## 3 Results and Discussion
### Analysis of Multi-Mode OAM Mode Recognition Based on AP-CNN
Therefore, even if the AP-CNN introduces an attention mechanism to mine the underlying image details, it cannot significantly improve the accuracy of OAM mode recognition. The confusion matrixes of superimposed vortex beams using ResNet18 and AP-CNN, with a transmission distance is 2000 m and when atmospheric refractive index structure constant \(C_{n}^{2}=5.0\times 10^{-13}\)m\({}^{-2/3}\), are given in Figure 9. The results show that {1, -2, 3, -5} has a 16% probability of being incorrectly identified as {-2, 3, -5}, {1, -2} has a 10% probability of being incorrectly identified as {1, -2, -5}, and {2, -6} has an 11% probability of being incorrectly identified as {4, -4}. In contrast, in the APP-CNN network, the accuracy of OAM mode detection improves by up to 7%, and the related incorrect identification rate is reduced by up to 3%, which confirms the necessity of designing similar OAM superposition mode datasets. The accuracy improvement and decrease of incorrect identifications may vary with the transmission conditions. Assuming the signal-to-noise ratio at the receiver side of the OAM communication system \(\gamma_{B}=10\)dB, the system BER can be calculated based on the recognition accuracy. When the transmission distance is 2000 m, the demodulation performance of the CNN demodulator, ResNet18 demodulator, ResNet18 demodulator with a specified mapping relationship, and the AP-CNN demodulator under six different turbulence intensities \(C_{n}^{2}\) and transmission distances, expressed as BER at the receiver end, are shown in Figure 10.  
It can be seen from Figure 10 that when the turbulence intensity and transmission distance are certain, ResNet18 can mine more OAM intensity map information due to the presence of more convolution layers compared to CNN. Additionally, the BER of the OAM communication system is lower when using the ResNet18 demodulator compared to the CNN demodulator. The CNN structure used here consists of three convolution layers and two full connection layers. Each convolution network layer is composed of a convolutional layer, a batch normalization layer, and a maxpool layer. The layers are connected by a rectified linear unit (Relu), and each layer uses dropout. The dropout probability is set to 0.3. The convolutional layers of the first, second, and third convolution network layers contains 16 kernels of size 5 \(\times\) 5, 32 kernels of size 3 \(\times\) 3, and 64 kernels with size of 3 \(\times\) 3, respectively. The maxpool layer size of the three convolution network layers is 2 \(\times\) 2 and the step size is 2; the difference is more obvious in a strong turbulence environment (\(C_{n}^{2}>1.0\times 10^{-13}\)m\({}^{-2/3}\)). Both the ResNet18 demodulator combined with specified mapping and the AP-CNN demodulator are optimized based on the ResNet18 demodulator, and both have lower BER than the ResNet18 demodulator. When \(C_{n}^{2}\leq 3.0\times 10^{-13}\)m\({}^{-2/3}\), the BER using the AP-CNN demodulator is lower than that using the ResNet18 demodulator combined with the specified mapping. However, when the turbulence is quite strong (e.g., \(C_{n}^{2}=5.0\times 10^{-13}\)m\({}^{-2/3}\)), the BER using the AP-CNN demodulator is higher than that of the ResNet18 demodulator with the specified mapping relationship. The reason for this is that the two optimization schemes (specifying the mapping relationship and introducing the attention pyramid) do not go in the same direction, as shown in Figure 11.