## 1 Introduction  
Free-space optical (FSO) communication technology can realize efficient wireless broadband communication by using a laser beam as a data carrier, which has obvious advantages with respect to data rate, confidentiality, terminal size, weight, power consumption, and anti-interference, so it is widely used in the satellite communication field [1]. The satellite laser link has the advantages of large capacity, comprehensive coverage, low power consumption, and low cost, meaning that it has garnered significant attention from the academic community [2, 3]. Satellite laser communication is divided into inter-satellite and satellite-ground laser communication, and satellite-ground laser communication links can be divided into uplink and downlink [4]. The optical effects generated by atmospheric turbulence are different for uplink and downlink. In addition to the influence of light intensity scintillation and the angle of arrival fluctuation, the uplink also has the phenomenon of beam wander, which will directly affect the communication performance of the system. When the downlink transmission beam reaches the atmosphere, its beam diameter is much larger than the vortex scale of the atmosphere. So, the influence of beam wander on the system can be ignored [5, 6]. Therefore, the effect of atmospheric turbulence on the uplink is more complicated. In the direct backhaul transmission between the ground and the satellite, the laser beam is susceptible to jitter and divergence due to atmospheric turbulence and cloud obstruction, which will reduce the communication performance of the system and even interrupt the communication link. A high-altitude platform (HAP) can be regarded as an effective solution to the above problems [7]. A HAP is a quasi-stationary aircraft with flexibility and maneuverability. It can adjust the spatial position and adaptive height to alleviate cloud interference and optimize the transmission quality of the laser beam [8; 9]. Concomitantly, a HAP has advantages such as low cost, low propagation delay, faster deployment, easy maintenance of ground communication, and high capacity and high-quality satellite communication. It can be used as a relay node to assist ground-satellite and satellite-ground backhaul laser communication [10; 11]. HAPs have mainly focused on researching backhaul communication between the ground and HAP in recent years. However, there are few studies on HAPs in backhaul laser communication between the ground and satellite. For example, [PERSON] et al. originally proposed the use of a HAP in addition to satellite-ground downlink and HAP and GEO satellites as relay stations to improve the efficiency of LEO satellite-to-ground data transmission [12]. [PERSON] et al. proposed the use of all-optical HAP-based relay technology to enhance the performance of free-space optical communication (FSO) systems from low Earth orbit (LEO) satellites to ground stations [11]. [PERSON] et al. studied the design of a HAP as a relay-assisted satellite free-space optical (FSO) quantum key distribution (QKD) system for secure vehicle networks. They analyzed security performance in terms of quantum bit error and traversal key rates [13]. [PERSON] et al. proposed a satellite communication system with adaptive FSO and RF switching schemes and analyzed outage performance and average symbol error rate (SER) [14]. [PERSON] et al. analyzed the outage probability of FSO communication links of ground-HAP-satellite, HAP-HAP, and satellite-HAP-ground under different atmospheric turbulence channel models [15]. Moreover, we propose the use of a HAP and reconfigurable intelligent surface (RIS) to improve the system performance in the downlink of satellite-ground laser communication and derive the closed BER expression of a satellite-quasi-stationary aircraft-RIS-ground laser communication system. Simultaneously, increasing the number of RIS components allows the system to obtain a lower bit error rate [16].