General statistical model of irradiance fluctuations in free space optics

Abstract

A model for the received irradiance statistical distribution for turbulence induced fading channels is derived. The derivation is based on expanding the extended Rytov method by associating a doubly stochastic process to model large scale scintillation. In particular, the large scale induced fluctuations are modeled as the product of arbitrary numbers of gamma and inverse gamma random variables, while the small scale induced irradiance fluctuations are modeled as a single gamma random variable. Closed form expressions for the probability density function (pdf), cumulative distributions, and moment generating function are given. Also, a procedure is proposed for associating the pdf parameters with the large and small scale induced variances. The proposed model is seen to contain many previously published models, such as gamma–gamma (GG) and Fischer–Snedicor F , as special cases. Moreover, two new fading distributions are introduced and analyzed, and plots for the proposed pdfs are generated and compared with often used models and measurements, thus showing the accuracies of the derived models.