On the Sum of Extended $\eta$-$\mu$ Variates with MRC Applications

TL;DR

This paper derives new closed-form expressions for the sum of extended η-μ variates, facilitating performance analysis of MRC systems under complex fading conditions.

Contribution

It introduces novel closed-form formulas for the PDF and CDF of the sum of extended η-μ variates, applicable to MRC performance metrics.

Findings

Derived closed-form PDF and CDF in hypergeometric and Fox's H-functions

Validated analytical results with numerical and Monte-Carlo simulations

Provided explicit outage probability and error rate expressions

Abstract

In this paper, the sum of L independent but not necessarily identically distributed (i.n.i.d.) extended $\eta$-$\mu$ variates is considered. In particular, novel expressions for the probability density function and cumulative distribution function are derived in closed-forms. The derived expressions are represented in two different forms, i.e., in terms of confluent multivariate hypergeometric function and general Fox's H-function. Subsequently, closed-form expressions for the outage probability and average symbol error rate are derived. Our analytical results are validated by some numerical and Monte-Carlo simulation results.