Transcript Resource Allocation for Mobile Multiuser Orthogonal Frequency Division Multiplexing Systems Prof. Brian L.

Resource Allocation for Mobile
Multiuser Orthogonal Frequency
Division Multiplexing Systems
Prof. Brian L. Evans
Embedded Signal Processing Laboratory
Dept. of Electrical and Computer Engineering
The University of Texas at Austin
July 5, 2006
[email protected]
Featuring work by PhD students Zukang Shen (now at TI) and Ian Wong
Collaboration with Prof. Jeffrey G. Andrews and Prof. Robert W. Heath
Outline
 Introduction
 Resource allocation in wireless systems
 Multiuser OFDM (MU-OFDM)
 Resource allocation in MU-OFDM
 MU-OFDM resource allocation with proportional rates
 Near-optimal solution
 Low-complexity solution
 Real-time implementation
 OFDM channel state information prediction
 Comparison of algorithms
 High-resolution joint estimation and prediction
 Multiuser OFDM resource allocation using predicted
channel state information
2
Resource Allocation in Wireless Systems
 Wireless local area networks (WLAN) 54--108 Mbps
 Metropolitan area networks (WiMAX) ~10--100 Mbps
 Limited resources shared by multiple users
Transmit power
Frequency bandwidth
Transmission time
Code resource
Spatial antennas
frequency
code/spatial





 Resource allocation impacts
 Power consumption
 User throughput
 System latency
user 4
user 1
user 5
user 2
user 6
user 3
time
3
Orthogonal Frequency Division Multiplexing
 Adopted by many wireless communication standards
 IEEE 802.11a/g WLAN
 Digital Video Broadcasting – Terrestrial and Handheld
 Broadband channel divided into narrowband subchannels
 Multipath resistant
 Receiver equalization simpler than single-carrier systems
magnitude
 Uses static time or frequency division multiple access
channel
subcarrier
frequency
Bandwidth
OFDM Baseband Spectrum
4
Multiuser OFDM
 Orthogonal frequency division multiple access (OFDMA)
 Adopted by IEEE 802.16a/d/e standards
 802.16e: 1536 data subchannels with up to 40 users / sector
 Users may transmit on different subcarriers at same time
 Inherits advantages of OFDM
 Exploits diversity among users
User 1
User 2
...
frequency
Base Station
(Subcarrier and power allocation)
5
User K
Exploiting Multiuser Diversity
 Downlink multiuser OFDM
 Users share subchannels and
basestation transmit power
 Users only decode their own data
Resource Allocation
Static
Adaptive
Rayleigh Fading Channel in a 10-user System
Users
transmission
order
Predetermined
Channel
state
information
Not
exploited
System
Performance
Poor
Dynamically
scheduled
Well
exploited
Channel gain (dB)
10
0
-10
-20
single user gain
max user gain
-30
Good
-40
0
6
0.1
0.2
0.3
Time (sec)
0.4
0.5
Multiuser OFDM Resource Allocation
Objective
Advantage
Disadvantage
Best sum
capacity
No data rate
proportionality
among users
Equal user
data rates
Inflexible user data
rates distribution
Data rate
fairness
adjustable
by varying
weights
No guarantee for
meeting proportional
user data rates
Max sum
capacity
[Jang et al., 2003]
Max minimum
user’s capacity
[Rhee et al., 2000]
Max weighted
sum capacity
[Cendrillon et al., 2004]
: user k’s capacity (bits/s/Hz) as continuous function for single cell
7
Outline

Introduction




MU-OFDM resource allocation with proportional rates




Near-optimal solution
Low-complexity solution
Real-time implementation
OFDM channel state information prediction



