## 4 Simulation Results
### Simulation Result
In this manner, when the feature with a large variability is used, the ranking of the efficiency value of each feature can be changed according to each SNR. However, since the performance is also changed to a similar trend, it becomes suitable even in environments using the feature with high volatility. The proposed method shows higher performance not only when using the second- and fourth-order cumulants but also when using the sixth-order cumulant. In the second set of simulations, in order to measure the classification performance according to the group, the cumulants were divided into three groups (top, middle, and bottom) based on the ranking obtained from the efficient feature-extraction method. The cumulants in each group were used as the inputs to the DNN algorithm to measure the classification performance. The parameters of the second DNN are summarized in Table 10.  
Figure 3 and Table 11 shows the simulation results of the proposed method and Figures 4 and 5 show the results of the conventional method. Tables 12-14 represent the features used for each group. In Figures 3-5, the desirable result is that the best classification performance is achieved when the top group is used as the input data, while the worst classification performance is achieved when the bottom group is used as the input data. In this respect, the conventional methods are unsatisfactory since the top group cannot always obtain the best performance in all SNR ranges. However, the proposed method shows a stable and the best performance over a wide SNR range of -2 dB to 10 dB. Even if the same amount of data is exploited, there is a large difference in performance depending on the features used. Also, even in the low SNR environment, the performance of the top group is better than that of the bottom group in the high SNR environment. Therefore, we conclude that the proposed method is very effective at extracting the useful feature group. Figure 6 shows the classification performance when only the features of the top group of each method is used as the input data. This figure also highlights that the proposed method shows superior performance in all SNR environments. Therefore, \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Number of input nodes & 5 \\ Number of hidden layer & 2 \\ Number of nodes of 1 st hidden layer & 30 \\ Number of nodes of 2 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 & 250,000 \\ Number of test data & 50,000 \\ Number of validation data & 50,000 \\ Epochs & 200 \\ Batch Size & 64 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The DNN parameters used in the second simulation for optimal feature group extraction and performance verification. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**SNR** & **-10 dB** & **-5 dB** & **0 dB** & **5 dB** & **10 dB** \\ \hline Proposed & 8.93 & 6.53 & 4.56 & 1.88 & 1.79 \\ Mutual information & 3.26 & 4.21 & 4.56 & 1.70 & 1.36 \\ Conventional & 3.47 & 6.53 & 4.56 & 1.70 & 1.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Difference in classification performance when all features are used and when the effective features are excluded by each method.