A Radar Active Jamming Identification Method Based on Multi-Domain Features and Decision Trees

Abstract

This invention belongs to the fields of radar electronic countermeasures, data classification, and signal recognition technology, and relates to a radar active jamming identification method based on multi-domain features and decision trees. It includes: obtaining high-dimensional feature vectors for each jamming signal from the time domain, frequency domain, wavelet domain, and bispectral domain; treating the high-dimensional feature vectors as data samples and labeling all samples to obtain a labeled dataset; standardizing the dataset and dividing it into training and test sets; in the feature selection stage, using the RF algorithm to select the optimal feature subsets for the training and test sets from the multi-domain feature dataset; and in the XGBoost training stage, constructing and training the XGBoost classifier. This method can effectively identify various types of active jamming; it improves the identification accuracy and generalization ability, reduces computational overhead, and enhances the accuracy and robustness of active jamming identification.

Description

Technical Field

[0001] This invention relates to a radar active jamming identification method based on multi-domain features and decision trees, and more particularly to a radar active jamming identification method based on a cascaded Random Forest (RF) algorithm and Extreme Gradient Boosting (XGBoost) algorithm, belonging to the fields of radar electronic countermeasures, data classification and signal recognition technology. Background Technology

[0002] In recent years, radar jamming techniques have become increasingly sophisticated and flexible, posing a significant threat to radar survivability. Active radar jamming, in particular, involves jammers actively emitting electromagnetic waves to suppress target echoes or deceive the radar with false target echoes, severely impacting radar operation. Especially with the continuous development of digital radio frequency storage technology, jammers can generate numerous highly realistic deceptive jamming signals that mimic radar target echoes through storage, modulation, and forwarding, greatly increasing the difficulty of radar anti-jamming. Jamming identification, as a prerequisite and crucial step in the radar anti-jamming process, determines the effectiveness of anti-jamming measures. Traditional radar jamming identification requires operators to judge the extent of radar interference based on experience, resulting in identification results heavily influenced by subjective experience and poor real-time performance and reliability. Furthermore, most methods are only applicable to traditional and single types of jamming, offering limited capabilities for identifying novel types such as intermittent sampling and forwarding jamming. Therefore, researching active radar jamming identification technology is of great practical significance in addressing the limitations of traditional jamming identification algorithms in accurately identifying new types of jamming and their low level of intelligence.

[0003] Currently, the problem of radar active interference identification can be viewed as a pattern recognition problem. Specifically, it involves analyzing the generation mechanism of radar interference, extracting effective features, and designing a reasonable classifier to identify the interference type. Feature extraction-based active interference identification methods are widely used and have achieved significant results. However, some problems still need to be solved. Regarding feature extraction, single-dimensional feature extraction is insufficient to handle the identification of multiple interference types, and it is difficult to extract robust and effective features under severe noise conditions. Regarding classifiers, most feature extraction-based interference identification methods are usually combined with machine learning methods, utilizing classifiers such as decision trees, support vector machines, and backpropagation neural networks. Although these classifiers perform well in radar active interference identification, they target relatively limited interference types and perform poorly in noisy environments, resulting in low identification accuracy. Furthermore, to more comprehensively reflect the characteristics of interference signals, multi-domain features are often extracted; however, high-dimensional feature vectors can easily lead to information redundancy and even the curse of dimensionality. Therefore, effective dimensionality reduction processing is needed before classification. Principal component analysis, a commonly used feature extraction method in dimensionality reduction, reduces computational complexity to some extent. However, it maps the original feature space to another feature space, and the physical meaning of the new features is different from that of the original features, resulting in weak interpretability and an unromantic dimensionality reduction process.

[0004] This invention aims to solve the problems of high-dimensional feature vector redundancy and low recognition accuracy in the above-mentioned active interference identification methods based on feature extraction. It proposes a radar active interference identification method based on multi-domain features and decision trees, which can effectively identify various types of interference under harsh noise environments. Summary of the Invention

[0005] The purpose of this invention is to address the problems of existing radar active jamming identification methods, such as the difficulty in effectively distinguishing various jamming types, especially novel jamming, due to the limitations of multi-domain features, the redundancy of high-dimensional feature vectors extracted from multiple domains, and the low identification accuracy under harsh noise environments. This invention proposes a radar active jamming identification method based on multi-domain features and a decision tree. The decision tree-based method is a cascaded RF and XGBoost method, hereinafter referred to as RF-XGBoost.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] The radar active jamming identification method includes a multi-domain feature extraction stage, a multi-domain feature dataset construction stage, a feature selection stage, and an XGBoost training and classification stage. The multi-domain feature extraction stage extracts features from the jamming signal in the time domain, frequency domain, fractal domain, wavelet domain, and bispectral domain to obtain high-dimensional feature vectors. The multi-domain feature dataset construction stage labels the obtained high-dimensional feature vectors with jamming types and divides the dataset into training and testing datasets. The feature selection stage uses the RF algorithm to select features from the feature dataset, obtaining training and testing sets. The XGBoost training and classification stage trains the feature-selected training set and tests the data in the testing set to identify the type of active jamming.

