Radar signals classification using energy‐time‐frequency distribution features

IET Radar, Sonar & NavigationVolume 14, Issue 5 p. 707-715 Research ArticleFree Access Radar signals classification using energy-time-frequency distribution features Zahra Seddighi, Corresponding Author Zahra Seddighi zseddighi0@gmail.com Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, 84156-83111 IranSearch for more papers by this authorMohammad Reza Ahmadzadeh, Mohammad Reza Ahmadzadeh Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, 84156-83111 IranSearch for more papers by this authorMohammad Reza Taban, Mohammad Reza Taban Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, 84156-83111 IranSearch for more papers by this author Zahra Seddighi, Corresponding Author Zahra Seddighi zseddighi0@gmail.com Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, 84156-83111 IranSearch for more papers by this authorMohammad Reza Ahmadzadeh, Mohammad Reza Ahmadzadeh Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, 84156-83111 IranSearch for more papers by this authorMohammad Reza Taban, Mohammad Reza Taban Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, 84156-83111 IranSearch for more papers by this author First published: 01 May 2020 https://doi.org/10.1049/iet-rsn.2019.0331Citations: 1AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract In this research, the authors extract features from intermediate frequency band radar signals in the time–frequency domain for classification. The extracted features are classified via support vector machine and K-nearest neighbour classifiers. They show the accuracy of classification is above 99% for different classes of radar signals except for frequency shift keying signal with accuracy 83% in negative signal-to-noise ratio (SNR). To identify the radars with the same class, the classification accuracy is 91% for SNR between 5 to 15 dB and 64% in the worst case for SNR between −1 to 10 dB. The proposed method is compared with some methods based on the empirical mode decomposition (EMD), cumulant and Zhao Atlas Mark Distribution (ZAMD). The results show that the classification error in the proposed method is less than that of EMD method 55% in the best case and 9% in the worst case. The performance of the cumulant-based method is weaker than that of the proposed method in common designed scenarios becoming almost similar only in one scenario. The ZAMD-based method could only distinguish the signals with different modulations in high SNR while it is unable to classify the signals with the same modulation but different parameters. 1 Introduction In passive electronic warfare systems, the primary purpose is to classify radar signals [1]. Since radar systems are becoming more complex to prevent detection, the importance of pulse separation is increasing. The signal classification from radar data is done using the measured characteristics of the signals. Some of these features are directly measured, and some of them are extracted from the received signal. Some important systems used to detect the presence of radars, extract specific characteristics from radar signals which are called pulse description word (PDW). These specifications include pulse amplitude, pulse width, pulse frequency, angle of arrival, time of arrival, and pulse repetition interval. There are several methods for the classification of different radar signals based on the characteristics of the PDW or other distinctive features extracted from the signal such as features based on cumulant [2], empirical mode decomposition (EMD) [3] and time–frequency measures [4-8]. The focus of the methods that work on the PDW features mainly is based on the classification methods such as neural network [9] and support vector machine (SVM) [10]. The neural network is used because of its non-linear mappings and its training capacity, while its structure is difficult to determine, and due to its generalisation constraint, it may suffer from overfitting. Since SVMs show more generalisation, it is less likely to be over-fitted, the accuracy of its classification is high and its implementation is much more straightforward than the neural network; therefore, it can be a proper alternative to the neural networks. There are two types of recognition for radar signals: radar emitter classification (REC) and specific emitter identification (SEI). The REC deals with radars with different types while in SEI radars are considered as with the same types and same signal modulation type, and their characteristics are very close to each other. The solutions on the SEI problem in the radar are usually based on the specific parameters of the pulses. These individual parameters are the structural details within each pulse and are referred to as unintentional modulation on pulse (UMOP), which will be introduced in the following. UMOP for each radar is unique like fingerprints. These characteristics are due to the internal structure of the radar and include pulse, frequency, and phase noise [11], which are described below. Pulse's envelope: Ideally, the received signal's envelope is rectangular and is constant relative to the frequency; however, in practice, it is not rectangular due to the continuous changes in the voltage and working current; hence each radar has a special shape that is invariant to the frequency. Spurious