Changes in the probability distribution for Gaussian processes subjected to phase jitter

Wave propagation is frequently accompanied by random phase variations. If X(t) is the transmitted signal and A(t) represents the time varying delay, the received signal may be expressed as U(t)=X(t-A(t)). In this paper we show that if X(t) is a Gaussian process then U(t) is in general non-Gaussian if A(t) is stochastic. With the aid of a simple example, we demonstrate this deviation from normality. Finally, we propose three different distance measurements between the original and jittered processes, and investigate their relative merits