## 1 Introduction  
Interest in the use of free-space optical links in satellite communication scenarios has been increasing in recent years. Compared to radio frequency (RF) communications, satellite laser communications have the advantages of a greater bandwidth, higher channel capacity, no spectrum licensing requirement, and better security [1; 2; 3]. However, when the optical signal passes through the atmospheric channel, its diameter is considerably larger than the atmospheric vortex size. Consequently, multiple independent atmospheric vortices will appear on the cross-section of the beam, and these vortices will create the independent diffraction and scattering of the beam. This phenomenon causes the beam received by the receiver to exhibit random energy fluctuations, i.e., the light intensity scintillation effect, which can seriously affect the performance of the entire communication system [4]. In addition, pointing errors due to the misalignment of the transmitter and receiver constitute another important factor that affects the performance of the communication system [5]. Various techniques have been proposed to alleviate the impact of these issues on the performance of satellite-terrestrial laser communication systems, such as the modulation technique, multiple-input and multiple-output technique, and relaying technique [6; 7; 8]. The satellite-terrestrial laser communication link can also be obstructed by clouds. Therefore, the availability of the downlink depends on the cloud conditions above the terrestrial receiver. A promising solution is the use of a high altitude platform (HAP), which is a quasi-stationary aircraft located at a cloud-free atmospheric altitude of about 20 km above the Earth's surface [9]. Using the HAP as a relay node for satellite-terrestrial laser communication also helps to improve the performance of the communication system [10]. Due to these advantages, studies on the use of HAP as a relay node to assist satellite-terrestrial laser communication have emerged in recent years [10; 11; 12]. For example, [PERSON] et al. derived the closed expression of the bit error rate (BER) for the downlink HAP relay system corresponding to satellite-terrestrial laser communication under the Gamma-Gamma atmospheric channel model. The authors found that the transmit power of the HAP-relays-assisted satellite-terrestrial laser communication system with the same BER is 25 dB lower than that of the system without the relay technique [10]. [PERSON] et al. introduced the HAP as a relay node into a satellite-terrestrial laser quantum key distribution system, and derived the ergodic secret-key rate of the system under the Gamma-Gamma atmospheric channel model [11]. [PERSON] et al. considered two scenarios for the satellite-terrestrial laser communication uplink: no HAP deployment and HAP deployment. The authors used the RF link as a backup for the laser link, and derived a unified expression for the outage probability (OP) and BER for this single-hop system and the two-hop (with HAP) system under the Gamma-Gamma atmospheric channel model [12]. However, the above-mentioned literature on satellite-to-HAP links uses the single-input single-output (SISO) technique. Unlike the SISO technique, the single-input multiple-output (SIMO) technique uses multiple receiving apertures to form multiple independent channels, and the diversity gain provided by these multiple independent channels can effectively combat channel fading caused by atmospheric turbulence. To the best of our knowledge, the use of the M distribution in satellite-high altitude platform-terrestrial laser communication (SHTLC) systems and SIMO technology for the satellite-to-HAP link has not been reported in existing literature. Reconfigurable intelligent surfaces (RIS) can passively reflect signals without any transmitting equipment, and it can also be seen as an alternative to active relay technology [13].