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In this paper, the authors consider how to achieve proportional fairness in multi-rate 802.11 WLANs by investigating an integrated problem of power control and AP Association in order to provide an effective tradeoff between network throughput and fairness. Since jointly considering power control and AP association for proportional fairness is NP-hard, they propose a centralized heuristic approach. By introducing a new concept of AP utility, they establish the relationship between the network utility and the AP utility according to proportional fairness. This relationship is exploited to design an algorithm PCAP to optimize the network utility by increasing the average and decreasing the variance of the AP utility.
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