# HCTC: Hybrid Convolutional Transformer Classifier for Automatic Modulation Recognition
## 4 Experimental Results and Discussion
### Classification Accuracy and Confusion Matrix
The WBFM class, although showing some misclassifications, with 38% of the instances misclassified as AM-DSB, still maintained a high level of correct classification, highlighting the overall improved accuracy of the HCTC model. Figure 5 shows an accuracy comparison plot for the proposed model and other algorithms in the RML2016a dataset. In Figure 5, the inset plots demonstrate how the proposed HCTC model achieved the best performance in the SNR range of 0-18 dB. The model was also tested in the RML2016B dataset, which contained a high number of samples and ten modulation classes. Figure 6 shows the confusion matrices of the proposed HCTC model across SNRs of \(-\)2 dB, 8 dB, and 18 dB. The accuracy of the proposed HCTC model compared with those of widely used AMR models across different modulations is shown in Table 5. Among the models evaluated, the proposed HCTC model consistently delivered the best results across most modulation types. For example, it achieved accuracies for BPSK of approximately 98.70% and for CPFSK of approximately 100.00%, indicating robust performance in these modulation schemes. In contrast, the 1 DCNN-PF [32] model demonstrated superior accuracy with AM-DSB (100.00%), though it had a lower performance with 16-QAM (41.50%). Models such as CGDNet [36] and CLDNN [28] generally performed well with AM-SSB, with accuracies of 96.00% and 94.50%, while the BPSK accuracy was 99.00% but fell short with 16-QAM and 64-QAM, where the accuracies were notably lower. DenseNet [34] excelled with CPFSK (99.00%) and performed competitively with other modulation schemes. Furthermore, CNN1 [24] and CNN2 [27] showed high accuracies with simpler modulation types, such as BPSK and CPFSK, but their performances receded with more complex schemes, such as 16-QAM and 64-QAM. Notably, the GRU [35] and IC-AMCNet [33] models exhibited good accuracies across various classes, but their performances were less consistent compared to those of the best-performing models. Figure 4: Confusion matrices of AMR models simulated in the RadioML2016a dataset at a 0 dB SNR: (i) ResNet; (j) IC-AMCNet; (k) MCNet; (l) CNN2; (m) DenseNet; (n) CLDNN2; (o) the proposed HCTC model. Figure 7 shows the accuracy and loss curves of the proposed HCTC model for training and validation. Figure 7 (left) shows the training loss (blue) and validation loss (orange) across 100 epochs. Both curves exhibit a steady decrease, and they stabilize toward the end of the training, indicating that the model does not overfit the training data. Figure 5: Accuracy comparison for the proposed HCTC model with other AMR models. Figure 6: Confusion matrices of the proposed HCTC model across SNRs of (**a**) \(-\)2 dB, (**b**) 0 dB, (**c**) and 18 dB in the RadioML2016b dataset. Figure 7: Training accuracy and loss curves for the proposed HCTC model. Figure 7 (right) presents the training and validation accuracy curves. The training accuracy increases rapidly before reaching a plateau, while the validation accuracy follows a similar trend, suggesting that the model is learning in a generalizable manner. During training, the training loss exhibited a general decreasing trend, signifying that the model was continuously learning and improving its predictions. Notably, in the first 20 epochs, the loss decreased significantly, indicating rapid learning in the initial stages. As the epochs progressed, the loss stabilized, showing the model's ability to converge. The validation loss followed a similar pattern, confirming that the model did not overfit the training data and generalized well to unseen data. This trend highlights the improved convergence speed and the promising performance of the proposed method. To ensure that the model did not overfit the data, several overfitting prevention strategies were employed during the training process, such as early stopping, reducing the learning rate on the plateau, dropout, and L2 regularization. We utilized early stopping to monitor the validation loss.