ECSE 6592 Wireless Ad Hoc and Sensor Networks Spatial Diversity in Wireless Networks Hsin-Yi Shen Nov 3, 2005 Introduction Main characteristic in wireless channelsrandomness in users’
Download ReportTranscript ECSE 6592 Wireless Ad Hoc and Sensor Networks Spatial Diversity in Wireless Networks Hsin-Yi Shen Nov 3, 2005 Introduction Main characteristic in wireless channelsrandomness in users’
Slide 1
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 2
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 3
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 4
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 5
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 6
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 7
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 8
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 9
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 10
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 11
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 12
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 13
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 14
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 15
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 16
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 17
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 18
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 19
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 20
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 21
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 22
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 23
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 24
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 25
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 26
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 27
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 28
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 29
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 30
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 31
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 32
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 33
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 34
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 35
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 36
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 37
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 38
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 39
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 40
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 41
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 42
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 2
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 3
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 4
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 5
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 6
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 7
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 8
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 9
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 10
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 11
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 12
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 13
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 14
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 15
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 16
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 17
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 18
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 19
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 20
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 21
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 22
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 23
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 24
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 25
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 26
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 27
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 28
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 29
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 30
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 31
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 32
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 33
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 34
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 35
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 36
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 37
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 38
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 39
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 40
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 41
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998
Slide 42
ECSE 6592 Wireless Ad Hoc and Sensor Networks
Spatial Diversity in Wireless
Networks
Hsin-Yi Shen
Nov 3, 2005
Introduction
Main characteristic in wireless channelsrandomness in users’ transmission channels
and randomness in users’ geographical
locations
Diversity- Convey information through
multiple independent instantiations of random
attenuations
Spatial diversity- through multiple antennas
or multiple users
Wireless Channel Characteristics
Three kind of attenuations-path loss,
shadowing loss, fading loss
Path loss: Signals attenuate due to distance
Shadowing loss : absorption of radio waves
by scattering structures
Fading loss :constructive and destructive
interference of multiple reflected radio wave
paths
Attenuation in Wireless Channels
Wireless Channel Characteristics
Key parameters of wireless channelscoherence time, coherence bandwidth
If symbol period>coherence time, the channel
is time selective
If symbol period< channel delay spread, the
channel is frequency selective
MIMO Channel Model
H(k;l) is the lth tap of the Mr x Mt channel response
matrix, z is noise vector
Theoretical Consideration
Information-Theoretic results for multipleantenna channels
Information-Theoretic results for multi-user
channels
Diversity order
Design consideration
Information-Theoretic results for multiple
antenna channels (1)
1. T hecapacityC of thechannelwith Mt transmitters and Mr receivers
and averagepower constraintP is
C
0
P Tmin 1 Tmax Tmin Tmax Tmin
k!
2
log(1
)
[ Lk
( )]
e d
Mt k 0
k Tmax Tmin
where Tmax max(Mt , Mr ),Tmin min(Mt , Mr ), and Lmk () is the
generalized Lagueree polynomialof order k with parameterm
2. For Mt Mr M , thecapacityC given above grows
asymptotic
ally linearlyin M , i.e.,
C
const
M M
lim
Information-Theoretic results for multiple
antenna channels (2)
3.
C ( SNR)
lim
min(M r , M t )
SNR log(SNR)
Assume the receiver had access to perfect
channel state information through training or
other methods
Information-Theoretic results for multiple
antenna channels (3)
T heoutage probability for a transmission rateof R and a
given transmission strategy p( X ) is defined as
Poutage ( R, p( X )) P{H : I ( X ; Y | H (k ) H ) R}
At high SNR the outage probability is the same as
frame error probability in terms of SNR exponent
For given rate, we can compare performance
through an outage analysis
Information-Theoretic results for multiuser channels
Two types of topology- multiple access channel
and broadcast channel
Information-Theoretic results for multiuser channels
Given a configuration C, thereexistsa scheduling and relayingpolicy
and a constantc 0 such that
lim P{ (n) cR is feasible | C} 1
n
for almost all configurations C as n
i.e, theprobability of theset of configurations for whichthe policy