[0008] The radar active interference identification method includes:

[0009] S1. In the multi-domain feature extraction stage, for the interference signal, extract time-domain skewness, time-domain kurtosis, normalized instantaneous amplitude absolute value standard deviation, normalized instantaneous frequency absolute value standard deviation, time-domain envelope undulation, and fast pulse modulation coefficients from the time domain; extract box dimension and information dimension from the fractal domain; extract frequency-domain skewness, frequency-domain kurtosis, frequency-domain envelope undulation, additive white Gaussian noise factor, carrier factor, spectral information entropy, spectral exponential entropy, and spectral norm entropy from the frequency domain; extract the energy proportion of low-frequency approximation coefficients, the energy proportion of high-frequency detail coefficients, wavelet energy spectrum entropy, and wavelet variance from the wavelet domain; and extract bispectral entropy, contour integral bispectral mean, contour integral bispectral variance, and bispectral waveform entropy from the bispectral domain to obtain the high-dimensional feature vector of each interference signal.

[0010] S2. The multi-domain feature dataset construction phase completes the construction of the feature dataset, specifically as follows:

[0011] S21. Take the high-dimensional feature vector of each interference signal in S1 as a data sample, and label all samples to obtain a labeled dataset.

[0012] S22. Standardize the dataset in S21;

[0013] S3. In the feature selection stage, the RF algorithm is used to select features from the multi-domain feature dataset in S2 to obtain the optimal feature subset. The dataset is then divided into training and test sets, specifically:

[0014] S31, the RF algorithm obtains multiple samples through random resampling;

[0015] The random resampling described in S31 specifically involves: randomly selecting N data points with replacement from the dataset and using them as a single sample.

[0016] S32. Construct a decision tree based on the samples in S31;

[0017] S33. Repeat S31 and S32 M times to generate M decision trees, forming a random forest;

[0018] S34. Calculate the importance score of each feature in S2 in the random forest in S33, complete the feature selection, and obtain the optimal feature subset;

[0019] The feature selection process involves calculating the importance score of each feature based on the Gini coefficient, sorting the features in descending order according to their importance scores, and eliminating features with low importance according to certain criteria.

[0020] S35. Divide the optimal feature subset in S34 into a training set and a test set according to a certain ratio;

[0021] Thus, from S31 to S34, the feature selection stage obtains the optimal feature subset and the training and test sets;

[0022] S4. The XGBoost training phase completes the construction and training of the XGBoost classifier, specifically as follows:

[0023] S41. Set the number of decision trees, decision tree depth, learning rate, penalty term coefficient γ, and regularization term coefficient λ of the XGBoost classifier to obtain the initial XGBoost classifier;

[0024] S42. Input the training set after feature selection in S3 into the initial XGBoost classifier. After training, the optimal XGBoost classifier is obtained.

[0025] In the S5 and XGBoost classification stages, the test set after feature selection in S3 is input into the optimal XGBoost classifier, which outputs the active interference type to achieve the identification of radar active interference.

[0026] The extraction of time-domain skewness, time-domain kurtosis, normalized instantaneous amplitude absolute standard deviation, normalized instantaneous frequency absolute standard deviation, time-domain envelope ripple, and fast pulse modulation coefficients from the time domain specifically includes:

[0027] The extraction of time-domain skewness from the time domain specifically involves: calculating the mean and standard deviation of the time-domain interference signal, subtracting the mean from the time-domain interference signal, dividing by the standard deviation, and then taking the mean of the third power to obtain the time-domain skewness.

[0028] The extraction of time-domain kurtosis from the time domain specifically involves: calculating the mean and standard deviation of the time-domain interference signal, subtracting the mean from the time-domain interference signal, dividing by the standard deviation, and then taking the mean of the fourth power to obtain the time-domain kurtosis.

[0029] The extraction of the standard deviation of the normalized instantaneous amplitude absolute value from the time domain is specifically as follows: based on the analytical expression of the time-domain interference signal obtained by Hilbert transform, the instantaneous amplitude is further calculated and the zero-center normalized instantaneous amplitude is calculated to obtain the standard deviation of the normalized instantaneous amplitude absolute value.

[0030] The step of extracting the normalized instantaneous frequency absolute standard deviation from the time domain specifically involves: extracting the instantaneous frequency of the interference signal and normalizing it to obtain the normalized instantaneous frequency absolute standard deviation.

[0031] The extraction of time-domain envelope variability from the time domain specifically involves: obtaining the signal analytical expression based on the Hilbert transform; the sum of the squares of the real part and the squares of the imaginary part of the signal analytical expression is the instantaneous envelope sum of squares; and further obtaining the time-domain envelope variability based on the ratio of the variance to the square of the mean of the instantaneous envelope sum of squares.

[0032] The extraction of fast intra-pulse modulation coefficients from the time domain specifically involves: calculating the autocorrelation function of the interference signal, taking the autocorrelation function values ​​of equally spaced sampling points of the interference signal, and calculating the fast intra-pulse modulation coefficients according to the definition of fast intra-pulse modulation coefficients.

[0033] The extraction of box dimension and information dimension from the fractal domain specifically includes:

[0034] The extraction of box dimension from the fractal domain specifically involves: performing spatial measurement on the temporal interference signal, selecting an appropriate box length, and ensuring that multiple boxes cover the entire interference signal to calculate the box dimension.

