On the Sum of Correlated Squared $\kappa-\mu$ Shadowed Random Variables and its Application to Performance Analysis of MRC

TL;DR

This paper derives the statistical distribution of the sum of correlated squared $ppa-mph{} shadowed random variables and applies it to analyze the performance of MRC over such channels, including diversity, BER, and capacity.

Contribution

It provides a novel power series PDF for the sum of correlated $ppa-mph{} shadowed variables and applies it to comprehensive performance analysis of MRC in correlated fading environments.

Findings

Diversity order depends on the number of branches and m parameter.

Derived closed-form expressions for BER for M-PSK and M-QAM.

Capacity expressed via Meijer-G function for correlated ppa-mph{} shadowed channels.

Abstract

In this paper, we study the statistical characterization of the sum of the squared $\kappa-\mu$ shadowed random variables with correlated shadowing components. The probability density function (PDF) of this sum is obtained in the form of a power series. The derived PDF is utilized for obtaining the performance results of the maximal ratio combining (MRC) scheme over correlated $\kappa-\mu$ shadowed fading channels. First, we derive the moment generating function (MGF) of the received signal-to-noise ratio of the MRC receiver. By using the derived MGF expression, the analytical diversity order is obtained; it is deduced on the basis of this analysis that the diversity of the MRC receiver over correlated $\kappa-\mu$ shadowed channels depends upon the number of diversity branches and $\mu$ parameter. Further, the analytical average bit error rate of the MRC scheme is also derived, which is applicable for $M$-PSK and $M$-QAM constellations. The Shannon capacity of the correlated $\kappa-\mu$ shadowed channels is also derived in the form of the Meijer-G function.