acheivesa throughtof goes to1 as n
(1) thrroughput is possible
Diversity Order and multiplexing gain
Diversityorder :
log(Pe ( SNR))
lim
d
SNR
log(SNR)
where Pe is averageerrorprobability
Multiplexing gain :
R( SNR))
lim
r
SNR log(SNR)
where R is transmission rate
Relation between Diversity Order and
Multiplexing Gain
For N M t M r 1, and
K min(M t , M r ), theoptimal
tradeoffcurve d * (r ) is given by
the piecewise linear function
connectingpointsin (k , d * (k )),
k 0,, K where
d * (k ) ( M t k )(M r k )
Relation between rate and SNR
Design Consideration
Space time code with low decoding
complexity and achieving maximum diversity
order
Trade-off between diversity order and rate
If system is delay-constrained, design with
high diversity order and lower data rate
Fairness for resource sharing between users
Cross layer design
Signal transmission
Transmitter Techniques- spatial multiplexing,
space-time trellis code and block codes
Receiver techniques- joint equalization with
channel estimation, space-time code
decoding
Spatial Multiplexing (Bell Labs Layered
Space-Time Architecture, BLAST)
Multiple transmitted data streams are separated and
detected successfully using a combination of array
processing (nulling) and multi-user detection
(interference cancellation) techniques
A broadband channel scenario using a MIMO
generalization of classical decision feedback
equalizer (DFE)
The nulling operation is performed as “feed-forward
filter” and the interference cancellation operation is
performed by the “feedback filter”
Spatial Multiplexing-continued
May have error propagation
The presence of antenna correlation and the
lack of scattering richness in the propagation
environment reduce the achievable rates of
spatial multiplexing techniques
Enhancement: Use MMSE interference
cancellation, perform ML detection for first
few streams
Space time coding
Improve downlink performance without
requiring multiple receive antennas
Easily combined with channel coding
Do not require channel state information at
the transmitter
Robust against non-ideal operating
conditions
Space-time Trellis codes
Maps information bit stream into Mt streams of
symbols
Decoding complexity increases exponentially as a
function of the diversity level and transmission rate
Example:
Space time block codes
Cons and pros of space time block codes
Achieve full diversity at full transmission rate for any
signal constellation
Does not require CSI at the transmitter
ML decoding involves only linear processing at the
receiver
Does not provide coding gain
A rate-1 STBC cannot be constructed for any
complex signal constellation with more than two
transmit antennas
Simple decoding rule valid only for flat-fading
channel where channel gain is const over two
consecutive symbols
Tradeoff between diversity and
throughput
BLAST achieves max spatial multiplexing
with small diversity gain
Space time codes achieves max diversity
gain with no multiplexing gain
Linear dispersion codes (LDC): achieve
higher rate with polynomial decoding
complexity for a wide SNR range
Build in the diversity into the modulation
Build Diversity into modulation
Receiver techniques
Coherent and non-coherent techniques
Coherent technique require channel state
information by channel estimation or training
sequences and feed this to joint
equalization/decoding algorithm
Non-coherent techniques does not require
CSI and more suitable for rapidly timevarying channels
Joint Equalization/Decoding techniques
M-BCJR algorithm: at
each trellis step, only M
active states associated
with the highest metrics
are retained
Significant reduction in
the number of
equalizer/decoder
states
Sphere decoder
Suitable for codes with lattice structures
Perform ML search with low computation
complexity
Joint Equalization/Decoding of space
time Block codes
Eliminate inter-antenna interference using a
low complexity linear combiner
Single-carrier frequency domain equalizer
(SC-FDE)
Performance of SC-FDE
Non-coherent techniques
Does not require channel estimation
Include blind identification and detection
schemes
Exploit channel structure (finite impulse
response), input constellation (finite alphabet),
output (cyclostationarity) to eliminate training
symbols
Use ML receiver which assumes statistics
about channel state but not knowledge of the
state itself
Summary in signal transmission
Mitigate fading effect by using space diversity
Use MIMO to realize spatial rate multiplexing
gains
Use equalization techniques (ex: M-BCJR,
SC-FDE) to mitigate channel frequency
selectivity
Use channel estimation and tracking,
adaptive filtering, differential
transmission/detection to mitigate time
selectivity
Networking issues
Medium sharing resource allocation
Mobility and routing
Hybrid networks
Resource allocation
Allocation criteria: rate-based criteria and jobbased criteria
Rate-based criteria provide average data
rates to users which satisfy certain properties
Job-based criteria schedule data delivery in
order to optimize various QoS guarantees
based on the job requests
Resource allocation-Rate-Based QoS
criteria
Utilize the multi-user diversity inherently available in
wireless channels
Schedule users when their channel state is close to
peak rate it can support
=> inherent unfairness
Keep track of the average throughput Tk(t) and rate
Rk(t), transmit the user with the largest Rk(t)/ Tk(t)
among the active users
If channel is slow time-varying, introduce random
phase rotations between the antennas to simulate
fast fading
Impact of spatial diversity
Multi-antenna diversity provide greater reliability by
smoothening channel variations
Multi-user diversity utilize the channel variability
across users to increase throughput
Choose diversity techniques according to channel
conditions, mobility and application constraints
For example, low delay-applications with high
reliability requirement may use multi-antenna
diversity with space time codes
Hybrid Networks
Two approaches to increasing TCP efficiency
in hybrid networks
Reduce error rate in wireless channel by
using more sophisticated coding schemes,
such as space-time codes
Use explicit loss notification (ELN) to inform
the sender that the packet loss occurred due
to wireless link failure rather than congestion
in wired part
Space time code and TCP throughput
STBC-enhanced 802.11a achieves a
particular throughput value at a much lower
SNR value than the standard 802.11a
STBC modify the SNR region under which a
particular transmission rate should be chosen
STBC increase the transmission range and
improve robustness of WLANs
STBC-enhanced 802.11a
The difference between
STBC 802.11a and
802.11a becomes
smaller when channel
quality is sufficiently
good
STBC-802.11a can
switch to faster
transmission mode at
much lower SNR
values
Conclusion
In wireless networks, power and spectral
bandwidth are limited
Limitation on signal processing at terminal
and requirement of sophisticated resource
allocation techniques due to variation in
capacity
Spatial diversity improves data rates and
reliability of individual links
Space time codes improves link capacity and
system capacity through resource allocation
Future works
Space time code design
Implementation issues-low-cost multiple RF
chains and low-power parallelizable
implementation of STC receiver signal
processing algorithm
Receiver signal processing-the development
of practical adaptive algorithm that can track
rapid variation of large number of taps in
MIMO channel and/or equalizer
Standardization activities
Reference
[1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis,
and A.R. Calderbank, “Great Expectations:
The Value of Spatial Diversity in Wireless
Networks,” Proceeding of The IEEE, Vol. 92,
No. 2, pp219-270, Feb 2004
[2] Sergio Verdu, “Multiuser Detection,”
Cambridge University Press, 1998