Stochastic models for long-term multipath fading channels and their statistical properties

Abstract

This paper discusses the use of stochastic differential equations and point processes to model the long-term fading effects during transmission of electromagnetic waves over large areas, which are subject to multipaths and power loss due to long distance transmission and reflections. When measured in dB's, the power loss follows a mean reverting Ornstein-Uhlenbeck process, which implies that the power loss is log-normally distributed. The arrival times of different paths are modeled using non-homogeneous Poisson counting processes and their statistical properties of the multipath power loss are examined. The moment generating function of the received signal is calculated and subsequently exploited to derive a central limit theorem, and the second-order statistics of the channel.