## 4 Simulations and Analysis  
In this section, the Monte Carlo simulation method with \(10^{8}\) independent runs is used to compare the theoretical results and numerical results. By adjusting some essential parameters, the communication performance of the downlink FSO communication system is assessed in terms of the average BER and the ergodic capacity. In the general case, some key parameters, from [9; 19; 28; 34], are shown in Table 1. Unless otherwise stated, the receiver FoV is \(\theta_{FoV}=80\) mrad, the orientation deviation is \(\sigma_{a}=15\) mrad, \(r_{L}/r_{r}=20\), \(L=2\) km, the average optical power is \(P_{t}=0\) dBm, and the FSO link undergoes moderate turbulence. In addition, \((\alpha,\beta)=\{(2.296,2),(4.2,3),(8,4)\}\) denote strong turbulence, moderate turbulence, and weak turbulence, respectively [18]. The asymptotic results of the average BER under various receiver FoV and pointing errors against the average optical power are illustrated in Figure 2. Larger the impact of the pointing errors, namely, the smaller the \(\xi\), the larger the average BER. Moreover, the average BER for the considered system without AoA fluctuations is lower than that of the system with AoA fluctuations for the same pointing errors. In addition, the average BER decreases as \(P_{t}\) and \(\theta_{FoV}\) increase. However, the system under AoA fluctuations with the same receiver FoV has the same average BER at a higher optical power regime. It is evident that the analytical and asymptotic results obtained from (15) at high optical power agree with the numerical results. The curves with different receiver FoVs have the same slope if the considered system is under the same pointing errors. As mentioned in the previous analysis, the diversity order depends on \(\min\left(\xi^{2},a,1\right)\). For example, the diversity order for \(\xi=0.74\) depends on \(\xi^{2}\), but that for \(\xi=1.05\) depends on \(1\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Name** & **Value** \\ \hline \multirow{2}{*}{\(\sigma_{c}\)} & Standard deviation of the random displacements of & \\  & beam centroid and receiver aperture & \\ \hline \multirow{2}{*}{\(\psi\)} & Visibility-related attenuation coefficient & 1.052 \\ \cline{2-3}  & Electron charge & \(1.6\times 10^{-19}\) C \\ \hline \multirow{2}{*}{\(\Delta f_{e}\)} & Receiver electrical bandwidth & 1 GHz \\ \hline \multirow{2}{*}{\(\Delta f_{o}\)} & Receiver optical bandwidth & 10 nm \\ \cline{2-3}  & Spectral radiance of the background radiations & 0.001 W/cm\({}^{2}\)-m-srad \\ \hline \multirow{2}{*}{\(\lambda\)} & Optical wavelength & 1500 nm \\ \cline{2-3}  & \multicolumn{1}{c}{Optoelectronic conversion efficiency of the PD} & 0.9 \\ \hline \multirow{2}{*}{\(p,q\)} & Two parameters that determine the binary & \\  & modulation method & \(0.5,1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Key parameters used in the simulation. To further investigate the correlation between \(\theta_{FoV}\) and the average BER, we present the average BER versus \(\theta_{FoV}\) in Figure 3 for various \(\sigma_{a}\). The Monte Carlo results coincide with the theoretical results. From this figure, as \(\theta_{FoV}\) increases, the average BER first decreases rapidly and then has a slight upward trend. It is because the influence of AWGN will be far more significant than that of the received light energy when \(\theta_{FoV}\) increases to a particular value. Mainly, when \(\sigma_{a}=10\) mrad, the average BER for \(\theta_{FoV}=50\) mrad is \(2.2\times 10^{-4}\), but the average BER for \(\theta_{FoV}=80\) mrad is only \(2.4\times 10^{-4}\). In addition, when \(\theta_{FoV}\) is low, the average BER increases as \(\sigma_{a}\) increases. Still, the degree of impact of orientation deviations on the average BER is nearly non-negligible when \(\theta_{FoV}\) is high.