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Ultra-wideband (UWB) communications is receiving significant attention recently due to its high data rates and low power, low interference transmission. This paper considers the issue of utilizing these advantages of UWB to design improved Wireless Sensor Networks (WSNs). In particular, we consider data gathering in wireless sensor networks using a mobile node for data collection. We first propose a network architecture where a mobile node equipped with both a UWB transceiver and a narrowband RF transceiver is used to collect data from sensor nodes. The sensor nodes are equipped with a narrowband RF transceiver and only a UWB transmitter (not receiver). This approach is chosen to strike a balance between cost of each sensor node and speed of data transfer, since a UWB transmitter is much less complex and expensive than a UWB receiver. We then propose a mobile Data Gathering (DGR) algorithm to find a minimal set of points in the sensor network, which will serve as data gathering points for the mobile node. We use a Voronoi diagram of the network as a starting point, considering each sensor node in the network as a site in the Voronoi diagram and finnding points in the network where data from multiple sites (sensor nodes) can be collected. We then use a weight function designed to reduce the number of these data collection points, and generate a new smaller set of points, such that the mobile node can collect data from multiple sites from each such point. With the aid of a discrete-event simulation model, we show significant savings in the total time for data collection while providing a high level of network coverage.