  In time hopping impulse radio, $N_f$ pulses of duration $T_c$ are transmitted
for each information symbol. This gives rise to two types of processing gain:
(i) pulse combining gain, which is a factor $N_f$, and (ii) pulse spreading
gain, which is $N_c=T_f/T_c$, where $T_f$ is the mean interval between two
subsequent pulses. This paper investigates the trade-off between these two
types of processing gain in the presence of timing jitter. First, an additive
white Gaussian noise (AWGN) channel is considered and approximate closed form
expressions for bit error probability are derived for impulse radio systems
with and without pulse-based polarity randomization. Both symbol-synchronous
and chip-synchronous scenarios are considered. The effects of multiple-access
interference and timing jitter on the selection of optimal system parameters
are explained through theoretical analysis. Finally, a multipath scenario is
considered and the trade-off between processing gains of a synchronous impulse
radio system with pulse-based polarity randomization is analyzed. The effects
of the timing jitter, multiple-access interference and inter-frame interference
are investigated. Simulation studies support the theoretical results.
