## 1 Introduction  
In recent years, with the changes in technology, 5G alone can no longer support the construction of future smart cities where everything is connected. A new generation of communication technology with faster speed, greater stability, and lower latency is needed [1]. The 6G mobile communication network has come into people's view with its terahertz frequency band carrier, microsecond latency, one-in-a-million interruption probability, and ultra-high communication rate [2; 3]. In order to truly realize the huge smart scene, a large number of communication satellites and terrestrial communication relay sites are needed to make up for the disadvantage of the small coverage area of the 6G single base station. Traditional satellite communication technology is far from being able to meet the needs of such high-speed data transmission scenarios. Free space optical communication (FSO) technology is undoubtedly an effective way to solve this problem [4; 5; 6; 7]. In order to achieve an ultra-high-speed FSO communication link, it is first necessary to couple the spatial signal light into a single-mode optical fiber and then perform subsequent optoelectronic signal processing. In inter-satellite communication links, since the channel is in a near vacuum state, the space optical signal is not disturbed by the medium, and the communication quality is only affected by the performance of the satellite platform and the communication terminal. However, when the communication terminal works in the atmospheric channel, a large number of turbulent eddies of different scales, affected by diffraction and scattering effects, make the light intensity at the receiving end fluctuate randomly, resulting in the phenomenon of light intensity scintillation. This leads to random fluctuations in the signal light wavefront incident to the receiving end of the system, which makes the coupling efficiency of the space light to the single-mode fiber deviate from the theoretical optimal value and become a random variable, seriously affecting the stability and reliability of the communication link transmission. The problem of light-intensity scintillation in atmospheric channels is one of the main bottlenecks limiting the development of laser communications. Over the years, in order to accurately analyze the scintillation effect of light intensity due to atmospheric turbulence, many statistical models and experimental studies have been proposed by numerous researchers to describe the channel state of the atmosphere. [PERSON] et al. established a model for calculating the variance of light intensity fluctuations, and the calculated results in weak turbulence channels were consistent with experimental test results [8]. [PERSON] and [PERSON] derived a calculation model for strong turbulent light intensity fluctuations based on the asymptotic analysis method. Then, [PERSON] studied the light intensity fluctuation model using the assumption that small-scale turbulent fluctuations are modulated by large-scale fluctuations and obtained a general solution for the variance of weak turbulent scintillation [9]. Through experiments, [PERSON] et al. found that the light intensity flicker variance first increases and then decreases during the light wave transmission process until it finally reaches a saturation state [10]. [PERSON] et al. proposed a dual gamma-gamma model and proposed the use of a two-scale modulation theory to characterize the changes in the probability distribution of light intensity ups and downs during atmospheric turbulence from weak to strong [11]. When measuring the impact of atmospheric light intensity scintillation on the performance of communication systems, researchers usually use signal-to-noise ratio and bit error rate [12; 13; 14; 15], and the coupling efficiency of spatial light to single-mode optical fiber is the primary parameter for analyzing the two.