## 5 Conclusions  
This paper studied the HAP-assisted ground-satellite uplink laser communication system under an anisotropic non-Kolmogorov turbulence model; hexagonal quadrature amplitude modulation (HQAM) and cross quadrature amplitude modulation (XQAM) techniques were adopted. Considering the influence of light intensity scintillation, beam drift, and the angle of arrival fluctuation on atmospheric turbulence, the closed expression of BER of the ground-HAP-satellite (G-H-S) uplink is derived. Concomitantly, the rela  
Figure 6: Relationship between the beam divergence 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 7: Relationship between the scintillation index and BER of HQAM, XQAM, RQAM, and QAM under different anisotropy factors in the ground–satellite uplink (**a**) u = 1; (**b**) u = 3.  
tionship between BER and zenith angle, receiving aperture, signal-to-noise ratio (SNR), beam divergence angle, and transmitter beam radius under different anisotropy factor u values was simulated and analyzed and compared with the modulation technology used in the satellite-to-ground laser system and the traditional ground-satellite (G-S) system without HAP. The simulation results showed that the BER of the HAP-assisted ground-satellite (G-S) system under an anisotropic non-Kolmogorov turbulence model is lower and decreases with the increase in the anisotropy factor. Concomitantly, in the case of the same communication performance, compared with QAM, RQAM, and XQAM, the ground-HAP-satellite (G-H-S) system using HQAM modulation can obtain better communication performance. For the same BER, the average transmit power required by HQAM is less than the power needed for the other three modulation schemes, which is beneficial in reducing the system power consumption and making the temperature control of the terminal laser easier. However, HQAM achieves a larger zenith angle, improves the coverage area of a single satellite, and can better control the antenna angle. Moreover, HQAM has the optimal transmitting aperture radius with the most extensive flat range, which can reduce the difficulty of beam control. In addition, HQAM has a smaller receiving aperture, which is conducive to reducing transmission costs. A smaller receiving aperture increases ground mobility and the flexibility of the laser network. Regarding the optimal beam divergence angle, HQAM is easier to obtain the optimal beam divergence angle than the other three modulation schemes. At the same time, HAP is used to connect communication between the ground and satellites. Due to the flexible deployment of HAP, it can be used as both a communication relay and for meteorological forecasting. Due to the influence of turbulence and weather in ground satellite communication, the HAP can be monitored in the atmosphere to obtain detailed meteorological data and ensure the quality of ground satellite communication. In summary, the HAP-assisted ground-satellite uplink studied under the anisotropic non-Kolmogorov turbulence model and the application of HQAM modulation to the ground-HAP-satellite (G-H-S) system can effectively optimize system performance and reduce the cost of satellite-ground laser communication. This design focuses on the ground-HAP-satellite uplink. In previous work, our team studied the satellite-HAP-ground downlink, as well as the ground-satellite uplink and satellite-ground downlink. The modulation techniques and turbulence models used in previous work were MSK, GMSK, and isotropic Kolmogorov turbulence models, respectively. The modulation techniques and turbulence models used this time were HQAM/XQAM and anisotropic non-Kolmogorov turbulence models, respectively. However, this study did not consider HAP hover fluctuations, which can also have a certain impact on the performance of the entire system. It is hoped that improvements can be made in future work. Conceptualization, [PERSON] and X.J. ; methodology, X.J. ; software, X.J. ; validation, [PERSON], X.J.