A New Expression for the Product of Two $\kappa-\mu $ Shadowed Random Variables and its Application to Wireless Communication

TL;DR

This paper derives new mathematical expressions for the product of two independent $ppa-mu$ shadowed random variables, enabling better analysis of complex wireless communication systems under various fading conditions.

Contribution

It introduces a general series expression for the PDF, CDF, and MGF of the product of two i.n.i.d. $ppa-mu$ shadowed variables, applicable to many fading channel models.

Findings

Derived series expressions for PDF, CDF, and MGF.

Applied the results to outage probability in wireless systems.

Validated findings with extensive Monte-Carlo simulations.

Abstract

In this work, the product of two independent and non-identically distributed (i.n.i.d) $\kappa - \mu $ shadowed random variables is studied. We derive the series expression for the probability density function (PDF), cumulative distribution function (CDF), and moment generating function (MGF) of the product of two (i.n.i.d) $\kappa - \mu $ shadowed random variables. The derived formulation in this work is quite general as they incorporate most of the typically used fading channels. As an application example, outage probability (OP) has been derived for cascaded wireless systems and relay-assisted communications with a variable gain relay. Extensive Monte-Carlo simulations have also been carried out.