# A Symmetric Matrix-Aided MIMO to Improve Reliability for Maritime Visible Light Communications
## 4 Numerical Results  
In this part, we first present the simulation parameter settings. Then we provide simulation results to verify the effectiveness of the proposed scheme. In the simulation, we assume that there are \(K=2\) users, and each user is equipped with \(N_{t}=2\) transmit apertures and \(N_{r}=2\) receiving apertures. We assume that a laser with a beam width of 3 mm and a beam wavelength of 550 nm is used as the light source. We set the photoelectric conversion efficiency \(\eta\) to be 1 and the field of view (FOV) semi-angle of the receiver to be \(\Psi_{1/2}=45^{\circ}\). The receiver aperture diameter is set as \(D=0.05\) m and the divergence semi-angle of transmitters is set as \(\Phi_{1/2}=0.5^{\circ}\). The distance between receivers is set to \(s_{r}=0.25\) m, while the distance between transmitters is set to \(s_{t}=0.25\) m.  
First of all, we set \(C_{n}^{2}=1\times 10^{-14}\), which means that the turbulence is weak. Additionally, we set the link distance in the atmosphere at 500 m and the distance underwater at 200 m, which can be obtained in the air channel \(\sigma_{I}^{2}=0.18\) and in the underwater channel \(\sigma_{I}^{2}=0.03\). From Figures 4 and 5, we can see that the theoretical results match the simulation ones. Moreover, we can see that the proposed scheme outperforms the other three benchmark schemes. As we can see in Figure 4, the proposed symmetric scheme outperforms the SMP scheme [14; 15] by about 4 dB at the SER = \(1\times 10^{-4}\) level in the atmospheric channel, while in the underwater channel, the proposed symmetric scheme obtains a performance gain of about 3 dB at SER = \(1\times 10^{-4}\) comparing to the SMP scheme [14; 15] in Figure 5. This also means the proposed symmetric scheme has a good advantage of improving reliability. Figure 4: Theoretical and simulation results in the atmospheric channel, \(\sigma_{I}^{2}=0.18\). Here we study the reliability performance of the four schemes for the air-water interface channel. In the simulation, we set the channel parameters as follows: wind speed is 1 m/s, atmospheric propagation distance is 100 m, and underwater propagation distance is 20 m. As can be seen from Figure 8, the proposed symmetric scheme is still superior to the other benchmark schemes in improving the reliability performance. It has a good performance gain of about 7 dB comparing to the RC scheme [14,15] when the SER is \(1\times 10^{-3}\). Subsequently, we investigate the reliability performance with different transmission distances of 500 m, 800 m, 1100 m, and 1400 m, respectively, in the atmosphere in Figure 9. We can notice that the reliability performance will become better when the transmission distance is shorter. We can see that at the 1 \(\times\) 10\({}^{-5}\) level, when the distance is 500 m, it outperforms by 6 dB compared to when the distance is 800 m, it has a performance gain of about 10 dB compared to when the distance is 1100 m, and is about 20 dB better than when the distance is 1400 m.  
Figure 8: Reliability performance comparisons for the air–water interface channel. Figure 7: Reliability performance comparisons for the underwater channel. Then, we studied the reliability of our proposed scheme underwater with different water types. Clear water, coastal water, and harbor water are considered. From Figure 10, we can see that in clear water it has a good performance gain of about 30 dB compared to when the water type is coastal water and about 98 dB when the water type is harbor. The transmission in the clear water is very good because the impurities and other small particles in the clear water are the least, and in the harbor water they are the greatest. Without these adverse factors that affect the communication propagation process, light propagation underwater is more convenient, so the reliability of the transmission will be better, while with these affecting the propagation, the propagation underwater is harder, so the reliability is worse.