## 3 Simulation Analysis and Results
### Results and Discussion
#### 3.3.2 Mean Square Error  
The received optical power fluctuation and uniformity of the three LED layouts under three typical seawater environments at different transmission depths are further analyzed by calculating the root mean square error (RMSE) of the received optical power. Dividing the receiving plane into a 100 \(\times\) 100 micro area, the RMSE of the received optical power can be given by  
Figure 5: Received optical power distribution for three layouts at different depths in coastal seawater. Ellipse-compensated layout at (**a**) 5 m; (**b**) 7 m; and (**c**) 9 m; ring-compensated layout at (**d**) 5 m; (**e**) 7 m; and (**g**) 9 m; and lemiscate-compensated layout at (**g**) 5 m; (**h**) 7 m; and (**i**) 9 m.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Transmission** & \multirow{2}{*}{**LED Layout**} & **Maximum Received** & **Minimum Received** \\
**Depth (m)** & & **Power (dBm)** & **Power (dBm)** & **PPD** \\ \hline \multirow{4}{*}{5 m} & ellipse-compensated layout & 27.42 & 5.20 & 0.81 \\  & ring-compensated layout & 28.93 & 3.27 & 0.89 \\  & lemniscate-compensated layout & 27.96 & 5.76 & 0.79 \\  & ellipse-compensated layout & 23.08 & 7.31 & 0.68 \\  & ring-compensated layout & 24.30 & 6.00 & 0.75 \\  & lemniscate-compensated layout & 23.07 & 7.94 & 0.66 \\  & ellipse-compensated layout & 18.60 & 6.01 & 0.68 \\  & ring-compensated layout & 19.54 & 5.60 & 0.71 \\  & lemniscate-compensated layout & 18.77 & 6.46 & 0.65 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Analysis of received optical power.  
\[\text{RMSE}=\sqrt{\sum_{i=1}^{N}{(P_{i}-P_{mean})^{2}/N}} \tag{21}\]  
where \(P_{i}\) is the receiving power of each micro area on the receiving plane, \(P_{mean}\) is the average receiving power, and \(N\) is the number of micro area sources on the receiving plane.  
In Figure 6, the RMSE of the three LED layouts at different transmission depths is measured under three typical seawater environments. In clean seawater, the overall fluctuation of the RMSE of the lemniscate-compensated layout is much better than that of the traditional ellipse-compensated and ring-compensated layouts. It can be seen from Figure 6a that, at a depth of 3 m, the RMSE of the lemniscate-compensated layout is 4.9, which is 0.2 less than the ellipse-compensated layout and 0.9 less than the ring-compensated layout. In coastal seawater, the overall RMSE of the lemniscate-compensated layout is lower than the traditional ellipse-compensated layout and ring-compensated layout. At a depth of 3 m in coastal seawater, the RMSE of the lemniscate-compensated layout is 4.6, which is 0.6 less than the ellipse-compensated layout and 1.2 less than the ring-compensated layout. In harbor seawater, the RMSE of the proposed lemniscate-compensated layout is 7 at a depth of 3 m, which is also lower than that of the traditional layouts. It can be seen that the lemniscate-compensated layout has relatively small received power fluctuation and can support more reliable communication under all three seawater types. Particularly, the RMSE of the received optical power increased at a transmission depth greater than 3 m, which indicates that the distribution uniformity of the received optical power becomes worse due to the larger attenuation coefficient of harbor seawater. Figure 7 shows the distribution of the received optical power at a transmission depth of 5 m in harbor seawater. It can be seen that the received optical power reduces to the range of \(-25\) dBm to \(-50\) dBm, which makes it difficult to achieve reliable communication for the UOWC system. Therefore, while analyzing the uniformity of the optical signal, the received optical power and system BER performance should be further analyzed based on the received optical power information obtained under different layouts to determine the reliable communication range of the proposed UOWC system.