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In this paper, we consider a shared wireless medium as employed in a mobile ad hoc wireless network. We develop an analytical approach to evaluate the single-hop performance of IEEE 802.11 DCF (Distributed Coordination Function) based MAC (Medium Access Control) algorithm that is combined with the use of directional transmitting and receiving antenna beams at each mobile entity. We characterize the saturation throughput performance of such directional CSMA/CA (Carrier Sensing Multiple Access with Collision Avoidance) protocol in terms of the number of channel contenders, packet size, selected beamwidth and location tracking imprecisions induced by entity mobility. The presented analytical framework provides valuable insights on the use of directional contention-based MAC protocols in mobile ad hoc wireless networks. Using our analytical, as well as simulation evaluations, we present an extensive set of performance results. We show that the directional CSMA/CA system can provide a significant upgrade of network performance when the beamwidth is properly selected.