## 5 Numerical Results and Discussion  
In this section, the impact of key system parameters on link performance is analyzed. It is worth noting that we make the assumption that all UAV relays experience the same atmospheric conditions and \(P_{f,j}=P_{r,j}=P_{l}\). The parameters are shown in Table 1.  
Figure 3a-d show the outage probability versus average transmitted power for different numbers of relays of case 1, case 2, case 3, and case 4, respectively. As these figures indicate, the transmit power increases significantly improve the overall outage probability performance. In addition, the simulation results of Figure 3a,c,d reveal that the outage probability generally decreases as the number of relays \(N\) increases. However, it is observed that the outage probability remains unaffected by the number of relays in case 2. It is noteworthy that the outage probability performance of \(N=5\) did not show any significant improvement compared to \(N=4\) across all four cases. Consequently, considering prudent cost management, the number of UAV relay deployments will not exceed four. In Figure 4, we observe the outage performance of the proposed modes, when the transmit power is equal to 25 dBm. As expected, increasing the velocity variance \(\sigma_{Sv}^{2}\) amplifies the pointing error as the jitter standard deviation of the AWACS-to-UAV link \(\sigma_{SR_{i}}^{2}\) increases, resulting in the deterioration of the overall outage performance. In Figure 4a, when the velocity variance of the GS \(\sigma_{Dv}^{2}=2\) and \(\sigma_{Sv}^{2}\) is below 8, case 1 exhibits optimal end-to-end outage performance ranges from about \(10^{-20}\) to \(10^{-10}\). It is worth noting that when \(\sigma_{Sv}^{2}\) exceeds 8, the outage probability curves of case 1 and case 4 coincide. Furthermore, when \(\sigma_{Sv}^{2}\) exceeds 15, the curve of case 2 aligns with those of cases 1 and 4. In other words, when \(\sigma_{Sv}^{2}\) exceeds 8, case 4 can replace case 1 to reduce the system's CSI requirements, and when \(\sigma_{Sv}^{2}\) surpasses 15, the simpler case 2 can substitute both cases 4 and 1. Therefore, in practical applications, there are some tradeoffs between the complexity and performance of these cases. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline The altitude of AWACS \(H_{AWACS}\) & 10 km \\ The zenith angle \(\xi_{UAV}=\xi_{GS}\) & \(\pi/3\) \\ Wavelength \(\lambda\) & 1550 nm \\ Responsivity \(\eta\) & 0.9 \\ Noise variance \(\sigma_{f}^{2}=\sigma_{rf}^{2}\) & \(2.5\times 10^{-14}\) \\ Turbulent factors of SR link \(\alpha_{1}\)-\(\beta_{1}\) & 7.2–6.2 \\ Turbulent factors of RD link \(\alpha_{2}\)-\(\beta_{2}\) & 5.6–4.1 \\ Cloud liquid water content \(M_{CLVNC}\) & 0.3128 mg/m\({}^{3}\) \\ Cloud droplet concentration \(N_{C}\) & 0.5 cm\({}^{-3}\) \\ Field-of-view angle \(\theta_{FoV,SR_{i}}=\theta_{FoV,R,D}\) & 8 mrad \\ Detector radius \(a\) & 0.1 m \\ SD of UAV position \(\sigma_{Rx}=\sigma_{Ry}\) & 0.1 m \\ SD of UAV orientation \(\sigma_{\theta}\) & 1.2 mrad \\ RF \(f_{RF}\) & 20 GHz \\ Antenna gain \(G_{t}\)=\(G_{r}\) & 45 dB \\ Threshold \(\gamma_{th}\) & 5 dB \\ Oxygen attenuation coefficient \(\kappa_{oxy}\) & 0.1 dB/km \\ Specific attenuation coefficient \(K\) & 0.5 (dB/km)/(g/m\({}^{3}\)) \\ Time interval \(\Delta t\) & 1 s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters and their values. The increase in \(\sigma^{2}_{Dv}\) to 10, as shown in Figure 4b, leads to a rise in the overall end-to-end outage probability and causes variability in the outage performance of different cases. As we can see from the figure, when \(\sigma^{2}_{Sv}\) is below 2, cases 1 and 3 exhibit optimal end-to-end outage performance ranges from about \(10^{-8}\), but with the increase in \(\sigma^{2}_{Sv}\), the outage performance of case 3 deteriorates rapidly. In contrast to Figure 4a, the outage performance of case 2 is consistently poor, remaining at approximately \(10^{-3}\).