## 5 Numerical Results
### Performance Analysis
As we can see, a high classification accuracy (approaching 75%) can be achieved even in a highly dynamic scenario (characterized by a maximum Doppler shift of 1400 Hz) with a low SNR (i.e., \(-5\) dB), demonstrating the robustness of the proposed approach in extreme conditions. As the received signal is inherently in the complex domain, in Figure 10, we compare the proposed approach, i.e., the proposed neural network (NN) architecture with Adam optimizer, with the complex-valued neural network (CVNN) model with different optimizers, including Adam, Adagrad, Adamax, Amagrad, and RMSprop, in terms of validation loss and accuracy. Apparently, when applied to CVNN, the Adagrad optimizer achieves lower validation loss and a faster convergence rate, while the Adam optimizer exhibits smoother \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Average Classification Acc. (\%)** & **Parameter** & **Average Classification Acc. (\%)** \\ \hline Time Domain + 1D-CNN \& & 97.8 & Time Domain + 1D-CNN & 79.0 \\ DD Domain + 2D-CNN & & & \\ Time Domain + 2D-CNN \& & & \\ DD Domain + 2D-CNN \& & & \\ Time Domain + 2D-CNN \& & & \\ DD Domain + 2D-CNN \& & & \\ Time Domain + 1D-CNN \& & & \\ DD Domain + 1D-CNN & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average classification accuracies of hybrid 1D/2D CNN models for time and DD domains. Figure 9: The performance of the proposed approach w.r.t. different maximum Doppler shifts. curves with greater stability. Last but not least, the proposed approach can achieve the lowest loss and highest accuracy. In Figure 11, the proposed approach is compared with different state-of-the-art baseline approaches. ResNet [14], originally designed for automatic modulation classification in OFDM systems, is adapted to OTFS systems and evaluated upon datasets with differentiated pilots, identical pilots, and no pilots. The baselines CLDNN [26], LSTM [24], CNN_LSTM [33], and CVNN with Adagrad optimizer [45] adopt differentiated pilot structures. The results for ResNet [14] further demonstrate the advantage of the proposed differentiated pilots. Compared to all the state-of-the-art baselines, the proposed approach, characterized by the dual-stream network architecture, shows superior classification performance (at least 90% accuracy) under both low- and high-SNR conditions. Table 6 records average metrics including accuracy, precision, recall, and F1-score over all the SNR values. The near-identical values of the metrics for the proposed approach indicate that the generated AMC model prevents biases among classification tasks well. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Model** & **Accuracy (\%)** & **Precision (\%)** & **Recall (\%)** & **F1-Score (\%)** \\ \hline Proposed Method & 97.81 & 97.81 & 97.81 & 97.81 \\ Differentiated pilot symbols + ResNet [14] & 92.50 & 92.57 & 92.52 & 92.54 \\ Same pilot symbols + ResNet [14] & 83.87 & 83.90 & 83.89 & 83.88 \\ no pilot symbols + ResNet [14] & 56.45 & 60.81 & 56.14 & 56.97 \\ CNN\_LSTM [33] & 79.09 & 79.06 & 79.14 & 79.09 \\ CLDNN [26] & 87.87 & 88.84 & 87.87 & 87.81 \\ LSTM [24] & 66.60 & 69.30 & 59.50 & 64.00 \\ CVNN + Adagrad [45] & 95.62 & 95.64 & 95.63 & 95.63 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Classification Performance Metrics of Different Approaches. Figure 10: Comparison between CVNN models with different optimizers and the proposed approach.