Accurate Performance Evaluation of Time-Hopping and Direct-Sequence UWB Systems in Multi-User Interference

An exact analysis is derived for precisely calculating the bit error probability of time-hopping and direct-sequence ultra-wideband systems with multi-user interference in an additive white Gaussian noise environment. The analytical expressions are validated by simulation and used to assess the accuracy of the Gaussian approximation proposed for estimating the performance of ultra-wideband communication systems. The Gaussian approximation is shown to be inaccurate for predicting the bit error rate for medium and large signal-to-noise ratio values. The performances of time-hopping and direct-sequence modulation schemes are accurately compared for different numbers of users and frame widths. It is shown that direct-sequence binary phase-shift keying outperforms time-hopping binary phase-shift keying for medium and large values of signal-to-noise ratio, which contradicts some previous results obtained using a Gaussian approximation.