1. Resource Allocation for Mobile Multiuser OFDM Systems
Prof. Brian L. Evans
Embedded Signal Processing Laboratory
Dept. of Electrical and Computer Engineering
The University of Texas at Austin
February 17, 2006
Featuring work by ESPL students Zukang Shen and Ian Wong Collaboration with Prof. Jeffrey G. Andrews and Prof. Robert W. Heath

2. 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 (CSI) prediction
Comparison of algorithms
High-resolution joint estimation and prediction
MU-OFDM resource allocation using predicted CSI 2

3. Resource Allocation in Wireless Systems
Wireless local area networks (WLAN) Mbps
Metropolitan area networks (WiMAX) ~ Mbps
Limited resources shared by multiple users
Transmit power
Frequency bandwidth
Transmission time
Code resource
Spatial antennas
Resource allocation impacts
Power consumption
User throughput
System latency
user 4
user 5
user 6
user 1
user 2
user 3
time
frequency
code/spatial 3

4. Orthogonal Frequency Division Multiplexing
Adopted by many wireless communication standards
IEEE a/g WLAN
Digital Video Broadcasting – Terrestrial and Handheld
Broadband channel divided into narrowband subchannels
Multipath resistant
Receiver equalization simpler than single-carrier systems
Uses static time or frequency division multiple access
subcarrier
frequency
magnitude
channel
Bandwidth
OFDM Baseband Spectrum 4

5. Multiuser OFDM
Orthogonal frequency division multiple access (OFDMA)
Adopted by IEEE a/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
frequency
Base Station
(Subcarrier and power allocation)
User 2
. . .
User K 5

6. Exploiting Multiuser Diversity
Downlink multiuser OFDM
Users share subchannels and basestation transmit power
Users only decode their own data
Resource Allocation
Static
Adaptive
Users transmission order
Pre-determined
Dynamically scheduled
Channel state information
Not exploited
Well exploited
System Performance
Poor
Good 6

7. MU-OFDM Resource Allocation
Objective
Advantage
Disadvantage
Max sum capacity [Jang et al., 2003]
Best sum capacity
No data rate proportionality among users
Max minimum user’s capacity [Rhee et al., 2000]
Equal user data rates
Inflexible user data
rates distribution
Max weighted sum capacity [Cendrillon et al., 2004]
Data rate fairness adjustable by varying weights
No guarantee for meeting proportional user data rates
: user k’s capacity (bits/s/Hz) as continuous function for single cell 7

8. 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 (CSI) prediction
Comparison of algorithms
High-resolution joint estimation and prediction
MU-OFDM resource allocation using predicted CSI 8

9. MU-OFDM with Proportional RatesB
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
Objective: Sum capacity
Constraints
Total transmit power
No subchannel shared by multiple users
Proportional rate constraints
Advantages
Allows different service privileges and different pricing 9

10. 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)
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
K - # users
N - # subchannels
n - # iterations 10

11. 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
Solution to sparse set of linear equations
Computational complexity O(K)
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 10 8 7 4
Example 11

12. Simulation Parameters
Value
Number of Subcarriers (N) 64
Channel Model
6-tap exponentially decaying power profile with Rayleigh fading
Number of Users (K)
4-16
Maximum Delay Spread
5 ms
Bit Error Rate Constraint
10-3
Doppler Frequency
30 Hz 12

13. Total Capacity Comparison
N = 64 subchannels
SNR = 38 dB
SNR Gap = 3.3 dB
Based on channel realizations
Proportions assigned randomly from {4,2,1} with probabilities [0.2, 0.3, 0.5]
Wong’s Method
Shen’s Method 13

14. Proportionality Comparison
Proportions
Wong’s Method
Shen’s Method
Based on the
16-user case,
10000 channel
realizations per
user
Normalized rate proportions for three classes of users using proportions
{4, 2, 1} 14