[0035] The extraction of information dimension from the fractal domain specifically involves: performing forward differencing on the interference signal to obtain the reconstructed signal, calculating the probability that the reconstructed signal falls into each box, and obtaining the information dimension using the Shannon information entropy formula.

[0036] The feature extraction from the frequency domain first involves performing a Fast Fourier Transform on the interference signal to obtain the signal spectrum and signal power spectrum, and then normalizing them. Then, it extracts frequency domain skewness, frequency domain kurtosis, frequency domain envelope ripple, additive white Gaussian noise factor, carrier factor, spectral information entropy, spectral exponential entropy, and spectral norm entropy from the frequency domain, specifically including:

[0037] The extraction of frequency domain skewness from the frequency domain specifically involves: calculating the mean and standard deviation of the signal power spectrum, subtracting the mean from the signal power spectrum and dividing by the standard deviation, then taking the mean of the third power to obtain the frequency domain skewness.

[0038] The extraction of frequency domain kurtosis from the frequency domain specifically involves: calculating the mean and standard deviation of the signal power spectrum, subtracting the mean from the signal power spectrum and dividing by the standard deviation, then taking the mean to the power of 4 to obtain the frequency domain kurtosis.

[0039] The extraction of frequency domain envelope undulation from the frequency domain specifically involves: obtaining the analytical expression of the signal power spectrum based on the Hilbert transform; the sum of the squares of the real part and the squares of the imaginary part of the analytical expression of the signal power spectrum is the instantaneous envelope sum of squares; and further obtaining the frequency domain envelope undulation based on the ratio of the variance to the square of the mean of the instantaneous envelope sum of squares.

[0040] The extraction of additive white Gaussian noise factors from the frequency domain is specifically as follows: First, the mean E1 of the signal power spectrum is calculated; second, the mean E2 of the portion of the signal power spectrum that is greater than the mean E1 is calculated; then, the mean E3 of the portion of the signal power spectrum that is greater than E2 is calculated; finally, two additive white Gaussian noise factors are obtained: the difference between E2 and E1 divided by E1 and the difference between E3 and E2 divided by E1.

[0041] The process of extracting the carrier factor from the frequency domain specifically involves: calculating the maximum and second-largest values ​​of the signal spectrum, and then taking the ratio of the maximum and second-largest values ​​to obtain the carrier factor;

[0042] The extraction of spectral information entropy from the frequency domain is specifically achieved by calculating the probability value of each frequency resolution unit in the signal spectrum and then obtaining the spectral information entropy according to the Shannon information entropy formula.

[0043] The extraction of spectral exponential entropy from the frequency domain is specifically achieved by calculating the probability value of each frequency resolution unit in the signal spectrum and then obtaining the spectral exponential entropy according to the exponential entropy formula.

[0044] The extraction of spectral norm entropy from the frequency domain is specifically achieved by calculating the p-th power of the signal spectrum and summing the results.

[0045] The feature extraction process in the wavelet domain first involves performing J-level wavelet decomposition on the interference signal to obtain the low-frequency approximation coefficients and high-frequency detail coefficients of the signal at J scales. Then, the total signal energy, the energy of the low-frequency approximation coefficients, and the energy of the high-frequency detail coefficients are calculated. Finally, the energy proportions of the low-frequency approximation coefficients, the high-frequency detail coefficients, the wavelet energy spectral entropy, and the wavelet variance are extracted. Specifically, this includes:

[0046] The extraction of the energy proportion of low-frequency approximation coefficients from the wavelet domain specifically involves: calculating the energy proportion of low-frequency approximation coefficients based on the ratio of the energy of the low-frequency approximation coefficients to the total energy after J-layer wavelet decomposition.

[0047] The extraction of the energy proportion of high-frequency detail coefficients from the wavelet domain specifically involves: calculating the energy proportion of high-frequency detail coefficients based on the ratio of the energy of the high-frequency detail coefficients to the total energy after J-level wavelet decomposition.

[0048] The extraction of wavelet energy spectrum entropy from the wavelet domain specifically involves: calculating the ratio of the energy of the low-frequency approximation coefficients and high-frequency detail coefficients under each scale decomposition to the total signal energy, using it as a probability value, and obtaining the wavelet energy spectrum entropy according to the Shannon information entropy formula;

[0049] The extraction of wavelet variance from the wavelet domain specifically involves calculating the variance of the low-frequency approximation coefficients and the high-frequency detail coefficients after wavelet decomposition.

[0050] The feature extraction from the bispectral domain first involves zero-mean normalizing the interference signal to obtain the bispectral matrix of the signal, and then extracting the bispectral entropy, the mean of the contour integral bispectral matrix, the variance of the contour integral bispectral matrix, and the bispectral waveform entropy, specifically including:

[0051] The extraction of bispectral entropy specifically involves: calculating the energy of the bispectral matrix, taking the ratio of the absolute value of a point in the bispectral matrix to the energy as the probability, and then obtaining the bispectral energy entropy, i.e., the bispectral entropy, according to the Shannon information entropy formula.

