# Hybrid Electromagnetic Signal Feature Extraction

Authors: Jianming Dong
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

In the complex electromagnetic environment, the large number of pulse loss (data loss) and the serious overlap of signal parameter space destroy the signal regularity used by the traditional sorting method and finally make the existing signal sorting algorithm difficult to obtain satisfactory sorting effect or even completely invalid. On the basis of considering several key characteristic indexes (pulse width, carrier frequency, and arrival time), a multiparameter and five-layer mutual coupling sorting algorithm is designed. In particular, a new key feature index extraction method is proposed to study the feature vectors contained in the data and establish the corresponding mathematical model, which is finally applied to the sorting of various communication signals. The numerical results show that the five-step sorting method can be used to separate signals with serious overlap and partial missing data.


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## Body

## 1. Introduction

With the rapid development of communication technology, the diversification and complexity of communication systems and the comprehensive utilization of various systems, electronic countermeasures are facing more and more complex electromagnetic environment. Reasonable management and control of spectrum resources is the basic guarantee for wireless communication services and security. It is an important task of reconnaissance how to carry out signal sorting in complex signal environment. It is one of the urgent and difficult tasks in the field of electronic reconnaissance to improve the ability of passive signal seeker to correctly select and track target signals in dense, complex, and changeable signal environment [1, 2].Commonly used signal feature extraction methods are as follows:(1)
Feature transformation methods are as follows: FFT, nonparametric power spectrum (periodogram method and Welch method), Hilbert-Huang transform, wavelet transform, parametric power spectrum estimation method (Burg, yale-worker AR), short-time Fourier transform method, MFCC (Mel cepstral coefficient), Wigner distribution (WDF), Radon transform, and Gabor transform(2)
Common characteristic indexes in time domain are as follows: waveform index, pulse index, kurtosis index, margin index, peak-to-peak value, zero-crossing rate, short-term energy, and short-term autocorrelation function(3)
Frequency domain indicators are as follows: center of gravity frequency, mean square frequency, root mean square frequency, frequency variance, frequency standard deviation, short-term power spectral density, spectral entropy, fundamental frequency, and formantTraditional signal sorting methods mainly adopt some matching, clustering, or classification methods based on five parameters (arrival time TOA, carrier frequency RF, pulse width PW, pulse amplitude PA, reach azimuth AOA, etc.). And many technologies related to electromagnetic space have been developed, including wireless device identification, radio frequency fingerprint identification, and electromagnetic signal identification. Research on relevant sorting methods began in the 1970s [3]. The early representative sorting algorithms include sequence search method proposed by Davies et al., small box matching method for setting quantitative tolerance of parameters proposed by Whittall and Rogers, and multiparameter clustering method based on spatial distance proposed by Andrews and Wilkinson et al. [4].In 2009, Franceschetti et al. divided the scattering centers into five types according to the different scattering structures and gave the analytical expressions of their scattering coefficients [5]. In 2016, Ou and Zhang applied Prony’s algorithm for the first time to solve the problem of one-dimensional inverse scattering [6]. In 2012, An et al. established the Prony scattering center model of the target, which uses an exponential function to model the frequency dependence of the scattering center [7]. For this model, they proposed the corresponding Prony method to extract the features of the target scattering center (Matlab demo of this paper can be downloaded from https://pan.baidu.com/disk/pdfview?fsid=175800526881488&path=%2Fprogramme.doc&size=46592&_at_=1647415854432/). Since the frequency-dependent characteristic is modeled as an exponential function, the model is also called the attenuation exponent and model, that is, the DE and model [8]. The attenuation index and model parameters have clear physical meanings and can be used to describe the frequency-dependent characteristics of some nonpoint scattering centers, but they do not consider the azimuth-dependent characteristics of the scattering centers. Based on theory, Professor Potter LC from Ohio University and others proposed to use power functions to model the frequency dependence of the amplitude of the scattering center [9]. Two years later, he proposed to use exponential function to model the dependence of scattering center amplitude on azimuth angle and established the original form of attribute scattering center model [10]. On this basis, they also gave a one-dimensional GTD model of the optical zone, but this model is only suitable for describing the scattering characteristics of targets at small angles. Since then, Yoshioka and Ohsugi improved the original attribute scattering center model based on GTD and PO theories in 1999 and proposed a specific form of attribute scattering center to describe the scattering characteristics of targets at wide angles [11]. Because the model is rich in various physical and geometric attribute parameters, it is called the attribute scattering center model, that is, the ASC model. According to the azimuth-dependent characteristics of the scattering center, the attribute scattering center can be divided into the localized scattering center (LSC) and the distributed scattering center model (DSC, distributed scattering center) [12]. The localized scattering center model and the distributed scattering center model, respectively, model the electromagnetic scattering echoes of the isotropic and anisotropic scattering centers along the azimuth direction. Generally, we collectively refer to the ideal point scattering center, attenuation index, model, and attribute scattering center model as the classical scattering center model. However, the actual echo obtained by radar is complex, and there are complex special scattering centers such as sliding scattering centers and dispersive scattering centers, which cannot be described by the attribute scattering center model. Therefore, Hamza et al. proposed a polynomial scattering center model and a semiparametric scattering center model to model such special scattering centers [13]. As the name implies, the polynomial scattering center model models the amplitude and phase of the scattering center into a polynomial form, but its parameters cannot correspond to specific physical or geometric meanings. The semiparametric scattering center model ignores the dependence of the scattering center amplitude on the frequency and azimuth angle in the distance direction and uses an arbitrary function to model the variation of the scattering center amplitude with the azimuth angle. Usually, we call these two models the nonclassical scattering center model. It is worth mentioning that in 1991, Ing further extended the GTD model to the two-base and three-dimensional situations [14]. The dual-base GTD scattering center model models six classic scatterer models of plane, dihedral angle, trihedral angle, cylinder, sphere, and hat top from the dependence characteristics of frequency, azimuth angle, pitch angle, and target attitude angle. Based on the dual-base GTD model, through the amplitude parameter correction, they also gave a three-dimensional attribute scattering center model. In addition, Babcock also proposed a wide-frequency and large-angle multipeak model based on the attribute scattering center model to approximate the distributed scattering center model in a wide-angle observation SAR system and gave the corresponding attribute parameter estimation and classification algorithm [15].Since the polarization information of the target is related to its structure, material, and other inherent characteristics, it is necessary to consider the influence of polarization characteristics when establishing the scattering center model. As early as 1965, Ayars and George gave the polarization characteristic parameters in the Prony