## 4 Numerical Results
### ABER Results  
Figure 9 shows the system's ABER versus \(P_{j}\) for different numbers of relay nodes \(M\) when \(Z_{m,j}=0.5\) km and \(\sigma^{2}_{\text{R},m,j}=1\). It can be seen that the system's ABER gradually decreases with the increase in \(P_{j}\) for a given \(M\) value. Under the same transmitted optical power condition, the system's ABER does not change with the increase in \(M\), because the system ABER is equal to the ABER of a single path and is independent of \(M\), when the states of each path are independent and identically distributed. Moreover, the system ABER does not decrease with the increase in \(P_{j}\), but approaches the same asymptotic bound. This indicates that increasing the \(P_{j}\) cannot always improve the system's ABER performance, which verifies the accuracy of Remark 2. Figure 10 shows the system's ABER versus \(P_{j}\) for different \(Z_{m,j}\) when \(\sigma^{2}_{\text{R},m,j}=1\) and \(M=2\). In Figure 10, the system's ABER dramatically decreases with the decrease in \(Z_{m,j}\) when \(P_{j}\) is small. This is obvious because the shorter the link transmission distance is, the better the channel quality is. However, when \(P_{j}\) is large, the system's ABER does not continuously decrease with the increase in \(P_{j}\), but gradually approaches the asymptotic bound, which verifies the accuracy of (37). This phenomenon suggests that when \(P_{j}\) is large enough, the average transmitted optical power does not affect the system's ABER. Moreover, the system's ABER curves approach the same asymptotic bound when \(P_{j}\) is large; that is, the asymptotic bound is independent of \(Z_{m,j}\) and the parameter that affects the system's ABER is no longer \(Z_{m,j}\), which verifies the accuracy of Remark 2. Figure 11 shows the system's ABER versus \(P_{j}\) for different \(\sigma^{2}_{\text{R},m,j}\) when \(M=2\) and \(Z_{m,j}=0.5\) km. In the figure, we find that the system BER increases with the increase in \(\sigma^{2}_{\text{R},m,j}\) when \(P_{j}\) is small. According to (9) and (10), we can conclude that the PDF of \(h^{a}_{m,j}\) is only determined by \(\sigma^{2}_{\text{R},m,j}\). Thus, when the average transmitted optical power is small, we can reduce the effect of atmospheric turbulence on the system's BER by decreasing \(\sigma^{2}_{\text{R},m,j}\). Under different \(\sigma^{2}_{\text{R},m,j}\) conditions, the system's BER curves approach the same asymptotic bound as when the average transmitted optical power is large; this asymptotic value  
is independent of \(P_{j}\) and the turbulence condition \(\sigma_{R,m,j}^{2}\), which verifies the accuracy of Remark 2. Figure 12 shows the system's ABER versus \(P_{j}\) for different FoVs \(\theta_{\mathrm{FoV},m,j}\) when \(M=2\) and \(Z_{m,j}=0.5\) km. In the figure, we find that the system's ABER gradually decreases with the increase in \(P_{j}\) for a given \(\theta_{\mathrm{FoV},m,j}\). When \(P_{j}\) is large, the system's ABER does not decrease with the increase in \(P_{j}\), but approaches different asymptotic bounds due to the different values of \(\theta_{\mathrm{FoV},m,j}\). This indicates that the system's ABER cannot always be decreased by increasing \(P_{j}\), which verifies the accuracy of Remark 2. Figure 13 shows the system's ABER versus the FoV \(\theta_{\mathrm{FoV},m,j}\) for different values of \(P_{j}\) when \(M=2\) and \(Z_{m,j}=0.5\) km. In this figure, we find that the system's ABER decreases first and then increases as \(\theta_{\mathrm{FoV},m,j}\) increases for a given \(P_{j}\). This indicates that there is an optimal \(\theta_{\mathrm{FoV},m,j}\) value for obtaining the minimum system ABER, and the optimal \(\theta_{\mathrm{FoV},m,j}\) value increases gradually with the increase in \(P_{j}\). Figure 14 shows the system ABER versus \(P_{j}\) for different standard deviations of the direction deviation \(\sigma_{\text{o}}\) when \(M=2\) and \(Z_{m,j}=0.5\) km. In this figure, we find that the system's ABER decreases with the increase in \(P_{j}\) for a given \(\sigma_{\text{o}}\).