output: The received signal is not usually so useful as we may expect it to be. Various reasons are associated with the unwanted components of a useful signal. For example, due to the use of non-linear devices and frequency mixers, additional frequency components are generated. Assume that the input signals are and , the output signal of a non-linear mixer can be (1) Here, the useful signals contain and frequencies; while the spurious signals are in frequencies [11]. Phase noise: Phase noise can be measured in the frequency domain, and is expressed as a ratio of signal power to the noise power in a 1 Hz bandwidth at a given offset from the central frequency , which is defined as follows [11]: (2) In the spectrum of the signal, the sidelobes around the central frequency are due to phase noise. Suppose that the unintentional phase modulation is as , then the output signal will be (3) Using Bessel function expansion and under the condition , it has been written as [11] (4) where is modulation index and is frequency offset. So will generate two sidebands at . Regarding the UMOP, the nth received pulse from radar is (5) where and . N is the length of the signal along the time, is the total number of received pulses, is the intentional modulation on the pulse, is the unintentional modulation on the pulse, is the initial phase, is the time delay, and is a Gaussian noise added to the received signal [11]. The methods used for SEI either are based on the same features of the PDW [12-14] or use a creative approach to extract new features such as wavelet [15], cyclostationary [11], EMD [16], and cumulants [17]. Unlike the methods in [11-17], our method is used mainly for the classification of radars with different classes. On the other hand, the PDW features are extracted in the time domain and are highly noise-affected; so they will lose the performance of classification at low signal-to-noise ratio (SNR). Although the wavelet transform does not have cross terms, it has poor resolution than the quadratic time–frequency transforms. The applied Choi Williams Distribution (CWD) has better resolution and attempts to minimise the cross terms. In [16], the EMD method is used for estimating the instantaneous parameters of non-stationary signals, while does not extract features and does not classify signals. Moreover, we will show that the EMD has a weaker performance in classification than the proposed method. In [11], feature estimation in the time domain is needed that can be very noise-affected. In [4], Rihaczek Distribution (RD) and Hough Transform (HT) have been used to derive the ratio of the minimum to the maximum of the HT and the peak number of the HT of the real part of the RD as two new characteristic features, to classify the modulation of the signal. In [5], the authors have obtained four characteristic features, namely, the ratio of sum of absolute slope (rsas), the coefficient of polynomial curve fitting, the number of ridge stairs, and the normalised coefficient of difference of the extreme, from the generalised time–frequency representation of Zhao, Atlas and Marks (ZAM). In [6], a method has been proposed based on the time–frequency distribution (TFD) and convolutional neural network. In [7], a new technique has been proposed for feature extraction of modulated signals which is based on a pattern recognition approach and Margenau-Hill distribution. This method is robust against noise up to ∼10 dB SNR. In [8], two classes of linear frequency modulation (LFM) signals have been classified using Wigner distribution and kernel principle component analysis in SNR above 5 dB. The methods proposed in [4-6] classify signals with different modulations, and in [7, 8] classify signals with the same modulation but different parameters in SNR = 10 dB. In this paper, we classify signals with the same modulation and different parameters. Our proposed method can even classify signals belonging to the same class radars and different UMOP parameters that is a solution for SEI. Unlike most other methods, our method is capable of separating signals in negative SNR (−4.5 dB: −0.5 dB). This is one of the first attempts to use CWD and energy-TFD features to classify radar signals. This research uses simulated labelled data and focuses on the extraction of the characteristic of radar signals in the IF. The basis of these features is the CWD and is divided into three categories: features along the time axis, features along the frequency axis, and features related to the entire time–frequency display. In the next step, the extracted properties are classified using the SVM classifier and the K-nearest neighbour (KNN). In Section 2, we describe the TFDs especially CWD. In Section 3, we introduce the proposed method including feature extraction and classification. At last, we design some scenarios to show the performance of the proposed method in Section 4. 