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In this paper, we present a computable bit error rate (BER) expression for the binary signals in the IEEE 802.15.3a ultra-wideband (UWB) channel. In the literature, the impacts of the RAKE receiver's finger numbers and lognormal shadowing on the BER performance have not been reported yet. We propose a characteristic function (CF) based BER formula to overcome the convergence problem of the existing moment generating function (MGF) approach when the BER calculation takes account of the shadowing effect. Simulation results demonstrate that the proposed CF-based computable BER formula can accurately estimate the complete effects of the cluster and ray arrival processes, the lognormal fading as well as shadowing, and the finger numbers at RAKE receivers.