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In the past few years, ultra-wideband (UWB) has emerged as a radio transmission scheme for short-range wireless communications. Its various benefits have attracted interests in studying UWB technologies in both academia and industry. Currently, several MAC protocols are being proposed for UWB networks. A number of these protocols are direct adaptations from the existing MAC protocols that have been designed for narrowband systems, and thus do not make use of the UWB's unique characteristics. In contrary, there are UWB MAC protocols that incorporate dynamic channel coding after revealing that it is unique for UWB channels to exhibit a linear Shannon capacity function with respect to signal-to-noise ratio (SNR) at the receiver. We show in this paper another characteristic of a UWB channel. Specifically, for a given bit error rate and a transmission rate, the optimal ratio of interfering distance to transmitting distance may become less than unity in a UWB channel as compared to a value larger than unity in a narrowband system. This implies UWB can effectively support concurrent transmissions within the receiving range of a receiver node as long as they are outside an exclusion region given by the optimal distance ratio. In view of this, this paper further propose a CSMA/CA based MAC protocol called medium access control with concurrent transmissions (CT-MAC) to capitalize on this UWB characteristic. Simulation results indicate that CT-MAC improve the throughput-delay performance by allowing concurrent transmissions without compromising the bit error rate requirement.