The performance of a binary phase shift keyed random time-hopping impulse radio system with pulse-based polarity randomization is analyzed. The effects of multiple access interference are investigated for both chip-synchronous and asynchronous systems. It is shown that the performance of a chip-synchronous system is the same as that for the symbol-synchronous case studied in . The asynchronous system is modelled as a chip-synchronous system with uniformly distributed timing jitter on the transmitted pulses of interfering users. This extends the analytical technique developed for the chip-synchronous case to the asynchronous case. An approximate closed-form expression for the probability of error, expressed in terms of the autocorrelation function of the transmitted pulse, is derived for the asynchronous case. The analysis shows that the chip-synchronous assumption can result in over-estimating the error probability, and hence that the system design based on this approximation will be on the safe side. The degree of overestimation mainly depends on the autocorrelation function of the UWB pulse and signal-to-interference-plus-noise-ratio (SIR) of the system. Simulations studies support this approximate analysis.