## 3 Proposed Effective Feature Selection Method  
### Conventional Effective Feature Selection Based on Mutual Information and Correlation  
The conventional method based on mutual information and correlation performs preprocessing before using it for input data. This is to reduce the computational complexity of the algorithm and maintain the identification performance. The conventional mutual information and correlation method for extracting an efficient feature is expressed as [15]:  
\[max_{x_{j}\in X-S_{m01}}\left[I\!\left(x_{j};c\right)-\frac{1}{m-1}\sum_{x_{i }\in S_{m-1}}I\!\left(x_{j};x_{i}\right)\right], \tag{4}\]  
where \(I\!\left(x_{j};c\right)\) denotes the mutual information value between the feature value and the corresponding module, \(S_{m}\) denotes a set of selected feature values up to \(m\) runs, and \(X\) denotes a set of all feature values. A representative value according to each feature can be obtained from (4) and a feature having a large representative value is the most efficient feature. Table 3 shows the representative values of the second-, fourth-, and sixth-order cumulants of the conventional method [15]. As can be observed from the table, the conventional method indicates that the most effective feature is \(C_{60}\) and the most ineffective feature is \(C_{21}\) in the 10 dB SNR environment. Thus, the effect of each feature on the classification performance should be numerically expressed as a representative value. The proposed method is expressed as:  
\[ECV_{i}=\sum_{j=1}^{M}\sum_{ \begin{array}{c}k=1\\ k\
eq j\end{array} }^{M}\Big{|}c\sigma\Big{(}x_{ik},x_{ij}\Big{)}\Big{|}, \tag{6}\]  
where \(M\) is the number of features, \(x_{ij}\) is the \(j\)-th feature of the \(i\)-th modulation type, and \(\text{cor}\Big{(}x_{ik},x_{ij}\Big{)}\) is the correlation coefficient between the two features. In this manner, one representative value can be obtained according to each characteristic. A characteristic with a large representative value has a little influence on the AMC performance. On the other hand, a feature with a small representative value has a strong influence on the classification performance and becomes the effective feature required for the AMC. As shown in Table 5, the proposed method indicates that the most effective feature is \(C_{40}\) and the most ineffective feature is \(C_{21}\) in the SNR 10 dB environment. As shown in Tables 3-5 the effective feature for each method is different, and the performance of each method is verified through two sets of simulations. In the AMC structure of this paper, the modulated signals to be classified are generated in the AWGN channel, and the cumulants are extracted for each signal. The extracted cumulants are represented by one representative value through the proposed method as shown in Equation (6). In order to reduce the computational complexity of the algorithm and to classify the modulation type quickly, it extracts the top feature and classifies the modulation type after learning by using it as input data to the DNN algorithm. The proposed AMC structure is shown in Figure 1. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**SNR** & \(-\)**10 dB** & \(-\)**5 dB** & **0 dB** & **5 dB** & **10 dB** \\ \hline \(C_{20}\) & 0.37 & 1.73 & 6.07 & 12.45 & 16.97 \\ \(C_{21}\) & 1.80 & 3.07 & 9.07 & 15.63 & 18.34 \\ \(C_{40}\) & 0.56 & 1.35 & 3.52 & 7.69 & 12.19 \\ \(C_{41}\) & 1.19 & 3.1 & 8.21 & 14.62 & 18.23 \\ \(C_{42}\) & 0.73 & 0.95 & 9.28 & 15.31 & 18.07 \\ \(C_{60}\) & 1.82 & 0.65 & 1.77 & 8.08 & 14.02 \\ \(C_{61}\) & 2.96 & 3.55 & 8.47 & 13.46 & 15.24 \\ \(C_{62}\) & 3.34 & 4.77 & 8.5 & 14.64 & 18.07 \\ \(C_{63}\) & 2.81 & 5.36 & 10.27 & 15.56 & 18.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Effective correlation values of each cumulant in various SNR environments for the proposed method. Unlike the other methods, small values indicate strong influence on the classification performance, meaning that the associated cumulants are more effective features for AMC systems.