## 4 Simulation Results and Analysis  
Based on the above theoretical analysis and derived expressions, the performance of the RIS-SHTLC system is simulated and analyzed under the M distribution channel model, and the accuracy of the numerical results is verified using Monte Carlo simulations. Under weak turbulence, the atmospheric refractive index structure constant is taken as \(7.5\times 10^{-17}\). Table 2 shows the specific parameters of the RIS-SHTLC system. Digital modulation techniques have now become an important means to enhance the performance of satellite-terrestrial laser communication systems. Figure 3 shows the effects of CBPSK modulation, CBPSK modulation, NBFSK modulation, and DBPSK modulation on the performance of the RIS-SHTLC system, respectively. Under all four modulation schemes, the BER of the RIS-SHTLC system decreases monotonically as the average SNR increases. The BER performance of the systems that use DBPSK and CBPSK modulations is almost the same. To achieve the same BER of \(10^{-5}\), the average SNR required for the RIS-SHTLC system with CBPSK modulation is 30 dB. Compared with the CBPSK modulation scheme, the system requires an average SNR of 4 dB higher with DBPSK and CBPSK modulations, and an average SNR of 10 dB higher with the NBFSK modulation. It can be observed that among the above four schemes, the RIS-SHTLC system with the CBPSK modulation method can obtain the optimal system performance. Therefore, the CBPSK modulation in RIS-SHTLC systems can achieve a better system performance compared with the CBPSK, NBFSK and DBPSK modulations. Figure 4 shows the average SNR versus BER for SHTLC and RIS-SHTLC systems with different numbers of RIS elements. We assume \(N_{E}=2\) with CBPSK modulation. The results show that the BERs of all four schemes decrease as the average SNR increases. When the average SNR is small, the BER difference between SHTLC and RIS-SHTLC systems is small. The difference between them increases as the average SNR increases. The SHTLC system has a higher BER than the system with the RIS technology, and the BER of the RIS-SHTLC system can be further reduced with the addition of RIS elements. For example, the BER of SHTLC systems is 4.3 \(\times\)\(10^{-4}\) at an average SNR of 30 dB. The \begin{table}
\begin{tabular}{c c c} \hline \hline
**System Parameters** & **Symbol** & **Value** \\ \hline Height of Satellite & H\({}_{8}\) & 36,000 km \\ Height of receiver above ground & h\({}_{0}\) & 10 m \\ Height of HAP & H\({}_{p}\) & 20 km \\ Laser wavelength & \(\lambda\) & 1550\(nm\) \\ Wind speed & v & 21\(m/s\) \\ Transmitter beam radius & \(\omega_{0}\) & 0.1 m \\ Receiver diameter & D & 0.2 m \\ Zenith angle & \(\zeta\) & 30\({}^{c}\) \\ The difference between the determined phase of LOS and & & \\ coupled-to-LOS scattering term & \(\phi_{A}-\phi_{B}\) & \(\pi/2\) \\ The average power of the total scatter component & \(2h_{0}\) & 0.2158 \\ The average power of the LOS component & \(\Omega\) & 1.3265 \\ Distance from HAP to RIS & \(L_{1}\) & 15 km \\ Distance from RIS to the ground receiver & \(L_{2}\) & 10 km \\ Reflected error angular variance & \(\sigma_{\tilde{\theta}}^{2}\) & 0.1 mrad \\ Pointing error angular variance & \(\sigma_{\theta}^{2}\) & 0.1 mrad \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Selection of simulation parameters for RIS-SHTLC laser communication system. Figure 3: Effect of different modulation techniques on the performance of RIS-SHTLC systems. values of the BER of \(N_{\rm r}=20,40,60\) RIS-SHTLC systems are 1.2 \(\times\)\(10^{-5}\), 9.6 \(\times\)\(10^{-7}\), and 1.2 \(\times\)\(10^{-7}\), respectively. The RIS-SHTLC system with \(N_{\rm r}=60\) has better BER performance. To meet the minimum requirement of BER = \(10^{-5}\) for a communication system, the required average SNR of SHTLC systems under weak turbulence exceeds 50 dB. However, in the RIS-SHTLC systems with \(N_{\rm r}=20\), \(N_{\rm r}=40\), and \(N_{\rm r}=60\) the average required SNR values are 30 dB, 20 dB, and 12 dB respectively.