Resource allocation in wireless systems
Multiuser-OFDM (MU-OFDM)
Resource allocation in MU-OFDM
Comparison of algorithms
High-resolution joint estimation and prediction
Multiuser OFDM resource allocation using predicted
channel state information
8
MU-OFDM with Proportional Rates
 Objective: Sum capacity
 Constraints
B
Transmission
bandwidth
K
# of users
N
# of subchannels
pk,n
power in user k’s
subchannel n
hk,n
channel gain of user k’s
subchannel n
N0
AWGN power density
Rk
User k’s capacity
System parameter for
proportional rates
 Total transmit power
 No subchannel shared by multiple users
 Proportional rate constraints
 Advantages
 Allows different service privileges and different pricing
9
Two-Step Near-Optimal Solution
 Subchannel allocation step
 Greedy algorithm – allow user with least
allocated capacity/proportionality to choose
best subcarrier [Rhee & Cioffi, 2000]
 Modified to incorporate proportional rates
 Computational complexity O(K N log N)
K - # users
N - # subchannels
n - # iterations
 Power allocation step [Shen, Andrews & Evans, 2005]
 Exact solution given a subcarrier allocation
 General case
 Solution to set of K non-linear equations in K unknowns
 Newton-Raphson methods are O(n K) where n is no. of iterations
 Special case: High channel-to-noise ratio
 Solution finds a root of a polynomial with O(n K) complexity
 Typically 10 iterations in simulation
10
Lower Complexity Solution
 In practical scenarios, rough proportionality is acceptable
 Key ideas to simplify Shen’s approach
[Wong, Shen, Andrews & Evans, 2004]
 Relax strict proportionality constraint
 Require predetermined number of subchannels
to be assigned to simplify power allocation
 Power allocation
10
8
7
4
 Solution to sparse set of linear equations
 Computational complexity O(K)
Example
 Advantages [Wong, Shen, Andrews & Evans, 2004]
 Waives high channel-to-noise ratio assumption of Shen’s method
 Achieves higher capacity with lower complexity vs. Shen’s method
 Maintains acceptable proportionality of user data rates
11
Simulation Parameters
Parameter
Value
Parameter Value
Number of
Subcarriers (N)
64
Channel
Model
Number of Users
(K)
Bit Error Rate
Constraint
4-16
Maximum
5 ms
Delay Spread
Doppler
30 Hz
Frequency
10-3
12
6-tap exponentially
decaying power
profile with
Rayleigh fading
Total Capacity Comparison
4.75
N = 64 subchannels
SNR = 38 dB
SNR Gap = 3.3 dB
capacity (bit/s/Hz)
4.7
4.65
Based on 10000
channel realizations
4.6
Proportions
assigned randomly
from {4,2,1} with
probabilities
[0.2, 0.3, 0.5]
4.55
Proposed
Method
Wong’s Method
Shen’s Method
Method
Shen's
4.5
4.45
4
6
8
10
12
number of users
13
14
16
Proportionality Comparison
0.16
Proportions
Proportions
Wong’s Method
Proposed
Method
Shen’sMethod
Method
Shen's
Normalized Rate Proportions
0.14
0.12
Based on the
16-user case,
10000 channel
realizations per
user
0.1
Normalized rate
proportions for
three classes of
users using
proportions
{4, 2, 1}
0.08
0.06
0.04
0.02
0
1
2
3
4
5
6 7 8 9 10 11 12 13 14 15 16
User Number (k)
14
Real-time Software Prototype
LabVIEW
7.0
Matlab
6.5
LabVIEW handles the
interface between Matlab
and the DSP and automates
allocation tests.
Matlab generates a frequencyselective Rayleigh channel for
each user.
TMS320C6701
Digital Signal
Processor
(DSP)
The DSP receives Channel
State Information and performs
resource allocation algorithm.
15
Computational Complexity
5
10
22% average
improvement
Channel Allocation-shen
Power Allocation-shen
Channel Allocation-wong
Power Allocation-wong
Total-shen
Total-wong
9
8
7
Clock cycles
DSP Imlementation Clock cycle count
x 10
Code developed
in floating point C
6
5
Run on 133 MHz
TI TMS320C6701
DSP EVM board
4
3
2
1
0
2
4
6
8
10
Number of users
12
16
14
16
Memory Usage
*Shen’s Method
Memory Type
Program
Memory
Subcarrier 1660
Allocation
2024
Power
Allocation
1976
2480
Total
Data
Memory
*Wong’s Method
4140
System
8KN+4K
Variables
O(KN)
Subcarrier 4N+8K
Allocation
O(N+K)
Power
4N+24K
Allocation
O(N+K)
* All values are in bytes
17
4000
8KN+4K
O(KN)
4N+12K
O(N+K)
4N+28K
O(N+K)
Performance Comparison Summary
Performance Criterion
Shen’s Method
Wong’s Method
Subcarrier Allocation
Computational Complexity
O(K N log N)
O(K N log N)
Power Allocation
Computational Complexity
O(N + nK), n~9
O(N+K)
Memory Complexity
O(NK)
O(NK)
Achieved Capacity
High
Higher
Adherence to
Proportionality
Tight
Loose
Assumptions on
Subchannel SNR
High
None
18
Outline

