# HCTC: Hybrid Convolutional Transformer Classifier for Automatic Modulation Recognition
## 4 Experimental Results and Discussion  
### Classification Accuracy and Confusion Matrix  
To evaluate the performance of the proposed HCTC model, it was compared with several other models across SNRs in the RadioML2016a dataset. The results, in bold letters in Table 4, demonstrate that the proposed HCTC consistently outperformed the other models in terms of accuracy across the SNRs. At different SNR levels, HCTC achieved high accuracy scores: 10.18% at \(-\)20 dB, 87.03% at 0 dB, and 90.61% at 18 dB. When averaging the accuracy across two SNR ranges, HCTC showed average accuracies of 38.04% from \(-\)20 dB to 0 dB and 90.45% from 0 dB to 18 dB, both of which were the highest among those of all the models tested. Overall, the average accuracy of the HCTC across the entire SNR range was 61.80%, which ranks it first among all the models. The highest accuracy achieved by the HCTC was 92.06%, which was also the best in comparison to those of the other models. These results demonstrate that the HCTC is highly effective and reliable, particularly for handling various levels of noise. To compare the performance of the proposed HCTC model to those of the other models, detailed confusion matrices are presented for all the widely used AMR models in Figures 3 and 4. In Figure 3, the confusion matrices of (a) CGDNet [36], (b) CLDNN [28], (c) 1 DCNN-PF [32], (d) MCLDNN [31], (e) CNN1 [24], (f) DAE [26], (g) PET-CGDNN [37], and (h) GRU [35] are presented, whereas in Figure 4, the confusion matrices of (i) ResNet [34], (j) IC-AMCNet [33], (k) MCNet [30], (l) CNN2 [27], (m) DenseNet [34], (n) CLDNN2 [34], and (o) the proposed HCTC model are shown. In Figures 3 and 4, each row represents an actual label, whereas each \begin{table}
\begin{tabular}{c c c} \hline
**Layer (Name)** & **Output Shape** & **Description** \\ \hline batch\_normalization (BatchNormalization) & (256) & Batch normalization applied to fc1 output \\  & & Number of units: 128 \\ fc2 (Dense) & (128) & Activation function: SELU \\  & & Kernel regularizer: L2 (1 \(\times\) 10\({}^{-4}\)) \\ batch\_normalization\_1 (BatchNormalization) & (128) & Batch normalization applied to fc2 output \\ softmax (Dense) & (11) & Number of units: 11 \\  & & Activation function: softmax \\ \hline \end{tabular}
\end{table} 
Table 3: _Cont._column represents a predicted label. Figures 3 and 4 show the classification accuracies of the modulation classes 8 PSK, AM-DSB, AM-SSB, BPSK, CPFSK, GFSK, 4-PAM, 16-QAM, 64-QAM, QPSK, and WBFM over the RadioML2016a dataset. The HCTC model achieved accurate classifications for CPFSK, 4-PAM, and BPSK, which were on par with or better than the highest performances of the other models. Notably, for 8 PSK, the HCTC model correctly classified 88% of the instances, outperforming models such as CLDNN [28]. Similarly, AM-DSB was classified correctly in 62% of the instances by the HCTC model, with some misclassifications in WBFM, but this performance is still comparable or superior to those of many of the previously proposed models. The performance of the HCTC model in classifying GFSK with 95% correct classifications and 16-QAM with 85% correct classifications also demonstrates its robustness and accuracy, showing fewer misclassifications compared to earlier models. For 64-QAM, the HCTC model accurately classified 83% of the instances, surpassing the performances of models  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**SNR**} & \multicolumn{2}{c}{**Proposed 1 DCNN-**} & \multirow{2}{*}{**FCTC**} & \multirow{2}{*}{**CODNet**} & \multirow{2}{*}{**CDDNN**} & \multirow{2}{*}{**CLDNN2**} & \multirow{2}{*}{**CNN1**} & \multirow{2}{*}{**CNN2**} & \multirow{2}{*}{**DAE**} & \multirow{2}{*}{**DenseNet**} & \multirow{2}{*}{**  
such as PET-CGDNN [37] and DenseNet [34]. Similarly, QPSK was correctly classified in 96% of the instances, indicating highly reliable classifications with minimal errors and improvement over models such as GRU [35] and CNN1 [24].