2 Time–frequency distributions Recently, great attention has been paid to time–frequency analysis in the signal processing field. The methods of time–frequency processing are the development of signal processing methods in the frequency domain and time domain using a signal display in a complete space that can provide more information of the signal. These methods are more useful for non-stationary signal processing. The amplitude or power spectrum of a signal does not provide information on how the signal frequency content varies with time, while this information is very vital for frequency modulated or non-stationary signals. An evaluation of a spectral value of a signal at a given frequency requires the presence of signal values at all times. Indeed for non-stationary signals, the frequency spectrum or auto-correlation signal function is time-dependent. TFDs are generally divided into two major groups. In the first group, the signal is represented by a time–frequency function, which is extracted from modulating or changing the scale of a base function with limited energy and frequency. Wavelet transform and orthogonal matching pursuit belong to this category. In the second category, a TFD is identified by a kernel function. In this method, where Cohen's ideas are used, the properties required for TFD are applied to the generating kernel. In such a case, the TFD representation for the signal is provided by [18] as (6) where is the kernel in the time-delay domain. The advantage of this TFD is that when the exterior and interior interfaces are minimised, it produces a high-resolution display. The cross-terms reduce the classification accuracy, especially for multi-component signals. These parts can be reduced by defining an appropriate kernel. A proper distribution must have some properties to describe the signal energy in the time and frequency domain. For example, a TFD should be a real-valued distribution such that the shift in time (or frequency) of a signal results in the corresponding shift of the distribution. Also, the integral of the distribution on the frequency (or time) domain must be equal to the spectral density (or instantaneous power) of the signal. Furthermore, the centroid frequency (or time) of the distribution at each time (or frequency) must give the instantaneous frequency (or group delay) of the signal [18]. CWD was introduced by Choie and Williams in 1989 [19], and their goal was to minimise cross terms of the WVD, while the optimal WVD properties, such as the marginal conditions and resolution of the main components, were maintained. Their effort led to the design of a kernel. The general form of CWD for the signal is provided by (7) The value of specifies the amount of removal of overlapping parts in the time–frequency plane. It can be verified that the CWD has above mentioned properties for a distribution. It can be shown that: (i) CWD is real valued; (ii) shift in time (or frequency) of a signal results in the corresponding shift of the distribution; (iii) the integral of the CWD over all times at each frequency f is equal to the spectral density of the signal at that frequency; (iv) the integral of the CWD over all frequencies at each time is the instantaneous power at that time; and (v) the integral over the whole plane is equal to the total signal energy [19]. In [20], a distribution has been provided based on the generalised S-Transform by extracting the parameters adapted to the instantaneous frequency of the signal. However, in this transform, the steps to obtain the TFD and computational volume are too large. Since we have a lot of computing volume in the feature extraction section, we use the simpler transform CWD. 3 Proposed method The procedure of the proposed method for radar signal classification is shown in Fig. 1. In the following subsections, we will explain each step of this procedure. As a novel approach, this paper uses CWD and extracts the energy-time–frequency features from this distribution for REC. Fig. 1Open in figure viewerPowerPoint Block diagram of the proposed method for radar classification There are so many time–frequency tools including Wigner, Spectrogram, Levin, Page, Choi-Williams etc. To compare the performance of these distributions in cross-term eliminating and signal denoising, we show these TFDs of a two components LFM signal with SNR = 4.2 dB in Fig. 2. We also use binary distributions shown in Fig. 3 for better comparison. It can be seen that the CWD is better-performance at cross-term eliminating and signal denoising. The Wigner distribution contains cross-terms despite robustness against noise. The spectrogram distribution does not have high resolution despite the lack of cross terms. The Page and Levin distributions have poor performance in denoising and resolution. Fig. 2Open in figure viewerPowerPoint TFDs of a two components LFM signal with SNR = 4.2 dB (a) Wigner, (b) Page, (c) Levin, (d) Spectrogram, (e) Choi-Williams Fig. 3Open in figure viewerPowerPoint Binary TFDs of a two components LFM signal with SNR = 4.2 dB (a) Wigner, (b) Page, (c) Levin, (d) Spectrogram, (e) Choi-Williams 3.1 Feature extraction One of the applications of the time–frequency transformation is detecting noisy signals. By taking the time–frequency transformation of the noisy signal, the energy of the noise will be spread over the time–frequency plane while the signal energy is concentrated in the small ranges in this plane. Particularly for a frequency modulated signal, in which the noise is added to the signal, it is much easier to detect the signal's characteristics in the time–frequency domain than the time or frequency domains alone. In this research, we use time–frequency transformation for feature extraction. In order to extract the discriminant features from radar