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The IEEE 802.11 protocol provides a physical multi-rate capability. Existing auto rate schemes concentrate on passively tuning the rate according to the channel strength, but cannot exploit the time-variation of fading channel. In this paper, by means of an analytical model, the authors derive the rule maximizing the throughput of RTS/CTS based multi-rate WLANs. Then, based on the obtained rule the authors propose a distributed fair auto rate medium access control scheme. With the proposed scheme, after receiving a RTS frame, the receiver selectively returns the CTS frame according to both the signal-to-noise ratio of the RTS frame and current network status. Moreover, the returned CTS carries a piggyback information indicating the maximum feasible rate. The key feature of the proposed scheme is that it is capable of positively exploiting time-varying fading channel and maintaining fairness in asymmetric situation where the distribution of SNR varies with stations. Extensive simulation results show that the proposed scheme outperforms the existing fairness schemes in time-varying channel conditions.