Researchers have recently considered the use of smart antennas in various packet-switched data networks. Previously, a single-beam system was described which employs a smart antenna basestation, operating in carrier-sense (CSMA) mode. Performance improvements are obtained by having the antenna dynamically point pattern nulls in the direction of interfering stations, thus reducing the frequency of channel collisions. In this paper, we consider the reverse-link performance of stations accessing a smart antenna basestation using multibeam SDMA. A basic CSMA/SDMA protocol is first proposed for this type of system. Following this, we also present a CSMA/SDMA protocol which incorporates basestation/portable signalling which mitigates the effects of hidden stations. The performance of these systems is characterized and compared using analytical throughput and capacity models. It is shown that when hidden stations are present, the capacity performance of the more sophisticated protocol may be much higher than that of the basic version.