signals, the time–frequency plane along the time and frequency axes, and finally the entire plane are divided into various areas, and then the energy-TFD features [21] are extracted for each area. These features detail the energy changes along the time axis, the frequency axis, and the entire time–frequency plane. Overall characteristics, such as the total energy of the time–frequency plane cannot help so much to solve the problem because the details of the energy changes are more informative. The results show that some well-known attributes can distinguish the signals. These attributes include entropy, energy-time distribution centre and energy-frequency distribution centre (which represents the amount of energy in each part of the time–frequency plane), kurtosis and skewness (which are dependent on the form of energy-time and energy-frequency distributions). First, we divide the time–frequency plane into small and equal windows; then calculate the energy of each window ( where i and j denote the partition indexes along the time and frequency, respectively). These energies are normalised to the entire energy of the time–frequency plane as . Then we extract the following overall features [21]: Energy-time–frequency entropy: (8) where and are the number of parts created along the time and frequency axes, respectively. Energy-time–frequency centre: (9) To extract the features along the time axis, we divide the time–frequency plane along the time axis into equal windows and normalise the energy of each window as where is the energy of the ith window along the time axis; therefore, considering the vector to display the distribution of energy along the time axis, the following features can be extracted: Energy-time distribution entropy: (10) Kurtosis of energy-time distribution: (11) where is the mean and is the standard deviation of the feature vector . Skewness of energy-time distribution: (12) Energy-time distribution centre: (13) To extract the features along the frequency axis, we divide the time–frequency plane along the frequency axis into equal windows; then compute and normalise the energy of each window as , where is the energy of the ith window along the frequency axis. Accordingly, we extract the following properties: Energy-frequency distribution entropy: (14) Kurtosis of energy-frequency distribution: (15) where is the mean and is the standard deviation of the feature vector . Skewness of energy-frequency distribution: (16) Energy-frequency distribution centre: (17) 3.2 Reduced feature dimension In many classifier training algorithms, the complexity of classifier depends on the number of inputs (input dimension). If the input data dimension is lower, the memory size and the computation will be smaller, the features' variance will be less and the classification results will become less dependent on the noise. Since the dimension of the extracted features in the previous section is 9, the dimension is firstly reduced, then the classification is done. In this paper, we use principal component analysis (PCA) to reduce the dimension. PCA maps data from a d-dimensional space to a new k-dimensional space, so that the variance of the data can be maximised. PCA represents the minimum mean square error compared to any other representation, and transforms a set of correlated variables into a set of uncorrelated variables, which are ordered by decreasing validity and have a lower dimension [22]. 3.3 Classification Usually, the neural network and SVM methods are used to classify radar signals. However, the SVM is less likely to be over-fitted than the neural network, and it also has more generalisation and ease of implementation; therefore we can use SVM here. The following explanations describe the SVM method. It is assumed that is the training data that d is the data dimension and L is the number of data. When two classes are linearly separable, the goal is to find the separating boundary that has the least classification error. This boundary will also be optimal when maximising the margin. The margin is the distance from the separating boundary to the nearest training data points of both classes. The nearest points, which are located on margins, are called the support vectors (SV) [23]. In practice, data is not always linearly separable. When data boundary is not linear, the data is mapped to a higher-dimensional space by a non-linear transformation. In this new space, data can be linearly separable as shown in Fig. 4. This non-linear function is called the kernel function. A kernel function in SVM can be in the following form (18) where maps the input data space from a lower dimension to a higher-dimensional space for each x data and 〈.,.〉 