## 5 Numerical Results
The capacity outage probability of our proposed scheme under different capacity thresholds is plotted in Figure 3. The turbulence level is assumed to be weak turbulence and \(\rho\) is set as 0.75. As shown in Figure 3, when considering clear weather conditions, the parallel FSO/RF scheme outperforms only the FSO scheme and only the RF scheme in different capacity thresholds. The parallel FSO/RF scheme has a similar performance to only the FSO scheme when the capacity threshold is 0.95 Gbps. The only FSO scheme is superior to only the RF scheme in clear weather conditions due to its large bandwidth. Considering clear weather conditions, the parallel FSO/RF scheme can achieve an outage probability of \(8.70\times 10^{-5}\), compared to \(4.15\times 10^{-3}\) for only RF scheme and \(2.23\times 10^{-4}\) for only the FSO scheme, at a capacity threshold of 0.5 Gbps. Limited by the outage probability of the GS-satellite and satellite-HAP FSO links, the capacity outage probability of parallel FSO/RF links cannot be further improved in a small value of capacity threshold in clear weather conditions. However, when considering the light fog weather, the performance of only the FSO scheme deteriorates sharply, which is due to the fact that the FSO link is largely affected by fog weather. Compared to only the FSO scheme, the parallel FSO/RF scheme has a smaller performance degradation, which is because the use of an RF link can reduce the effect of foggy weather. Interestingly, considering light fog weather, when \(\rho\) is no more than 0.20, the parallel FSO/RF scheme even has a better capacity outage performance than only the RF scheme. This can be attributed to the fact that the FSO link can effectively supplement the capacity of the parallel FSO/RF links with a very small portion of power. As such, the parallel FSO/RF scheme is a desirable choice in clear weather and can also be adopted in light fog with a small value of \(\rho\). The effect of atmospheric turbulence under different detection techniques was depicted in Figure 4, and three nominal ground turbulence levels were assumed for parallel FSO/RF links, which are \(C_{n}^{2}(0)=1\times 10^{-12}m^{-\frac{2}{3}}\), \(C_{n}^{2}(0)=5\times 10^{-13}m^{-\frac{2}{3}}\) and \(C_{n}^{2}(0)=2.5\times 10^{-13}m^{-\frac{2}{3}}\). According to ([15], Equation (54)) and ([15], Equation (61)), the scintillation parameters are calculated as \(\alpha=4.51\), \(\beta=2.73\) for strong turbulence, \(\alpha=6.06\), \(\beta=4.48\) for moderate turbulence, \(\alpha=8.98\), \(\beta=7.47\) for weak turbulence. The average SNR for OGS-to-satellite and satellite-to-HAP FSO links is set as 40 dB, and \(\rho\) is set as 0.75. The capacity threshold is assumed as 0.5 Gbps and \(m=1\), \(N_{t}=1\) are also assumed. It can be obviously seen that the HD technique owns better outage performance than the IM/DD technique in different turbulence levels. Considering moderate turbulence and to achieve a capacity outage probability of \(1\times 10^{-4}\), the HD technique can achieve an 11.6 dB gain compared to the IM/DD technique. This is because the HD technique has better spectral efficiency and higher sensitivity than the IM/DD technique [31; 32; 33]. The HD technique suffers a 1.6 dB and 4.8 dB performance loss when the turbulence level changes from weak turbulence to  
Figure 2: Capacity outage probability under different weather conditions with different power allocation coefficients. moderate turbulence and strong turbulence at an outage probability of \(1\times 10^{-6}\). Limited by the GS-satellite and satellite-HAP FSO links, performance saturation appears in the IM/DD technique under weak turbulence when SNR exceeds 22 dB. When considering that the diversity order in Figure 4 is mainly limited by the value of \(\xi_{3}\), we give a further analysis of asymptotic analysis in Figure 5, assuming \(\xi_{3}=5.2\). The black dashed line in Figure 5 represents the asymptotic analysis at a high SNR region, and its slope is defined as the diversity order.