## 4 Numerical Results
### OP Results  
Figure 2 shows the OP versus the average transmitted optical power \(P_{j}\) for different relay numbers \(M\) when \(Z_{m,j}=0.5\) km and \(\sigma_{\text{R},m,j}^{2}=1\). As can be observed, for a given \(M\), the OP gradually decreases with the \(P_{j}\). Under the same \(P_{j}\), the OP decreases significantly with an increase in \(M\). This means that increasing the number of parallel relay nodes can significantly improve the system's outage performance. In addition, when \(P_{j}\) is large, the OP of the system does not decrease with the increase in \(P_{j}\) but tends to the corresponding asymptotic bound. This indicates that increasing the average transmitted optical power cannot always improve the outage performance of the system, which verifies the conclusion in Remark 1. Figure 3 shows the OP versus \(P_{j}\) for different \(Z_{m,j}\) when \(M=2\) and \(\sigma_{\text{R},m,j}^{2}=1\). As can be seen, when \(P_{j}\) is small, the system's OP gradually decreases with the decrease in \(Z_{m,j}\). Obviously, the smaller the link transmission distance is, the better the channel quality is. However, when \(P_{j}\) is sufficiently large, the OP does not continuously decrease with the increase in \(P_{j}\) but gradually approaches its asymptotic bound, which verifies the accuracy of (25). Such an observation suggests that when \(P_{j}\) is sufficiently large, the average transmitted optical power will no longer affect the OP performance of the system. In this situation, the relay numbers \(M\), the FoV \(\theta_{\text{FoV},m,j}\), and the standard deviation of the direction deviation \(\sigma_{\text{o}}\) limit the system's outage performance. In addition, when \(P_{j}\) is large, the system's OP curves tend to the same asymptotic bound under different \(Z_{m,j}\). That is to say, its asymptotic \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Symbols** & **Values** \\ \hline Standard deviation of direction deviation & \(\sigma_{\text{o}}\) & 1.2 mrad \\ \hline Noise variance at \(\text{R}_{j}\) & \(\sigma_{\text{r}}^{2}\) & \(2.5\times 10^{-14}\) \\ \hline SNR threshold & \(\gamma_{\text{th}}\) & 10 dB \\ \hline Noise variance at D & \(\sigma_{\text{d}}^{2}\) & \(2.5\times 10^{-14}\) \\ \hline Beam waist radius at distance \(Z_{m,j}\) & \(\omega_{\text{Z}_{m,j}}\) & 2 m \\ \hline Receiver FoV & \(\theta_{\text{FoV},m,j}\) & 5 mrad \\ \hline Receiver sensitivity & \(S_{\text{v}}\) & \(-30\) dBm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._bound is independent of \(Z_{m,j}\). Therefore, the limiting factor affecting the system's OP is no longer \(Z_{m,j}\), which verifies the conclusion in Remark 1. Figure 4 shows the OP versus \(P_{j}\) for different \(\sigma^{2}_{\mathbb{R},m,j}\) when \(M=2\) and \(Z_{m,j}=0.5\) km. As can be observed, when \(P_{j}\) is small, the OP performance becomes worse as \(\sigma^{2}_{\mathbb{R},m,j}\) increases. By observing (9) and (10), we can conclude that the PDF of \(h^{\alpha}_{m,j}\) is only affected by \(\sigma^{2}_{\mathbb{R},m,j}\). Therefore, when \(P_{j}\) is small, the effect of atmospheric turbulence on the OP is reduced by reducing \(\sigma^{2}_{\mathbb{R},m,j}\). When \(P_{j}\) is large, the OP curves of the system tend to the same asymptotic bound under different \(\sigma^{2}_{\mathbb{R},m,j}\). It should be noted that the asymptotic value is independent of \(P_{j}\) and the turbulence condition of \(\sigma^{2}_{\mathbb{R},m,j}\), which verifies Remark 1. Figure 5 shows the OP versus \(P_{j}\) for different SNR threshold values \(\gamma_{\text{th}}\) when \(M=2\) and \(Z_{m,j}=0.5\) km. It can be observed from the figure that when \(P_{j}\) is small, the system's OP performance becomes worse as the \(\gamma_{\text{th}}\) increases, which suggests that a better OP performance for the system can be obtained by reducing the value of \(\gamma_{\text{th}}\).