## 5 Numerical Results
### Performance Analysis  
First of all, we evaluate the impact of the dropout rate on the model training in Figure 5. We measure fitting degree as the average difference between training set accuracy and validation set accuracy over the batches from convergence until the end of training. As can be seen, the model with the dropout rate of 0.6 reaches the best trade-off between classification accuracy and regularization effectiveness; it achieves highest average accuracy while effectively preventing overfitting and thus guaranteeing generalization. Therefore, a dropout rate of 0.6 is employed in the neural network model design. Figure 6 shows the confusion matrices of modulation classification at different SNRs ranging from 0 dB to 15 dB. As can be seen, the classification accuracy is significantly improved as the SNR is raised from 0 dB to 15 dB. Moreover, in Figure 5(a),b, it is obvious that even under low SNR conditions (i.e., 0 dB and 5 dB), the confusion matrices exhibit apparent diagonal patterns, with 100% classification accuracy for some modulation schemes. Figure 5(c),d further demonstrate that our approach shows excellent classification performance at high SNRs. In Table 3 and Figure 7, we investigate the effect of the proposed differentiated embedded pilot insertion scheme on the neural network training and modulation classification performance. Compared with data structures using identical pilot symbols, the ones embedded with differentiated pilot values show higher classification accuracy thanks to the  
Figure 5: Accuracy and fitting degree across different dropout rates. feature differences introduced among modulation schemes. Moreover, the number of embedded pilots also has an impact on the classification accuracy. Furthermore, we conduct experiments for multi-domain and single-domain approaches whose results are shown in Figure 8 and Table 4. As can be seen, the DD domain NN branch, especially the one with the 2D-CNN, substantially contributes to a high modulation classification accuracy. Based on that, the incorporation of the time-domain NN branch can significantly boost the performance as the SNRs vary within \([-5,5]\) dB. This accounts for why the proposed combination of DD domain and time domain can achieve high classification accuracy under varying SNR conditions, including even \(-5\) and \(0\) dB. Note that the structure (i.e., 1D-CNN/2D-CNN) of the time domain NN branch has limited effects on the performance; therefore, it is sufficient for the time-domain NN branch to adopt 1D-CNN for computational efficiency. Figure 6: Confusion matrix of modulation classification results. Figure 8: Comparison in terms of different NN architectures. \begin{table}
\begin{tabular}{c c} \hline \hline
**Pilot Symbol Configuration** & **Average Classification Acc. (\%)** \\ \hline
3 \(\times\) 3 differentiated pilot symbols & 97.8 \\
3 \(\times\) 3 same pilot symbols & 93.7 \\
2 \(\times\) 2 differentiated pilot symbols & 92.8 \\
2 \(\times\) 2 same pilot symbols & 92.6 \\
1 \(\times\) 1 differentiated pilot symbols & 92.4 \\
1 \(\times\) 1 same pilot symbols & 81.2 \\ No pilot symbols & 74.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average classification accuracy under different pilot symbol configurations. Figure 7: Comparison in terms of different pilot structures. The impact of maximum Doppler shifts on the classification performance of the proposed approach is investigated in Figure 9 and Table 5. The experiments are conducted with a carrier frequency of 5 GHz and maximum Doppler shifts of 400 Hz, 1000 Hz, 1200 Hz, and 1400 Hz, which correspond to the moving speeds of 86 km/h, 216 km/h, 260 km/h, and 302 km/h, covering common speed ranges of transportation. Therefore, the robustness of the proposed approach under various mobility conditions is comprehensively evaluated. Table 5 presents the classification accuracy, precision, recall, and F1-score over SNRs ranging from \(-5\) dB to 25 dB under four different maximum Doppler shift conditions.