On the Computation of the Higher Order Statistics of the Channel Capacity over Generalized Fading Channels

TL;DR

This paper introduces a unified MGF-based method to accurately compute the higher-order statistics of channel capacity in generalized fading channels, applicable to MRC receivers in correlated fading environments.

Contribution

A novel, exact analytical approach using MGF to evaluate higher-order channel capacity statistics in complex fading scenarios.

Findings

Method effectively computes HOS for generalized fading channels.

Applicable to correlated Rician and chi-squared distributions.

Numerical examples demonstrate accuracy and versatility.

Abstract

The higher-order statistics (HOS) of the channel capacity $\mu_n=\mathbb{E}[\log^n(1+\gamma_{end})]$, where $n\in\mathbb{N}$ denotes the order of the statistics, has received relatively little attention in the literature, due in part to the intractability of its analysis. In this letter, we propose a novel and unified analysis, which is based on the moment generating function (MGF) technique, to exactly compute the HOS of the channel capacity. More precisely, our mathematical formalism can be readily applied to maximal-ratio-combining (MRC) receivers operating in generalized fading environments (i.e., the sum of the correlated noncentral chi-squared distributions / the correlated generalized Rician distributions). The mathematical formalism is illustrated by some numerical examples focussing on the correlated generalized fading environments.