## 5 Numerical Results  
In this section, we provide performance evaluation for our proposed system in terms of capacity outage probability, weighted average BER, and energy efficiency. The optimal power allocation coefficients of parallel FSO/RF links under different weather conditions are also obtained. Additionally, we have discussed the performance of our proposed parallel FSO/RF scheme with the existing schemes, including the only FSO scheme and only RF scheme. System parameters are listed as shown in Table 3 unless otherwise specified, and the weather-dependent attenuation coefficients are given in Table 4[29]. Three types of turbulence conditions are assumed similar to [2]. Without loss of generality, we assume that the maximum acceptable capacity outage probability of users inside or outside the hotspot areas is \(1\times 10^{-3}\). Note that ten terms in (27) are sufficient to achieve a relative error of \(1\times 10^{-7}\). Monte Carlo simulations are also adopted over \(10^{7}\) realizations to validate the correctness of analytical results [30]. In Figure 2, the capacity outage probability of our proposed system under different weather conditions is plotted as a function of the power allocation coefficient \(\rho\). We assume that the average SNR of both OGS-to-satellite and satellite-to-HAP FSO links is 40 dB. The total transmit power of HAP is 14 dBW, and moderate turbulence is assumed. It can be clearly observed that severe weather conditions can seriously deteriorate the capacity outage probability of parallel FSO/RF links. For a given weather condition and target capacity threshold, there exists an optimal power allocation coefficient that can minimize the system capacity outage probability. Specifically, \(\rho*\) is 0.75 for clear weather while \(\rho*\) also equal to 0.75 for moderate rain and light fog weather conditions. It is worth noting that \(\rho*\) is not sensitive to the target capacity threshold and a larger capacity threshold, resulting in a worse capacity outage performance. Compared to clear weather, the performance of parallel FSO/RF links decreases in moderate rain weather, which is due to the fact that both the FSO and the RF links are affected by the attenuation caused by rainfall. The light fog weather owns the worst capacity outage performance due to the large attenuation of the FSO link caused by foggy weather. Moreover, we have also marked the minimum value of \(\rho\) in Figure 2, which satisfies the maximum acceptable capacity outage probability of users inside the hotspot areas. Therefore, we should flexibly set the value of \(\rho\) according to different weather conditions to optimize system capacity outage probability. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Weather Conditions** & \(\omega_{fg}\)**(dB/km)** & \(\omega_{rain}\)**(dB/km)** \\ \hline Clear Weather & 0.43 & 0 \\ \hline Haze weather & 3.34 & 0 \\ \hline Moderate rain & 5.84 & 5.69 \\ \hline Heavy rain & 9.29 & 10.09 \\ \hline Light fog & 16.67 & 0 \\ \hline Moderate fog & 35.38 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Weather-Dependent Variables [29]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Satellite altitude & \(h_{S}\) & 550 km \\ \hline HAP altitude & \(h_{H}\) & 20 km \\ \hline AP height & \(h_{G}\) & 10 m \\ \hline Wind speed & \(\omega_{d}\) & 21 m/s \\ \hline Capacity threshold & \(C_{thr}^{1},C_{th}^{2}\) & 0.3 Gbps, 0.5 Gbps \\ \hline \multicolumn{3}{c}{FSO subsystem} \\ \hline Link bandwidth & \(W_{f}\) & 1 GHz \\ \hline Wavelength & \(\lambda\) & 1550 nm \\ \hline Conversion coefficient & \(\rho\) & 0.8 \\ \hline Beam radius & \(w_{0}\) & 0.05 m \\ \hline Fixed relay gain & \(Q\) & 1.2 \\ \hline \multicolumn{3}{c}{RF subsystem} \\ \hline Carrier frequency & \(f\) & 28 GHz \\ \hline Link bandwidth & \(W_{r}\) & 300 MHz \\ \hline Fading parameter & \(m\) & 1, 2 \\ \hline Antenna number & \(N_{t}\) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: System Parameters.