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

Abstract

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, Ricean Nakagami etc. distributions to their non-stationary analogs and thus generalizing channel models to include time variations. From these computations the second order statistics of the received signal are obtained.