Stochastic models for short-term multipath fading channels: chi-square and Ornstein-Uhlenbeck processes

This paper discusses the use of stochastic differential equations to model signal envelope variations over areas, which are subject to short-term fading effects. The short-term fading effects are modeled using Ornstein-Uhlenbeck processes and they are derived from first principles, using the scattering assumption of electromagnetic waves. This gives rise to signal envelope variations which follow a mean-reverting square-root process, which is elastically pulled towards a long-term mean which characterizes the propagation environment. The derived signal envelope distributions include generalizations of Rayleigh, Rician, Nakagami etc. distributions to their nonstationary analogs and thus generalizing channel models to include time variations. From these computations the second order statistics of the received signal are obtained.