Free-Space Optical Systems over Correlated Atmospheric Fading Channels: Spatial Diversity or Multihop Relaying?

Both spatial diversity and multihop relaying are considered to be effective methods for mitigating the impact of atmospheric turbulence-induced fading on the performance of free-space optical (FSO) systems. Multihop relaying can significantly reduce the impact of fading by relaying the information over a number of shorter hops. However, it is not feasible or economical to deploy relays in many practical scenarios. Spatial diversity could substantially reduce the fading variance by introducing additional degrees of freedom in the spatial domain. Nevertheless, its superiority is diminished when the fading sub-channels are correlated. In this paper, our aim is to study the fundamental performance limits of spatial diversity suffering from correlated Gamma-Gamma (G-G) fading channels in multihop coherent FSO systems. For the performance analysis, we propose to approximate the sum of correlated G-G random variables (RVs) as a G-G RV, which is then verified by the Kolmogorov-Smirnov (KS) goodness-of-fit statistical test. Performance metrics, including the outage probability and the ergodic capacity, are newly derived in closed-form expressions and thoroughly investigated. Monte-Carlo (M-C) simulations are also performed to validate the analytical results.