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

Abstract

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.

Fade statistics of ℳ ${\mathcal {M}}$ -turbulent optical links

“…Nevertheless, we can assume the assumption made in [1] for the gamma-gamma in which it was discussed that, although the conditional PDF of i is not known, however, based on physical grounds, it can be approximated to a zero-mean Gaussian PDF. Supporting that statement, and as detailed in [13], the Málaga distribution tends to a zero-mean Gaussian PDF if α → 1, β → 1, and m k = 1, with m k representing the probability that certain portion of the transmitted optical power travels through the k-th optical path, for which the probability of the optical power to be coupled to the line-of-sight component is established by an additional factor inherent to m k , as shown in [14].…”

“…Then, substituting (14) in (12) then we can obtain a relationship between the quasi-frequency and the turbulence correlation time:…”

Performance analysis of FSO communications under LOS blockage

“…As detailed in [9,10], the RV X follows a Gamma distribution, while Y has the form of a Rician-Shadowed distribution. In this scheme, the small-scale fading characteristic of the atmospheric channel is modeled by three different signal components: a main LOS component, denoted as U L , and two additional scattering components U C S , and U G S , as shown in Fig.…”

“…Note that for ρ → 1 the M-distribution reduces to the Gamma-Gamma distribution with parameters α and β. Following the notation of [10], the average optical power of the LOS component is given…”

“…As detailed in [10], Eq. (4) can be seen as the superposition of k Generalized-K sub-channels, K G (I; α, k, µ k ), corresponding each one to a different physical optical path.…”