Analytical expressions based on the Gauss-Chebyshev quadrature (GCQ) rule technique are derived to evaluate the bit-error rate (BER) for the time-hopping pulse position modulation (TH-PPM) ultra-wide band (UWB) systems under a Nakagami-m fading channel. The analyses are validated by the simulation results and adopted to assess the accuracy of the commonly used Gaussian approximation (GA) method. The influence of the fading severity on the BER performance of TH-PPM UWB system is investigated.