Level Crossing Rate and Average Fade Duration of the Multihop Rayleigh Fading Channel

TL;DR

This paper develops a new analytical framework to evaluate the level crossing rate and average fade duration of multihop Rayleigh fading channels, providing accurate formulas and approximations validated by simulations.

Contribution

It introduces novel analytical expressions and simple approximations for second order statistics of N*Rayleigh channels, extending previous dual-hop results.

Findings

Derived exact formulas for LCR and AFD of multihop Rayleigh channels.

Proposed efficient closed-form approximations validated by simulations.

Results applicable to cascade fading models in wireless communications.

Abstract

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, which can be modelled as the product of N fading amplitudes, we derive novel analytical expressions for the average LCR and 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 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.