[0052] The extraction of the mean value of the contour integral bispectral from the bispectral domain is specifically as follows: take multiple squares centered at the origin in the bispectral matrix as integration paths, calculate the contour integral bispectral sequence, and then calculate its mean value to obtain the mean value of the contour integral bispectral.

[0053] The extraction of the bispectral variance of the contour integral from the bispectral domain is specifically achieved by calculating the variance of the bispectral sequence of the contour integral.

[0054] The extraction of bispectral waveform entropy from the bispectral domain specifically involves: calculating the sum of integrals for all integration paths, using the ratio of the integral of each integration path to the sum of integrals as a probability, and then obtaining the bispectral waveform entropy according to the Shannon information entropy formula.

[0055] The extracted time-domain skewness, time-domain kurtosis, normalized instantaneous amplitude absolute standard deviation, normalized instantaneous frequency absolute standard deviation, time-domain envelope ripple, fast pulse modulation coefficient, box dimension, information dimension, frequency-domain skewness, frequency-domain kurtosis, frequency-domain envelope ripple, additive white Gaussian noise factor, carrier factor, spectral information entropy, spectral exponential entropy, spectral norm entropy, low-frequency approximation coefficient energy proportion, high-frequency detail coefficient energy proportion, wavelet energy spectrum entropy, wavelet variance, bispectral entropy, bispectral domain extracted contour integral bispectral mean, contour integral bispectral variance, and bispectral waveform entropy are merged to form a high-dimensional feature vector for each interference signal.

[0056] The labeling described in S21 specifically involves using a positive integer n as a label to represent different types of interference, serving as the last dimension of each high-dimensional feature vector.

[0057] The construction of the decision tree described in S32 is as follows: k features are randomly selected without repetition, and the optimal feature is selected for splitting according to the minimum Gini coefficient criterion. The splitting stops when all samples of a node belong to the same class, thus completing the construction of the decision tree.

[0058] Beneficial effects

[0059] The radar active jamming identification method based on multi-domain features and decision trees described in this invention has the following advantages compared with existing active jamming identification methods:

[0060] 1. The identification method extracts features from multiple perspectives, including time domain, frequency domain, fractal domain, wavelet domain, and bispectral domain. In addition to being able to identify four traditional types of interference, such as radio frequency noise interference, amplitude modulation noise interference, frequency modulation noise interference, and range false target interference, it also has an effective identification effect on four new types of active interference, such as smart noise interference, spectrum dispersion interference, slice reconstruction interference, and intermittent sampling forwarding interference.

[0061] 2. The identification method benefits from multi-domain feature extraction, which extracts features with high discriminative power and insensitivity to noise. Under harsh noise environments, it can robustly and effectively identify active interference types, thereby improving the identification accuracy and generalization ability of the method.

[0062] 3. The identification method adopts a cascaded approach of RF algorithm and XGBoost algorithm. The RF algorithm, which has excellent dimensionality reduction performance and good noise resistance, is used for feature selection, which effectively addresses the problem of redundancy in high-dimensional feature vectors and reduces computational overhead. The accurate and efficient XGBoost classifier completes type identification, which improves the accuracy and robustness of active interference identification. Attached Figure Description

[0063] Figure 1 This invention describes the stage composition and connection relationship of a radar active interference identification method based on multi-domain features and decision trees.

[0064] Figure 2 This is a flowchart illustrating the specific implementation of the radar active interference identification method based on multi-domain features and decision trees in Embodiment 1 of the present invention.

[0065] Figure 3 This is the optimal feature subset after RF feature selection in Embodiment 1 of the radar active interference identification method based on multi-domain features and decision trees of the present invention;

[0066] Figure 4 This is a curve showing the change in recognition accuracy of different interference types with interference-to-noise ratio in Embodiment 1 of the radar active interference identification method based on multi-domain features and decision trees of the present invention.

[0067] Figure 5 This is the recognition accuracy curve of different feature dimensionality reduction methods based on SVM classification in Embodiment 1 of the radar active interference identification method based on multi-domain features and decision trees of the present invention;

[0068] Figure 6This is a comparison of the recognition accuracy curves of different interference recognition methods in Embodiment 1 of the radar active interference recognition method based on multi-domain features and decision trees of the present invention. Detailed Implementation

[0069] To better illustrate the purpose and advantages of this method, the specific implementation details of the radar active jamming identification method based on multi-domain features and decision trees of the present invention will be further described in detail with reference to the accompanying drawings and specific embodiments.

[0070] Example 1

[0071] This embodiment illustrates the specific implementation of the method described in this invention for identifying eight types of active interference, including radio frequency noise interference, amplitude modulation noise interference, frequency modulation noise interference, range false target interference, agile noise interference, spectrum dispersion interference, slice reconstruction interference, and intermittent sampling forwarding interference.

[0072] The simulation environment includes software and hardware configurations, as detailed below:

[0073] 1. Software Configuration:

[0074] Operating system: Windows 10; Simulation software: Tensorflow 2.6.0 (Keras library), Python 3.9.0;

[0075] 2. Hardware configuration: CPU: AMD Ryzen 7 5800H with Radeon Graphics, 3.20GHz; Memory: 16GB.

