Random phase tracking of non-uniformly sampled signals

Random phase tracking of discrete time signals perturbed by an additive White Gaussian Noise channel (AWGN) and also a fading channel is presented in this paper. The zero-crossing sampling detector employed causes the sampling of the incoming signal to be non-uniform. The fading channel assumed is a Log-Normal channel and causes random pertubations in both amplitude and phase of the incoming signal. Mathematical description of the phase detector with a second order digital filter is presented and its performance is characterized by the phase error process statistics. Under the assumption of weak amplitude fluctuations and for a frequency step-input an approximate analytic solution in the steady state has been obtained by solving the corresponding Chapman-Kolmogorov (C-K) equation. These results have been verified by numerical and simulation methods.