Second Order Statistics of -Fisher-Snedecor Distribution and Their Application to Burst Error Rate Analysis of Multi-Hop Communications

An advantage of using the composite fading models (CFMs) is their ability to concurrently address the impact of multi-path and shadowing phenomena on the system performance in wireless communications. A Fisher-Snedecor (FS)
$\mathcal{F}$
CFM has been recently proposed as an experimentally verified and tractable fading model that can be efficiently applied for 5G and beyond 5G wireless communication systems. This paper provides second-order (s-order) performance analysis of the product of
$N$
independent but not identically distributed (i.n.i.d) FS
$\mathcal{F}$
random variables (RVs). In particular, accurate and closedform approximations for level crossing rate (LCR) and average fade duration (AFD) of the product of
$N$
i.n.i.d FS
$\mathcal{F}(N-{\mathrm {FS}}~ \mathcal{F})$
RVs are successfully derived by exploiting a general property of a Laplace approximation method for evaluation of the
$N$
-folded integral-form LCR expression. Based on the obtained s-order statistical results, the burst error rate and maximum symbol rate of the
$N$
-FS
$\mathcal{F}$
distribution are addressed and thoroughly examined. The numerical results of the considered performance measures are discussed in relation to the
$N-\mathrm{FS}~ \mathcal{F}$
multi-path and shadowing severity parameters. Moreover, the impact of the number of hops
$(N)$
of the
$N$
-FS
$\mathcal{F}$
CFM on the s-order metrics, the burst error rate and maximum symbol rate are numerically evaluated and investigated. The derived s-order statistical results can be used to address the cooperative relay-assisted (RA) communications for vehicular systems. Monte-Carlo
$(\mathrm{M}-\mathrm{C})$
simulations for the addressed statistical measures are developed in order to confirm the provided theoretical results.