## 3 Channel Model
### Turbulence Model  
The Malaga distribution model is suitable for describing the ocean turbulence channel with arbitrary levels of strength from weak to strong, with \(\alpha\) being a positive parameter related to the effective number of large-scale cells in the scattering process that determines the turbulence strength. \(\beta\) represents the value of the fading parameter and is a natural number. The probability density function (PDF) of \(h_{\mathrm{t}}(t)\) can be represented as [21]:  
\[f_{h_{\mathrm{t}}}(h_{\mathrm{t}})=A\sum_{k=1}^{\beta}a_{k}h_{\mathrm{t}}^{ \frac{\alpha+k}{2}-1}K_{\alpha-k}\left(2\sqrt{\frac{\alpha\beta h_{\mathrm{t}} }{g\beta+\Omega^{\prime}}}\right) \tag{4}\]  
where \(A=\frac{2\alpha\frac{\beta}{\beta}}{g^{1+\frac{\alpha}{2}}\Gamma(\alpha)} \left(\frac{g\beta}{g\beta+\Omega^{\prime}}\right)^{\beta+\frac{\alpha}{2}}\), \(a_{k}=\left( \begin{array}{c}\beta-1\\ k-1\end{array} \right)\frac{(g\beta+\Omega^{\prime})^{1-\frac{\beta}{2}}}{(k-1 )! }\left(\frac{\Omega^{\prime}}{g}\right)^{k-1}\left(\frac{\alpha}{\beta} \right)^{\frac{k}{2}}\), and \(\left( \begin{array}{c}\beta\\ k\end{array} \right)\) is the binomial coefficient. \(\mathrm{K}_{\mathrm{p}}(\cdot)\) is a modified Bessel function of the second kind with the order of \(v\). \(g=2b_{0}(1-\delta)\) denotes the average power of the energy scattered to the receiver by off-axis eddies. \(2b_{0}\) indicates the average power of the total scatter components. The parameter \(\delta\) is the factor expressing the amount of scattering power coupled to the line-of-sight (LOS) component, \(0\leq\delta\leq 1\). \(\Omega^{\prime}=\Omega+2\delta b_{0}+2\sqrt{2b_{0}\Omega\delta}\cdot\cos( \varphi_{\mathrm{A}}-\varphi_{\mathrm{B}})\) symbolizes the average power from the coherent contribution, whereas \(\Omega\) represents the average power of the LOS term. The parameters \(\varphi_{\mathrm{A}}\) and \(\varphi_{\mathrm{B}}\) are the deterministic phases of the LOS scattering term and the coupled-to-LOS scatter term, respectively. The parameters \(\alpha\) and \(\beta\) can be expressed as follows for a plane wave [3]:  
\[\alpha=\left[\exp\left(\frac{0.49\sigma_{\mathrm{R}}^{2}}{\left(1+1.11\sigma_{ \mathrm{R}}^{12/5}\right)^{7/6}}\right)-1\right]^{-1},\beta=\left[\exp\left( \frac{0.51\sigma_{\mathrm{R}}^{2}}{\left(1+0.69\sigma_{\mathrm{R}}^{12/5} \right)^{5/6}}\right)-1\right]^{-1}, \tag{5}\]  
where \(\sigma_{\mathrm{R}}^{2}\) is the Rytov variance for a plane wave. The scintillation index can be described by the Rytov variance for a plane wave. Thus, \(\sigma_{\mathrm{R}}^{2}=\sigma_{1}^{2}\) for a plane wave. In general, \(\sigma_{1}^{2}\) describes the turbulence strength; e.g., \(\sigma_{1}^{2}<1\) for weak turbulence, \(\sigma_{1}^{2}\approx 1\) for moderate turbulence, and \(\sigma_{1}^{2}>1\) for strong turbulence. \(\sigma_{1}^{2}\) can be calculated as follows [3; 13]:  
\[\sigma_{\mathrm{I}}^{2}(z)=8\pi^{2}k^{2}z\int_{0}^{1}\int_{0}^{\infty}\kappa \Phi(\kappa)\bigg{\{}1-\cos\left[\frac{z\kappa^{2}}{k}\zeta(1-(1-\Theta) \zeta)\right]\bigg{\}}dx\delta, \tag{6}\]  
where \(k=2\pi/\lambda\) denotes the optical wave number at the wavelength of \(\lambda\). \(\Theta=1\) and \(0\) for plane and spherical waves, respectively. \(\kappa\) is the magnitude of the spatial frequency and \(\zeta\) is the normalized distance variable, \(0\leq\zeta\leq 1\). \(\Phi_{n}\) (\(\kappa\)) represents the power spectrum in isotropic and heterogeneous ocean conditions [22]; i.e.,  
\[\Phi_{n}(\kappa)=\frac{\mathrm{C}_{0}}{4\pi}\frac{a_{k}^{2}\chi_{T}}{\omega^{2 }}\varepsilon^{-1/3}\kappa^{-11/3}\left[1+\mathrm{C}_{1}(\kappa\eta)^{2/3} \right]\left[\omega^{2}\mathrm{e}^{-A_{T}\delta}+d_{t}\mathrm{e}^{-A_{S}\delta }-\omega(1+d_{r})\mathrm{e}^{-A_{T}\delta}\right], \tag{7}\]where \(\varepsilon\) is the rate of dissipation of kinetic energy per unit mass of fluid, as given by \(\varepsilon=v^{3}\eta^{-4}\), where \(v\) denotes the kinematic viscosity.