## 4 Simulation Analysis

Table 4: Relationship between the hidden layers and accuracy. \begin{table}
\begin{tabular}{c c} \hline \hline
**Learning Rate** & **Accuracy Rate** \\ \hline
0.00002 & 88.54371\% \\
0.00020 & 98.96791\% \\
0.00200 & 99.99514\% \\
0.02000 & 99.67210\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Relationship between learning rate and accuracy. \begin{table}
\begin{tabular}{c c} \hline \hline
**Cycle Index** & **Accuracy Rate** \\ \hline
20 & 98.976791\% \\
30 & 99.995140\% \\
40 & 99.995151\% \\
50 & 99.995201\% \\
60 & 99.989432\% \\
70 & 98.673576\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Relationship between the cycle index and accuracy. \begin{table}
\begin{tabular}{c c} \hline \hline
**Hidden Layers** & **Accuracy Rate** \\ \hline
6 & 97.632746\% \\
7 & 98.921215\% \\
8 & 99.950473\% \\
9 & 99.091451\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of accuracy between the LSTM network and LSTM attention network. The comparison of accuracy of the LSTM network and LSTM attention network is shown in Table 5. It is clear that the accuracy of the LSTM attention network is significantly higher than that of the LSTM network. It is well known that rain, snow, sheet, fog, haze, pollution, and so on are atmospheric factors that impact the laser beams. Their presence causes reflection, refraction, scattering, and attenuation of optical signals. It has been proven that atmospheric turbulence follows the Gamma-Gamma distribution, and weak, moderate, and strong turbulence intensity can be expressed by the refractive-index structure constant of \(C_{n}^{2}=2\times 10^{-18}\), \(C_{n}^{2}=2\times 10^{-15}\), and \(C_{n}^{2}=2\times 10^{-12}\), respectively [35] The curves of different atmospheric turbulence intensities versus BER are shown in Figure 6, where the roll-off factor is 0.6, \(\tau=0.8\), and the transmission distance is 500 m. It is evident from the figure that the BER performance is gradually improving with the decrease in turbulence intensity. When BER = 3.8 \(\times\) 10\({}^{-3}\), the BER performance of weak turbulence is about 2 dB and 5 dB better than that in moderate and strong turbulence, respectively. Figure 7 shows the influence of the roll-off factor of FTN shaping filter on BER with a different decoder, where the acceleration factor is 0.8. As shown in Figure 7a, when BER = 10\({}^{-4}\), the LSTM attention decoder improves the BER performance by about 1 dB compared with the BP algorithm. Figure 7b shows that the LSTM attention decoder improves the BER performance by about 2.5 dB compared with the MLSE algorithm when BER = 10\({}^{-4}\). Therefore, LSTM attention is beneficial to improve the BER performance compared with the traditional decoder. Figure 8 shows the impact of acceleration factor on the system BER performance. When the BER is 10\({}^{-4}\) and the acceleration factor decreases from 1 to 0.9 and to 0.8, the BER performance decreases about 2 dB and 4 dB, respectively. When the BER is 10\({}^{-3}\) and acceleration factor decreases from 1 to 0.9 and to 0.8, the BER performance declines by about 1 dB and 4.5 dB, respectively. It can be concluded from the figure that the BER curves decrease rapidly as the acceleration factor decreases. However, under the premise of improving the spectrum efficiency, the system can still ensure good communication quality when the acceleration factor is 0.8. Thus, the proposal is beneficial to improve the performance of the system. Figure 6: BER under different atmospheric turbulence channels. Figure 8: Relationship of BER and acceleration factor \(\tau\). Figure 7: Relationship between BER and roll factor: (**a**) LSTM attention and BP decoding algorithms; (**b**) LSTM attention and MLSE decoding algorithms.