The Tradeoff Between Processing Gains of an Impulse Radio UWB System in the Presence of Timing Jitter

In time hopping impulse radio, N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> pulses of duration T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> are transmitted for each information symbol. This gives rise to two types of processing gains: (i) pulse combining gain, which is a factor Nf, and (ii) pulse spreading gain, which is N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> = T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> /T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> , where T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> is the mean interval between two subsequent pulses. This paper investigates the tradeoff between these two types of processing gains 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 (BEP) 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 (MAI) and timing jitter on the selection of optimal system parameters are explained through theoretical analysis. Finally, a multipath scenario is considered, and the tradeoff between processing gains of a synchronous impulse radio system with pulse-based polarity randomization is analyzed. The effects of the timing jitter, MAI, and interframe interference (IFI) are investigated. Simulation studies support the theoretical results.