# Cooperative Terrestrial-Underwater FSO System: Design and Performance Analysis
## 5 Results
In this respect, to illustrate the large degradation of the underwater channel, Figure 2 shows the received signal level, expressed in \(A^{2}\), for different water types and transmitted powers as a function of link depth, assuming only geometrical and path loss. Regarding ocean turbulence, three intensities are considered (strong, moderate-to-strong, weak-to-moderate). The scintillation index of the ocean turbulence, \(\sigma_{u}^{2}\), depends on parameters such as wavelength, underwater link length, and salinity and temperature variations of the medium. In our analysis, values of \(\sigma_{u}^{2}=0.2453\), \(0.7885\) and \(1.0652\) are considered for weak-to-moderate, moderate-to-strong and strong turbulence, respectively [24; 41]. Finally, for the repeater, a gain of \(g=1/A_{0}\) is assumed. In order to properly analyze the behavior of the FSO-TU system, different realistic scenarios were considered in which the impact of the main degradation phenomena for the terrestrial link and the underwater link on the BER performance were analyzed separately. \begin{table}
\begin{tabular}{l c c} \hline \hline \multicolumn{3}{c}{**Terrestrial Optical Link**} \\ \hline
**Parameter** & **Symbol** & **Value** \\ \hline Wavelength & \(\lambda_{1}\) & 1550 nm \\ \hline Responsivity & \(R_{1}\) & 0.5 A/W \\ \hline Distance & \(L\) & 1 km \\ \hline Transmitter divergence & \(\theta_{T}\) & 1 mrad \\ \hline Transmitted beamwidth at 1 km & \(\omega_{l}\) & 1 m \\ \hline Receiver radius & \(r\) & 10 cm \\ \hline Jitter standard deviation & \(\sigma_{\rho}\) & 10/30/60 cm \\ \hline Atmospheric turbulence (weak) & & 0.37 \\ Atmospheric turbulence (moderate) & \(\sigma_{a}^{2}\) & 0.5 \\ Atmospheric turbulence (strong) & & 1.17 \\ \hline Attenuation coefficient (very clear air) & & 0.0647 dB/km \\ Attenuation coefficient (clear air) & \(a\) & 0.2208 dB/km \\ Attenuation coefficient (haze) & & 0.7360 dB/km \\ \hline \multicolumn{3}{c}{**Underwater optical link**} \\ \hline
**Parameter** & **Symbol** & **Value** \\ \hline Wavelength & \(\lambda_{2}\) & 532 nm \\ \hline Responsivity & \(R_{2}\) & 0.5 A/W \\ \hline Depth & \(z\) & 20/30/40 m \\ \hline Transmitter divergence & \(\theta_{T}\) & 10 mrad \\ \hline Transmitted beamwidth at z & \(\omega_{z}\) & 30.8/46.2/61.6 cm \\ \hline Receiver radius & \(r\) & 10 cm \\ \hline Underwater turbulence (moderate-weak) & & 0.2453 \\ Underwater turbulence (moderate-strong) & \(\sigma_{u}^{2}\) & 0.7885 \\ Underwater turbulence (strong) & & 1.0652 \\ \hline Extinction coefficient (clear ocean water) & c\({}_{T}\) & 0.151 m\({}^{-1}\) \\ Extinction coefficient (coastal water) & & 0.398 m\({}^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System parameters. First, Figure 3 presents the results of the impact of terrestrial link degradation factors on the BER of the FSO-TU system. Therefore, in this figure, the underwater channel conditions are not modified, assuming the most favorable conditions, i.e., moderate-weak ocean turbulence, clean ocean water and a depth of 20 m. In particular, Figure 3 shows the BER obtained with Equation (36) as a function of the SINR for three different atmospheric turbulence conditions and three different weather conditions. We note that the SINR depicted in the figure is the maximum achievable SINR and therefore includes the minimum losses of both links, i.e., the geometric losses and the underwater channel path loss for \(z=20\) m. Values of \(\sigma_{1}=10^{-7}\) A and \(\sigma_{2}=10^{-6}\) A are assumed in our analysis. We note that both values are consistent with the noise variance measured in [42]. Here, solid, dashed and dotted curves correspond to scenarios with strong, moderate and weak turbulence, respectively, while black, red and blue curves correspond to haze, clear air and very clear air conditions, respectively. A fixed jitter with \(\sigma_{\rho}=10\) cm is assumed in all cases due to pointing error.