model. They believe that the polarization characteristic parameters are mainly reflected in the complex amplitude of the scattering center, independent of the frequency, and azimuth dependence of the target [16]. The attribute scattering center model proposed in 1997 continued this idea, thinking that the target changes with frequency and angle under each polarization channel are the same, and the complex amplitude under each polarization channel is different with different polarization modes [17]. In 2013, Peng-Peng et al. also proposed a theoretical model of coherent polarization diffraction of the target to describe the dispersion and polarization characteristics of the target scattering center and gave the corresponding feature extraction algorithm [18]. In recent years, the model modeling of the polarization mode of the scattering center has continued to use this idea [19].Generally speaking, the parameter estimation methods of the scattering center can be divided into two categories: parametric methods and nonparametric methods. The nonparametric method does not need to establish a scattering center model and directly uses Fourier analysis to extract the peak characteristic parameters of the scattering center. According to the different operating domains, nonparametric methods can be divided into time-domain non-parametric methods and frequency-domain nonparametric methods. Typical time-domain nonparametric methods include time-domain matched filtering methods. Typical frequency domain nonparametric methods include Fourier analysis, CLEAN, RELAx, and other high-resolution spectrum estimation methods [20]. The nonparametric method has the characteristics of low computational complexity and time-consuming, but its resolution is limited by the constraints of hardware conditions such as radar emission bandwidth, and the estimation accuracy is low. The feature extraction technology of the scattering center is an important technology for studying the electromagnetic feature extraction of the target, and it is of great significance for the classification and recognition of the target [21]. The parametric extraction method based on the scattering center model is the mainstream algorithm for the feature extraction of the scattering center. First, it effectively describes the scattering characteristics of the target in the high-frequency region by parametric modeling of the scattering center of the target; then, it extracts the characteristic parameter set of the scattering center by parameter estimation to realize the feature extraction. Classical scattering center model includes point scattering center model, attenuation index and model, and attribute scattering center model. Among them, the attribute scattering center model can use different combinations of attribute parameters to describe the physical and geometric properties of the basic scattering center through continuous improvement of the first two models. Therefore, it has received extensive attention and attention from scholars at home and abroad. The feature extraction methods of the attribute scattering center model can be divided into two types: nonparametric methods and parameterized methods. For complex scattering centers, there is often more than one peak corresponding to the image domain. It is difficult for nonparametric methods to obtain accurate and effective estimates, and the performance of nonparametric methods depends on the imaging resolution. Therefore, the current mainstream algorithm of target scattering center feature extraction method is a parameterized method. The essence of the parameterization method is based on the parameter estimation of the parameterized model [22]. Different from the traditional point scattering model, the feature extraction of the attribute scattering center model is a high-dimensional mixed parameter estimation problem. The earliest frequency domain attribute feature extraction method is to optimize and solve the estimated parameters of multiple attribute scattering centers at the same time. There are problems of difficulty in order determination and huge calculation amount. Therefore, it is only suitable for feature extraction of radar target images with a small number of scattering centers. The parameter estimation method based on the image domain effectively reduces the amount of calculation by segmenting the scattering center in the image domain. Among them, the most commonly used algorithm is the ML estimation algorithm based on image domain segmentation, which is mainly divided into four steps: image segmentation, model category selection, parameter initial value selection, and parameter optimization. First, the radar image is divided into several subimages with a few or independent scattering centers through image segmentation to reduce the amount of calculation. Then, the type of the scattering center is judged according to the azimuth envelope of the scattering center in each subimage. Then, the initial value of each scattering center is roughly set using numerical methods and prior conditions. Finally, the optimization method is used to optimize and solve each characteristic parameter. However, due to its nonconvex cost function, it requires high precision for the initial values of the parameters; otherwise, it is easy to fall into local extreme values. However, the existing parameter initialization methods often fail to meet the precise requirements and eventually lead to misunderstandings.The signal is the carrier of information. The key to information processing lies in the extraction and analysis of key features in the signal. In the field of electromagnetic information security, by analyzing the characteristics of electromagnetic leakage or wireless transmission signal data, potentially useful information can be excavated, and then, the existing security risks can be solved. The feature analysis of electromagnetic signals includes data collection, feature extraction, and feature statistics. Feature extraction can more intuitively present the characteristics of the signal, so that the signal can display its data value. In the field of machine learning, feature extraction extracts features from raw data and converts them into a format suitable for machine learning models to obtain better training data features, so that the performance of machine learning models can be effectively improved. Feature statistics are necessary means for feature selection and further feature extraction in order to respond to data with richer types, real-time, and higher accuracy requirements, so as to improve the accuracy of signal processing. When electromagnetic signals are monitored, the first concern is the identification of electromagnetic signals. Image recognition technology and convolutional neural network are used to classify and recognize electromagnetic leakage signals. However, in the application of this method, it is found that weak changes in the signal will affect the recognition results. How weak signal changes affect the recognition results, signal feature extraction, and statistical distribution are the basis. At present, signal recognition methods based on feature extraction and statistics have been applied in different fields, and certain results have been achieved. Zhang Yingnan and others conducted statistics on the instantaneous frequency and complex envelope modulus characteristics of intercepted signals in the field of space electronic countermeasures and realized the rough classification of signal types. Kim et al. carried out statistical distribution research on the machine tool sound signal features extracted in the time domain, amplitude domain, and frequency domain and achieved good recognition results [23]. Some scholars introduced this method into the field of communication to solve the problems of modulation recognition of communication signals and individual recognition of radiation sources [24]. From the perspective of electromagnetic information security, this paper conducts feature extraction and statistical analysis of typical electromagnetic leakage signals. By establishing feature extraction methods in the time domain and frequency domain, the distribution of feature parameters is analyzed, and effective features are further screened out, and the electromagnetic signals are excavated. A large amount of information provides effective analysis methods for the classification and identification of electromagnetic signals and then provides strong support for applications such as abnormal signal detection and equipment behavior recognition.


