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Although asymptotic bounds of wireless network capacity have been heavily pursued, the answers to the following questions are still critical for network planning, protocol and architecture design: Given a three-dimensional (3D) network space with the number of active users randomly located in the space and using the wireless communication technology, what are the expected per-flow throughput, network capacity, and network transport capacity? In addition, how can the protocol parameters be tuned to enhance network performance? In this paper, we focus on the ultra wideband (UWB) based wireless personal area networks (WPANs) and provide answers to these questions, considering the salient features of UWB communications, i.e., low transmission/interference power level, accurate ranging capability, etc. Specifically, we demonstrate how to explore the spatial multiplexing gain of UWB networks by allowing appropriate concurrent transmissions. Given 3D space and the number of active users, we derive the expected number of concurrent transmissions, network capacity and transport capacity of the UWB network. The results reveal the main factors affecting network (transport) capacity, and how to determine the best protocol parameters, e.g., exclusive region size, in order to maximize the capacity. Extensive simulation results are given to validate the analytical results.