## 4 Simulation Results
### Simulation Result  
In this paper, we propose an efficient feature extraction method to reduce training time while maintaining AMC performance. In order to evaluate the proposed method, the representative value was selected from various cumulants by using each method and two sets of simulations were conducted. In the first simulation, in order to find the effective feature values, we ranked the cumulants based on the calculation from each method. Then, we measured the classification performance sequentially by excluding the feature values one by one. The structure of DNN is the same environment except for the input layer. Table 8 summaries the classification performance according to elimination of each feature. In the 10 dB SNR environment, the most essential or effective feature is \(C_{40}\) and the most unnecessary or ineffective feature is \(C_{21}\). In the case of the proposed method, these features \(C_{40}\) and \(C_{21}\) are identified precisely. On the other hand, the mutual information method identified \(C_{62}\) as the most essential feature and \(C_{21}\) as the most unnecessary feature. In the case of the conventional method, the most effective feature was extracted as \(C_{60}\) and the most unnecessary feature was extracted as \(C_{21}\). In the proposed method, the most effective feature and the most unnecessary feature were accurately identified in the 10 dB SNR environment, while the other two methods accurately identified the unnecessary feature but failed to extract the most effective feature. In other words, the proposed method shows superior performance in extracting effective features compared to the conventional methods. Table 9 shows the difference in the classification performance when all the features are used and when the effective features are excluded by each method. If a method shows the highest value for a given SNR value in the table, that method is the best in correctly identifying the effective features. \begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Value** \\ \hline Number of input nodes & 9 \\ Number of hidden layer & 3 \\ Number of nodes of 1 st hidden layer & 40 \\ Number of nodes of 2 st hidden layer & 20 \\ Number of nodes of 3 st hidden layer & 10 \\ Number of output nodes & 5 \\ Activation function of hidden layer & ReLU \\ Activation function of output layer & Softmax \\ Number of training data & 450,000 \\ Number of test data & 90,000 \\ Number of validation data & 90,000 \\ Epochs & 200 \\ Batch Size & 64 \\ \hline \end{tabular}
\end{table} 
Table 7: The DNN parameters used in the first simulation for optimal feature extraction and performance verification. \begin{table}
\begin{tabular}{c c c c c c} \hline
**SNR** & **\(-\)10 dB** & **\(-\)5 dB** & **0 dB** & **5 dB** & **10 dB** \\ \hline ALL & 86.37 & 89.67 & 95.70 & 98.61 & 99.91 \\ C\({}_{20}\) & 77.44 & 83.99 & 92.05 & 93.03 & 98.38 \\ C\({}_{21}\) & 83.10 & 84.60 & 91.85 & 97.56 & 98.92 \\ C\({}_{40}\) & 79.16 & 83.91 & 91.03 & 96.73 & 98.12 \\ C\({}_{41}\) & 83.19 & 84.93 & 91.92 & 97.52 & 98.40 \\ C\({}_{42}\) & 82.90 & 83.67 & 91.47 & 97.47 & 98.69 \\ C\({}_{60}\) & 83.09 & 83.14 & 91.14 & 96.91 & 98.35 \\ C\({}_{61}\) & 83.17 & 84.53 & 91.52 & 97.30 & 98.27 \\ C\({}_{62}\) & 83.28 & 84.87 & 92.14 & 97.42 & 98.55 \\ C\({}_{63}\) & 83.11 & 85.46 & 91.40 & 97.34 & 98.73 \\ \hline \end{tabular}
\end{table} 
Table 8: Classification performance according to elimination of each feature [%]. The feature with the lowest value is the most essential for the classification. In [14], only the second and the fourth-order cumulants are considered, and the variation of characteristic values is small even in low SNR environments. Therefore, there was little variation in efficiency ranking in a low SNR environment. However, in this paper, it can be seen that the order of efficiency fluctuates significantly in a low SNR environment due to the sixth-order cumulant with high variability.