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In this paper, we first present the challenges involved in the design of media access control (MAC) protocols for UWB based wireless networks. We formulate the radio resource allocation problem as a theoretical optimization problem that maximizes the system throughput under different constraints that reflect the UWB physical layer, the system topology as well as the traffic patterns. We introduce a suboptimal practical MAC protocol that allocates the nodes' transmission power and bit rates. In the proposed method, we differentiate between two different classes, best effort and real-time classes. We implemented our scheme in MATLAB and the simulation results show that the proposed method results in significant higher throughput compared to a random access MAC protocol.