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Optimal OFDMA Resource Allocation with Linear Complexity to Maximize Ergodic Weighted Sum Capacity

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 weighted sum ergodic capacity 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 capacity 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.