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There is growing interest in employing ultra-wideband (UWB) communication systems at the physical layer for multihop wireless networks. Recent efforts show that networking problems involving UWB systems should follow a cross-layer approach with consideration at multiple layers. Due to the nonlinear nature of the optimization problem, there are very limited theoretical results for this important problem. In this paper, we address this problem by considering a UWB-based ad hoc network. We study how to maximize capacity (in the form of a data rate utility) for a set of communication sessions. Via a cross-layer approach, we formulate this utility maximization problem into a nonlinear programming (NLP) problem, which takes into consideration routing, scheduling, and power control. We develop a solution procedure based on the so-called branch-and-bound framework. Within this framework, we employ a powerful optimization technique called reformulation linearization technique (RLT). We use numerical results to validate the efficacy of this solution procedure and offer insights on UWB-based ad hoc networks. This work provides a theoretical result for the achievable performance bound for a UWB-based ad hoc network.