Abstract-Binary signaling over the IEEE 802.15.3a ultra-wideband channel model is considered. For received waveforms observed during a finite time window, a formula is derived for the average bit error probability (BEP). The formula can be rapidly evaluated using Gaussian quadratures, and is used to study average BEP curves as a function of window size, which is then related to the percentage of energy captured. These techniques should be useful to system designers in assessing the performance impact of various signaling rates, guard times, etc.Index Terms-Cluster process, lognormal distribution, point process, Saleh-Valenzuela model, shot noise, ultra-wideband (UWB).

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The IEEE 802.15.3a standards body has developed a modification of the Saleh-Valenzuela multipath channel model as the accepted model for ultra-wideband channel investigations. Although it is straightforward to simulate channel realizations according to the model, doing so many thousands of times in order to estimate bit-error probabilities is computationally intensive. To overcome this burden, this paper derives an exact analytical formula for the average bit-error probability that can be quickly evaluated using Gaussian quadrature.

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