On the second order statistics of N-Hop FSO communications over N-gamma-gamma turbulence induced fading channels

Abstract

The paper explores N-hop FSO communications assisted by amplify-and-forward relays (AFRs) over N-gamma-gamma (N-gg) turbulence induced (TI) fading channels. We model TI fading signal as the product of independent but not necessarily identically distributed (i.n.i.d) N number of gg random processes (RPs) in order to address N-hop AFR FSO communications in moderate to strong TI fading conditions. The closed form statistical measures such as: probability density function (PDF), cumulative distribution function (CDF), average level crossing rate (LCR) and average fade duration (AFD) approximated by general Laplace integration formula (LIF) and exponential LIF are derived. The CDF and AFD derived expressions are in terms of finite sums and valid only for an integer value of the parameter related to small-scale atmospheric cells in the first link of N-hop AFR FSO system. The numerical examples for moderate to strong TI fading conditions as well as for various number of hops for the proposed N-hop AFR FSO systems are presented and discussed. Moreover, LIF approximate numerical results are compared with numerical results evaluated from exact integral expressions for the observed system model parameters.