Novel formulation of the ℳ model through the Generalized-K distribution for atmospheric optical channels

• Published in: Optics express Vol. 23; no. 5; pp. 6345 - 6358
• Main Authors: Garrido-Balsells, José María, Jurado-Navas, Antonio, Paris, José Francisco, Castillo-Vazquez, Miguel, Puerta-Notario, Antonio
• Format: Journal Article
• Language: English
• Published: United States 09.03.2015
• ISSN: 1094-4087; 1094-4087
• DOI: 10.1364/OE.23.006345

In this paper, a novel and deeper physical interpretation on the recently published Málaga or ℳ statistical distribution is provided. This distribution, which is having a wide acceptance by the scientific community, models the optical irradiance scintillation induced by the atmospheric turbulence. Here, the analytical expressions previously published are modified in order to express them by a mixture of the known Generalized-K and discrete Binomial and Negative Binomial distributions. In particular, the probability density function (pdf) of the ℳ model is now obtained as a linear combination of these Generalized-K pdf, in which the coefficients depend directly on the parameters of the ℳ distribution. In this way, the Málaga model can be physically interpreted as a superposition of different optical sub-channels each of them described by the corresponding Generalized-K fading model and weighted by the ℳ dependent coefficients. The expressions here proposed are simpler than the equations of the original ℳ model and are validated by means of numerical simulations by generating ℳ -distributed random sequences and their associated histogram. This novel interpretation of the Málaga statistical distribution provides a valuable tool for analyzing the performance of atmospheric optical channels for every turbulence condition.