In time hopping impulse radio, N f pulses of duration Tc 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 Nc = T f /Tc, 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

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... bability 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 Nc 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. 4 In coded systems, the polarity of all pulses are determined by a random polarity code sequence and a binary information bit, as will be explained later.