Transcript Communications through High Delay Spread x Bandwidth (HDB) Channels: Opportunities and Challenges M.

Communications through High Delay
Spread x Bandwidth (HDB) Channels:
Opportunities and Challenges
M. Emami, F. Lee and A. Paulraj
Stanford University
October 18, 2004
AIM Workshop on Time-Reversal Communications in Richly Scattering Environments
Agenda





What is a HDB Channel and the “TR” Effect
Experimental Data
Characterization of Spatial Focusing
Communications in HDB Channels
Single User



Multi User



Capacity
Equalization
Capacity
Equalization
Concluding Remarks
What is a HDB Channel?
Amplitude
Amplitude
Amplitude
Rich Channel - HDSBW
Delay
Delay
Delay
Low Delay Spread
High Delay Spread
Sparse Channel
High Delay Spread
Rich Channel
Few resolved paths
Few resolved paths
Many resolved paths
HDB Metric


The TR effect depends on the number of
significant resolvable taps (N) in the channel
response
Typically, N > 30 represents a good HDB channel
Time Reversal (TR) Experiment
Step 1
h(t)
h(t)
Tx
(t)
Rx
Step 2
s(t)
Tx
x(t)
x(t) = s(t)  h*(-t)
h(t)
Rx
r(t)
r(t) = s(t)  h*(-t)  h(t)
TR Effects


Spatial focusing
Temporal focusing
Channel hardening
Magnitude PDF of One Tap
Number of Occurrences

After
TR
Original
Channel
Normalized Magnitude
Agenda





What is a HDB Channel and the “TR” Effect
Experimental Data
Characterization of Spatial Focusing
Communications in HDB Channels
Single User



Multi User



Capacity
Equalization
Capacity
Equalization
Concluding Remarks
Experimental Evidence for TR Effects

Indoor (Intel/Stanford)




Outdoor (Nokia)


Large office space with cubicles (40 x 60 yards)
Bandwidth 2 to 8 GHz (UWB)
Channel measured with fixed Tx and Rx in a grid of
.5m x .5m at (approx.) every 3 cm
Bandwidth 100 MHz
Underwater Acoustics
Indoor Wireless: Spatial Focusing Effect
NLOS Data
Power
Power
LOS Data
Distance in Wavelength

Distance in Wavelength
Spatial power profile strongly localized at
intended receiver location
Indoor Wireless: Temporal Focusing Effect
Impulse Response after TR
Normalized Magnitude
Normalized Magnitude
Channel Impulse Response
Tap Index


Tap Index
Temporal power profile at intended receiver
strongly localized in time
Side lobes double channel length
Outdoor Wireless: Temporal Focusing Effect
Impulse Response after TR
Normalized Magnitude
Normalized Magnitude
Channel Impulse Response
Tap Index

N 17 for this case
Tap Index
Underwater Acoustics
Time (µs)
High N
Distance
Low N
Agenda





What is a HDB Channel and the “TR” Effect
Experimental Data
Characterization of Spatial Focusing
Communications in HDB Channels
Single User



Multi User



Capacity
Equalization
Capacity
Equalization
Concluding Remarks
Characterizing Spatial Focusing



Single Ring (SR) Model
h(τ,R) is the channel from Tx to r = R
r=0 represents center of circle
2
Tx
d
N i.i.d.
uniformly
distributed
scatterers
r=0
rm
rM
1
Spatial Focusing Statistics


Space-time (S-T) random field generated by a one
shot TR pulse offers multiple characterization
Influencing parameters





N - HDB metric
λ - wavelength
BW - bandwidth
Δθ = θ2 -θ1 (receive angle spread)
Define
E{(R )} = [max {s(, R)}]2
where s(, R) = h*(-, 0)  h(, R)
Spatial Focusing Statistics - Metrics

Long range spatial focusing:
p  lim|R| η(R) η(0)

3-dB contour of (R ) around Rx (Ga and Gx are
the range and cross-range widths of contour)
 D (Gau a ) /  D (0)  0.5
 D (Gxu x ) /  D (0)  0.5
One-Shot Results: Single Tx Antenna
Distance in Wavelength
Typical one-shot realizations of (R ) around target point
N=1
Ga
N = 100
Gx
Distance in Wavelength
One-Shot Results: 5 Tx Antennas
Distance in Wavelength
Typical one-shot realizations of (R ) around target point
N=1
N = 100
Distance in Wavelength
Peak Power (dB)
Spatial Focalization: E{(R)}
Distance in Wavelength
Pulse Bandwidth (MHz)
S-T Focalization: Empirical Relationships for SR
Model
Ep  p  0.28 
Ga   0.62 
 0.1
RMS
 0.4
RMS
B
B
 0.2

 0.1
 0.2
0.17  RMS B



Gx   

 0.1
 0.2
0
.
62

B
RMS




 0.35
2 
0.6
   sin  


2



2 
1.3
   sin  


2



 0.05
2 
1.2
   sin  


2



M T1
 0.05
M T1
  3 4
 0.05
M T1
  3 4
1
   sin  


2


 0.2
M T1.5
Agenda




What is a HDB Channel and the “TR” Effect
Experimental Data
Communications in HDB Channels
Single User



Multi User



Capacity
Equalization
Capacity
Equalization
Concluding Remarks
What is a HDB Communication System?