15. Real-time Software Prototype
LabVIEW 7.0
LabVIEW handles the interface between Matlab and the DSP and automates allocation tests.
TMS320C6701 Digital Signal Processor (DSP)
Matlab 6.5
Matlab generates a frequency-selective Rayleigh channel for each user.
The DSP receives Channel State Information and performs resource allocation algorithm. 15

16. Computational Complexity
22% average improvement
Code developed in floating point C
Run on 133 MHz TI TMS320C6701 DSP EVM board 16

17. Memory Usage 1660 2024 2480 1976 4140 4000 8KN+4K O(KN) 4N+8K O(N+K)
Memory Type
*Shen’s Method
*Wong’s Method
Program
Memory
Subcarrier Allocation
1660
2024
Power Allocation
2480
1976
Total
4140
4000
Data Memory
System Variables
8KN+4K
O(KN)
4N+8K
O(N+K)
4N+12K
4N+24K
4N+28K
* All values are in bytes 17

18. Performance Comparison Summary
Performance Criterion
Shen’s Method
Wong’s Method
Subcarrier Allocation Computational Complexity
O(KNlogN)
Power Allocation Computational Complexity
O(N+nK), n~9
O(N+K)
Memory Complexity
O(NK)
Achieved Capacity
High
Higher
Adherence to Proportionality
Tight
Loose
Assumptions on Subchannel SNR
None 18

19. 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 (CSI) prediction
Comparison of algorithms
High-resolution joint estimation and prediction
MU-OFDM resource allocation using predicted CSI 19

20. Delayed CSI  t=0: Mobile estimates channel and
Internet
Back haul 
mobile
t=0: Mobile estimates channel and
feeds this back to base station
t=: Base station receives estimates,
adapts transmission based on these
t=
t=0
Higher BER
Lower bps/Hz
Channel Mismatch 20

21. Prediction of Wireless Channels
Use current and previous channel estimates to predict future channel response
Overcome feedback delay
Adaptation based on predicted channel response
Lessen amount of feedback
Predicted channel response may reduce how often direct channel feedback is provided
h(n-p)
h(n-)
h(n)
h(n+) ? … 21

22. … 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
Data Subcarriers
IFFT
Time-domain channel taps 22

23. OFDM Channel Prediction Comparison
Compared three approaches in unified framework [Wong, Forenza, Heath & Evans, 2004]
Analytical and numerical MSE comparison
All-subcarrier and pilot-subcarrier methods have similar MSE performance
Time-domain prediction performs much better than the two other frequency domain prediction methods
Complexity comparison
All-subcarrier > Pilot-subcarrier ¸ Time-domain 23

24. 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

25. 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
Used in modeling and simulation of wireless channels [Jakes 1974]
Used in ray-tracing channel characterization [Rappaport 2002]
n OFDM symbol index k subchannel index 25

26. 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

27. 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
Time-delay estimation
Doppler-frequency estimation 27

28. IEEE e Simulation 28

29. Mean-square Error vs. SNR
Prediction 2  ahead
ACRLB – Asymptotic Cramer-Rao Lower Bound
CRLB – Cramer-Rao Lower Bound 29

30. Mean-square Error vs. Prediction Length
SNR = 7.5 dB
ACRLB – Asymptotic Cramer-Rao Lower Bound
CRLB – Cramer-Rao Lower Bound 30

31. Performance Comparison Summary
L - No. of paths M - No. of rays per path
Explain last two lines more 31

32. MU-OFDM Resource Allocation with Predicted CSI (Future Work)
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

33. Conclusion Resource allocation for MU-OFDM with proportional rates
Allows tradeoff between sum capacity and user rate “fairness”
Enables 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

34. Embedded Signal Processing Laboratory
Director: Prof. Brian L. Evans
WiMAX (OFDM) related research
Algorithms for resource allocation in MU-OFDM
Algorithms for OFDM channel estimation and prediction
Key collaborators: Prof. Jeff Andrews and Prof. Robert Heath
Key graduate students:
Zukang Shen, PhD
Ian C. Wong, PhD Candidate
Kyungtae Han, PhD Candidate
Daifeng Wang, MS Student
Hamood Rehman, MS Student 34

