## 4 Performance Analysis
### Secrecy Outage Probability (SOP)
#### 4.2.1 Exact Analysis
The results also depict that the analytical results perfectly matched with the simulation results, which indicate the accuracy of the derived expressions. The impact of pointing error on the system SOP performance under the different detection schemes is presented in Figure 4. Under both detec  
Figure 3: Impact of atmospheric turbulence on the system SOP performance under different detection schemes when \(\overline{\gamma}_{2}=10\) dB, \(\overline{\gamma}_{e}=5\) dB, and \(\xi=6.5\). Figure 2: COP performance of the system under atmospheric conditions for different detection scheme at \(\overline{\gamma}_{e}=5\) dB, \(\overline{\gamma}_{1}=35\) dB, \(\overline{\gamma}_{2}=15\) dB. error value (\(\xi=1.1\)) causes an increase in the effect of pointing errors, which leads to degradation in the system SOP performance. On the other hand, higher values of PE (\(\xi=6.5\)) decrease the effect of PE and improve the system SOP. It is observed from the results that the system performance is better under the heterodyne detection compared to the IMDD detection. In Figure 5, the effect of \(\overline{\gamma}_{e}\) level on the system SOP performance is demonstrated under the different detection schemes. It can be seen that the analytical results collaborate perfectly with the simulation results, which proves the accuracy of the derived expressions. Moreover, it can be deduced from the results that the higher the values of \(\overline{\gamma}_{e}\), the worse the system SOP performance, with heterodyne detection outperforming the IMDD detection. It can also be observed from the result that the asymptotic results follow the SOP results at high SNR. This shows that the quality of eavesdropper channel improves at higher valves of \(\overline{\gamma}_{e}\), which significantly leads to degradation in system SOP performance. The effect of Rican factor level of the eavesdropper link on the system SOP performance is depicted in Figure 6. It can be observed that the higher value of \(K\) factor has lower system SOP performance. This is because, at large values of \(K\) factor, there is strong LOS for the eavesdropper to wiretap the confidential message from HAP, and this degrades the system SOP performance. The analytical results match well with simulation results, confirming the validity of the derived expressions. Figure 4: Effect of pointing errors on the system SOP under different detection schemes at \(\overline{\gamma}_{e}=5\) dB, \(\overline{\gamma}_{2}=10\) dB. The system SOP performance under different shadowing fading severities is presented in Figure 7. It can be observed that the system becomes degraded as the shadowing fading effect increases from AS to FHS. Under the same channel conditions, the results show that heterodyne detection offers the system better SOP performance compared with IMDD detection. In addition, analytical results of the system SOP closely match with simulation results, showing the accuracy of our derivations. Figure 5: Impact of \(\overline{\gamma}_{e}\) levels on the system SOP under different detection schemes when \(\overline{\gamma}_{2}=10\) dB and \(\xi=1.1\). The effect of the number of terrestrial users on the system SOP performance under strong turbulence condition is presented in Figure 8. It can be deduced that the system SOP performance significantly improves as the number of ground users increases. This is because multiuser diversity gain is achieved, which, in turn, enhances the system SOP performance. The results indicate that the heterodyne detection offers the system better performance compared to the IMDD detection. Figure 8: Effect of number of terrestrial users on the system SOP performance under the heterodyne detection for different pointing errors when \(\overline{\gamma}_{1}=35\) dB and \(\overline{\gamma}_{e}=5\) dB. Figure 7: Impart of shadowing fading severities on the system SOP performance under different detection schemes when \(\overline{\gamma}_{1}=45\) dB, \(\overline{\gamma}_{e}=5\) dB, and \(\xi=6.5\).