In this article we propose the use of the so-called Fisher-Snedecor $\mathcal {F}$-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 $\mathcal {F}$-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 $\mathcal {F}$ turbulence is assessed. The proposed analysis is substantiated by numerically evaluated results and Monte Carlo simulations.

中文翻译：

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自由空间光学系统中湍流诱导衰落的 Fischer-Snedecor F 分布模型

在本文中，我们建议使用所谓的 Fisher-Snedecor $\mathcal {F}$-分布以模拟自由空间光通信系统中大气湍流引起的衰落。提出的模型是一个双参数分布，定义为两个独立伽马随机变量的比率。在这种情况下，所提出的模型基于湍流引起的衰落的双重随机理论，假设传播波的小尺度辐照度变化（由伽马分布建模）是大尺度辐照度波动的主题，建模为逆伽马分布。结果表明，$\mathcal {F}$与众所周知的伽马-伽马分布相比，-分布对实验和计算机模拟数据的拟合效果至少一样好，甚至更好。此外，重要的统计指标，例如累积分布函数 (CDF) 和矩生成函数 (MGF) 在数学上比伽马-伽马分布更简单。在这些事实的推动下，单输入多输出 (SIMO) 和多输入多输出 (MIMO) 系统的性能在存在$\mathcal {F}$湍流被评估。提议的分析得到了数值评估结果和蒙特卡罗模拟的证实。