On the Distribution of the Ratio of Products of Fisher-Snedecor $\mathcal{F}$ Random Variables and Its Applications

TL;DR

This paper derives exact and approximate statistical characterizations for the ratio of products of Fisher-Snedecor F-distributed variables, facilitating performance evaluation in advanced wireless communication systems.

Contribution

It provides the first closed-form expressions and tight approximations for the ratio of products of F-distributed variables, enabling practical system performance analysis.

Findings

Exact closed-form expressions for PDF, CDF, and MGF of the ratio of products.

Simple, tight approximations for the distribution of products and ratios.

Numerical and simulation results validate the analytical expressions.

Abstract

The Fisher-Snedecor $\mathcal{F}$ distribution has been recently proposed as a more accurate and mathematically tractable composite fading model than traditional established models in some practical cases. In this paper, we firstly derive exact closed-form expressions for the main statistical characterizations of the ratio of products of $\mathcal{F}$-distributed random variables, including the probability density function, the cumulative distribution function and the moment generating function. Secondly, simple and tight approximations to the distribution of products and ratio of products of $\mathcal{F}$-distributed random variables are presented. These analytical results can be readily employed to evaluate the performance of several emerging system configurations, including full-duplex relaying systems operating in the presence of co-channel interference and wireless communication systems enhanced with physical-layer security. The proposed mathematical analysis is substantiated by numerically evaluated results, accompanied by equivalent ones obtained using Monte Carlo simulations.