Introduction




MU-OFDM resource allocation with proportional rates




Near-optimal solution
Low-complexity solution
Real-time implementation
OFDM channel state information prediction



Resource allocation in wireless systems
Multiuser-OFDM (MU-OFDM)
Resource Allocation in MU-OFDM
Comparison of algorithms
High-resolution joint estimation and prediction
Multiuser OFDM resource allocation using predicted
channel state information
19
Delayed Channel State Information
Internet

Back haul
t=0: Mobile estimates channel and
feeds this back to base station
t=: Base station receives estimates,
adapts transmission based on these
Channel mismatch
[Souryal & Pickholtz, 2001]
Higher BER
Lower bits/s/Hz
20
mobile
t=0 t=
Prediction of Wireless Channels
 Use current and previous channel estimates to predict
future channel response
 Overcome feedback delay
 Adaptation based on predicted channel response
 Reduce amount of feedback
 Predicted channel response
may reduce how often direct
channel feedback is provided
h(n)
h(n-)
h(n-p)
21
h(n+) ?
Related Work
 Prediction on each subcarrier [Forenza & Heath, 2002]
 Each subcarrier treated as a narrowband autoregressive process
[Duel-Hallen et al., 2000]
 Prediction using pilot subcarriers [Sternad & Aronsson, 2003]
 Used unbiased power prediction [Ekman, 2002]
 Prediction on time-domain channel taps
[Schafhuber & Matz, 2005]
 Used adaptive prediction filters
Pilot Subcarriers
…
…
IFFT
Data Subcarriers
Time-domain channel taps
22
OFDM Channel Prediction Comparison
 Compared three approaches in unified framework
[Wong, Forenza, Heath & Evans, 2004]
 Analytical and numerical mean squared error comparison
 All-subcarrier and pilot-subcarrier methods have similar mean
squared error performance
 Time-domain prediction performs much better than the two other
frequency domain prediction methods
 Complexity comparison
 All-subcarrier > Pilot-subcarrier ¸ Time-domain
N p  N and Nt  N and p  N
23
High-resolution OFDM Channel Prediction
 Combined channel estimation and prediction
[Wong & Evans, 2005]
 Outperforms previous methods with similar order of
computational complexity
 Allows decoupling of computations between receiver and
transmitter
 High-resolution channel estimates available as a
by-product of prediction algorithm
24
Deterministic Channel Model
 Outdoor mobile macrocell scenario
 Far-field scatterer (plane wave assumption)
 Linear motion with constant velocity
 Small time window (a few wavelengths)
 Channel model
n
k
 Used in modeling and simulation of
wireless channels [Jakes 1974]
 Used in ray-tracing channel
characterization [Rappaport 2002]
25
OFDM symbol index
subchannel index
Prediction via 2-D Frequency Estimation
 If we accurately estimate parameters in channel model,
we could effectively extrapolate the fading process
 Estimation and extrapolation period should be within time
window where model parameters are stationary
 Estimation of two-dimensional complex sinusoids in noise
 Well studied in radar, sonar, and other array signal processing
applications [Kay, 1988]
 Many algorithms available, but are computationally intensive
26
Two-step 1-D Frequency Estimation


