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This paper considers the bandwidth reservation problem in a mobile ad hoc network (MANET) to support QoS (quality-of-service) routing. We approach this problem by assuming a common channel shared by all hosts under a TDMA (time division multiple access) channel model. Existing solutions have addressed this problem by assuming a stronger multi-antenna model, where the bandwidth of a link is independent of the transmitting/receiving activities of its neighboring links, or a less strong CDMA-over-TDMA channel model, where the use of a time slot on a link is only dependent on the status of its one-hop neighboring links. While more practical and less costly, using a TDMA model needs to face the challenge of radio interference problems. In this paper, we propose a new protocol that can reserve routes by addressing both the hidden-terminal and exposed-terminal problems. The protocol can conduct accurate bandwidth calculation while performing route discovery. Simulation results are presented to verify how this new protocol performs.