# Relay Selection Schemes for FSO Communications over Turbulent Channels
## 4 Simulation Results  
A target of \(10^{-6}\) for the ABER is assumed and the FSO link distance is 1 km with different first-hop and second-hop link distances. Derived analytical results that were corroborated via Monte Carlo simulation are performed with \(10^{7}\) bits transmitted for each depicted SNR and the Gauss-Laguerre quadrature approximation order is \(S\leq 50\). Table 1 shows the system parameters under investigation that are used in various FSO communication systems [13; 19; 20]. Using Table 2, the atmospheric turbulence conditions are calculated through Equations (13), (18), (19) and (20). Table 2 illustrates \(\sigma_{x1}\)\(a_{1}\), \(b_{1}\), and \(\sigma_{R_{1}}^{2}\) turbulence parameters for the first-hop and \(\sigma_{x_{2}}\), \(a_{2}\), \(b_{2}\), and \(\sigma_{R_{2}}^{2}\) turbulence parameters for the second-hop [11]. The simulation and analytical results that are shown in four when considering a relation between ABER and SNR over L-N channel for a weak turbulence with distance 400-600 m, the number of relays is 3 and the beam waist is 2 m. The following schemes R-D, S-R, and S-R-D are compared with the performance of the direct-link (DL) transmission. The results show the accuracy of the derived approximated ABER. It is worth noting that, for all three cases enhancing the ABER, performance needs to increase the transmitted power. By comparing the three scenarios in terms of power consumption, it shows that, to achieve an ABER of \(10^{-6}\) bit/s, the R-D case gives the best performance for weak turbulence regime. It shows that the R-D scheme has a higher SNR gain than the S-R-D, S-R, and DL schemes by 0.4 dB, 3.6 dB, and 14.8 dB, respectively. While comparing the two other techniques, it is noticed that the direct link needs higher transmitted power than S-R and S-R-D by 11.2 dB, 14.4 dB, respectively. It is clear that increasing the turbulence effect requires more SNR to achieve the same ABER. Whether it is weak, as in Figure 4, or moderate turbulence, as in Figure 5, the R-D proved to be better than S-R-D and S-R. Moreover, the R-D scheme has higher SNR gain than the S-R-D and S-R schemes \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Wavelength & \(\lambda\) & 1550 nm \\ \hline Receiver diameter & \(D_{R}\) & 0.2 m \\ \hline Transmitter diameter & \(D_{T}\) & 0.2 m \\ \hline Divergence angle & \(\theta_{T}\) & 2 mrad \\ \hline Distance between source and destination & D & 1 km \\ \hline Attenuation coefficient & \(\alpha\) & 0.43 dB/km \\ \hline Jitter standard deviation & \(\sigma_{s}\) & 0.3 m \\ \hline Beam waist (weak-to-strong pointing error) & \(\omega_{z}\) & 2 m or 0.5 m \\ \hline Refractive index coefficient & \(C_{n}^{2}\) & \(0.5\times 10^{-14}\), \(2\times 10^{-14}\) \\ (weak-to-strong turbulence) & & and \(5\times 10^{-14}\) m\({}^{-2/3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: SYSTEM Parameters. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Atmospheric Turbulence** & **Link Type** & \(\sigma_{x_{1}}\) & \(\sigma_{x_{2}}\) & \(\mathbf{a_{1}}\) & \(\mathbf{a_{2}}\) & \(\mathbf{b_{1}}\) & \(\mathbf{b_{2}}\) & \(\sigma_{R_{1}}^{2}\) & \(\sigma_{R_{2}}^{2}\) \\ \hline
**Direct Link** & 0–1000 & 0.16 & & & & & \\ \hline \multirow{4}{*}{**Weak Turbulence**} & 500–500 & 0.08 & 0.08 & & & & \\ \cline{2-6}  & 600–400 & 0.1 & 0.07 & & & & \\ \cline{2-6}  & 400–600 & 0.07 & 0.1 & & & & \\ \hline \multirow{4}{*}{**Moderate Turbulence**} & 0–1000 & 0.31 & & & & & \\ \cline{2-6}  & 500–500 & 0.17 & 0.17 & & & & \\ \cline{2-6}  & 600–400 & 0.2 & 0.14 & & & & \\ \cline{2-6}  & 400–600 & 0.14 & 0.2 & & & & \\ \hline \multirow{4}{*}{**Strong Turbulence**} & 0–1000 & & 4.39 & 2.57 & 0.99 & \\ \cline{2-6}  & 500–500 & & 7.26 & 7.26 & 7.4 & 7.4 & 0.28 & 0.28 \\ \cline{2-6}  & 600–400 & & 5.5 & 10.8 & 5.5 & 10.9 & 0.4 & 0.19 \\ \cline{2-6}  & 400–600 & 10.8 & 5.5 & 10.9 & 5.5 & 0.19 & 0.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: ATMOSPHERIC CONDITIONS. by 0.4 dB and 8.9 dB, respectively.