## 4 Simulation and Discussion
### Received Light Spots  
Figure 5 shows the spatial intensity distributions of the received spots after an 80 m distance underwater transmission. Four cases are considered: in the vacuum (see Figure 5a), in the water with turbulence only (see Figure 5b), in the water with attenuation only (see Figure 5c), and in the water with turbulence and attenuation simultaneously (see Figure 5d). The turbulence properties in Figure 5b, d are set as follows: \(\varepsilon=10^{-10}\)m\({}^{2}\)/s\({}^{3}\), \(\chi_{\rm T}=10^{-4}\)K\({}^{2}\)/s, and \(\omega=-0.2\). The absorption and scattering coefficients in Figure 5c,d are \(a=0.0405\) m\({}^{-1}\) and \(b=0.0025\) m\({}^{-1}\). A comparison of the results in Figure 5a,b shows that the turbulence effect results primarily in the beam diffusion and uneven spatial distribution of light intensity, which subsequently deteriorates the communication performance. In Figure 5a,c, the absorption and scattering effects cause uniform attenuation of light intensity. Considering the receiving intensity threshold, the attenuation in ocean water may bring more challenges to signal receiving in a UWOC system.  
Figure 6 shows the spatial intensity distributions of the received spots after passing through different turbulence channels. The parameters in Figure 6a are as follows: \(\varepsilon=10^{-8}\)m\({}^{2}\)/s\({}^{3}\), \(\chi_{\rm T}=10^{-5}\)K\({}^{2}\)/s, and \(\omega=-0.5\). The parameters are changed to \(\varepsilon=10^{-10}\)m\({}^{2}\)/s\({}^{3}\) in Figure 6b, \(\chi_{\rm T}=10^{-4}\)K\({}^{2}\)/s in Figure 6c, and \(\omega=-0.1\) in Figure 6d. The decrease of \(\varepsilon\), which means the slower consumption of the turbulence kinetic energy, the increase of \(\chi_{\rm T}\), which means the larger temperature gradient of water, and the approach of \(\omega\) to 0, which means more contributions from salinity than temperature, all imply the aggravation of the turbulence effect in a UWOC system.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Value** \\ \hline Source wavelength, \(\lambda\) & 450 nm \\ Beamwidth, \(\sigma\) & 4 mm \\ The curvature radius of Gaussian waver, \(R\) & \(\infty\) \\ Kolmogorov microscale length, \(\eta\) & 1 mm \\ The rate of dissipation of kinetic energy per unit mass, \(\varepsilon\) & \(10^{-8}\) m\({}^{2}\)/s\({}^{3}\) \\ The rate of dissipation of mean-squared temperature, \(\chi_{\rm T}\) & \(10^{-5}\) K\({}^{2}\)/s \\ The ratio of temperature to salinity contributions, \(\omega\) & \(-0.5\) \\ Velocity of water flow, \(\
u\) & 1 \\ Absorption coefficient, \(a\) & 0.0405 m\({}^{-1}\) \\ Scattering coefficient, \(b\) & 0.0025 m\({}^{-1}\) \\ Transmission distance, \(z\) & 50 m \\ Receiver aperture diameter, \(D\) & 1 cm \\ Observation region of interest, \(D_{1},D_{2}\) & 4 cm \\ Number of phase screens, n & 4 \\ Number of subharmonic phase screen layers, \(N_{p}\) & 5 \\ Grid spacing of the screen, \(d\) & \(5\times 10^{-5}\) m \\ Number of sampling points on one dimension of the screen, \(N\) & 512 \\ Number of sampling points of the long-size screen, \(N_{L}\) & 800 \\ The original mean light intensity, \(I\) & 1 mW \\ The AWGN intensity, \(\sigma_{N}\)\({}^{2}\) & 0.1 mW \\ The receiving sensitivity threshold, \(I_{th}\) & 0.01 mW \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameter values in the simulation.