On the Second Order Statistics of the Multihop Rayleigh Fading Channel

TL;DR

This paper develops new analytical expressions for second order statistics, specifically level crossing rate and average fade duration, in multihop Rayleigh fading channels, aiding in the design of wireless systems.

Contribution

It introduces a novel analytical framework for evaluating second order statistics of multihop Rayleigh channels, including closed-form approximations and validation.

Findings

Derived new expressions for LCR and AFD of N*Rayleigh channels.

Validated accuracy of formulas through simulations.

Provided efficient approximations using multivariate Laplace theorem.

Abstract

Second order statistics provides a dynamic representation of a fading channel and plays an important role in the evaluation and design of the wireless communication systems. In this paper, we present a novel analytical framework for the evaluation of important second order statistical parameters, as the level crossing rate (LCR) and the average fade duration (AFD) of the amplify-and-forward multihop Rayleigh fading channel. More specifically, motivated by the fact that this channel is a cascaded one and can be modeled as the product of N fading amplitudes, we derive novel analytical expressions for the average LCR and the AFD of the product of N Rayleigh fading envelopes (or of the recently so-called N*Rayleigh channel). Furthermore, we derive simple and efficient closed-form approximations to the aforementioned parameters, using the multivariate Laplace approximation theorem. It is shown that our general results reduce to the corresponding ones of the specific dual-hop case, previously published. Numerical and computer simulation examples verify the accuracy of the presented mathematical analysis and show the tightness of the proposed approximations.