Typically, many propagation paths share the same
resolvable time delay
We can thus break down the problem into two steps
1. Time-delay estimation
2. Doppler-frequency estimation
27
IEEE 802.16e Simulation
0.5
Path power
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
Time delay
2
2.5
3
x 10
-6
28
Mean-square Error vs. SNR
Prediction 2  ahead
-10
ACRLB
CRLB
2-Step 1-Dimensional
Burg
-15
-20
MSE in dB
-25
-30
-35
-40
-45
-50
10
15
20
25
SNR in dB
30
35
ACRLB – Asymptotic Cramer-Rao Lower Bound
CRLB – Cramer-Rao Lower
Bound
29
Mean-square Error vs. Prediction Length
-9
SNR = 7.5 dB
-10
ACRLB
CRLB
2-Step 1-Dimensional
Burg
-11
MSE in dB
-12
-13
-14
-15
-16
-17
-18
-19
0.5
1
1.5
2
2.5
3
3.5
Prediction length ()
4
4.5
ACRLB – Asymptotic Cramer-Rao Lower Bound
CRLB – Cramer-Rao Lower Bound
30
5
Performance Comparison Summary
L - No. of paths
M - No. of rays per path
31
MU-OFDM Resource Allocation with
Predicted Channel State Infomation (Future)
 Combine MU-OFDM resource allocation with long-range
channel prediction
 Using the statistics of the channel prediction error, we
can stochastically adapt to the channel
 Requires less channel feedback
 More resilient to channel feedback delay
 Improved overall throughput
32
Conclusion
 Resource allocation for MU-OFDM with proportional rates
 Allows tradeoff between sum capacity and user rate “fairness” to
enable different service privileges and pricing
 Derived efficient algorithms to achieve similar performance with
lower complexity
 Prototyped system in a DSP, showing its promise for real-time
implementation
 Channel prediction for OFDM systems
 Overcomes the detrimental effect of feedback delay
 Proposed high-performance OFDM channel prediction algorithms
with similar complexity
 Resource allocation using predicted channels is important for
practical realization of resource allocation in MU-OFDM
33
Embedded Signal
Processing Laboratory

Director: Prof. Brian L. Evans


http://www.ece.utexas.edu/~bevans/
WiMAX (OFDM) related research




Algorithms for resource allocation in Multiuser OFDM
Algorithms for OFDM channel estimation and prediction
Key collaborators: Prof. Jeffrey Andrews and Prof. Robert Heath
Key graduate students:
Aditya
Chopra
Youssof
Mortazavi
Marcel
Nassar
34
Hamood
Rehman
Ian
Wong
Backup
35
Subchannel Allocation

Modified method of [Rhee et al., 2000], but we keep the
assumption of equal power distribution on subchannels