A communication system that exploits the “TR
effect” to improve performance factors.
The transmitter uses a pre-filter derived from the
time reversed channel for transmission to the
intended receiver.
Encode /
Mod.
f (h* ( ))
Tx
h()
Demod. /
Decode
Rx
Important Questions for HDB Communications


How is capacity affected by HDB channels in
single and multi-user scenarios?
What are the key communication problems?





Equalization for ISI
Channel coding
Can spatial focusing be preserved
Are there any “LPI” or CCI reduction effects
Design tradeoffs
Agenda




What is a HDB Channel and the “TR” Effect
Experimental Data
Communications in HDB Channels
Single User



Multi User



Capacity
Equalization
Capacity
Equalization
Concluding Remarks
Capacity of Single User HDB Channels



Capacity of a communication channel determines
maximum rate of transmission per channel use.
HDB channels are frequency selective fading
channels. They will suffer a capacity penalty w.r.t.
AWGN channels at high SNR.
Optimum approach to maximizing capacity is
water-filling (WF). TR is close to but not true WF.
Effect of HDB Channels on Capacity
h ( )
p( ) 
for T R
h
p( )
x(t )

h( )
y(t )
TR rate:
ITR

u( )
n(t )
1

2
 | H ( ) |4 
 log2 1   2 || h ||2 d

Max. achievable rate:
IWF
1
 max
 E ( ) d  P 2
Tx power
spectral
density
 E ( ) | H ( ) |2 
d
2
 log2 1 



Water-Filling

In order to obtain IWF , the input energy must
satisfy the water-filling solution:




1


E ( )    
 IWF 
2 
| H ( ) | 
2

2

  | H ( ) |2 
 log2   2 d

2
| H ( ) |2
Capacity: TR vs. WF
50 taps
SNR


Probability
Average Rate (bits/s/Hz)
Cumulative Distribution
Rate (bits/s/Hz)
Ergrodic capacity of TR is near optimal at low SNR
Outage capacity decreases with increase in # of taps
Equalization Options for HDB Channels
Tx Eq.
h()
Rx Eq.
Tx Equalization
Rx Equalization
TR
None
None
LE / DFE / MLSE
LE
None
TR
LE
THP
THP
LE – Linear Equalizer
DFE – Decision Feedback Equalizer
MLSE – Maximum Likelihood Sequence Estimator – Too complex (exponential)
THP – Tomlinson-Harashima Precoding
Equalization



HDB = high Inter Symbol Interference Problem
Modulation schemes can be used to “mitigate” ISI
problem. e.g. Spread spectrum, OFDM.
We discuss Single carrier schemes where the ISI problem
is severest.
TR at Tx – No Receive Processing
n(t )
x(t )
h ( )
h
u( )

This channel has a severe
ISI problem.
Power of main tap =
Power in ISI taps.
TR does not solve the ISI
problem.

Mitigation: Rate back-off
h( )
y(t )
ISI
Rate back-off (RB)

Rate back-off refers to signaling at symbol rate <
1/BW. This effectively sub-samples the channel,
reducing the effective ISI while capturing full
diversity
Normal Channel after TR
Effective Channel with RB = 2
Peak
ISI
ISI vs. Rate back-off for TR

Assuming the channel
taps are i.i.d. Gaussian,
the ratio of peak to ISI
power is related to rate
back-off as follows:
 TR
Peak

 RB as N  
ISI
Plot of γTR for No Rate back-off (RB = 1)
Intel Indoor Data
Theoretical
Rx-Only Equalization: LE and DFE
LE
sk
H(z)
sk '
C(z)
nk
DFE
sk
H(z)
nk
Performance
LE
DFE
sk '
F(z)
Poor
(Noise enhancement)
1–B(z)
Complexity
Time domain: O(n)
Frequency domain: O(log2n)
Close to MLSE at high SNR Time domain: O(2n)
(Error propagation negligible) Frequency domain: O(n) + O(log2n)
Tx-Only Equalization: LE
nk
sk

G (z )
uk
H (z )

Minimize mean square error (MSE) subject to
power constraint:
2
min
E
[|
y

x
|
]
k
k 
H
g g 1




is the delay of the equalizer and the channel
 is for removing the bias
Peak
We investigate SNReff 
ISI  Noise
yk
TR vs. Tx-LE: Effect of Rate back-off
SNReff (dB)
RB=25
RB=1
RB=2
RB=5
SNRMFB (dB)

Rate back-off improves effective SNR
Joint Tx & Rx Equalization: TR & LE
nk
sk
H ( z 1 )
uk
H (z )
C(z )
yk

