The trade-off between processing gains of impulse radio systems in the presence of timing jitter

In time hopping impulse radio, N_f pulses of duration T_c are transmitted for each 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 with and without random polarity codes in the presence of timing jitter. Approximate expressions for bit error probability are derived for both coded and uncoded systems over additive white Gaussian noise channels and are used as the criterion to choose optimal N_f and N_c values. The effects of timing jitter and multiple access interference on the selection of optimal system parameters are explained through theoretical analysis. Simulation studies support the theoretical results.