35. Backup 35

36. 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 (Allocate best subchannel for each user)
Find satisfying for all
Let , and update
While (Iteratively give lowest rate user first choice)
Find satisfying for all
For the found , find satisfying for all
For the found and , Let , and update
Back 36

37. 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
subchannels
Water-level 37

38. Power Allocation among Many Users
Use proportional rate and total power constraints
Solve nonlinear system of K equations: /iteration
Two special cases
Linear case: , closed-form solution
High channel-to-noise ratio: and
where
Back 38

39. Comparison with Optimal Solution
Back 39

40. Comparison with Max-Min Capacity40

41. Comparison with Max Sum Capacity41

42. 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

43. Wong’s 4-Step Approach
Determine number of subcarriers Nk for each user
Assign subcarriers to each user to give rough proportionality
Assign total power Pk for each user to maximize capacity
Assign the powers pk,n for each user’s subcarriers (waterfilling)
O(K)
O(KNlogN)
O(K)
O(N) 43

44. Desired proportionality among data rates
Simple Example
N = 4 subchannels
K = 2 users
Ptotal = 10
Desired proportionality among data rates 10 8 7 4
1 = 3/4 9
2 = 1/4 6 5 3 44

45. Step 1: # of Subcarriers/UserNk 3 1 10 8 7 4
1 = 3/4 9
2 = 1/4 6 5 3
N = 4 subchannels
K = 2 users
Ptotal = 10 1 2 3 4 45

46. Step 2: Subcarrier Assignment10 8 4 7 10 10 8 10 8 7 Rk
Rtot 8 4 7 4 7
log2(1+2.5*10)=4.70
log2(1+2.5*8)=4.39 4
log2(1+2.5*7)=4.21
13.3 3 6 5 9 9
log2(1+2.5*9)=4.55
4.55 3 6 5  Nk
3/4 3
1/4 1 1 2 3 4 1 2 3 4 46

47. Step 3: Power per user P1 = 7.66 P2 = 2.3410 8 7 9
P1 = 7.66
P2 = 2.34
N = 4 subchannels; K = 2 users; Ptotal = 10
Back 47

48. Step 4: Power per subcarrier
Waterfilling across subcarriers for each user
P1 = 7.66
P2 = 2.34
p1,1= 2.58
p1,2= 2.55
p1,3= 2.53
p2,1= 2.34  Nk
3/4 3
1/4 1 1 2 3 4 10 8 7 9
Data Rates:
R1 = log2( *10) + log2( *8)
+ log2( *7) =
R2 = log2( *9) =
Back 48

49. Pilot-based Transmission
Comb pilot pattern
Least-squares channel estimates t f … Dt Df
Get rid of pattern, legend of LS estimates, remind key parameters, Nt nf,… 49

50. Prediction over all the subcarriers
Design prediction filter for each of the Nd data subcarriers
Mean-square error 50

51. 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 e OFDM)
Use the same prediction filter for the data subcarriers nearest to the pilot carrier …
Pilot Subcarriers
Data Subcarriers 51

52. 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

53. Simulation Parameters (IEEE 802.16e)
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

54. Prediction Snapshot 54

55. NMSE vs. Channel Estimation Error55

56. NMSE vs. Prediction Horizon56

57. 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

58. 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

59. Prediction as parameter estimation
Channel is a continuous non-linear function of the 4M-length channel parameter vector 59

60. Cramer-Rao Lower Bound (CRLB)
Fix this slide… add legend for notation 60

61. 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
Add box to equation , legend for notation Nf Nt Dt Df, n, k kbar, add bullet lead in to equation 61

62. Insights from the MSE expression
Amplitude & phase error variance
Doppler frequency & phase cross covariance
Doppler frequency error variance
Time-delay & phase cross covariance
Time-delay error variance
Linear increase with 2 and M
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
Fix equations, put arrows or animation to explain quadratic increase, say what is new and known, explain some tradeoffs… 62