## 3 Channel Model  
In this paper, we consider a \(\mathcal{M}\) probability density function (PDF) to model atmospheric scintillation, \(h_{1}\)[26]. Thus, \(h_{1}\) is described by a modulation process as a product of two stationary random terms: one arising from large-scale turbulent eddy effects, mainly due to refractive effects; and the other one representing the small scale atmospheric fading characteristic, which is primarily due to diffraction effects. Accordingly, Figure 2 shows its associated small-scale laser propagation scheme. There, the observed field at the receiver is supposed to consist of three terms: the line-of-sight contribution \(U_{L}\); a new scattering component, \(U_{S}^{C}\), that is quasi-forward scattered on the propagation axis and assumed to be coupled to \(U_{L}\); and, in addition to the classical scattering optical field, \(U_{S}^{G}\), due to energy that is scattered to the receiver by off-axis eddies. A detailed description of this model can be found in [26]. Precisely, following [26], the model defines some other parameters to completely characterize the received irradiance fluctuation. Thus, parameter \(\Omega=E[U_{L}^{2}]\) represents the LOS average optical power, whereas \(\xi=E[|U_{S}^{C}|^{2}+|U_{S}^{C}|^{2}]=\xi_{c}+\xi_{g}\) denotes the average power of the total scattering components: either the coupled-to-LOS and the classic one, respectively. On another note, the relationship between those two scattering components is described by parameter \(\rho\), representing the amount of scattering power coupled to the LOS component, with \(0\leq\rho\leq 1\). Hence, their average powers are, respectively, \(\xi_{c}=\rho\xi\) and \(\xi_{g}=(1-\rho)\xi\), and the total average optical power is given by \(E[h_{1}]=\Omega+\xi\). Figure 2: Laser beam propagation scheme under an \(\mathcal{M}\)-distributed FSO link [45]. In addition, as detailed in [45], the Malaga PDF can be reformulated by involving a mixture of continuous Generalized-K and a discrete Binomial distributions. This fact results in a novel and interesting physical interpretation of the \(\mathcal{M}\) statistical model, where the optical channel are considered as a superposition of different independent subchannels described by a generalized-K PDF, \(K_{G}\), with each subchannel with a different probability and \(m_{k}\) is associated with a Binomial PDF. In this respect, the received irradiance PDF can be written as follows:  
\[f_{h_{1}}(h_{1})=\sum_{r=1}^{\beta}m_{r}K_{G}(h_{1};\alpha,r,\mathcal{I}_{r}), \tag{4}\]  
where \(m_{r}\) is the probability that the optical signal travels through the \(r\)-th optical path, with \(\alpha\) being a positive parameter related to the effective number of large-scale cells of the scattering process and \(\beta\in\mathbb{N}\) being the shape parameter of the Nakagami-m distribution related to the slow fluctuation of the line-of-sight component, as discussed in [26]. Moreover, \(\mathcal{I}_{r}\) represents the mean optical irradiance of the \(r\)-th Generalized-K term. On the other hand, the large-scale effects are assumed to be common for every small-scale subchannel. Namely these small-scale subchannels are governed by small-scale diffraction effects, with the lower subchannel orders referring to more adverse turbulence regimes. On a different matter and following the works introduced in [18; 59], we employ a Weibull function model to characterize the fading associated with salinity-induced turbulent underwater channels. For this case, the Weibull model offers an excellent accuracy when it is utilized to predict experimental data, becoming particularly interesting in transition areas between seas and oceans where different masses of water meet. Furthermore, it provides a good fit when the receiver aperture is much larger than the coherence radius of the medium, which is something feasible considering the short-range links involved in underwater FSO systems.