## 3 Performance Analysis
As the receiving aperture increases and the incident light power increases, the receiving intensity of the optical signal increases. The BER of the two gradually decreases, and the BER of the G-H-S system decreases faster, leading to a gradual increase in the difference in bit error rate between the two. When u = 3 and the receiving aperture is 0.8 m, the BERs of the G-H-S system and G-S system under QAM modulation are 2.1 \(\times\) 10\({}^{-2}\) and 3.9 \(\times\) 10\({}^{-3}\), respectively. The communication performance of the G-H-S system is superior to that of the traditional G-S system. In the uplink, a small receiving aperture can reduce the influence of beam distortion on system performance, minimize transmission cost, and effectively avoid the problems of high manufacturing cost and complex processing caused by large aperture reception. Figure 5a,b show the variation in the transmit radius 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 not only decreases first and then increases with the increase in the emission radius but also decreases with the increase in the anisotropy factor. When the system reaches the optimal transmission radius, the performance of the HQAM modulation scheme is the best, and the BER is lower with the increase in the anisotropy factor. For example, when u = 1, the BERs of HQAM, XQAM, RQAM, and QAM at the optimal transmission half a cattle are 8.54 \(\times\) 10\({}^{-8}\), 5.12 \(\times\) 10\({}^{-7}\), 3.7 \(\times\) 10\({}^{-6}\), and 2.16 \(\times\) 10\({}^{-5}\), respectively. When u = 3, the BERs of HQAM, XQAM, RQAM, and QAM at the optimal transmission half a cattle are 5.03 \(\times\) 10\({}^{-9}\), 4.15 \(\times\) 10\({}^{-8}\), 2.6 \(\times\) 10\({}^{-7}\), and 5.68 \(\times\) 10\({}^{-7}\), respectively. However, compared with the system using HAP, the BER of the G-S system is higher. When u = 1, the BERs of the G-H-S and G-S systems under QAM modulation are 5.59 \(\times\) 10\({}^{-6}\) and 1.7 \(\times\) 10\({}^{-5}\), respectively. Therefore, the G-H-S system has better communication performance, and HQAM modulation has a lower bit error rate and the best transmission aperture in a more comprehensive flat range. In practical application,  
Figure 4: Relationship between the receiving aperture and BER of HQAM, XQAM, RQAM, and QAM under different anisotropy factors in the ground–satellite uplink. (**a**) u = 1; (**b**) u = 3.  
the radius of the emission beam may change. It will not be kept at the optimal value; the more extensive the emission radius range, the more accessible the laser beam is to control the system. Figure 6a,b show the variation in the beam divergence angles 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 not only decreases first and then increases with the increase in the divergence angle but also decreases with the increase in the anisotropy factor. As can be seen from the Figure 6a,b, all four modulation methods have the best beam divergence angle to minimize the BER. When the system reaches the optimal beam divergence angle, the performance of the HQAM modulation scheme is the best, and the BER is lower with the increase in the anisotropy factor. For example, when u = 1, the BERs of HQAM, XQAM, RQAM, and QAM at the optimal beam divergence angle are \(1.91\times 10^{-7}\), \(1.04\times 10^{-6}\), \(5.59\times 10^{-6}\), and \(1.19\times 10^{-5}\), respectively. When u = 3, the BERs of HQAM, XQAM, RQAM, and QAM at the optimal beam divergence angle are \(5.03\times 10^{-9}\), \(4.15\times 10^{-8}\), \(2.6\times 10^{-7}\), and \(2.48\times 10^{-6}\), respectively. Moreover, when the system BER reaches the minimum, the optimal beam divergence angles of HQAM, XQAM, RQAM, and QAM are \(55\times 10^{-5}\) rad, \(51\times 10^{-5}\) rad, \(46\times 10^{-5}\) rad, \(45\times 10^{-5}\) rad, respectively, and the beam divergence angle of HQAM is the largest.