[0076] The basic radar simulation parameters for the dataset are shown in Table 1, and the interference simulation parameters are shown in Table 2. The interference-to-noise ratio (JNR) ranges from -14dB to 14dB. For eight types of active interference, 400 interference signals are simulated and their features are extracted every 2dB within the JNR range, resulting in a total of 48,000 interference samples.

[0077] Table 1 Simulation parameters of radar transmitted signal

[0078]

[0079] Table 2 Simulation parameters for interference feature extraction

[0080]

[0081]

[0082] Figure 1 This describes the stage composition and connection relationships of the radar active jamming identification method based on multi-domain features and decision trees. From... Figure 1It can be seen that the radar active interference identification method includes four stages: multi-domain feature extraction stage, multi-domain feature dataset construction stage, feature selection stage, and XGBoost training and classification stage. The stages are connected sequentially.

[0083] Figure 2 This is a flowchart illustrating the specific implementation of a radar active interference identification method based on multi-domain features and decision trees, as described in Embodiment 1 of the present invention. Figure 2 It can be seen that the simulated active interference signal is superimposed with Gaussian white noise to obtain the original received signal, which is then processed... Figure 1 The four stages shown indicate the interference type, thus completing the active interference identification. The specific implementation steps include the following:

[0084] S1. In the multi-domain feature extraction stage, for the interference signal, extract time-domain skewness, time-domain kurtosis, normalized instantaneous amplitude absolute value standard deviation, normalized instantaneous frequency absolute value standard deviation, time-domain envelope undulation, and fast intra-pulse modulation coefficients from the time domain; extract box dimension and information dimension from the fractal domain; extract frequency-domain skewness, frequency-domain kurtosis, frequency-domain envelope undulation, additive white Gaussian noise factor, carrier factor, spectral information entropy, spectral exponential entropy, and spectral norm entropy from the frequency domain; extract the energy proportion of low-frequency approximation coefficients, the energy proportion of high-frequency detail coefficients, wavelet energy spectrum entropy, and wavelet variance from the wavelet domain; and extract bispectral entropy, contour integral bispectral mean, contour integral bispectral variance, and bispectral waveform entropy from the bispectral domain to obtain the high-dimensional feature vector of each interference signal, specifically:

[0085] The extraction of time-domain skewness, time-domain kurtosis, normalized instantaneous amplitude absolute standard deviation, normalized instantaneous frequency absolute standard deviation, time-domain envelope ripple, and fast pulse modulation coefficients from the time domain specifically includes:

[0086] The extraction of time-domain skewness from the time domain specifically involves: calculating the mean μ and standard deviation σ of the time-domain interference signal x[n] (n=1,2,…,N), and then subtracting the mean from the time-domain interference signal, dividing by the standard deviation, and taking the mean of the third power to obtain the time-domain skewness F1=E{(x[n]-μ) / σ] 3}; where E{·} represents the mean function;

[0087] The extraction of time-domain kurtosis from the time domain specifically involves: calculating the mean μ and standard deviation σ of the time-domain interference signal, subtracting the mean from the time-domain interference signal, dividing by the standard deviation, and then taking the mean of the fourth power to obtain the time-domain kurtosis F2=E{[(x[n]-μ) / σ] 4};

[0088] The extraction of the normalized instantaneous amplitude absolute value standard deviation from the time domain specifically involves:

[0089] The analytical expression of the time-domain interference signal x[n] is obtained from the Hilbert transform. Further calculation of instantaneous amplitude

[0090] And calculate the zero-center normalized instantaneous amplitude a cn (i)=a(i) / E[a(i)]-1;

[0091] The standard deviation of the normalized instantaneous amplitude absolute value is obtained as follows:

[0092]

[0093] The extraction of the normalized instantaneous frequency absolute value standard deviation from the time domain specifically involves: extracting the instantaneous frequency f[n] of the interference signal and normalizing it to obtain...

[0094] Where, max{ f (i)} represents traversal f (i) Find the maximum value, where i ranges from 1 to N; then obtain the standard deviation of the normalized instantaneous frequency absolute value:

[0095]

[0096] The extraction of the temporal envelope ripple from the time domain specifically involves: obtaining the signal analytical expression z[n] based on the Hilbert transform; the sum of the squares of the real and imaginary parts of the signal analytical expression is the instantaneous envelope sum of squares.

[0097] Further, based on the variance of the instantaneous envelope sum of squares:

[0098] With mean μ a The ratio of squares yields the time-domain envelope variability:

[0099] The extraction of fast intra-pulse modulation coefficients from the time domain specifically involves: calculating the autocorrelation function R[n] of the interference signal x[n], taking the autocorrelation function values ​​of three equally spaced sampling points n1, n2, n3 of the interference signal, and calculating the fast intra-pulse modulation coefficients according to the definition of fast intra-pulse modulation coefficients.

[0100]

[0101] The extraction of box dimension and information dimension features from the fractal domain specifically includes:

[0102] The extraction of box dimension from the fractal domain specifically involves: performing spatial measurement on the time-domain interference signal, selecting an appropriate box length q = 1 / N, ensuring multiple boxes cover the entire interference signal, and calculating the box dimension according to the definition of box dimension.

