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In a wireless network, with the aid of rate adaptation, multiuser diversity can be exploited by allowing the mobile user with the best channel to use the channel. However, the overhead that results from polling mobile stations to obtain channel state information (CSI) in large networks can outweigh the multiuser diversity gain. In this paper, we propose a wireless medium access control protocol, namely multiuser diversity with capture (MDC), which explicitly employs the capture effect to obviate the overhead problem. We analyze the good put performance of MDC and compare it with the medium access diversity (MAD) scheme proposed in the literature. Our results show that MDC is effective in networks with radio receivers possessing reasonably good capture properties and in networks where the number of mobile stations is reasonably large.