Initialization (Enforce zero initial conditions)
Set
,
for
. Let

For



to
Find
Let
While



(Allocate best subchannel for each user)
satisfying
for all
and update
,
(Iteratively give lowest rate user first choice)
Find
satisfying
For the found , find
For the found
and
update
for all
satisfying
, Let
for all
,
and
Back
36
Power Allocation for a Single User
 Optimal power distribution for user
 Order
 Water-filling algorithm
 How to find
for
K
# of users
N
# of subchannels
pk,n
power in user k’s nth
assigned subchannel
Hk,n
Channel-to-noise ratio
in user k’s nth assigned
subchannel
Nk
# of subchannels
allocated to user k
Pk,tot
Total power allocated to
user k
Water-level
subchannels
37
Power Allocation among Many Users
 Use proportional rate and total power constraints
where
 Solve nonlinear system of K equations:
 Two special cases
 Linear case:
 High channel-to-noise ratio:
/iteration
, closed-form solution
and
38
Back
Comparison with Optimal Solution
Overall capacity (bits/s/Hz)
3.5
3
2.5
2
1.5
1
optimal, E(ch1)/E(ch2)=1
decoupled, E(ch1)/E(ch2)=1
optimal, E(ch1)/E(ch2)=0.1
decoupled, E(ch1)/E(ch2)=0.1
optimal, E(ch1)/E(ch2)=10
decoupled, E(ch1)/E(ch2)=10
0.5
0
-10
-5
0
10*log10(1/2)
39
5
10
Back
Minimum User's Capacity (bit/s/Hz)
Comparison with Max-Min Capacity
1.6
proposed
max-min:equal power
TDMA
1.4
1.2
1
0.8
0.6
0.4
0.2
8
10
12
14
Number of users K
40
16
Ergodic Sum Capacity (bits/s/Hz)
10
9
8
max sum capacity
single user (higher SNR)
proposed
static TDMA
single user (lower SNR)
7
6
0
1
2
3
4
5
Fairness Index m
6
7
Normalized Ergodic Capacity Per User
Comparison with Max Sum Capacity
0.8
ideal, m=3
proposed m=3
max sum capacity
static TDMA
0.6
0.4
0.2
41
0
1
2
3
4 5 6
User Index k
7
8
Summary of Shen’s Contribution
 Adaptive resource allocation in multiuser OFDM systems
 Maximize sum capacity
 Enforce proportional user data rates
 Low complexity near-optimal resource allocation algorithm
 Subchannel allocation assuming equal power on all subchannels
 Optimal power distribution for a single user
 Optimal power distribution among many users with proportionality
 Advantages




Evaluate tradeoff between sum capacity and user data rate fairness
Fill the gap of max sum capacity and max-min capacity
Achieve flexible data rate distribution among users
Allow different service privileges and pricing
42
Wong’s 4-Step Approach
1. Determine number of subcarriers Nk
for each user
2. Assign subcarriers to each user to
give rough proportionality
3. Assign total power Pk for each user to
maximize capacity
4. Assign the powers pk,n for each user’s
subcarriers (waterfilling)
43
O(K)
O(KNlogN)
O(K)
O(N)
Simple Example
N = 4 subchannels
K = 2 users
Ptotal = 10
10
8
Desired
proportionality
among data rates
1 = 3/4
7
4
2 = 1/4
9
6
5
3
44
Step 1: # of Subcarriers/User
Nk
3
10
1
8
1 = 3/4
7
4
2 = 1/4
9
6
5
3
1
2
3
N = 4 subchannels
K = 2 users
Ptotal = 10
4
45
Step 2: Subcarrier Assignment
Rk
10
8
10
7
log2(1+2.5*10)=4.70
8
7
4
9
6
9
5
3
1
2
3
4
1
Rtot
2
3
4
46
log2(1+2.5*8)=4.39
log2(1+2.5*7)=4.21
13.3
log2(1+2.5*9)=4.55
4.55

Nk
3/4
3
1/4
1
Step 3: Power per user
10
1
8
2
7
3
9
4
P1 = 7.66
P2 = 2.34
N = 4 subchannels; K = 2 users; Ptotal = 10
47
Back
Step 4: Power per subcarrier
• Waterfilling across subcarriers for each user
P1 = 7.66
P2 = 2.34
10
1
8
2
7
3
p1,1= 2.58
p1,2= 2.55
p1,3= 2.53
p2,1= 2.34
9
4