[0103]

[0104] Wherein, N(q) is defined as:

[0105]

[0106] The extraction of information dimension from the fractal domain specifically involves: performing forward differencing on the interference signal to obtain the reconstructed signal s[n] = x[n+1] - x[n], and calculating the probability that the reconstructed signal falls into the i-th box. The information dimension was obtained using Shannon's information entropy formula.

[0107] The feature extraction from the frequency domain first involves performing a Fast Fourier Transform on the interference signal [n] to obtain the signal spectrum X(w) and the signal power spectrum, which are then normalized to obtain P(w). Then, frequency domain skewness, frequency domain kurtosis, frequency domain envelope ripple, additive white Gaussian noise factor, carrier factor, spectral information entropy, spectral exponential entropy, and spectral norm entropy are extracted from the frequency domain. Specifically, this includes:

[0108] The extraction of frequency domain skewness from the frequency domain specifically involves: calculating the mean μ of the signal power spectrum. p and standard deviation σ p The frequency domain skewness is obtained by subtracting the mean from the signal power spectrum P(w), dividing by the standard deviation, and then taking the mean of the third power.

[0109] The extraction of frequency domain kurtosis from the frequency domain specifically involves: calculating the mean μ of the signal power spectrum. p and standard deviation σ p The frequency domain kurtosis is obtained by subtracting the mean from the signal power spectrum P(w), dividing by the standard deviation, and then taking the mean to the fourth power.

[0110] The extraction of frequency domain envelope undulation from the frequency domain specifically involves obtaining the analytical expression of the signal power spectrum based on the Hilbert transform: The sum of the squares of the real and imaginary parts of the analytical expression for the signal power spectrum is the sum of squares of the instantaneous envelope: Further based on the variance σ of the instantaneous envelope sum of squares A 2 With mean μ A The ratio of squares yields the frequency domain envelope ripple.

[0111] The extraction of additive white Gaussian noise factors from the frequency domain specifically involves: first, calculating the mean E1 of the signal power spectrum P(w); second, calculating the mean E2 of the portion of the spectrum greater than E1; then, calculating the mean E3 of the portion of the spectrum greater than E2; and finally obtaining two additive white Gaussian noise factors, which are the ratio of the difference between E2 and E1 to E1, respectively. The ratio of the difference between E3 and E2 to E1

[0112] The extraction of the carrier factor from the frequency domain specifically involves: calculating the maximum and second-largest values ​​of the signal spectrum X(w), and then taking the maximum value {X(w)}. max and the second largest value {X(w)} sec The ratio of these values ​​yields the carrier factor:

[0113] F 14 ={X(w)} max / {X(w)} sec ;

[0114] The extraction of spectral information entropy from the frequency domain is specifically achieved by calculating the probability value of each frequency resolution unit in the signal spectrum X(w). Then, based on Shannon's information entropy formula, the spectral information entropy is obtained.

[0115] Where, p i satisfy Let the base 'a' be 'e'.

[0116] The extraction of spectral exponential entropy from the frequency domain is specifically achieved by calculating the probability value p of each frequency resolution unit of the signal spectrum X(w). i Then, based on the exponential entropy formula, the spectral exponential entropy is obtained.

[0117] The extraction of the spectral norm entropy from the frequency domain is specifically achieved by calculating the p-th power of the signal spectrum X(w) and summing the results.

[0118] The feature extraction process in the wavelet domain first involves performing J-level wavelet decomposition on the interference signal to obtain the low-frequency approximation coefficients cA of the signal at J scales. j and high-frequency detail coefficients cD j And calculate the total signal energy E and the energy E of the low-frequency approximation coefficients respectively. a and the energy E of high-frequency detail coefficients j (1≤j≤J), then extract the energy proportion of low-frequency approximation coefficients, the energy proportion of high-frequency detail coefficients, wavelet energy spectrum entropy, and wavelet variance, specifically including:

[0119] The extraction of the energy proportion of low-frequency approximation coefficients from the wavelet domain specifically involves: calculating the energy proportion of low-frequency approximation coefficients based on the ratio of the energy of the low-frequency approximation coefficients to the total energy after J-level wavelet decomposition.

[0120] In this embodiment, J=5, and the signal is decomposed using the Haar wavelet basis function;

[0121] The extraction of the energy proportion of high-frequency detail coefficients from the wavelet domain specifically involves: calculating the energy proportion of high-frequency detail coefficients based on the ratio of the energy of the high-frequency detail coefficients to the total energy after J-level wavelet decomposition.

[0122] The extraction of wavelet energy spectrum entropy from the wavelet domain specifically involves: calculating the ratio of the energy of the low-frequency approximation coefficients and high-frequency detail coefficients under each scale decomposition to the total signal energy, and using this ratio as the probability value p. j =E j / E, and obtain the wavelet energy spectrum entropy according to the Shannon information entropy formula.

[0123] The extraction of wavelet variance from the wavelet domain specifically involves calculating the variances of the low-frequency approximation coefficients and high-frequency detail coefficients after wavelet decomposition.

[0124] Among them, (Df) j,n The wavelet coefficients are at scale j;

[0125] The feature extraction from the bispectral domain first involves zero-mean normalization of the interference signal to obtain the bispectral matrix of the signal.