## 2. Denoising Processing of Mixed Electromagnetic Signals

### 2.1. Decompression Process Design

During the detection of mixed electromagnetic signals, there are many electromagnetic interferences on site. Usually, there are pulse electromagnetic interference signals, white noise, and periodic narrowband electromagnetic interference signals. Pulse electromagnetic interference signals can be divided into random and periodic pulse electromagnetic interference signals. Among them, the periodic pulse electromagnetic interference signal mainly comes from electromagnetic interference caused by the action of the SCR device. Random electromagnetic interference signals are generally electromagnetic interference generated by lightning and relays. White noise interference is mainly a variety of random noise, including noise interference generated by transmission lines and thermal noise of windings. Periodic narrowband interference is mainly electromagnetic interference signals such as radio communication and carrier communication.In the currently published related literature, research on the recognition of modulation of communication signals is carried out basically on the assumption that there is only one signal in the same receiving channel. In fact, with the widespread popularity of radio communication in military and civilian fields, signals in the radiocommunication frequency band are becoming denser, coupled with the presence of a large number of intentional or unintentional interfering signals, even in ordinary narrowband communication receivers, both appear in the same. It is difficult to avoid the phenomenon of more than one signal, and it is extremely common to have many signals simultaneously in special broadband receivers such as electronic reconnaissance and radio monitoring. In this case, the current modulation technology is no longer applicable and it is necessary to learn new methods, process the observation data appropriately, and determine the modulation form of each signal. It is a problem of recognizing the modulation of many signals in the same channel.In particular, multisignal modulation recognition refers to the following: in noncooperative communication or communication, the observation data received by the receiver (typically a sampling sequence derived from the receiver’s intermediate frequency) contains two or more noise contaminated modulated signals, based on an evaluation of the presence or absence of a signal, estimation number of signals (signal detection), and estimating some parameters (parameter estimation) such as center frequency and signal bandwidth using a particular method for determining the received or modulation type of the signal of interest. It can be seen that multiple signals to be identified are completely associated in the time domain; therefore, existing modulation identification algorithms for a single signal cannot be directly used for multisignal modulation identification.These noise interferences are usually less than 200 MHz, and there are relatively few interference sources in ultrahigh frequency electromagnetic waves, mainly mobile phone mobile communication interference, such as GSM wave is 900 MHz, but its frequency band is fixed. Although the UHF electromagnetic wave method can effectively avoid a large amount of electromagnetic interference, there will still be other electromagnetic interference signals on site. These electromagnetic interference signals have similar characteristics to white noise [25]. In this paper, white noise signals are used to simulate electromagnetic interference signals around the scene. Because the mixed electromagnetic signal is very weak and its signal-to-noise ratio is very low, effective denoising can keep the mixed electromagnetic signal at a low distortion rate, so that the recognition result of the mixed electromagnetic signal will not be affected.Regardless of whether single-channel or multichannel reception is used, the collected observation data is a mixed waveform of the plurality of signals to be identified and additional noise, and appropriate preprocessing is required prior to processing. In signal processing, preprocessing in the narrow sense mainly refers to simple data processing such as subtracting the mean value, removing outliers, and eliminating trend elements from the original observation data to facilitate subsequent signal processing. In this article, in addition to the basic data processing mentioned above, preprocessing is mainly concerned with the separation of multiple signals, i.e., the application of appropriate temporal filtering or spatial filtering methods such as FIR filters or beamforming to aliasing multiple signals in the time domain. Identified signals are separated from them. Mixed runs one by one. Its purpose is to turn the multisignal identification problem into the multisignal identification problem and then use the existing modulation identification method proposed for a single signal to identify the modulation form of each separated signal and realize the multisignal modulation identification. At the same time, filtering can also improve the signal-to-noise ratio of the identified signal, so it is beneficial to improve the efficiency of modulation identification. For a complete multisignal modulation recognition process, the separation of multiple signals is only preprocessing.In practical applications, the specific method of signal separation used depends on the distribution characteristics of the plurality of signals to be identified in a mixed waveform in the frequency domain and in the spatial domain. In the case of multiple signals that can be separated in the frequency domain, a relatively simple separation method based on time filtering can be used, and at the same time, only a single-channel receiving system is required to obtain observation data of the multiple signals. To identify a plurality of signals that can be separated in the spatial domain, whether or not the frequency domain can be separated, a spatial filtering-based separation method can be used. A complex receiving system is required. Receive these signals. Of course, the latter method is a more versatile method of signal separation than the former, but its implementation is very complicated. As we all know, whether it is temporal or spatial filtering, there are many mature algorithms available. Therefore, our main problem is to choose a filtering algorithm suitable for use in noncooperative communication conditions for signal separation. Under noncooperative communication conditions, since the receiving system receives unknown signals including the number of signals and signal parameters, the signal detection part can only provide the number of signals and the center frequency or direction of arrival of each signal, etc.The basic idea of the multisignal modulation recognition method with signal separation as preprocessing is to transform the multiple signal processing problem into multiple single signal processing. For a plurality of signals that are time domain separable, this is actually a single signal modulation recognition problem; for a plurality of signals that are frequency and space separable, the appropriate time-space filtering methods can be used to separate the signals one by one and then use the single signal modulation recognition method to recognize the modulation form of each signal; when multiple signals are associated in time domain, frequency domain, and space domain, only other signal processing methods can be used to separate each signal, such as independent component analysis. Recognition of multisignal modulation, which extracts each signal feature directly, differs from the method based on signal separation. However, since many signals are completely aliased in the time domain, it is usually necessary to distinguish features in the transform domain, such as a multisignal modulation recognition method based on a periodic spectrum, etc. The proposed method based on the AR or GAR model in this article uses cochannel observation Limited data parameter modeling technology and the specificity of the solution of AR or GAR model parameters, feature extraction is entirely carried out in the time domain, so it can be considered direct.At present, many kinds of denoising algorithms have been applied to the denoising of mixed electromagnetic signals, especially the wavelet denoising algorithm has become mature day by day, but the energy of mixed electromagnetic signals is mainly distributed in the high frequency band, while the wavelet transform is mainly used for the low frequency band. The resolution of wavelet packet transformation is higher than that of wavelet analysis, and the frequency domain is more detailed, which can determine the frequency contained in the signal. In this paper, a wavelet packet algorithm with improved threshold function is first used to reduce noise [26]. Although this method has a good denoising effect, the method lacks a certain degree of adaptability due to its fixed basis function and constant multiresolution. The signal is related to the measurement system and the measurement environment, which causes some difficulties in the selection of wavelet packet basis functions. The empirical mode decomposition (EMD) method processes the signal adaptively, which is suitable for the processing of nonstationary signals. In recent years, many scholars have applied the empirical mode decomposition algorithm to the denoising of mixed electromagnetic signals. Therefore, on this basis, this paper applies the EMD denoising algorithm based on the combination of autocorrelation function and interval threshold to the processing of mixed electromagnetic signal.


