Product and Ratio of Two $\alpha-\kappa-\mu$ Shadowed Random Variables and its Application to Wireless Communication

TL;DR

This paper derives statistical expressions for the product and ratio of independent $ ext{ extalpha- extkappa- extmu}$ shadowed random variables and applies these results to analyze wireless communication performance metrics.

Contribution

It provides new series and integral expressions for the product and ratio distributions of $ ext{ extalpha- extkappa- extmu}$ shadowed variables and applies them to wireless system performance analysis.

Findings

Derived series and integral expressions for PDFs, CDFs, and MGFs.

Analyzed outage probability in cascaded wireless systems.

Evaluated secrecy metrics and RIS-assisted communication performance.

Abstract

This work studies the product and ratio statistics of independent and non-identically distributed (i.n.i.d) $ \alpha-\kappa - \mu $ shadowed random variables. We derive the series expression for the probability density function (PDF), cumulative distribution function (CDF), and moment generating function (MGF) of the product and ratio of i.n.i.d $ \alpha - \kappa - \mu $ shadowed random variables. We then give the single integral representation for the derived PDF expressions. Further, as application examples, 1) outage probability has been derived for cascaded wireless systems, and 2) physical-layer security metrics like secrecy outage probability and strictly positive secrecy capacity are derived for the classic three-node model with $\alpha-\kappa-\mu$ shadowed fading. Next, we discuss an intelligent reflecting surface-assisted communication system over $\alpha-\kappa-\mu$ shadowed fading.