[0126]

[0127] Then, the bispectral entropy, the mean of the contour integral bispectral value, the variance of the contour integral bispectral value, and the bispectral waveform entropy are extracted, specifically including:

[0128] The extraction of bispectral entropy specifically involves: calculating the energy of the bispectral matrix, using the ratio of the absolute value of a point in the bispectral matrix to its energy as a probability, and then obtaining the bispectral energy entropy according to the Shannon information entropy formula. That is, bispectral entropy;

[0129] in

[0130] The extraction of the contour integral bispectral mean from the bispectral domain specifically involves: taking multiple squares centered at the origin in the bispectral matrix as integration paths, calculating the contour integral bispectral sequence B'[n] (1≤n≤M), and then calculating its mean to obtain the contour integral bispectral mean F. 23 =E(B'[n]);

[0131] The extraction of the contour integral bispectral variance from the bispectral domain is specifically achieved by calculating the variance of the contour integral bispectral sequence.

[0132] The extraction of bispectral waveform entropy from the bispectral domain specifically involves: calculating the sum of integrals for all integration paths, and using the ratio of the integral of each integration path to the sum of integrals as the probability. Then, based on Shannon's information entropy formula, the bispectral waveform entropy is obtained.

[0133] The extracted time-domain skewness, time-domain kurtosis, normalized instantaneous amplitude absolute standard deviation, normalized instantaneous frequency absolute standard deviation, time-domain envelope ripple, fast intra-pulse modulation coefficient, box dimension, information dimension, frequency-domain skewness, frequency-domain kurtosis, frequency-domain envelope ripple, additive white Gaussian noise factor, carrier factor, spectral information entropy, spectral exponential entropy, spectral norm entropy, low-frequency approximation coefficient energy proportion, high-frequency detail coefficient energy proportion, wavelet energy spectrum entropy, wavelet variance, bispectral entropy, bispectral domain extracted contour integral bispectral mean, contour integral bispectral variance, and bispectral waveform entropy are merged to form a high-dimensional feature vector for each interference signal, each with 29 feature parameters, i.e., the high-dimensional feature vector is 29-dimensional.

[0134] This completes the multi-domain feature extraction of radar active interference;

[0135] S2. The multi-domain feature dataset construction phase completes the construction of the feature dataset, specifically as follows:

[0136] S21. Take the high-dimensional feature vector of each interference signal in S1 as a data sample, and label all samples to obtain a labeled dataset.

[0137] The labeling is specifically as follows: a positive integer n (1≤n≤8) is used as the label to represent different types of interference, which is the last dimension of each high-dimensional feature vector;

[0138] S22. Standardize the dataset in S21;

[0139] Thus, from S21 to S22, the construction of the multi-domain feature dataset is complete;

[0140] S3. In the feature selection stage, the RF algorithm is used to select features from the multi-domain feature dataset in S2 to obtain the optimal feature subset. The dataset is then divided into training and test sets, specifically:

[0141] S31, the RF algorithm obtains multiple samples through random resampling;

[0142] The random resampling specifically refers to: randomly selecting N data points with replacement from the dataset and using them as a sample;

[0143] S32. Construct a decision tree based on the samples in S31;

[0144] The construction of the decision tree is specifically as follows: k features are randomly selected without repetition, and the optimal feature is selected for splitting according to the minimum Gini coefficient criterion. The splitting stops when all samples of a node belong to the same class, thus completing the construction of the decision tree.

[0145] S33. Repeat S31 and S32 M times to generate M decision trees, forming a random forest;

[0146] S34. Calculate the importance score of each feature in S2 in the random forest in S33, complete the feature selection, and obtain the optimal feature subset;

[0147] The feature selection process involves calculating the importance score of each feature based on the Gini coefficient, sorting the features in descending order according to their importance scores, and eliminating features with low importance according to certain criteria.

[0148] S35. Divide the optimal feature subset in S34 into a training set and a test set according to a certain ratio;

[0149] Thus, from S31 to S34, the feature selection stage obtains the optimal feature subset and the training and test sets;

[0150] Figure 3 This is the optimal feature subset after RF feature selection in this invention. At this point, JNR = -6dB, and Table 3 provides the feature names and importance scores. Figure 3 It can be seen that, under the current interference-to-noise ratio conditions, more effective features appear in the frequency domain and wavelet domain, and entropy features play an important role.

[0151] Table 3 Importance scores of the optimal feature subset with JNR = -6dB

[0152]

[0153]

[0154] S4. The XGBoost training phase completes the construction and training of the XGBoost classifier, specifically as follows:

[0155] S41. Set the number of decision trees in the XGBoost classifier to 100, the depth of the decision trees to 5, the learning rate to 0.05, the penalty term coefficient γ to 1, and the regularization term coefficient λ to 1 to obtain the initial XGBoost classifier.

[0156] S42. Input the training set after feature selection in S3 into the initial XGBoost classifier. After training, the optimal XGBoost classifier is obtained.

[0157] Thus, from S41 to S42, the construction and training of the XGBoost classifier are complete;

[0158] In the S5 and XGBoost classification stages, the test set after feature selection in S3 is input into the optimal XGBoost classifier, which outputs the active interference type to achieve the identification of radar active interference.