### 2.2. Wavelet Packet Denoising Algorithm

Under the wavelet packet transform, the white noise and the mixed electromagnetic signal show different change characteristics with the scale transformation. Choose an appropriate threshold to process the wavelet packet coefficients: keep the wavelet packet coefficients larger than the threshold, and discard the coefficients smaller than the threshold. The wavelet packet threshold denoising process is shown in the flowchart.It can be seen from the flowchart (Figure1) that to obtain a better denoising effect, the main thing is the selection of the threshold and the design of the threshold function. The wavelet packet coefficients smaller than the threshold are discarded, and the coefficients larger than the threshold are used to reconstruct the signal. If the threshold is too large, the signal energy loss is too much; if the threshold is too small, the filtering effect will not be too good.Figure 1
Flowchart of wavelet packet threshold denoising.


### 2.3. Simulation Analysis of Electromagnetic Signal

It can be seen from the denoising effect that the wavelet packet algorithm after the improved threshold causes greater waveform distortion and filters out some weak discharge pulse signals, while the EMD denoising based on the combination of autocorrelation function and interval threshold has less distortion. Therefore, the EMD denoising effect based on the combination of the autocorrelation function and the interval threshold is better. Figures2–7 are the simulation analysis process and results of signal denoising.Figure 2
Measured mixed signal denoising results.Figure 3
Sampling period square wave signal.Figure 4
Carrier frequency signal.Figure 5
Modulated signal.Figure 6
The effect of point targets on electromagnetic signals.Figure 7
Electromagnetic signal scattered back to the antenna by the target.