denotes internal product operator [23]. Fig. 4Open in figure viewerPowerPoint Mapping input data into a higher-dimensional space to provide linear separation [24] (a) Input space, (b) Feature space The separator function of SVM is (19) where is the number of training data, , is the training data, and is the Lagrange coefficient [23]. SVM is used to classify two-class data, while simulated data and actual radar data are multi-class. One method to classify the multi-class data using the SVM is the pair-wise method, which is less time-consuming and better in comparison to other methods. This method involves estimating class probabilities for each pair of classes, and then coupling the estimates together. Another classifier used in this paper is KNN. In machine learning, the KNN method is a non-parametric algorithm used for classification and regression. In both cases, the input contains the k closest training examples in the feature space [24]. In the KNN classification method, the output is a class membership. An object is classified by a plurality vote of its neighbours, with the object being assigned to the class most common among its k nearest neighbours (k is a positive integer, typically small). If , then the object is simply assigned to the class of that single nearest neighbour. 4 Experimental results 4.1 Proposed method evaluation In this section, we examine the proposed method in different scenarios. In the first scenario, we use simulated data with different modulation signals that are binary phase shift keying (BPSK), non-linear frequency modulation (NLFM), LFM and frequency shift keying (FSK). The window length used to segment the time–frequency plane is selected based on the length of the signal in the time domain and the frequency domain and computational complexity. It is clear that if window length is too small, the volume of calculation will become too large. The simulated signal's length except FSK signal is 1100 and the windows size is 100. The FSK signal's length is 693 and window's length is 50. As mentioned in the following tables, we simulate three data groups in different SNRs. The data in the scenarios are obtained by simulation belong to four radars that each radar has 98 signals in the IF band. Two features for two classes of the signal in scenario 1 are plotted in Fig. 5. As can be seen, the most feature vectors are separable. The classification error percentages of signals in the first scenario are shown in Table 1. Table 1. Classification error percentage for signals in scenario 1 SNR 3 dB: 7.5 dB −2 dB: 3 dB −4.5 dB: −0.5 dB proposed method's classification error 2.5 3 2.5 Fig. 5Open in figure viewerPowerPoint Sample graph spanning two columns In the second scenario we classify data with the same modulation but different parameters and different SNR. In this scenario, we simulate four groups of signals with modulations presented in Table 2, then we classify signals in each group. Table 2. Classification error percentage for signals in scenario 2 Modulation type SNR 3 dB: 7.5 dB −2 dB: 3 dB −4.5 dB: −0.5 dB LFM 0.25 0.25 0.25 BPSK 0 0.5 0.25 NLFM 0.25 0.25 0.5 FSK (group1) 0 4.3 17 FSK (group2) 0 0.25 1.53 The classification error percentage for each group is shown in Table 2. In the next scenario, we use real data from four different radars, each of which has 48 signals in IF band in different SNRs. The experimental results are shown in Table 3 for SVM with different kernels. Table 3. Classification error percentage for signals in scenario 3 Linear SVM Gaussian SVM Polynomial SVM proposed method's classification error 11.97 0 8.8 As a result, the SVM with non-linear kernel has better performance in classification. To illustrate whether the proposed method can solve the SEI problem, or whether the proposed method is able to separate radars with the same class and type, we design another scenario that uses simulated signal with the same modulation and parameters (the fourth scenario). The simulated signals in this scenario belong to four radars, each of which has 100 signals in different SNRs between −1 and 10 dB. It should be noted that each pulse of radars has a delay time, and initially pre-processing is conducted on the pulses to balance them in time. Here, we assume that the time shift is applied to the pulses, and the data is simulated in the form of (5). Signal differences in this scenario are in the characteristics of UMOP that occur on the signal, which include the signal envelope and the amount of . The values of are selected as [0.011, 0.012, 0.013, 0.014] for four classes. The signal envelope for four classes that have a slightly different are shown in Fig. 6. The value is fixed to 0.01 for four classes. Fig. 6Open in figure viewerPowerPoint Pulse envelope of signal in scenario 4 [25] In this scenario, the KNN with provides better performance than the SVM. Here the combination of training and test data is determined by one-leave-out method, in which each data is used once as a test data and the rest as training data. The result of classification for this scenario is shown in Table 4. Table 4. Classification error percentage for signals in scenario 4 Modulation type Classification's error SNR LFM 9 5 dB: 15 dB BPSK 36.5 −1 dB: 10 dB NLFM 33.25 −1 dB: 10 dB FSK 35.5 −1 dB: 10 dB It should be noted that in the CWD, the value of specifies the removal of the cross-terms. According to Fig. 7, although sigma value reduction results in the reduction of cross-term value, it also reduces the resolution of original parts of the signal and there is a trade-off between the cross-term reduction and resolution. According to this point, we have experimentally determined the value of . For example in scenario 2, is 1. Fig. 7Open in figure viewerPowerPoint CWD of a two components LFM signal with different sigma values (a) sigma = 1, (b) sigma = 0.01 As seen in Table 2, the percentage of correct classification except for FSK is above 99%. Although the error rate for the FSK is higher than that