OFDMA Downlink Resource Allocation for Ergodic Capacity Maximization with Imperfect Channel Knowledge

In this paper, we derive an optimal resource allocation algorithm for ergodic weighted-sum capacity maximization in OFDMA systems assuming the availability of only partial (imperfect) CSI. Using a dual optimization framework, we show that the optimal power allocation is multi-level waterfilling based on the conditional expected value of the channel-to-noise ratio, and the optimal user is selected based on the maximum weighted conditional expected capacity penalized by the required power. The algorithm is shown to have O(MK) complexity for an OFDMA system with K used subcarriers and M active users, and achieves relative duality gaps of less than 10^-5 (99.99999% optimal).