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We consider the medium access control (MAC) protocol design for nodes in a wireless LAN that use a wide-azimuth switched beam smart antenna system comprised of a multiple beam antenna array. The one-hop performance of carrier sense multiple access (CSMA) as well as slotted aloha for such a system is presented analytically and through simulation. The problem of synchronization of multiple beams in CSMA is investigated in our analysis. Our results show that, under heavy offered load conditions, CSMA is a good choice with nodes that have multiple-beam smart antennas, despite the performance loss due to the beam synchronization, providing a stable throughput that approaches unity and is invariant to fluctuations in the offered load. Slotted Aloha, on the other hand, is capable of higher peak throughput in a narrow range of offered loads as more switched beams are employed, but performance drastically reduces beyond optimum offered loads. We also introduce a method, expanded receive rule (ERR), whereby the tight synchronization among different beams of a receiver node in CSMA is relaxed, which is observed to provide better throughput. Finally, we also present performance results for a 4-way-handshake-type carrier sense mechanism using multiple beam antennas.