## 4 Simulation Results and Analysis
It can be observed that in order to achieve the same BER performance, the RIS-SHTLC system requires a lower average SNR compared to the SHTLC scheme. This trend signifies that the use of RIS technology can effectively reduce the difficulty of on-board laser temperature control and system energy consumption. Figure 5 shows the effect of the zenith angle on the BER of the system for a different number of RIS elements. The SNR is set to 30 dB, and CBPSK modulation is used. The results show that the BER increases as the zenith angle increases, and decreases as the number of RIS elements increases. For a small zenith angle, the trend of BER variation is flatter for schemes with different numbers of RIS elements. The system BER increases rapidly and the performance of the RIS-SHTLC system decreases rapidly as the zenith angle increases. In addition, for a small zenith angle, the schemes with different numbers of RIS elements have a greater impact on the system BER, and the difference between them gradually decreases as the zenith angle increases. For example, for a zenith angle of \(30^{\circ}\), the BER values of RIS-SHTLC systems with \(N_{\rm r}=20,40,60\) are 1 \(\times\)\(10^{-6}\), 1.3 \(\times\)\(10^{-8}\), and 1.9 \(\times\)\(10^{-10}\), respectively. When the zenith angle is \(70^{\circ}\), the BER values of the above three schemes are 1.7 \(\times\)\(10^{-5}\), 5.9 \(\times\)\(10^{-6}\), and 5.4 \(\times\)\(10^{-6}\), respectively. In addition, an increase in the number of RIS elements can result in a larger zenith angle for the same communication performance conditions. In satellite-terrestrial laser communication, the larger the zenith angle, the larger the communication coverage. Therefore, the use of RIS technology can optimize the performance of the SHTLC system and reduce the communication cost. Figure 4: Average SNR versus BER for SHTLC systems and RIS-SHTLC systems with different numbers of RIS. Figure 5: Effect of zenith angle on the performance of RIS-SHTLC system with different numbers of RIS elements. Figure 6 shows the relationship between the receiving aperture and the BER for the RIS-SHTLC system with different RIS elements. It can be observed that at an average SNR of 40 dB in the weak turbulence case, the BER of the system with different numbers of RIS elements decreases as the receiving aperture increases. As the receiving aperture increases, the BER difference between systems with different number of RIS elements gradually increases. For a constant size of the receiving aperture, the BER of the system can be reduced effectively by increasing the number of RIS elements. To meet the same requirement of BER = \(10^{-5}\) at \(N_{\mathrm{r}}=20\), the RIS-SHTLC system requires a receiving aperture of 0.65 m. The required receiving apertures for RIS-SHTLC systems with \(N_{\mathrm{r}}=40\) and \(N_{\mathrm{r}}=60\) are 0.5 m and 0.4 m, respectively. It is obvious that as the number of RIS elements increases, the requirement for the system to achieve the same BER performance for the receiving aperture gradually becomes less strict. A small receiving aperture reduces the impact of beam distortion on system performance and reduces the transmission costs. In addition, a small receiving aperture facilitates the movement of ground terminals and increases the flexibility of the optical network. Figure 7 illustrates the effect of the divergence angle on the BER performance of the RIS-SHTLC system for different numbers of RIS elements. In the systems with different numbers of RIS elements, the system BER tends to increase and then decrease, and finally increase again as the divergence angle increases. When the divergence angle is less than 20 \(\times\) 10\({}^{-5}\) rad, the system BER increases as the divergence angle increases, and increasing the number of RIS elements does not improve system performance. When the divergence angle is greater than 20 \(\times\) 10\({}^{-5}\) rad, the BER of the system decreases and then increases as the divergence angle increases.