The Fischer–Snedecor F-Distribution Model for Turbulence-Induced Fading in Free-Space Optical Systems

In this article we propose the use of the so-called Fisher-Snedecor F-distribution to model atmospheric turbulence-induced fading in free space optical communication systems. The proposed model is a two-parameter distribution, defined as the ratio of two independent gamma random variables. In this context, the proposed model is based on a doubly stochastic theory of turbulence-induced fading, assuming that small-scale irradiance variations of the propagating wave, modeled by a gamma distribution, are a subject to large-scale irradiance fluctuations, modeled by an inverse gamma distribution. It is shown that the F-distribution yields at least as good, or even a better fit to experimental and computer simulation data as compared to the well known gamma-gamma distribution. Also, important statistical measures such as cumulative distribution function (CDF) and moment generating function (MGF) are mathematically simpler than those of the gamma-gamma distribution. Motivated by these facts, the performance of single-input-multiple output (SIMO) and multiple-input-multiple output (MIMO) systems operating in the presence of F turbulence is assessed. The proposed analysis is substantiated by numerically evaluated results and Monte Carlo simulations.