## 3 Coherent Feature Extraction and Evaluation
### Coherent Feature Evaluation  
To evaluate the comprehensive identification performance of SMR and the typical five feature parameters, AHP [25] is introduced in this paper. AHP is a systematic method that takes a complex multiobjective decision-making problem as a system and decomposes the objective into several levels, namely, multiobjective, multicriteria, and multiattribute. Through quantitative and qualitative analyses, the single ranking and total ranking of the levels are calculated as a systematic method of objective and optimized decision-making. Evaluation steps based on AHP are given as below. _Step 1:_ Establish a model of the evaluation system  
To establish a suitable feature evaluation system as the basis of efficient evaluation, the feature evaluation system needs to follow certain evaluation criteria, such as purposefulness, a scientific nature, and systematization. In this paper, the feature evaluation system is designed as a three-layer structure, namely, a target layer, an index layer, and a scheme layer. The target layer denotes the radar emitter identification. In the index layer, three metrics--reliability, accuracy, and robustness--are adopted to evaluate the performance of the parameters. The scheme layer is the parameters to be evaluated, which are CF, PRI, PW, AOA, PA, and SMR. The model of the evaluation system is shown in Figure 6.  
Figure 5: SMRs (the ratios of the secondary peak value to the main peak value) of different signal types in different signal-to-noise ratios (SNRs). Figure 6: Evaluation system model. _Step 2:_ Construct the judgment matrix. According to the Saaty relative importance hierarchy table [26], reliability, accuracy, and robustness in the index layer are taken to make a comprehensive evaluation of the evaluated feature. The judgment matrix is constructed in terms of these three indexes, which are compared with each other by the expert's scoring. Judgment matrix \(A\) is computed below. \[\mathbf{A}=\left[a_{ij}\right]_{3\times 3}=\left[\frac{\alpha_{i}}{\alpha_{j}} \right]_{3\times 3}=\left[ \begin{array}{ccc}1&3&8\\ 1/3&1&6\\ 1/8&1/6&1\end{array} \right] \tag{15}\]  
where \(a_{13}=a_{1}/a_{3}=8\) denotes that the influence of reliability on the evaluation system is much higher than that of robustness for radar emitter identification. The definition of the other elements in matrix \(A\) can be deduced in the same way. In the same way, judgment matrices \(B_{1}\), \(B_{2}\), \(B_{3}\) can be obtained below. \[\mathbf{B}_{1}=\left[ \begin{array}{cccccc}1&1/5&1/7&1/9&3&1/7\\ 5&1&1/3&1/5&7&1/3\\ 7&3&1&1/3&7&1\\ 9&5&3&1&9&3\\ 1/3&1/7&1/7&1/9&1&1/7\\ 7&3&1&1/3&7&1\end{array} \right] \tag{16}\]  
\[\mathbf{B}_{2}=\left[ \begin{array}{cccccc}1&3&4&4&5&7\\ 1/3&1&3&3&4&6\\ 1/4&1/3&1&1&3&5\\ 1/4&1/3&1&1&3&5\\ 1/5&1/4&1/3&1/3&1&3\\ 1/7&1/6&1/5&1/5&1/3&1\end{array} \right] \tag{17}\]  
\[\mathbf{B}_{3}=\left[ \begin{array}{cccccc}1&3&3&3&5&9\\ 1/3&1&1&1&3&7\\ 1/3&1&1&1&3&7\\ 1/3&1&1&1&3&7\\ 1/5&1/3&1/3&1/3&1&5\\ 1/9&1/7&1/7&1/7&1/5&1\end{array} \right] \tag{18}\]  
In judgment matrix \(B_{1}\), \(\beta_{1}/\beta_{2}=1/5\) denotes the reliability of CF is weaker than that of PW, \(\beta_{1}/\beta_{5}=3\) denotes the reliability of CF is better than that of AOA. The definition of other elements in matrices \(B_{1}\), \(B_{2}\), \(B_{3}\) can be deduced in this way. _Step 3:_ Calculate the weight vector of judgment matrices \(A\), \(B_{1}\), \(B_{2}\), \(B_{3}\) and check their consistency. In this step, we need to introduce three definitions [27]: compatibility index (\(CI\)), random consistency index (\(RI\)), and compatibility ratio (\(CR\)). The mathematical expression of \(CI\) and \(CR\) are given below. \[CI=\frac{(\lambda_{\max}-n)}{(n-1)} \tag{19}\]  
\[CR=\frac{CI}{RI} \tag{20}\]  
In the formulas mentioned above, \(n\) denotes the order of matrix \(A\), \(\lambda_{\max}\) is the maximum eigenvalue of the judgment matrix \(A\). When \(n=3\), \(RI=0.58\); \(n=4\), \(RI=0.96\); \(n=5\), \(RI=1.12\); \(n=6\), \(RI=1.24\)[28].