On the asymptotic distribution of the correlation receiver output for time-hopped UWB signals

In ultra-wideband (UWB) communications based on time-hopping (TH) impulse radio, one of the most frequently studied receivers is the correlation receiver. The multiuser interference (MUI) at the output of this receiver is sometimes modeled as a Gaussian random variable. In order to justify this assumption, the conditions of validity of the Central Limit Theorem (CLT) have to be studied in an asymptotic regime where the number of interferers and the processing gain grow toward infinity at the same rate, with the channel degree being kept constant. An asymptotic study is made in this paper based on the so-called Lindeberg's condition for the CLT for martingales. Nonsynchronized users sending their signals over independent multipath channels are considered. These users may also have different powers. It is shown that when the frame length grows and the repetition factor is kept constant, then the MUI does not converge in distribution toward a Gaussian random variable. On the other hand, this convergence can be established if the repetition factor grows at the rate of the frame length. In this last situation, closed-form expressions for the signal-to-interference-plus-noise ratio (SINR) are given for TH pulse amplitude modulation (PAM) and pulse position modulation (PPM) UWB transmissions.