A Unified Fading Model Using Infinitely Divisible Distributions

TL;DR

This paper introduces a unified fading model for wireless channels by representing the channel gain as an infinitely divisible random variable, enabling comprehensive analysis of various fading phenomena.

Contribution

It proposes a novel unification framework for fading distributions using infinitely divisible random variables, encompassing many existing models in wireless communications.

Findings

Most common fading distributions are included in the infinitely divisible class.

The model simplifies performance analysis of wireless systems.

It subsumes several previously proposed unifications of fading models.

Abstract

This paper proposes to unify fading distributions by modeling the magnitude-squared of the instantaneous channel gain as an infinitely divisible random variable. 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 $n$. Infinitely divisible random variables have many interesting mathematical properties, which can be applied in the performance analysis of wireless systems. It is shown that the proposed unification subsumes several unifications of fading distributions previously proposed in the wireless communications literature. In fact, almost every distribution used to model multipath, shadowing and composite multipath/shadowing is shown to be included in the class of infinitely divisible random variables.