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

Orthogonal Frequency Division Multiple Access (OFDMA) Adopted by IEEE 802.16a/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

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

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

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:

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

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

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

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

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

Simulation Parameters (3GPP-LTE) Channel Snapshot

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

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

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

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

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.