Optimal Downlink OFDMA Resource Allocation with Linear Complexity to Maximize Ergodic Rates

OFDMA resource allocation assigns subcarriers and power, and possibly data rates, to each user. Previous research efforts to optimize OFDMA resource allocation with respect to communication performance have focused on formulations considering only instantaneous per-symbol rate maximization, and on solutions using suboptimal heuristic algorithms. This paper intends to fill gaps in the literature through two key contributions. First, we formulate continuous and discrete ergodic weighted sum rate maximization in OFDMA assuming the availability of perfect channel state information (CSI). Our formulations exploit time, frequency, and multi-user diversity, while enforcing various notions of fairness through weighting factors for each user. Second, we derive algorithms based on a dual optimization framework that solve the OFDMA ergodic rate maximization problem with O(MK) complexity per OFDMA symbol for M users and K subcarriers, while achieving data rates shown to be at least 99.9999% of the optimal rate in simulations based on realistic parameters. Hence, this paper attempts to demonstrate that OFDMA resource allocation problems are not computationally prohibitive to solve optimally, even when considering ergodic rates.