# Cooperative Terrestrial-Underwater FSO System: Design and Performance Analysis
## 5 Results
We note that along with the analytical results provided by the closed expression for the BER mentioned above, numerical results obtained by Monte Carlo simulations are also plotted in the figure. These numerical results are plotted with circular markers. It is important to note that, in all cases, a perfect match is shown between the simulated results and those obtained from the derived expression. As can be seen from Figure 3, the FSO-TU system has a different behavior under strong, moderate and weak turbulence. For weak and moderate turbulence, the BER decreases rapidly as the SINR increases; however, under strong turbulence, the decay of the BER curves is much slower. We notice that under weak and moderate turbulence, the BER curves change behavior for SINR values above 40 dB. From this SINR level onwards, a BER floor occurs. The appearance of this BER floor for high SNR ratios is an expected phenomenon in a turbulent environment as shown by the analysis published in [43]. This floor imposes a limit on the BER performance achievable by the system. In particular, for the most favorable scenario in Figure 3, the BER cannot be less than \(10^{-7}\) in any case. Furthermore, the detailed analysis of the figure shows that the BER floor of the curves corresponding to weak turbulence and moderate turbulence tend to coincide as the SINR increases. In fact, it would also coincide with the BER floor of the curves with strong turbulence whenever sufficiently high SINR values are drawn. This behavior leads to the important conclusion that the BER floor of the FSO-TU system is independent of the intensity of atmospheric turbulence and, therefore, is imposed by the intensity of the underwater turbulence of the second link. Lastly, as far as weather conditions are concerned, Figure 3 shows that their effect on BER degradation is less pronounced than that  
Figure 2: Received signal level as a function of the depth of the underwater link for different types of seawater and transmitted powers. Only geometrical and loss path are assumed. of turbulence, which is understandable for short links of up to 1 km. However, a higher degradation is seen in the case of haze. Next, the impact of pointing errors occurring in the terrestrial link on BER performance is analyzed separately in Figure 4. As in the previous figure, in order to reduce the influence of the underwater link, the most favorable conditions are assumed for this link, i.e., moderate-weak ocean turbulence, clean ocean water and a depth of 20 m. In addition, the strong atmospheric turbulence condition is assumed for the terrestrial link in all cases. This figure shows the average BER obtained analytically (depicted with lines) from Equation (36) and numerically (represented with circular markers) by Monte Carlo simulations for three levels of pointing errors and three atmospheric transparency conditions. We note that, as expected, the analytical and numerical results coincide again. The three jitter levels chosen in the figure, \(\sigma_{\rho}=0.1\), \(0.3\) and \(0.6\) m, model real situations with pointing errors of different severity. The severity of the pointing error depends on the \((\sigma_{\rho}/\omega_{l})\) ratio, so that the higher the \((\sigma_{\rho}/\omega_{l})\), the higher the severity. In the figure, the dotted line curves shows the BER corresponding to a low-severity pointing error, while the dashed and solid line curves show the BER for low-moderate and high-severity errors, respectively. As expected, the impact of pointing errors at \(\sigma_{\rho}=0.1\) m and \(\sigma_{\rho}=0.3\) m causes a moderate increase in BER; however, at \(\sigma_{\rho}=0.6\) m there is a sharp increase in BER that seriously compromises the performance of the FSO-TU system. Higher \(\sigma_{\rho}\) values with \((\sigma_{\rho}/\omega_{l})\sim 1\) result in link failure. Again, we can see how the effect on BER degradation is less pronounced with very clear air than with haze, although the difference is small due to the short distance of the link.