## 2.1. Decompression Process Design

During the detection of mixed electromagnetic signals, there are many electromagnetic interferences on site. Usually, there are pulse electromagnetic interference signals, white noise, and periodic narrowband electromagnetic interference signals. Pulse electromagnetic interference signals can be divided into random and periodic pulse electromagnetic interference signals. Among them, the periodic pulse electromagnetic interference signal mainly comes from electromagnetic interference caused by the action of the SCR device. Random electromagnetic interference signals are generally electromagnetic interference generated by lightning and relays. White noise interference is mainly a variety of random noise, including noise interference generated by transmission lines and thermal noise of windings. Periodic narrowband interference is mainly electromagnetic interference signals such as radio communication and carrier communication.In the currently published related literature, research on the recognition of modulation of communication signals is carried out basically on the assumption that there is only one signal in the same receiving channel. In fact, with the widespread popularity of radio communication in military and civilian fields, signals in the radiocommunication frequency band are becoming denser, coupled with the presence of a large number of intentional or unintentional interfering signals, even in ordinary narrowband communication receivers, both appear in the same. It is difficult to avoid the phenomenon of more than one signal, and it is extremely common to have many signals simultaneously in special broadband receivers such as electronic reconnaissance and radio monitoring. In this case, the current modulation technology is no longer applicable and it is necessary to learn new methods, process the observation data appropriately, and determine the modulation form of each signal. It is a problem of recognizing the modulation of many signals in the same channel.In particular, multisignal modulation recognition refers to the following: in noncooperative communication or communication, the observation data received by the receiver (typically a sampling sequence derived from the receiver’s intermediate frequency) contains two or more noise contaminated modulated signals, based on an evaluation of the presence or absence of a signal, estimation number of signals (signal detection), and estimating some parameters (parameter estimation) such as center frequency and signal bandwidth using a particular method for determining the received or modulation type of the signal of interest. It can be seen that multiple signals to be identified are completely associated in the time domain; therefore, existing modulation identification algorithms for a single signal cannot be directly used for multisignal modulation identification.These noise interferences are usually less than 200 MHz, and there are relatively few interference sources in ultrahigh frequency electromagnetic waves, mainly mobile phone mobile communication interference, such as GSM wave is 900 MHz, but its frequency band is fixed. Although the UHF electromagnetic wave method can effectively avoid a large amount of electromagnetic interference, there will still be other electromagnetic interference signals on site. These electromagnetic interference signals have similar characteristics to white noise [25]. In this paper, white noise signals are used to simulate electromagnetic interference signals around the scene. Because the mixed electromagnetic signal is very weak and its signal-to-noise ratio is very low, effective denoising can keep the mixed electromagnetic signal at a low distortion rate, so that the recognition result of the mixed electromagnetic signal will not be affected.Regardless of whether single-channel or multichannel reception is used, the collected observation data is a mixed waveform of the plurality of signals to be identified and additional noise, and appropriate preprocessing is required prior to processing. In signal processing, preprocessing in the narrow sense mainly refers to simple data processing such as subtracting the mean value, removing outliers, and eliminating trend elements from the original observation data to facilitate subsequent signal processing. In this article, in addition to the basic data processing mentioned above, preprocessing is mainly concerned with the separation of multiple signals, i.e., the application of appropriate temporal filtering or spatial filtering methods such as FIR filters or beamforming to aliasing multiple signals in the time domain. Identified signals are separated from them. Mixed runs one by one. Its purpose is to turn the multisignal identification problem into the multisignal identification problem and then use the existing modulation identification method proposed for a single signal to identify the modulation form of each separated signal and realize the multisignal modulation identification. At the same time, filtering can also improve the signal-to-noise ratio of the identified signal, so it is beneficial to improve the efficiency of modulation identification. For a complete multisignal modulation recognition process, the separation of multiple signals is only preprocessing.In practical applications, the specific method of signal separation used depends on the distribution characteristics of the plurality of signals to be identified in a mixed waveform in the frequency domain and in the spatial domain. In the case of multiple signals that can be separated in the frequency domain, a relatively simple separation method based on time filtering can be used, and at the same time, only a single-channel receiving system is required to obtain observation data of the multiple signals. To identify a plurality of signals that can be separated in the spatial domain, whether or not the frequency domain can be separated, a spatial filtering-based separation method can be used. A complex receiving system is required. Receive these signals. Of course, the latter method is a more versatile method of signal separation than the former, but its implementation is very complicated. As we all know, whether it is temporal or spatial filtering, there are many mature algorithms available. Therefore, our main problem is to choose a filtering algorithm suitable for use in noncooperative communication conditions for signal separation. Under noncooperative communication conditions, since the receiving system receives unknown signals including the number of signals and signal parameters, the signal detection part can only provide the number of signals and the center frequency or direction of arrival of each signal, etc.The basic idea of the multisignal modulation recognition method with signal separation as preprocessing is to transform the multiple signal processing problem into multiple single signal processing. For a plurality of signals that are time domain separable, this is actually a single signal modulation recognition problem; for a plurality of signals that are frequency and space separable, the appropriate time-space filtering methods can be used to separate the signals one by one and then use the single signal modulation recognition method to recognize the modulation form of each signal; when multiple signals are associated in time domain, frequency domain, and space domain, only other signal processing methods can be used to separate each signal, such as independent component analysis. Recognition of multisignal modulation, which extracts each signal feature directly, differs from the method based on signal separation. However, since many signals are completely aliased in the time domain, it is usually necessary to distinguish features in the transform domain, such as a multisignal modulation recognition method based on a periodic spectrum, etc. The proposed method based on the AR or GAR model in this article uses cochannel observation Limited data parameter modeling technology and the specificity of the solution of AR or GAR model parameters, feature extraction is entirely carried out in the time domain, so it can be considered direct.At present, many kinds of denoising algorithms have been applied to the denoising of mixed electromagnetic signals, especially the wavelet denoising algorithm has become mature day by day, but the energy of mixed electromagnetic signals is mainly distributed in the high frequency band, while the wavelet transform is mainly used for the low frequency band. The resolution of wavelet packet transformation is higher than that of wavelet analysis, and the frequency domain is more detailed, which can determine the frequency contained in the signal. In this paper, a wavelet packet algorithm with improved threshold function is first used to reduce noise [26]. Although this method has a good denoising effect, the method lacks a certain degree of adaptability due to its fixed basis function and constant multiresolution. The signal is related to the measurement system and the measurement environment, which causes some difficulties in the selection of wavelet packet basis functions. The empirical mode decomposition (EMD) method processes the signal adaptively, which is suitable for the processing of nonstationary signals. In recent years, many scholars have applied the empirical mode decomposition algorithm to the denoising of mixed electromagnetic signals. Therefore, on this basis, this paper applies the EMD denoising algorithm based on the combination of autocorrelation function and interval threshold to the processing of mixed electromagnetic signal.


