## 3 Results and Discussion
### Experiments and Discussion  
We first explore the impact of the number of hybrid parallel modules. Figure 6 illustrates the performance of different hybrid parallel modules. We choose \(m=0.1\) and \(s=10\). The average accuracy from one hybrid parallel module to 6 hybrid parallel modules is 71.77%, 87.76%, 88.84%, 90.51%, 87.36% and 86.69%, respectively. We can find that only one hybrid parallel module is not enough to learn the distribution of dataset. However, when the number of modules is larger than 4, the performance of network is also not ideal. This can be explained by too few modules not being enough to learn the distribution of dataset. Nevertheless, too many modules will make back propogation difficult, which will result in the problem of network degradation. As a result, our proposed method needs a proper number of modules. In Figure 6, we find that the best number is 4. The recognition rate of each modulation category for different SNRs is shown on Figure 7. The network we applied stacks with 4 hybrid parallel module and sets \(m=0.1\) and \(s=10\), the average accuracy is 90.42%. We find that AM-DSB has always been misclassified a lot with WBFM. 8 PSK is misclassified at first but the accuracy add up fast, while at 0 dB, the accuracy surpasses 90%. Although the performance of some modulation categories is not good at \(-4\) dB, with the increase of SNR, the performance of all modulation categories can exceed 95% except AM-DSB, which means that our proposed method has a great performance on the digital-modulated signal and can also recognize some types of analog modulation categories. \begin{table}
\begin{tabular}{c c c} \hline \hline
**First Inception Channels** & **Second Inception Channels** & **Stride** \\ \hline
64 & 40 & 1 \\
40 & 40 & 2 \\
20 & 20 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The structure of our proposed hybrid parallel network. Figure 6: The performance of different number of hybrid parallel modules. Next we analyze different confusion matrixs for an SNR of \(-4\) dB, \(0\) dB and \(6\) dB. The value \(-4\) dB in Figure 8 is the lowest SNR so we can observe the confusion at low SNR. When it comes to \(0\) dB, the SNR has increased and we can see the change in the confusion matrix. The performance of our method becomes stable for an SNR of \(6\) dB. AM-DSB has always been misclassified with WBFM, but WBFM can be successfully recognized. \(16\)QAM and \(64\)QAM are misclassified for each other at \(-4\) dB and the accuracy improves gradually with the increase of SNR. This is owing to the fact that \(16\)QAM and \(64\)QAM both belong to QAM modulation category. The same thing happens between \(8\)PSK and QPSK. they are misclassified with each other at \(-4\) dB, and the accuracy reaches \(99\%\) at \(6\) dB. In summary, the performance of digital-modulated signal is much better than analog-modulated signal. We hold the opinion that this is because of two reasons: at the first, the number of analog-modulated signal included in this dataset is less than digital-modulated signal. Secondly, the distance between analog-modulated signal is shorter than the digital-modulated signal. Figure 9 displayed the distribution of extracted features at \(-4\) dB, \(0\) dB and \(6\) dB. The features are extracted at the penultimate layer of our proposed method, where the last layer is the AM-softmax layer. The features from the penultimate layer are \(128\) dimensions. Figure 8: Confusion matrix of the hybrid parallel network for different Signal to Noise Ratios (SNRs). **(a)** The confusion matrix of the hybrid parallel network for an SNR of \(-4\) dB. **(b)** The confusion matrix of the hybrid parallel network for an SNR of \(0\) dB. **(c)** The confusion matrix of the hybrid parallel network for an SNR of \(6\) dB. Figure 7: Classification accuracy of different modulation categories. We utilized t-SNE [54] to reduce dimension. We show in Figure 9 that, for an SNR of \(-4\) dB, the cosine distance between 16 QAM and 64 QAM is very close, 8 PSK and QPSK severely overlap.