Lately, spread spectrum systems are being increasingly used for commercial wireless communications because of their ability to reject various types of interference. This ability allows them to be used in multiple access systems. Direct sequence and frequency hopping systems have been the primary spread spectrum techniques used in practice. One technique which has not received much attention until recently is time hopping. In time hopping, a symbol is transmitted at a random position within the symbol period using a pulse width which is much smaller than the symbol period. Ultra-wideband (UWB) technology is a radar technology which shows promise for an relatively simple implementation of a time hopping system. This thesis looks at the error probability performance of a UWB time hopping multiple access system. Previous work has led to an estimate of the performance using a Gaussian approximation similar to that used for direct sequence systems. Through the use of a fast simulation technique, it will be shown that in certain situations, the Gaussian approximation fails to accurately predict the performance. A numerical analysis which uses characteristic functions is developed and shown to correctly predict the system’s performance under a wide range of situations. This numerical analysis also contributes to the understanding of the system. / Master of Science