## 5 Numerical Results and Discussion
In other words, when the system imposes a requirement on outage probability (such as not exceeding \(10^{-10}\)), the altitude of UAVs in cases 1 and 3 should be limited to a maximum of 700 m. In case 4, the altitude of UAVs should not exceed 500 m, and for case 2 it should not exceed 300 m.  
Figure 7 shows the impact of \(\sigma^{2}_{S_{U}}\) on the average BER performance of the system for \(\sigma^{2}_{Dv}=2\sigma^{2}_{Dv}=10\), and \(\sigma^{2}_{Dv}=20\) considering \(H_{UAV}=0.5\) km and \(P_{t}=25\) dBm. As expected, increasing the velocity variance deteriorates the overall BER performance as the pointing error increases. Also, we can see that increasing the \(\sigma^{2}_{Dv}\) results in a significant rise in the average BER when the value of \(\sigma^{2}_{S_{U}}\) is small. Conversely, the BER of the three curves tend to converge when \(\sigma^{2}_{S_{U}}\) is large. Similarly, an increase in \(\sigma^{2}_{S_{U}}\) leads to a rapid escalation in the BER from \(10^{-5}\) to \(10^{-1}\) when \(\sigma^{2}_{Dv}=2\); however, when \(\sigma^{2}_{Dv}=20\), although there is still an increment with \(\sigma^{2}_{S_{U}}\) it only exhibits a slight rise. Figure 8 shows the average BER results for different weather conditions, according to the attenuation values corresponding to weather conditions in [24]. The attenuation coefficient \(\omega=[0.43,\,4.2,\,20,\,42.2,\,125]\times 10^{-3}\) m\({}^{-1}\) corresponds to clear air, haze, light fog, moderate fog, and heavy fog. It is found that the increase in \(\omega\) results in a slight increase in the average BER. The parallel FSO/RF hybrid link and the utilization of UAV relays enhance the system's capability to adapt to weather variations. Design Guidelines:  
In summary, we provide important design guidelines that can help design the UAV-based hybrid FSO/RF aeronautical communication system:  
* The use of UAV relays improves the system's performance. The increase in the number of relays improves outage performance to some extent when \(N\leq 4\). However, when  
Figure 8: Impact of the weather conditions in terms of the average BER. Figure 7: Impact of the velocity variance of the AWACS and GS in terms of the average BER. N > 4, increasing the number of relays does not have a positive impact on outage probability. Considering cost-saving, it is recommended that the total number of relays in this system should not exceed four. * In mobile scenarios, the velocity variance of the AWACS and GS directly impact the outage and average BER performance of the hybrid FSO/RF aeronautical communication system. Excessive velocity variance in either AWACS or GS can lead to degradation in system performance. * In the multi-UAV relay system, the outage performance varies among different relay selection modes. Generally, the Max-Select mode demonstrates the best performance; however, it requires the most feedback channels. In fact, for lower \(\sigma_{S_{0}}^{2}\) values and higher \(\sigma_{Dv}^{2}\), the simpler Relay-Destination-Select mode can replace Max-Select mode. In addition, for higher \(\sigma_{S_{0}}^{2}\) values and lower \(\sigma_{Dv}^{2}\), the Source-Relay-Select mode can replace Max-Select mode. When both \(\sigma_{S_{0}}^{2}\) and \(\sigma_{Dv}^{2}\) exhibit large values, the Dual-Distributed-Select mode can also serve as a viable alternative for approximating performance. The tradeoffs between complexity and performance vary depending on the actual usage. * The end-to-end outage probability of the system is influenced by the deployment altitude of UAV relays. Within the acceptable range of UAV flight characteristics, lower flight altitudes result in enhanced outage performance. When \(P_{t}=25\) dBm, to ensure that the outage probability is controlled within \(10^{-5}\), the flight altitude should not exceed 1 km for cases 1 and 3, 800 m for case 4, and 500 m for case 2.