  In this paper, the performance of a binary phase shift keyed random
time-hopping impulse radio system with pulse-based polarity randomization is
analyzed. Transmission over frequency-selective channels is considered and the
effects of inter-frame interference and multiple access interference on the
performance of a generic Rake receiver are investigated for both synchronous
and asynchronous systems. Closed form (approximate) expressions for the
probability of error that are valid for various Rake combining schemes are
derived. The asynchronous system is modelled as a chip-synchronous system with
uniformly distributed timing jitter for the transmitted pulses of interfering
users. This model allows the analytical technique developed for the synchronous
case to be extended to the asynchronous case. An approximate closed-form
expression for the probability of bit error, expressed in terms of the
autocorrelation function of the transmitted pulse, is derived for the
asynchronous case. Then, transmission over an additive white Gaussian noise
channel is studied as a special case, and the effects of multiple-access
interference is investigated for both synchronous and asynchronous systems. The
analysis shows that the chip-synchronous assumption can result in
over-estimating the error probability, and the degree of over-estimation mainly
depends on the autocorrelation function of the ultra-wideband pulse and the
signal-to-interference-plus-noise-ratio of the system. Simulations studies
support the approximate analysis.