TR performs near-optimal WF while LE & rate
back-off mitigate ISI

For further complexity reduction, only the largest
10 or 20 taps in impulse response after TR and
rate back-off are used to design LE
TR & LE: Performance Results
RB = Rate-back-off Factor
RB
RB
RB
LE only uses largest 20 taps
of impulse response after TR
RB
RB
RB
LE only uses largest 10 taps
of impulse response after TR
(Full impulse response after TR contains 499 taps)
Joint Tx & Rx Equalization: THP
sk
mod
1–B(z)



xk
H(z)
F(z)
mod
sk '
nk
Modulo operator at transmitter limits average &
peak power of xk
Better BER performance than DFE, especially at low
SNR, since there is no error propagation
Capacity penalty of 0.255 bits/transmission at high
SNR compared to DFE (shaping loss)
Effect of HDB on LE & THP
Effect of Equalization on Spatial Focusing


Rx-only equalization: No spatial focusing
Tx-only equalization

TR: Shown previously (use as reference)
N
p
N  RB  1

LE: Similar to TR with a small penalty
Spatial Focusing: Simulation Results
S to I Ratio vs Rate Back-off
S to I Ratio vs Rate Back-off
18
16
16
14
14
12
12
10
TR
MMSE
8
10
6
8
4
6
2
4
0
20
40
60
80
Rate Back-off


100
20
40
60
Rate Back-off
80
100 i.i.d. Gaussian taps (N=100)
We have that S  RB for both MMSE and TR
I
100
SNReff (dB)
TR vs. Tx-LE: Effect of Multiple Antennas
SNRMFB (dB)

Effective SNR increases with # of Tx antennas (MT)
Single-User MIMO Systems

The capacity for a frequency selective MIMO
channel is given by:
CFS
MN
E
1


 MNmax  log2 1  s i2 i 
N  i  MN i 1
 M

i 1

λi is the energy of space-frequency mode i of the
channel
n(t )
x1 ( )
x2 ( )
xM ( )
H ( )
+
+
y1 (t )
+
yM (t )
y 2 (t )
Multi-User Systems
User 1
...
...
BS
H()
User K

Assumption



Each user has 1 antenna
Base station (BS) has MT antennas
Key questions


What is the effect of HDB on capacity regions?
What are the appropriate equalization techniques for
HDB channels?
Capacity Regions of Multiple Access Channels
Single Antenna
Multiple Antennas
R2
R2
Flat
No ISI
R1
R2
R1
R2
Flat
ISI
R1
R1
Broadcasting Channels

Dirty Paper Coding (DPC)
interference
sn
w2nR

noise
zn
xn(w,sn)
Examples of practical DPC schemes




THP
Trellis precoding
Flexible precoding
Lattice coding
yn
ŵ(yn)
Tx Equalization for Broacast Channels
n1k
x1k
h1
g1
h2
g2
1
y1k
2
y2 k
n2 k
+
x2 k
+
+
2
2
min
max{
E
[|
y

x
|
],
E
[|
y

x
|
1k
1k  1
2k
2 k   2 ]}
H
g g 1
g  [ g1T
g 2T ]T
THP for Broadcast Channels
sk
mod
I-B
x
Channel
(Flat or ISI)
F
y1
H
Feedforward
Filter
mod
s1 '
...
Element-Wise
Operation
n
yK
mod
sK'
Feedback Filter (Triangular)
Joint (vector/matrix) processing at BS
Individual (scalar) processing
for each user
THP for Broadcast Channels

Equivalent to VBLAST at Rx


Sources of capacity loss relative to optimum DPC



No error propagation
Shaping loss induced by modulo operation
Symbol-by-symbol encoding
Secure communication possible

Difficult for one user to decode other users’ data based on
its own received signal
Performance Example: [2]
2-Tap ISI Channel with Equal Power, # of Users = 4
Simulation
Theoretical
Approximation
MT = 4
MT = 5
MT = 6
References
[1] R. Schober and W. H. Gerstacker, “On the Distribution of Zeros of
Mobile Channels with Application to GSM/EDGE,” IEEE JSAC, July
2001.
[2] L. U. Choi and R. D. Murch, “ A Pre-BLAST-DFE Technique for the
Downlink of Frequency-Selective Fading MIMO Channels,” IEEE
Trans. Commun., May 2004.
Publications of TR Group
[1] M. Emami, et al., “Predicted Time Reversal Performance in Wireless
Communications Using Channel Measurements,” to appear in IEEE
Commun. Letters.
[2] J. Hansen, et al., “Design Approach for a Time Reversal Test Bed for
Radio Channels,” Special Session on MIMO Prototyping, 12th
European Signal Processing Conference, Sept. 2004.
[3] C. Oestges, et al., “Time Reversal Techniques for Broadband Wireless
Communications,” European Microwave Week, Oct. 2004. (Invited
Paper)
[4] T. Strohmer, et al., “Application of Time Reversal with MMSE
Equalizer to UWB Communications,” to appear in GLOBECOM’04.
[5] M. Emami, et al., “Matched Filtering with Rate Back-off for Low
Complexity Communications in Very Large Delay Spread Channels,” to
appear in Asilomar Conference on Signals, Systems, and Computers,
Nov. 2004.