# Cooperative Terrestrial-Underwater FSO System: Design and Performance Analysis
## 5 Results  
In this section, the closed-form mathematical expression for the average BER derived in the previous section is used to evaluate the performance of the proposed cooperative FSO-TU system. The aim of this analysis is to better understand the BER performance of the hybrid FSO-TU system under realistic scenario conditions, as well as to draw some ideas and conclusions that may lead to a better future design of cooperative FSO-TU systems based on the scheme investigated here. Table 1 summarizes the realistic parameters considered in our analysis for the terrestrial an underwater links. On the one hand, as far as the terrestrial link is concerned, this first link operates at \(\lambda_{1}=1550\) nm over a distance \(L=1\) km, as shown in Figure 1. Here, the transmitter laser emits an average optical power \(P_{1}\) with a divergence angle of \(\theta_{T}=10\) mrad, resulting at the receiver end in a beam footprint with a waist of \(\omega_{l}=1\) m. With this optical beam broadening, only a fraction of the transmitted power is collected for the detector of \(r=10\) cm radius and responsiveness \(R_{1}=0.5\) A/W. Thus, this terrestrial link operates with a ratio of \((\omega_{l}/r)=10\). Moreover, with regard to the limiting factors of the networking environment, three atmospheric turbulence conditions are considered for the terrestrial channel: strong, moderate, and weak. As discussed in Section 3, the intensity of atmospheric turbulence, \(\sigma_{a}^{2}\), depends on the wavelength, \(\lambda_{1}\), the link distance, \(L\), the link inclination angle, \(\theta\), and the refractive index structure parameter \(C_{n}^{2}\). In turn, parameter \(C_{n}^{2}\) changes with height, as shown by different models such as the Hundagle-Valley and the SLC models [16]. In our analysis, we use different values of \(\theta\) and \(C_{n}^{2}\) according to the aforementioned models in order to obtain, by means of Equations (12) and (13), the values of \(\alpha\) and \(\beta\) required by the Gamma-Gamma model to emulate the mentioned turbulent conditions. In particular, the values of \(\alpha\) and \(\beta\) considered in our calculations are \(6.76\) and \(5.22\), \(5.383\) and \(3.753\), and \(4.345\) and \(1.307\), which correspond to weak (\(\sigma_{a}^{2}=0.37\)), moderate (\(\sigma_{a}^{2}=0.5\)), and strong (\(\sigma_{a}^{2}=1.17\)) turbulence conditions, respectively. In addition, three climatic conditions such as very clear air, clear air, and haze are also considered. The values of the attenuation coefficient, \(a\), for these three climatic conditions are taken from [31]. Finally, concerning the misalignment effect, three values of jitters are used with standard deviations of \(\sigma_{\rho}=\)10, 30, and 60 cm, which corresponds to ratios \((\sigma_{\rho}/\omega_{l})=0.1\), \(0.3\), and \(0.6\), respectively. On the other hand, as far as the underwater link is concerned, this second link operates at a \(\lambda_{2}=532\) nm for three different depths of \(z=20\), 30 and 40 m. We note that the distances in this second link are much smaller than in the terrestrial link due to the huge degradation of the underwater channel. Here, the transmitter emits average optical power \(P_{2}\) with a divergence angle of \(\theta_{T}=10\) mrad which results, for a detector size of 10 cm radius, in \((\omega_{z}/r)\) ratios of two, three and four for each of the above-mentioned depths. The value of \(P_{2}\) can be obtained from the terrestrial link parameters and the gain of the relay node as \(P_{2}=gR_{1}P_{1}A_{0}h_{l}\gamma_{\rho}^{2}/(1+\gamma_{\rho}^{2})\). Moreover, to calculate coefficient \(h_{lg}\) that takes into account the path loss and geometric losses, we use the values of extinction coefficient \(c_{T}\) and of coefficients \(k_{1}\) and \(k_{2}\) published in [33], according to the type of water and depth considered in each case.