Performance Analysis of N-Fisher-Snedecor F Fading and Its Application to N-Hop FSO Communications

The Fisher-Snedecor $F$ distribution has been recently proposed as an experimentally verified and tractable turbulence induced fading model (TIFM) for free space optical (FSO) communications. This paper provides outage probability (OP) and higher-order (HO) performance analysis of the product of $N$ independent but not identically distributed (i.n.i.d) Fisher-Snedecor $F$ random variates (RVs). Accurate and closed-form (C-F) expressions for cumulative distribution function (CDF), level crossing rate (LCR) and average fade duration (AFD) of N-Fisher-Snedecor $F$ distribution are successfully derived. The general property of a Laplace approximation approach for evaluation of N-folded complex integral-form (I-F) LCR expressions has been applied. The obtained statistical results are directly related to the performance evaluation of N-hop FSO communication links over weak, moderate and strong atmospheric turbulence conditions.