## 1 Introduction  
Since the 1960s, as one of the advanced satellite communication technologies, satellite laser communication technology has attracted much attention from the scientific community because it has some potential advantages, including higher data rates, larger communication capability, better anti-disturbance, low probability of intercept, less volume, less mass, lower power consumption, no restrictions for frequency use, etc. [1]. At the same time, the integration of the newly developed satellite communication technology and satellite laser communication technology can also be expected [2, 3, 4]. In the late 1990s, the United States, Europe, and Japan successively carried out verification experiments on the ground. In the first two decades of the 21 st century, satellite laser communication technology has made great progress. As the representatives of space optical communication pioneer, the European Space Agency, the German Space Agency, the Japan aerospace exploration agency, the National Association of Information and Communications Technology, and the Jet Propulsion Laboratory involve comprehensive and in-depth research, and key technologies have been developed. Several sets of satellite laser communication terminals have been developed and successfully completed a number of on-orbit experiments. The space-based laser communication network with global coverage are being planned to demonstrate the huge potential of satellite laser communications and lay a solid foundation for the commercialization and application of satellite laser communication technology. For satellite-to-ground and ground-to-satellite links, since the Earth's atmosphere is one part of the communication channel, the atmospheric turbulence deteriorates the performance level of satellite laser communication system. To solve this problem, several experiments have been carried out to study the effects of atmospheric turbulence on satellite-ground laser communication. The results have shown that the laser uplink is more seriously affected by atmospheric turbulence than the downlink. The main performance is that the bit error rate of the uplink is much higher than that of the downlink [5; 6; 7; 8]. In the downlink, the above 90 percent path of the laser beam is the ideal transmission environment close to vacuum, and there will be atmospheric attenuation and phase distortion until it is close to the ground. On the contrary, in the uplink, the laser beam is affected by the dense atmosphere of the troposphere as soon as it leaves the pupil. In addition to atmospheric attenuation and scintillation, the downlink is also affected seriously by the beam wander, which is equivalent to increase the pointing error of the satellite laser communication system. Up until now, the uplink of satellite-ground laser communication can only barely establish in all on-orbit experiments, and cannot guarantee the continuous symbol tracking and clock synchronization, and there is often the phenomenon of communication interruption. Therefore, it is of great significance to study the influence of atmospheric turbulence on satellite laser communication, especially on uplink. In recent years, data from stellar scintillation measurements, airborne tether balloon temperature measurements, and ground-based radar measurements have shown turbulence deviations from [PERSON]'s model in parts of the Earth's atmosphere [9; 10; 11; 12; 13]. For example, [PERSON] et al. [10] measured the power spectrum of one-dimensional temperature fluctuations along the inclined path of the Earth's atmosphere by using balloons and radar. The results showed that the upper troposphere and the entire stratospheric turbulent atmosphere did not follow the [PERSON] statistical law, and the three-dimensional power spectrum of \(-5\) power rate was also confirmed.