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Receiver design for impulse radio (IR) based ultra-wideband (UWB) communication is a challenge, because full-resolution digital receiver is difficult to implement under today's technology due to high sampling rate required. Some trade-offs can be made to the digital receiver, such as limiting amplitude resolution to only 1 bit, which results in a previously considered so-termed mono-bit receiver. In this paper, we consider the design of finite-resolution digital UWB receiver. We derive the optimal post-quantization processing, and analyze the achievable bit-error rate (BER) performance using an approximation of the log-likelihood ratio. We evaluate the effect of quantization threshold. The optimal threshold for two-bit quantization is obtained. Our work discloses the incremental gain that each sampling bit could bring and the results provide guidelines for designing IR UWB digital receivers.receivers.