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The use of directional antennas in mobile ad hoc networks has shown to offer large potential throughput gains relative to omnidirectional antennas. When used in ad hoc networks, directional medium-access-control (DMAC) protocols usually require all nodes, or part of nodes, to be aware of their exact locations. This location information is typically provided using a global positioning system (GPS) which, typically, requires a line of sight in order to avoid the large signal attenuation and hence is not suitable for indoor applications. Moreover, as the inaccuracy associated with the GPS position estimation increases, the system throughput dramatically degrades. In this paper, we propose an efficient two-channel two-mode DMAC protocol. Our protocol employs two frequency division multiplexed channels: channel one used for omni-mode transmission and channel two for directional mode transmission. Signal parameter estimation via the rotational invariance technique (ESPRIT) is used for direction-of-arrival (DOA) estimation. By avoiding the reliance on GPS for obtaining the position information, our protocol is suitable for both outdoor and indoor applications. Under different operating conditions and channel models, our simulation results clearly show the throughput improvement achieved using the proposed protocol relative to the IEEE 802.11.