Nk
3/4
3
1/4
1
Data Rates:
R1 = log2(1 + 2.58*10) + log2(1 + 2.55*8)
+ log2(1 + 2.53*7)
= 13.39008
Back
R2 = log2(1+ 2.34*9)
= 4.46336
48
Pilot-based Transmission
 Comb pilot pattern
 Least-squares
channel estimates
…
f
Df
Dt
49
t
Prediction over all the subcarriers
 Design prediction filter for each of the Nd data
subcarriers
 Mean-square error
50
Prediction over the pilot subcarriers
 Design filter on the Npilot pilot subcarriers only
 Less computation and storage needed
 Npilot << Nd (e.g. Npilot = 8; Nd = 192 for 802.16e OFDM)
 Use the same prediction filter for the data subcarriers
nearest to the pilot carrier
Pilot Subcarriers
…
…
Data Subcarriers
51
Prediction on time-domain channel taps
 Design filter on Nt · Npilot time-domain channel taps
 Channel estimates typically available only in freq. domain
 IFFT required to compute time-domain channel taps
 MSE:
52
Simulation Parameters (IEEE 802.16e)
Parameter
Value
Parameter
Value
N
256
Bandwidth
5 MHz
Guard Carriers
(7)
[0-27] &
[201:256]
Fcarrier
2600 MHz
Channel Model
ETSI Vehicular A
Mobile Velocity
75 kmph
Prediction
Order
75
Downsampling rate
25
(4*fd)
53
Prediction Snapshot
54
NMSE vs. Channel Estimation Error
55
NMSE vs. Prediction Horizon
56
Step 1 – Time-delay estimation
 Estimate autocorrelation function using the modified covariance
averaging method [Stoica & Moses, 1997]
 Estimate the number of paths L using minimum description length
rule [Xu, Roy, & Kailath, 1994]
 Estimate the time delays
using Estimation of Signal Parameters
via Rotational Invariance Techniques (ESPRIT) [Roy & Kailath, 1989]
 Estimate the amplitudes cp(l) using least-squares
 Discrete Fourier Transform of these amplitudes could be used to
estimate channel
 More accurate than conventional approaches, and similar to parametric
channel estimation method in [Yang, et al., 2001]
57
Step 2 – Doppler Frequency Estimation
 Using complex amplitudes cp(l) estimated from Step 1 as the left
hand side for (2), we determine the rest of the parameters
 Similar steps as Step 1 can be applied for the parameter estimation
for each path p
 Using the estimated parameters, predict channel as
58
Prediction as parameter estimation
 Channel is a continuous non-linear function of the 4Mlength channel parameter vector
59
Cramer-Rao Lower Bound (CRLB)
60
Closed-form expression for asymptotic CRLB
 Using large-sample limit of CRLB matrix for general 2-D complex
sinusoidal parameter estimation [Mitra & Stoica, 2002]
 Much simpler expression
 Achievable by maximum-likelihood and nonlinear least-squares
methods
 Monte-Carlo numerical evaluations not necessary
61
Insights from the MSE expression
Amplitude & Doppler
phase error frequency &
phase cross
variance
covariance
 Linear increase with 2 and M
Doppler
frequency
error
variance
Time-delay
& phase
cross
covariance
Time-delay
error
variance
 Dense multipath channel environments are the hardest to predict [Teal, 2002]
 Quadratic increase in n and |k| with f and  estimation error variances
 Emphasizes the importance of estimating these accurately
 Nt, Nf, Dt and Df should be chosen as large as possible to decrease the
MSE bound
62
Selected Wireless Standards
 Selected wireless data communication standards.
 On June 8, 2006, IEEE suspended its 802.20 Mobile
Broadband Wireless Access standard activities.
 IEEE 802.20 is intended to operate at carrier frequencies
below 3.5 GHz
Standard
Primary Use
Carrier Frequency
Transmission
Bandwidth
Channels
Bluetooth
Personal Area Network
2.4 GHz
1 MHz
79
IEEE 802.11a
Wireless LAN (Wi-Fi)
5.2 GHz
20 MHz
12
IEEE 802.11b
Wireless LAN (Wi-Fi)
2.4 GHz
22 MHz
3
IEEE 802.11g
Wireless LAN (Wi-Fi)
2.4 GHz
30 MHz
3
IEEE 802.11n
High-Speed Wireless LAN
(expected July 2007)
2.4 GHz
30 MHz
3
IEEE 802.16e
Mobile Broadband
Wireless Access
(Wi-Max)
Varies by maker:
2.5–2.69 GHz,
3.3–3.8 GHz, or
5.725–5.850 GHz
1.25 – 20 MHz
Varies by
maker
7 – 400
63