On the Computation of the Higher-Order Statistics of the Channel Capacity for Amplify-and-Forward Multihop Transmission

TL;DR

This paper introduces a novel MGF-based method to efficiently compute higher-order statistics of channel capacity in amplify-and-forward multihop systems over generalized fading channels, aiding in assessing transmission reliability.

Contribution

It presents a unified, easy-to-use mathematical framework for calculating higher-order channel capacity statistics using reciprocal MGFs, applicable to generalized fading environments.

Findings

Method accurately computes higher-order statistics

Numerical results match simulations perfectly

Applicable to various fading channel models

Abstract

Higher-order statistics (HOS) of the channel capacity provide useful information regarding the level of reliability of the signal transmission at a particular rate. We propose in this letter a novel and unified analysis, which is based on the moment-generating function (MGF) approach, to efficiently and accurately compute the HOS of the channel capacity for amplify-and-forward multihop transmission over generalized fading channels. More precisely, our mathematical formulism is easy-to-use and tractable specifically requiring only the reciprocal MGFs of the instantaneous signal-to-noise ratio distributions of the transmission hops. Numerical and simulation results, performed to exemplify the usefulness of the proposed MGF-based analysis, are shown to be in perfect agreement.