## 2.2. Wavelet Packet Denoising Algorithm

Under the wavelet packet transform, the white noise and the mixed electromagnetic signal show different change characteristics with the scale transformation. Choose an appropriate threshold to process the wavelet packet coefficients: keep the wavelet packet coefficients larger than the threshold, and discard the coefficients smaller than the threshold. The wavelet packet threshold denoising process is shown in the flowchart.It can be seen from the flowchart (Figure1) that to obtain a better denoising effect, the main thing is the selection of the threshold and the design of the threshold function. The wavelet packet coefficients smaller than the threshold are discarded, and the coefficients larger than the threshold are used to reconstruct the signal. If the threshold is too large, the signal energy loss is too much; if the threshold is too small, the filtering effect will not be too good.Figure 1
Flowchart of wavelet packet threshold denoising.


## 2.3. Simulation Analysis of Electromagnetic Signal

It can be seen from the denoising effect that the wavelet packet algorithm after the improved threshold causes greater waveform distortion and filters out some weak discharge pulse signals, while the EMD denoising based on the combination of autocorrelation function and interval threshold has less distortion. Therefore, the EMD denoising effect based on the combination of the autocorrelation function and the interval threshold is better. Figures2–7 are the simulation analysis process and results of signal denoising.Figure 2
Measured mixed signal denoising results.Figure 3
Sampling period square wave signal.Figure 4
Carrier frequency signal.Figure 5
Modulated signal.Figure 6
The effect of point targets on electromagnetic signals.Figure 7
Electromagnetic signal scattered back to the antenna by the target.


## 3. Feature Extraction of Mixed Electromagnetic Signals Based on EMD Decomposition

### 3.1. EMD Decomposition Analysis of Mixed Electromagnetic Signals

The mixed electromagnetic signal is denoised preprocessing first, and then, the EMD decomposition is carried out, but there will be overdecomposition and false components in the EMD decomposition, which will result in excessive extraction of the feature quantity of the mixed electromagnetic signal. Theoretically, the eigenmode function components of each order obtained by EMD decomposition are the actual components of the original signal, and due to the limited signal length and the criteria for termination of screening, there are errors between the actual signal components and the eigenmode function components.. Through analysis, it can be found that although there are errors between the two, they must be similar and there will be correlation. The difference between the actual signal component and the IMF component causes the false component to be generated. The correlation between the false component and the actual signal will be very small, and it can be judged by the correlation analysis between each component and the original signal. In addition, the EMD decomposition of the actual mixed electromagnetic signal has more IMF components, and the following IMF components also contain relatively little information. The main information components can be selected to extract their characteristic parameters. Therefore, the correlation coefficient can be used to select the main IMF components.


### 3.2. Feature Extraction of the Fractal Dimension of Mixed Electromagnetic Signals Based on EMD

In 1977, the fractal theory was proposed by the American mathematician Mandelbrot. This theory is very suitable for solving nonlinear problems and has been widely used in engineering, signal processing, computers, and other fields. The fractal fractus is derived from the Latin fractus, which means fragmentation and division. The concept of fractal provides a new way of thinking about the relationship between the whole and the part and provides a tool for analyzing complex things in nature. Fractal dimension is the main characteristic parameter of fractal theory and the main tool to describe fractal bodies with complex structures. People call those noninteger dimensions as fractal dimensions. Fractal dimensions mainly describe the complexity and irregularity of fractal sets.Fractal dimensions have the following basic properties:(1)
The fractal dimensionD has nothing to do with scale(2)
The fractal dimensionD is a relative quantity(3)
The fractal dimensionD reflects the irregularity, fineness, and complexity of the contour in the space. The larger the D value, the richer the details, and the smaller the D value, the less the detailsAt present, the main measurement tool in fractal signal processing technology [65, 66] is the fractal dimension. The fractal dimension can measure the irregularity of the signal. In addition, the fractal dimension can remain unchanged under multiscale and multiresolution changes. The noninteger nature of the fractal dimension is used to indicate the smoothness of the signal. The smaller theD, the smoother the signal; the larger the D, the rougher the signal. There are many ways to calculate the fractal dimension, such as box dimension, Hausdorff dimension, similarity dimension, correlation dimension, information dimension, Lyapunov dimension, and Perkin dimension.The EMD method can linearly solve the nonlinear signal problem and smoothly solve the nonstationary signal, while the mixed electromagnetic signal is a sudden change signal, and different discharge types have different frequency information. The discharge signal can be processed by EMD decomposition. Because EMD is adaptively decomposed according to the local characteristic information of the mixed electromagnetic signal itself, the obtained eigenmode function (IMF) not only contains the different characteristic scale information of the mixed electromagnetic signal but also the local characteristic information of the signal, so it can reflect the discharge essential information. The denoised mixed electromagnetic signal is decomposed by EMD to obtainn IMF components. The IMF components of each order represent different frequency bands. The discharge information contained in different frequency bands is different, and the performance complexity is also different. This makes different frequency bands different.The fractal characteristics of the frequency bands are different, that is, the fractal dimensions of the discharge signals in different frequency bands are different. Therefore, the fractal dimension ofkk<n IMF components containing the main information can be calculated as the feature quantity.The improved difference box counting method is used to calculate the fractal dimension of the IMF component containing the main information of the mixed electromagnetic signal, and the eigenvector can be obtained. In order to better process the signal later, the fractal dimension of the IMF component of the mixed electromagnetic signal is normalized, and because the fractal dimension is distributed in the range of 1 to 2, the actual fractal dimension is reduced. The fractal dimensions of each order of eigenmode components of different discharge types are quite different. The fractal dimension distribution of corona discharge and creeping discharge is relatively concentrated, while the fractal dimension distribution of the first two IMF components of the air gap discharge is relatively concentrated, and the fractal dimension of the latter IMF is relatively different from the other two discharges.


