# HCTC: Hybrid Convolutional Transformer Classifier for Automatic Modulation Recognition
## 4 Experimental Results and Discussion
### Numbers of Parameters and FLOPs and Accuracy at 0 dB and the Average Accuracy from 0 to 18 dB  
Table 6 presents a comprehensive evaluation of various AMR methods across machine-learning models for the numbers of parameters and floating-point operations per second (FLOPs) and the accuracy at 0 dB and the average accuracy from 0 to 18 dB for the RML2016a dataset. This allowed for a direct comparison of the performances, complexities, and computational efficiencies of the models. The proposed HCTC model achieved the highest performance and a competitive number of parameters and FLOPs and, thus, robustness. Models such as DenseNet and ResNet [34] had higher numbers of parameters and FLOPs and offered superior performances; however, their computational costs increased. There are tradeoffs between the accuracy and the numbers of FLOPs and parameters, which help to select a specific model according to the application requirements. \begin{table}
\begin{tabular}{l 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}{*}{**CGDNet**} & \multirow{2}{*}{**CLDNN**} & \multirow{2}{*}{**CLDNN2**} & \multirow{2}{*}{**CNN1**} & \multirow{2}{*}{**CNN2**} & \multirow{2}{*}{**DAE**} & \multirow{2}{*}{**DenseNet**} & \multirow{2}{*}{**GRU**} & \multicolumn{2}{c}{**IC-**} & \multirow{2}{*}{**MCLDNN**} & \multirow{2}{*}{**MCNET**} & \multirow{2}{*}{**PET-**} \\  & & & **HCTC** & & & & & & & & & & **AMCNet** & & & **CGDNN** \\ \hline
8 PSK & 88.00 & 74.00 & 68.00 & 81.00 & 92.50 & 87.50 & 88.00 & 70.50 & 88.00 & 78.00 & 80.00 & 86.00 & 78.50 & 81.00 & 57.50 \\ AM- & 62.00 & 100.00 & 91.50 & 96.00 & 82.00 & 93.00 & 97.00 & 93.00 & 75.50 & 74.00 & 96.50 & 55.50 & 98.50 & 90.00 & 89.00 \\ CMB & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - \\ SSB & 88.00 & 92.00 & 96.00 & 94.50 & 93.00 & 92.50 & 97.00 & 95.50 & 96.00 & 92.50 & 95.00 & 95.00 & 94.50 & 95.00 & 92.50 \\ BPSK & 98.00 & 98.50 & 99.00 & 99.00 & 99.00 & 99.50 & 99.00 & 99.00 & 97.50 & 99.00 & 99.00 & 99.00 & 99.00 & 97.50 & 99.50 & 95.00 \\ CPFSK & 100.00 & 98.50 & 99.50 Performance metrics, such as the accuracy and numbers of parameters and FLOPs, are shown in Figures 8-11. Figure 8 presents a bar chart illustrating the accuracy of the various models when evaluated at an SNR of 0 dB with the RML2016a dataset, indicating that the proposed HCTC model performed better than the other models in terms of the accuracy. Furthermore, the proposed HCTC model and the MCLDNN [31] and PET-CGDNN [37] models achieved the highest accuracies, demonstrating their superior performances. In contrast, models such as ResNet [34] and CGDNet [36] exhibited lower accuracies, indicating that they are less effective at an SNR of 0. Figure 9 shows the average accuracies of the various models over a range of SNRs from 0 to 18 dB with the RML2016a dataset. This broader range of SNR values provided a comprehensive view of the performance of each model. Models such as the proposed HCTC and the MCLDNN [31] and PET-CGDNN [37] models consistently maintained high average accuracies, whereas models such as MCNet [30] and CGDNet [36] showed low average accuracies across the SNR range. This figure shows the overall robustness and reliability of the models and provides insights into how well they perform across a spectrum of practical noise environments.