1. Ian C. Wong and Brian L. Evans ICASSP 2007 Honolulu, Hawaii
Optimal Downlink OFDMA Subcarrier, Rate, and Power Allocation for Ergodic Rate Maximization with Imperfect Channel Knowledge
Ian C. Wong and Brian L. Evans
ICASSP 2007
Honolulu, Hawaii

2. Orthogonal Frequency Division Multiple Access (OFDMA)
Adopted by IEEE a/d/e and 3GPP-LTE
Multiple users assigned different subcarriers
Inherits advantages of OFDM
Granular exploitation of diversity among users through channel state information (CSI) feedback
User 1
frequency
Base Station
(Subcarrier and power allocation)
. . .
User M

3. Summary of Contributions
Previous Research
Our Contributions
Solution
Constraint-relaxation
One large constrained convex optimization problem
Resort to sub-optimal heuristics (O(MK2) complexity)
Dual optimization
Multiple small optimization problems w/closed-form solutions
99.999% optimal with O(MK) complexity
Previous Research
Our Contributions
Solution
Constraint-relaxation
One large constrained convex optimization problem
Resort to sub-optimal heuristics (O(MK2) complexity)
Dual optimization
Multiple small optimization problems w/closed-form solutions
99.999% optimal with O(MK) complexity
Assumption
Perfect channel knowledge
Unrealistic due to channel estimation errors and delay
Imperfect channel knowledge
Allocate based on statistics of channel estimation/prediction errors

4. OFDMA Signal Model Downlink OFDMA with K subcarriers and M users
Perfect time and frequency synchronization
Delay spread less than guard interval
Received K-length vector for mth user at nth symbol
Diagonal gain matrix
Diagonal channel matrix
Noise vector

5. Partial Channel State Information Model
Stationary and ergodic channel gains
MMSE channel prediction
MMSE Channel Prediction
Ehat
Conditional PDF of channel-to-noise ratio (CNR) – Non-central Chi-squared
CNR:
Normalized error variance:

6. Discrete Rate Function
Uncoded
BER = 10-3
Average rate function given partial CSI:

7. BER, Power, and Rate Functions
Impractical to impose instantaneous BER constraint when only partial CSI is available
Find power allocation function that fulfills the average BER constraint for each discrete rate level
Given the power allocation function for each rate level, the average rate can be computed
Derived closed-form expressions for average BER, power, and average rate functions

8. Weighted-Sum Rate Maximization with Partial CSI
Nonlinear integer
program
Rate levels:
Average rate:
Feasible set:
Power:
User weights:

9. Dual Optimization Method
“Dualize” the power constraint
Multiple small optimization problems with simple solutions
Continuous and convex (may not be continuously differentiable)
Find optimal multiplier using derivative-free line search
Bottleneck: computing rate and power functions
Rate and power functions independent of multiplier
Can be computed and stored before running search

10. Optimal Subcarrier, Rate, and Power Allocation
Optimal rate level selection:
Optimal user selection:
Optimal power allocation:
Optimal rate allocation:

11. Simulation Parameters (3GPP-LTE)
Channel Snapshot

12. Power Allocation Functions
Optimal Power Allocation:
Multilevel Fading Inversion
(MFI):
Predicted CNR:

13. Two User Capacity Region
No. of line search
iterations (I)
5 dB
21.33
10 dB
21.12
15 dB
21.15
Relative
Gap
(x10-4)
71.48
7.707
5.662
Complexity
O(MK(I+L))
M – No. of users
K – No. of subcarriers;
I – No. of line search iterations
L – No. of discrete rate levels

14. Average BER Comparison
Per-subcarrier Average BER
Per-subcarrier Prediction Error Variance
Subcarrier Index

15. Conclusion
Derived downlink OFDMA resource allocation algorithms assuming partial CSI
Maximizes ergodic weighted-sum rates conditioned on partial CSI
Requires linear complexity
Achieves negligible optimality gaps (99.999% optimal)
Ignoring CSI errors causes average BER degradation
Level of degradation depends on CSI error variance

16. Further reading: continuous rate and perfect CSI cases
MAHALO!
Further reading: continuous rate and perfect CSI cases
[1] I.C. Wong and B. L. Evans, "Optimal OFDMA resource allocation with linear complexity to maximize ergodic weighted-sum capacity," Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Proc., April 16-20, 2007, Honolulu, HI USA [Poster Session: Fri, 9:30-11:30am, Poster Area 2].
[2] I. C. Wong and B. L. Evans, "Optimal Resource Allocation in OFDMA Systems with Imperfect Channel Knowledge,“ IEEE Trans. on Communications., submitted.
[3] I. C. Wong and B. L. Evans, "Optimal OFDMA Resource Allocation with Linear Complexity to Maximize Ergodic Rates," IEEE Trans. on Wireless Communications, submitted.