#### 3.2.1. Feature Extraction of Singular Value Decomposition of Mixed Electromagnetic Signals Based on EMD

Singular value decomposition (SVD) has become an important method of modern signal processing. In signal processing, it can reflect the situation of signal inclusion and energy concentration. The extraction of feature quantities based on singular values is widely used in signal noise reduction and vibration signal analysis [27].The collected mixed electromagnetic signals are preprocessed for denoising first, and the denoised partial electromagnetic signals are decomposed by EMD to obtainn IMF components. Because the IMF components of each order represent different frequency bands, the discharge information contained in different frequency bands is different. Therefore, kk<n IMF components containing main information can be formed into an eigenvector matrix. Singular values have better stability. When the elements in the matrix have small changes, their singular values also have small changes. The singular value obtained by singular value decomposition can reflect the concentration of the energy of the IMF component in the original matrix (intrinsic mode matrix), so the energy of the IMF component can be judged by the magnitude of the singular value. The feature extraction of singular value decomposition of mixed electromagnetic signals based on EMD is to use the IMF components (including main information) obtained by EMD decomposition to construct an eigenmode matrix for singular value decomposition and obtain singular values that can reflect the energy concentration of IMF components. As the feature quantity, pattern recognition is performed.


## 3.1. EMD Decomposition Analysis of Mixed Electromagnetic Signals

The mixed electromagnetic signal is denoised preprocessing first, and then, the EMD decomposition is carried out, but there will be overdecomposition and false components in the EMD decomposition, which will result in excessive extraction of the feature quantity of the mixed electromagnetic signal. Theoretically, the eigenmode function components of each order obtained by EMD decomposition are the actual components of the original signal, and due to the limited signal length and the criteria for termination of screening, there are errors between the actual signal components and the eigenmode function components.. Through analysis, it can be found that although there are errors between the two, they must be similar and there will be correlation. The difference between the actual signal component and the IMF component causes the false component to be generated. The correlation between the false component and the actual signal will be very small, and it can be judged by the correlation analysis between each component and the original signal. In addition, the EMD decomposition of the actual mixed electromagnetic signal has more IMF components, and the following IMF components also contain relatively little information. The main information components can be selected to extract their characteristic parameters. Therefore, the correlation coefficient can be used to select the main IMF components.


## 3.2. Feature Extraction of the Fractal Dimension of Mixed Electromagnetic Signals Based on EMD

In 1977, the fractal theory was proposed by the American mathematician Mandelbrot. This theory is very suitable for solving nonlinear problems and has been widely used in engineering, signal processing, computers, and other fields. The fractal fractus is derived from the Latin fractus, which means fragmentation and division. The concept of fractal provides a new way of thinking about the relationship between the whole and the part and provides a tool for analyzing complex things in nature. Fractal dimension is the main characteristic parameter of fractal theory and the main tool to describe fractal bodies with complex structures. People call those noninteger dimensions as fractal dimensions. Fractal dimensions mainly describe the complexity and irregularity of fractal sets.Fractal dimensions have the following basic properties:(1)
The fractal dimensionD has nothing to do with scale(2)
The fractal dimensionD is a relative quantity(3)
The fractal dimensionD reflects the irregularity, fineness, and complexity of the contour in the space. The larger the D value, the richer the details, and the smaller the D value, the less the detailsAt present, the main measurement tool in fractal signal processing technology [65, 66] is the fractal dimension. The fractal dimension can measure the irregularity of the signal. In addition, the fractal dimension can remain unchanged under multiscale and multiresolution changes. The noninteger nature of the fractal dimension is used to indicate the smoothness of the signal. The smaller theD, the smoother the signal; the larger the D, the rougher the signal. There are many ways to calculate the fractal dimension, such as box dimension, Hausdorff dimension, similarity dimension, correlation dimension, information dimension, Lyapunov dimension, and Perkin dimension.The EMD method can linearly solve the nonlinear signal problem and smoothly solve the nonstationary signal, while the mixed electromagnetic signal is a sudden change signal, and different discharge types have different frequency information. The discharge signal can be processed by EMD decomposition. Because EMD is adaptively decomposed according to the local characteristic information of the mixed electromagnetic signal itself, the obtained eigenmode function (IMF) not only contains the different characteristic scale information of the mixed electromagnetic signal but also the local characteristic information of the signal, so it can reflect the discharge essential information. The denoised mixed electromagnetic signal is decomposed by EMD to obtainn IMF components. The IMF components of each order represent different frequency bands. The discharge information contained in different frequency bands is different, and the performance complexity is also different. This makes different frequency bands different.The fractal characteristics of the frequency bands are different, that is, the fractal dimensions of the discharge signals in different frequency bands are different. Therefore, the fractal dimension ofkk<n IMF components containing the main information can be calculated as the feature quantity.The improved difference box counting method is used to calculate the fractal dimension of the IMF component containing the main information of the mixed electromagnetic signal, and the eigenvector can be obtained. In order to better process the signal later, the fractal dimension of the IMF component of the mixed electromagnetic signal is normalized, and because the fractal dimension is distributed in the range of 1 to 2, the actual fractal dimension is reduced. The fractal dimensions of each order of eigenmode components of different discharge types are quite different. The fractal dimension distribution of corona discharge and creeping discharge is relatively concentrated, while the fractal dimension distribution of the first two IMF components of the air gap discharge is relatively concentrated, and the fractal dimension of the latter IMF is relatively different from the other two discharges.


