## 2 Comprehensive Multiparameter Model for UWOC Channels  
The underwater optical channel is affected by absorption, scattering, and turbulence. The random effect of the turbulence is related to the light position, whereas absorption and scattering uniformly affect the whole light beam. Meanwhile, the laser transmission process can be considered by the split-step beam propagation method [19] as alternate steps of partial propagation in the isotropic material, and interactions with the material with the inhomogeneous refractive index n(x, y, z). In this way, the absorption and scattering effects, as well as the turbulence effect, can be both considered in such alternate steps. Figure 1 shows the schematic description of the channel model. The transmission process can be separated into refraction parts and diffraction parts [20]. The turbulence effect is treated as thin phase screens that only change the light propagation directions [21]. Then, all the light keep their own directions until reaching the next phase screen, with the light intensity attenuating due to absorption and scattering effects along the path. In the end, a Fresnel diffractive lens is set to converge the spatial light to the receiver. Figure 1: Schematic description of the beam propagation model of the UWOC channel. The collimated laser source is modeled by a Gaussian beam as \(U_{0}\). The optical field on the \(i\)th screen plane is \(U(\mathbf{r}_{i})\) and the optical field on the \(i+1\)th screen plane can be expressed as:  
\[U(\mathbf{r}_{i+1})\sim\hat{P}(\Delta z,\mathbf{r}_{i},\mathbf{r}_{i+1})\hat{R}(\Delta z,\bm {r}_{i},\mathbf{r}_{i+1})\{U(\mathbf{r}_{i})\} \tag{1}\]  
where \(\mathbf{r}_{i}\) and \(\mathbf{r}_{i+1}\) are spatial coordinates on the screens and \(\Delta z\) is the distance of each propagation segment. \(\hat{R}=e^{-j\varphi(\mathbf{r}_{i+1})}\) is the refraction operator. The phase \(\varphi\) can be obtained from the underwater turbulence refractive index power spectrum density (PSD). \(\hat{P}\sim\mathcal{F}^{-1}(\mathbf{r}_{i+1},\mathbf{f}_{i})\hat{H}(\mathbf{f}_{i}) \mathcal{F}(\mathbf{f}_{i},\mathbf{r}_{i})\) is the diffraction operator, where \(\mathbf{f}_{i}\) is the spatial frequency of the optical field on the \(i\)th screen. Fourier transforms and a transfer function \(\hat{H}\) are used here to describe the Fresnel diffraction process. Regarding the refraction part, the phase values \(\varphi\) on a screen can be written as:  
\[\varphi(x,y)=\sum_{n}\sum_{m}c_{n,m}exp\big{[}j\big{(}k_{xn}x+k_{ym}y\big{)} \big{]} \tag{2}\]  
where \(k_{xn}\) and \(k_{ym}\) are the discrete spatial frequencies in \(x\) and \(y\) directions, respectively. The Fourier coefficients \(c_{n,m}\) obey the complex Gaussian distribution with zero mean and the variance given by [22]:  
\[\langle|c_{n,m}|^{2}\rangle=2\pi k^{2}\Delta z\Phi_{n}(k)/\big{(}L_{x}L_{y} \big{)} \tag{3}\]  
where \(L_{x}\) and \(L_{y}\) are the sizes of the screen, and \(\Phi_{n}\) is the underwater turbulence refractive index PSD as [23]:  
\[ \begin{array}{c}\Phi_{n}(k)=0.388\times 10^{-8}e^{-\frac{1}{3}}k^{-\frac{11}{3} }\times\Big{[}1+2.35(k\eta)^{\frac{2}{3}}\Big{]}\times\\ \frac{\Upsilon}{\omega^{2}}\times\big{[}\omega^{2}exp(-A_{T}\delta)+exp(-A_{S} \delta)-2\omega exp(-A_{T}\delta)\big{]}\end{array}  \tag{4}\]  
where \(\delta=8.284(k\eta)^{4/3}+12.978(k\eta)^{2}\), \(k=2\pi/\lambda=2\pi f\) is the optical wavenumber, \(\varepsilon\) is the dissipation rate of turbulent kinetic energy per unit mass of fluid ranging from \(10^{-1}\)m\({}^{2}\)/s\({}^{3}\) to \(10^{-10}\)m\({}^{2}\)/s\({}^{3}\), \(\chi_{T}\) is the dissipation rate of mean-squared temperature ranging from \(10^{-4}\) K\({}^{2}\)/s to \(10^{-10}\) K\({}^{2}\)/s, \(\omega\) defines the ratio of the temperature contribution to the salinity contribution to the refractive index spectrum, ranging from \(-5\) to \(0\), and \(\eta\) is the Kolmogorov microscale length. The constants are \(A_{T}=1.863\times 10^{-2}\), \(A_{S}=1.9\times 10^{-4}\), and \(A_{TS}=9.41\times 10^{-3}\).