## 3 Results and Discussion
### Analysis of Single-Mode OAM Mode Detection Based on AP-CNN  
The detection accuracies of OAM mode with the ResNet18 network and AP-CNN are shown in Table 2 after 100 training cycles under different turbulence intensities and transmission distances. It can be concluded that the stronger the turbulence, the lower the accuracy of OAM detection. In addition, it can be seen from the data in Table 3 that no matter whether the transmission distance is 2000 m or 3000 m, under different turbulence intensities, AP-CNN has improved accuracy compared with ResNet18. In strong turbulence (\(C_{n}^{2}=5.0\times 10^{-13}\)m\({}^{-2/3}\)); the detection accuracy of AP-CNN is 85.2%, a 1.3% improvement compared with ResNet18, whereas in medium turbulence conditions (\(C_{n}^{2}=5.0\times 10^{-14}\)m\({}^{-2/3}\)), the detection accuracy of AP-CNN has a 3.4% improvement compared with ResNet18 at the transmission distance of 3000 m. When the transmission distance is reduced to 2000 m, the detection accuracy of AP-CNN shows 5.5% and 4.3% improvements compared with ResNet18 at \(C_{n}^{2}=3.0\times 10^{-13}\)m\({}^{-2/3}\) and \(C_{n}^{2}=5.0\times 10^{-13}\)m\({}^{-2/3}\), respectively. It should be emphasized that when the transmission  
Figure 10: Performance comparison of four OAM demodulators with (**a**) atmospheric refractive index structure constant \(C_{n}^{2}\) (**b**) transmission distance. distance is long and there is strong turbulence, the light intensity distribution captured at the receiving end is damaged (because the vortex beam is greatly affected by the turbulent distortion during transmission), and the AP-CNN detection rate cannot be significantly improved. A comparison of the demodulation performance of CNN, ResNet18, ResNet18 combined with plane wave interference, and AP-CNN combined with plane wave interference with a 2000 m transmission distance under six different turbulence intensities is shown in Figure 12a. The performance of the communication link under different transmission distances when \(C_{n}^{2}=5.0\times 10^{-14}\)m\({}^{-2/3}\) is compared in Figure 12b. It can be seen from Figure 12 that no matter which demodulation scheme is adopted, when the transmission distance is fixed, the stronger the turbulence, the lower the accuracy of the OAM mode detection at the receiving end. When the turbulence intensity is constant, the longer the transmission distance, the lower the OAM mode detection rate. The detection accuracy of the CNN demodulator with three convolutional layers, a simple structure, and  
Figure 11: Comparison of the optimization direction of the AP-CNN and specified mapping relationship. Figure 12: Performance of four OAM demodulators for detecting single-mode vortex light (**a**) under different turbulence intensities and (**b**) different transmission distances. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{\(\text{Cn}^{2}/(\text{m}^{-2/3})\)} & \multicolumn{2}{c}{**ResNet18**} & \multicolumn{2}{c}{**AP-CNN**} \\  & **2000 m** & **3000 m** & **2000 m** & **3000 m** \\ \hline \(1.0\times e^{-14}\) & 100.0\% & 100.0\% & 100.0\% & 100.0\% \\ \(3.0\times e^{-14}\) & 98.9\% & 98.5\% & 99.2\% & 99.8\% \\ \(5.0\times e^{-14}\) & 97.2\% & **92.4\%** & 98.3\% & **95.8\%** \\ \(1.0\times e^{-13}\) & 93.5\% & 89.8\% & 96.6\% & 93.5\% \\ \(3.0\times e^{-13}\) & **85.9\%** & 84.2\% & **91.4\%** & 87.1\% \\ \(5.0\times e^{-13}\) & **84.6\%** & **83.9\%** & **88.9\%** & **85.2\%** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Detection accuracy comparison of single mode OAM mode using ResNet18 and AP-CNN. no plane wave interference is low. The ResNet18 has a more complex network structure, including 17 layers of convolution, and has a stronger ability to mine light intensity information. However, it directly identifies the light intensity distribution of single-mode vortex light without interference. Although its detection accuracy is improved compared with that of CNN, it is still not satisfactory.