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In this paper, we investigate the problem of achieving proportional fairness via access point (AP) association in multirate WLANs. This problem is formulated as a nonlinear programming with an objective function of maximizing the total user bandwidth utilities in the whole network. Such a formulation jointly considers fairness and AP selection. We first propose a centralized algorithm Non-Linear Approximation Optimization for Proportional Fairness (NLAO-PF) to derive the user-AP association via relaxation. Since the relaxation may cause a large integrality gap, a compensation function is introduced to ensure that our algorithm can achieve at least half of the optimal in the worst case. This algorithm is assumed to be adopted periodically for resource management. To handle the case of dynamic user membership, we propose a distributed heuristic Best Performance First (BPF) based on a novel performance revenue …