### 3.2.1. Feature Extraction of Singular Value Decomposition of Mixed Electromagnetic Signals Based on EMD

Singular value decomposition (SVD) has become an important method of modern signal processing. In signal processing, it can reflect the situation of signal inclusion and energy concentration. The extraction of feature quantities based on singular values is widely used in signal noise reduction and vibration signal analysis [27].The collected mixed electromagnetic signals are preprocessed for denoising first, and the denoised partial electromagnetic signals are decomposed by EMD to obtainn IMF components. Because the IMF components of each order represent different frequency bands, the discharge information contained in different frequency bands is different. Therefore, kk<n IMF components containing main information can be formed into an eigenvector matrix. Singular values have better stability. When the elements in the matrix have small changes, their singular values also have small changes. The singular value obtained by singular value decomposition can reflect the concentration of the energy of the IMF component in the original matrix (intrinsic mode matrix), so the energy of the IMF component can be judged by the magnitude of the singular value. The feature extraction of singular value decomposition of mixed electromagnetic signals based on EMD is to use the IMF components (including main information) obtained by EMD decomposition to construct an eigenmode matrix for singular value decomposition and obtain singular values that can reflect the energy concentration of IMF components. As the feature quantity, pattern recognition is performed.


## 3.2.1. Feature Extraction of Singular Value Decomposition of Mixed Electromagnetic Signals Based on EMD

Singular value decomposition (SVD) has become an important method of modern signal processing. In signal processing, it can reflect the situation of signal inclusion and energy concentration. The extraction of feature quantities based on singular values is widely used in signal noise reduction and vibration signal analysis [27].The collected mixed electromagnetic signals are preprocessed for denoising first, and the denoised partial electromagnetic signals are decomposed by EMD to obtainn IMF components. Because the IMF components of each order represent different frequency bands, the discharge information contained in different frequency bands is different. Therefore, kk<n IMF components containing main information can be formed into an eigenvector matrix. Singular values have better stability. When the elements in the matrix have small changes, their singular values also have small changes. The singular value obtained by singular value decomposition can reflect the concentration of the energy of the IMF component in the original matrix (intrinsic mode matrix), so the energy of the IMF component can be judged by the magnitude of the singular value. The feature extraction of singular value decomposition of mixed electromagnetic signals based on EMD is to use the IMF components (including main information) obtained by EMD decomposition to construct an eigenmode matrix for singular value decomposition and obtain singular values that can reflect the energy concentration of IMF components. As the feature quantity, pattern recognition is performed.


## 4. Conclusion

According to the characteristics of the mixed electromagnetic signal, firstly, the wavelet packet denoising is used to improve the deficiencies of the wavelet packet threshold function. Through the denoising processing verification of the partial discharge simulation signal, the wavelet packet algorithm of the soft threshold function is used to denoise. The signal-to-noise ratio is 8.962, and the waveform correlation coefficient is 0.968. The wavelet packet denoising after the improved threshold function has a signal-to-noise ratio of 11.150 and a waveform correlation coefficient of 0.971, which suppresses the oscillation phenomenon caused by the wavelet packet transform. Due to the relatively fixed basis function of wavelet packet and constant multiresolution, the wavelet packet algorithm lacks adaptability, and the mixed electromagnetic signal is related to the measurement system and the measurement environment, which causes some difficulties in the selection of the wavelet packet basis function.This paper applies the EMD denoising method based on the combination of autocorrelation function and interval threshold to the denoising of mixed electromagnetic signals and compares the denoising of partial discharge simulation signals through the EMD combined with autocorrelation function and soft threshold. The results are as follows: the signal-to-noise ratio of the EMD denoising with the combination of autocorrelation and interval threshold is 11.345, and the waveform correlation coefficient is 0.974; the signal-to-noise ratio of the EMD denoising with the combination of autocorrelation function and soft threshold is 9.712. Therefore, the EMD with the combination of autocorrelation and interval threshold has a better denoising effect. Finally, the EMD algorithm combining the autocorrelation function and the interval threshold and the wavelet packet algorithm after the improved threshold function are used to denoise the actual mixed electromagnetic signal. It is found that the EMD denoising effect based on the combination of the autocorrelation function and the interval threshold is better. The waveform distortion rate is lower, and it has good adaptability. Therefore, this method is used to denoise the mixed electromagnetic signal and achieve a good denoising effect. EMD decomposition of the mixed electromagnetic signal caused by three different insulation defects, and use the correlation coefficient method to determine the eigenmode component containing the main information, and construct the two eigenmodes of the mixed electromagnetic signal by calculating its fractal dimension and singular value. As feature quantity, through the discovery of two identification methods, singular value as a feature quantity, its recognition rate is higher.



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*Source: 3693790-2022-05-12.xml*