This paper provides the bit error rate (BER) analysis of the antipodal and orthogonal binary signals under the ultra-wideband (UWB) channel. We offer an analytical expression and its evaluation formula for the BER. The channel model we consider is the IEEE 802.15.4a UWB channel. We take into account of the impact of all the key parameters, including inter-cluster arrival rate, cluster decay constant, the inter-ray arrival rate, ray decay constant, parameters of the power delay profile (PDP), and the distribution of a Nakagami fading signal. For the IEEE 802.15.4a UWB channel, the effects of clustering are characterized by a Poisson process, and the inter-ray arrival time is modeled as the hyperexponential random variable. We propose a systematic analytical method to evaluate the BER performance of the UWB signal associated with such joint continuous Nakagami and discrete Poisson random variable. Thus, the developed analytical model is useful in evaluating the performance of an UWB signal in the IEEE 802.15.4a channel without time consuming simulations.