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

In this paper, a novel and deeper physical interpretation on the recently published Malaga 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 Malaga 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 Malaga statistical distribution provides a valuable tool for analyzing the performance of atmospheric optical channels for every turbulence condition.