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We derive bounds on the expected capacity and outage capacity of a three-node relay network for UWB communications. We also provide a simple tight approximation for the derived upper bound on the capacity and then using this bound we obtain the outage probability of the network. Numerical results show that a significant improvement in the system capacity and outage probability is obtained by adding a relay node. Moreover, our theoretical results reveal that the diversity gain of a relay channel substantially increases by using UWB links instead of NB links. We also derive these bounds when we have a constraint on the total transmitted power of the source and the relay nodes.