A Unified Approach for Modeling Fading Channels Using Infinitely Divisible Distributions

Abstract

This paper proposes to unify fading distributions by modeling the instantaneous SNR as an infinitely divisible random variable, which is a known class of random variables from the probability theory literature. A random variable is said to be infinitely divisible if it can be written as a sum of $n \geq 1$ independent and identically distributed random variables for each $n$ . The proposed unification subsumes several classes of multipath and shadowing fading distributions previously proposed in the wireless communication literature. We show that infinitely divisible random variables have many useful mathematical properties that are applied in the performance analysis of wireless systems. Specific applications include diversity analysis and partial ordering of fading distributions.