## 5 Numerical Results
The average SNR for OGS-to-satellite and satellite-to-HAP FSO links is assumed to be 40 dB, and clear weather conditions are considered with \(\rho=0.75\). We can observe that strong turbulence can deteriorate weighted average BER performance, which is due to the fact that strong turbulence will reduce the average BER performance of the FSO link. For the IM/DD technique, to achieve a weighted average BER of \(1\times 10^{-2}\), an additional 5.9 dB is needed for strong turbulence compared to weak turbulence. In addition, the HD technique can outperform the IM/DD technique in different turbulence levels. Considering weak turbulence conditions, a 7.1 dB gain can be achieved by the HD technique compared to the IM/DD technique at a weighted average BER of \(1\times 10^{-3}\). The weighted average BER for different modulation schemes is shown in Figure 9, where we assume the average SNR for OGS-to-satellite and satellite-to-HAP FSO links as 40 dB and \(\rho=0.75\) is adopted. It can be observed that the BPSK modulation can achieve the best weighted average BER performance; 10.2 dB, 7.0 dB, and 12.5 dB gains can be achieved compared to 16 PSK modulation, 16 QAM modulation, and 64 QAM modulation at a weighted average BER of \(1\times 10^{-3}\). The 16 QAM owns a better weighted average BER performance than 16 PSK, which is consistent with [34]. The 16 PSK modulation can outperform OOK modulation when the total transmit power is larger than 15 dBW, while the 64 QAM modulation can outperform OOK modulation when the total transmit power is larger than 20 dBW. Limited by the average BER of the RF link, the weighted average BER performance gap between BPSK and 16-QAM becomes smaller in a high total transmit power region. Figure 7: Weighted average BER under different weather conditions with different transmission schemes. Figure 10 presents the system's energy efficiency under different weather conditions, in which the optimal values of \(\rho\) are also marked. In addition, the capacity outage probability of users outside the hotspot area under different weather conditions is given in Figure 11. From Figure 11, we can find that the value of \(\rho\) should not exceed 0.94 in clear weather to satisfy the maximum acceptable capacity outage probability of \(1\times 10^{-3}\) for users outside the hotspot area. Similarly, the values of \(\rho\) should not exceed 0.77 and 0.37 in moderate rain and heavy rain weather, respectively. From Figure 2, the value of \(\rho\) should not be less than 0.05 in clear weather to ensure the QoS of users inside the hotspot area and \(\rho\) should not be less than 0.20 and 0.35 in moderate rain and light fog weather, respectively. From Figure 10, it can be clearly seen that the largest energy efficiency can be achieved in clear weather with an optimal \(\rho\) of 0.80, which also satisfies the QoS of users inside and outside the hotspot area. Compared to clear weather, hazy weather has a smaller energy efficiency, and the optimal \(\rho\) equals 0.80. When considering moderate fog weather, system energy efficiency decreases with the increase of \(\rho\), and more power should be allocated to RF links to achieve a higher energy efficiency. This is due to the fact that the FSO link has poor availability in moderate fog weather. Compared to moderate fog, optimal energy efficiency can be obtained in light fog weather with \(\rho=0.70\), which also satisfies the QoS of users inside and outside the hotspot area. Moreover, \(\rho\) equals 0.80 for both moderate rain and heavy rain weather; however, considering the QoS of users, \(\rho\) should be set as 0.77 and 0.37 in moderate rain weather and heavy rain weather, respectively. The optical values of \(\rho\) are also given in Figure 3.0 Furthermore, when \(\rho\) is less than 0.55, the light fog weather can achieve a higher energy efficiency than heavy rain weather, while instead when \(\rho\) is less than 0. \(\rho\) is larger than 0.55.