of other modulations when SNR is decreased, the accuracy of FSK signals classification is still above 83% in the worst case. The reason is that the differences in the signals from each class to the other class are negligible. Obviously, if we select more different signals, the error rate will decrease. We consider another group of signals with FSK modulation belonging to four classes that each class has 98 signals. Note that the differences between the signals from each class to the other class are more than the first group of FSK signals. We can see the results of the classification for this group in Table 2. As it is observed, the percentage error of classification is 1.53% in the worst case. This shows that CWD has enough strength for classification the radar signals using the TFD features. The error rates for NLFM, FSK and BPSK modulations are higher than that of LFM modulation. Generally, the time–frequency transformation is a better tool for displaying signals with LFM modulation, because the LFM signals can be represented by a straight line in the time–frequency domain, and in the low SNR, the detection and estimation of their characteristics using time–frequency transform are simpler than the signals with FSK and BPSK modulations. 4.2 Compare with other works To compare the performance of our method with some of the most known methods used in REC and SEI, we apply cumulant method (that is used in SEI), wavelet-EMD method (that is used in SEI and REC), and Zhao Atlas Mark Distribution (ZAMD)-based method (that is used in REC), on the same data for different SNR values and extract features that are mentioned in [3, 5, 17]. The results of the classification are in Table 5. Table 5. Classification error percentage in scenarios 1 to 3 using EMD, cumulant and proposed methods Scenario number 1 2 3 SNR −2 to 3 dB −0.5 to −4.5 dB Real data-Unknown SNR modulation type different modulation LFM BPSK NLFM FSK different modulation wavelet-EMD's based method 18 52 33.16 56.12 26 1.5 cumulant based method 70 58 53 65 62 0 proposed method 2.5 0.25 0.2 0.5 17.09 0 It can be seen that the proposed method has better performance than that of EMD. The reduction percentage of the error rate for classification in scenario 1, scenario 2, scenario 3 are 30, 55 and 1.5%, respectively. It can be concluded that the TFDs especially CWD have better potential to denoise signals than that of EMD-based method. The reason is that in the time–frequency domain, the energy of the signal is concentrated in special spaces while the energy of noise is distributed in the whole space. This causes signal denoising to be more effective. The cumulant-based method has used three-order and four-order cumulants to extract the average and dispersion features and entropy like features. We apply this method on simulated data in four scenarios whose results are shown in Tables 5 and 6. In Table 6, we used KNN classifier. Based on the results, the cumulant method has poor performance in the first and second scenarios. According to [17], the cumulant method is designed to separate signals belonging to the same class radars. In the fourth scenario, the cumulant performance is close to the performance of the proposed method. Table 6. Classification error in scenarios 1:3 in cumulant and proposed methods Scenario number SNR SNR 5 to 15 dB −1 to 10 dB modulation type LFM BPSK NLFM FSK proposed method 9 36.5 33.25 35.5 cumulant-based method 15.25 25 39.5 37.5 Another well-known method is ZAMD-based method [5]. This method classifies the signals with different modulation by extracting four features namely the ratio of the sum of the absolute slope, the coefficient of polynomial curve fitting, the number of ridge stairs and the normalised coefficient of difference of the extreme, from the generalised time–frequency representation of ZAM. The limitations of this method are as follows: Can apply only on signals with different modulations. As mentioned in [5], the performance of method changes with the signal's parameter. This means that in some ranges of the parameter, this method has poor performance. For example for a scenario in which the data are LFM, 2FSK, 4FSK, BPSK and Mono Pulse modulation, from each modulation we have 100 signals in SNR = 5 dB. Based on [5], if the rsas becomes lower than one, the signal should be BPSK. The rsas is defined in [5] as (20) where (21) (22) where is ZAMD of x [5]. In this scenario, 82% of the LFM signals, 77% of the 2FSK signals and 44% of the 4FSK signals have rsas lower than one while in the proposed method we do not have any error in the classification of the LFM and 2FSK; also the classification errors of the 4FSK and BPSK signals are 1 and 11%, respectively. 5 Conclusion In this paper, we proposed a new method for radar signal classification, and showed that the proposed method could be used for SEI problem. The proposed method is based on CWD and the Energy-TFD features. We designed four scenarios to show and evaluate the performance of the proposed method. As seen in the results, the accuracy percentage of classification for radar with different classes is above 99% except for FSK signal that is 83%. To identify the radar with the same class, the accuracy percentage of classification is 91% in the best case and 64% in the worst case. 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