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In this paper, we present the bit error probability (BEP) of a relay network employing UWB links between its nodes. Since UWB systems can resolve many paths and are thus rich in multipath diversity, the use of the Rake diversity combining is very effective. However, because of the complexity, it is impractical in the scenarios with portable terminals or in the networks with multiple relays. Time-reversal technique, in which the transmitting nodes can do the pre-diversity filtering of UWB signal before transmission, is known as an approach to achieve the performance equivalent to the Rake combining without increasing the receiver complexity. The performance of such a network with simple correlators for each link at the receiver side is analyzed considering some realistic channel estimation errors. The results show that there is a great potential in combining time reversal and UWB techniques with respect to both reducing the receiver complexity and improving the system performance. The system robustness to imperfect channel estimation is also shown in the numerical analysis and compared to traditional UWB system with All-rake receiver. The analytical expressions are also validated by computer simulations which confirm the accuracy of the approximations used in obtaining these results.