## 3 Performance Analysis
\begin{table}
\begin{tabular}{c c c} \hline \hline
**System Parameters** & **Symbol** & **Value** \\ \hline Height of satellite ground station & H & 3600 km \\ Height of the transmitter from the ground & h\({}_{0}\) & 100 m \\ Wind speed & p & 21 m/s \\ Light wavelength & \(\lambda\) & 1.55 um \\ Atmospheric structure constant of refractive index & \(C_{n}^{2}\) & \(7.5\times 10^{-17}\) \\ Receiving diameter & D & 0.2 m \\ Zenith angle & \(\zeta\) & 30\({}^{\circ}\) \\ anisotropic factor & u & 1 and 3 \\ Height of HAP & Hp & 20 km \\ FSO link length from ground transmitter to HAP & L1 & 40 km \\ FSO link length from HAP to satellite & L2 & 7160 km \\ Inclination angle of HAP to the ground & \(\zeta_{1}\) & 60\({}^{\circ}\) \\ Inclination angle of HAP to the satellite & \(\zeta_{2}\) & 30\({}^{\circ}\) \\ Transmitter beam radius & \(\omega\)0 & 0.1 m \\ \hline \end{tabular}
\end{table} 
Table 1: Simulation parameter selection of G-H-S laser communication system. \(3.87\times 10^{-4}\), respectively. However, the BER of HQAM modulation is always lower than that of XQAM, RQAM, and QAM. Moreover, the BER of the G-H-S and G-S systems increases monotonically with the increase in the zenith angle, which indicates that a high zenith angle has a more severe influence on atmospheric turbulence than a low zenith angle. Regarding trends, when the zenith angle is small, the difference in bit error rate between the two is the largest, and the distance between the two lines is large. As the zenith angle increases, the BER of the G-H-S system shows a greater upward trend than that of G-S. The difference between them gradually decreases, and the two lines are closer but do not overlap. For example, when u = 1 and the zenith angle is \(10^{\circ}\), the BERs of the G-H-S and G-S systems are \(1.8\times 10^{-4}\) and \(7.1\times 10^{-3}\), respectively. When u = 1 and the zenith angle is \(37^{\circ}\), the BERs of the G-H-S and G-S systems are 0.08 and 0.1, respectively. Therefore, it is better to use a HAP to assist ground-satellite uplink and adopt HQAM modulation. Figure 4a,b show the variation in the receiving aperture of HQAM, XQAM, RQAM, and QAM with BER at different anisotropy factors of u = 1 and u = 3, respectively. The results show that the BER of the system decreases not only with the increase in the receiving aperture but also with the increase in the anisotropy factor, mainly because the rise of the aperture will increase the power of the incident light and lead to a decrease in the BER. As can be seen from Figure 4a,b, the BER of the four modulation schemes decreases with the  
Figure 3: Relationship between the zenith angle and BER of HQAM, XQAM, RQAM, and QAM under different anisotropy factors in the ground–satellite uplink. (**a**) u = 1; (**b**) u = 3. Figure 2: Relationship between SNR and BER of HQAM, XQAM, RQAM, and QAM under different anisotropy factors in the ground–satellite uplink. (**a**) u = 1; (**b**) u = 3.  
increase in the acceptance aperture and decreases with the increase in the anisotropy factor under the same acceptance aperture. For example, when u = 1 and the receiving aperture is 1 m, the BERs of HQAM, XQAM, RQAM, and QAM are 1.16 \(\times\) 10\({}^{-2}\), 2.84 \(\times\) 10\({}^{-2}\), 6.76 \(\times\) 10\({}^{-2}\), and 1.17 \(\times\) 10\({}^{-1}\), respectively. When u = 3 and the receiving aperture is 1 m, the BERs of HQAM, XQAM, RQAM, and QAM are 5.93 \(\times\) 10\({}^{-4}\), 1.61 \(\times\) 10\({}^{-3}\), 4.64 \(\times\) 10\({}^{-3}\), and 8.62 \(\times\) 10\({}^{-3}\), respectively. However, when u = 3 and the BER of the G-H-S system is 10\({}^{-3}\), the receiving apertures required for HQAM, XQAM, RQAM, and QAM are 0.8 m, 1 m, 1.2 m, and 1.4 m, respectively. Therefore, under the same communication performance, the receiving aperture required by HQAM is relatively tiny. Moreover, the BER of the G-H-S and G-S systems decreases monotonically with the increase in receiving aperture. Regarding trends, the initial BER distance between the two is similar but does not overlap.