Ian C. Wong and Brian L. Evans ICASSP 2007 Honolulu, Hawaii OPTIMAL OFDMA RESOURCE ALLOCATION WITH LINEAR COMPLEXITY TO MAXIMIZE ERGODIC WEIGHTED SUM CAPACITY Ian C. Wong and Brian L. Evans ICASSP 2007 Honolulu, Hawaii

Mobile Broadband Wireless Access (IEEE 802.16e, 3GPP-LTE) Ubiquitous and high-speed video, data, and voice Ease of deployment, lower total cost of ownership Scalable infrastructure Figure from http://www.wi-lan.com/library/WiMAX_Intro_CES_2005.pdf

Orthogonal Frequency Division Multiple Access (OFDMA) Adopted by IEEE 802.16a/d/e and 3GPP-LTE Allows multiple users to transmit simultaneously on different subcarriers Inherits advantages of OFDM Exploits diversity among users . . . User 1 frequency Base Station (Subcarrier and power allocation) User M

OFDMA Resource Allocation How do we allocate K data subcarriers and total power P to M users to optimize some performance metric? E.g. IEEE 802.16e: K = 1536, M¼ 40 / sector Voice applications Minimize transmit power required to support a set of data rates Data applications Maximize data rates subject to power constraints Very active research area Difficult discrete optimization problem Brute force optimal solution: Search through MK subcarrier allocations and determine power allocation for each

Summary of Contributions Previous Research Our Contributions Formulation Instantaneous rate Unable to exploit time-varying wireless channels Ergodic rate Exploits time-varying nature of the wireless channel Solution Constraint-relaxation One large constrained convex optimization problem Resort to sub-optimal heuristics (O(MK2) complexity) Dual optimization Multiple small unconstrained problems w/closed-form solutions 99.9999% optimal with O(MK) per iteration, <10 iterations

Weighted-Sum Capacity Maximization Constant weights Powers to determine Channel gain to noise ratio Average power constraint Space of feasible power allocation vectors Subcarrier capacity

Dual Optimization Method “Dualize” the power constraint Multiple small unconstrained problems with closed-form solutions Find optimal geometric multiplier using line search Derived closed-form PDF of dual 1-dimensional integral per iteration “Multi-level waterfilling” Geometric multiplier “Max-dual user selection”

Optimal Subcarrier and Power Allocation “Multi-level waterfilling” “Max-dual user selection”

Numerical Results 5 dB 8.091 8.344 10 dB 7.727 8.333 15 dB 7.936 8.539 SNR Erg. Rates Inst. No. of Iterations (I) 5 dB 8.091 8.344 10 dB 7.727 8.333 15 dB 7.936 8.539 Relative Gap (x10-6) .0251 5.462 .0226 5.444 .0159 Initialization Complexity O(INM) - Runtime Complexity O(MK) O(IMK) M – No. of users; K – No. of subcarriers; N – No. of function evaluations for integration

Conclusion Derived downlink OFDMA resource allocation algorithms Requires linear complexity Maximizes ergodic weighted-sum capacity Achieves negligible optimality gaps (99.9999% optimal) Extensions to discrete rate and partial CSI cases: [1] I. C. Wong and B. L. Evans, "Optimal Resource Allocation in OFDMA Systems with Imperfect Channel Knowledge,“ IEEE Trans. on Communications., submitted. [2] I. C. Wong and B. L. Evans, "Optimal OFDMA Resource Allocation with Linear Complexity to Maximize Ergodic Rates," IEEE Trans. on Wireless Communications, submitted. [3] I.C. Wong and B. L. Evans, "Optimal OFDMA Subcarrier, Rate, and Power Allocation for Ergodic Rates Maximization with Imperfect Channel Knowledge," Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Proc., April 16-20, 2007, Honolulu, HI USA, accepted.