The error probability and capacity of a time-hopping ultra-wideband (UWB) communication system with receive diversity are investigated. We consider pulse amplitude modulation (PAM) and pulse-position modulation (PPM) over additive white Gaussian channels for a single-user system. A multiuser environment with PPM is also investigated. It is shown that the communication distance and error performance are improved by employing receive diversity. The channel capacity of PPM and PAM is determined subject to the power constraints of FCC part 15 rules to illustrate the relationship between reliable communication distance and signal-to-noise ratio. The error probability with PAM and receive diversity is derived for the single-user case. The error probability and performance bounds with PPM are derived for both the single-user and multiuser cases.