General non-stationary models for short-term and long-term fading channels

This paper discusses the use of stochastic differential equations to model signal envelope variations over large areas, which are subject to long-term fading effects from the transmitter to local areas, followed by short-term fading effects in local areas around the receiver. Based on first principles, we model the dynamics of the instantaneous power received of each multipath component, in the case of the short-term model, and power loss in dBs in the case of the long-term channel model using mean-reverting Ornstein-Uhlenbeck processes. With these models at hand, explicit expressions for signal envelope distributions are derived. They include generalizations of Rayleigh, Rician, log-normal, etc., distributions to their time-varying analogs. From these computations the second order statistics of the received signal are obtained.