[0159] Thus, from S1 to S5, a radar active jamming identification method based on multi-domain features and decision trees has been completed.

[0160] Figure 4 These are curves showing the variation of the interference ratio with the recognition accuracy of different interference types in this invention. Figure 4 It can be seen that, overall, the recognition rate of all eight types of interference signals improves with the increase of the interference-to-noise ratio (JNR). When JNR = -4dB, the recognition rate of each interference type on the test set is close to 100%, meaning that the algorithm can accurately identify interference signals. It is worth noting that, except for spectral dispersion interference and slice reconstruction interference, other interference types still exhibit excellent recognition accuracy at -14dB. This demonstrates that the feature parameters extracted in S1 in the time domain, frequency domain, wavelet domain, fractal domain, and bispectral domain have high discriminative power and good noise resistance, verifying the effectiveness of this invention in identifying interference signals in complex electromagnetic environments.

[0161] In practical implementation, to test the recognition performance of the RF-XGBoost cascaded interference recognition method, the following two experiments were designed based on the multi-domain feature dataset constructed in S2:

[0162] Experiment 1: Three commonly used feature dimensionality reduction methods were selected, including Principal Component Analysis (PCA), Recursive Feature Elimination (RFE), and the RF algorithm. Using the traditional Support Vector Machine (SVM) classifier, the recognition results of multi-domain feature datasets under different JNR conditions were simulated to verify the advantages of the RF algorithm as a feature selection algorithm.

[0163] As shown in S1, 29-dimensional features were extracted from the time domain, frequency domain, wavelet domain, and bispectral domain. Here, the high-dimensional feature vector was reduced to 10 dimensions using three dimensionality reduction methods. The parameters of the SVM classifier were set, using a linear kernel function and a penalty coefficient c of 0.3. The ratio of the training set to the test set was set to 6:4.

[0164] Figure 5 These are the recognition accuracy curves of different feature dimensionality reduction methods based on SVM classification in this invention; (The remaining text appears to be a fragment and requires further context for accurate translation.) Figure 5It can be seen that, based on the multi-domain feature dataset, the interference recognition rate of all three methods increases with the increase of JNR. Overall, when JNR is between -14dB and 0dB, the recognition performance of RF-SVM and RFE-SVM methods is better than that of PCA-SVM, and both approach 100% recognition accuracy at -2dB. When JNR = -14dB, the interference recognition rate of RF and RFE methods is only 60%, which is low because the extracted features reflect noise characteristics more. When JNR = -6dB, the recognition rate of PCA-SVM is 78.28%, while the other two methods reach 92%, a decrease of 13.72%. The interference recognition performance of PCA-SVM is poor under low interference-to-noise ratio conditions. For RFE-SVM and RF-SVM methods, the recognition performance is not significantly different, and their trends with JNR are roughly the same.

[0165] Table 4 shows the computation times of the three dimensionality reduction methods. RFE takes the longest time (3.087s), followed by RF and PCA. Although PCA takes only 0.006s, less than RF, its data recognition rate after dimensionality reduction is lower. Therefore, considering both the recognition and time performance of the feature selection algorithms, RF performs best.

[0166] Table 4. Computation time for different feature reduction methods

[0167]

[0168] Experiment 2: This experiment investigates the overall recognition and time performance of SVM, XGBoost, PCA-SVM, and RF-XGBoost to test the superiority of the present invention. The simulation conditions are the same as those described above.

[0169] Figure 6 This is a comparison of the recognition accuracy curves of different interference recognition methods in this invention. Figure 6It can be observed that the recognition performance of different algorithms improves with the increase of JNR. Specifically, at lower JNR, the PCA-SVM algorithm has a lower recognition accuracy, even lower than the SVM algorithm, reflecting that PCA dimensionality reduction leads to a decrease in the discriminative power of feature parameters, proving that dimensionality reduction using feature extraction methods is not robust. For the XGBoost algorithm, it has a higher recognition rate in the -14dB to 14dB range, which is generally greater than the recognition results of the SVM and PCA-SVM algorithms. This reflects that the XGBoost algorithm is very effective in solving the problem of radar active interference recognition based on the multi-domain feature dataset constructed in this invention. It is worth noting that the recognition rate change curve of the XGBoost algorithm basically coincides with that of the RF-XGBoost algorithm, proving that the RF algorithm effectively reduces the number of features while maintaining recognition accuracy, thereby reducing the computational cost of the algorithm. Overall, the proposed RF-XGBoost maintains a high interference recognition rate within the range of -14dB to 14dB. At JNR = -6dB, the recognition rate is 99.69%, close to 100%, representing a 7.74% improvement over the traditional SVM algorithm and a 21.49% improvement over the PCA-SVM algorithm. Furthermore, the invention performs well even in noisy environments, achieving a recognition rate of 90.55% at JNR = -14dB, demonstrating the algorithm's superiority and robustness.

[0170] Therefore, it can be concluded that the interference identification method based on multi-domain feature extraction and decision tree described in this invention, especially the RF-XGBoost identification method, can effectively deal with novel interference identification problems. Under low interference-to-noise ratio conditions, it can effectively reduce computational overhead and improve identification accuracy, thereby further improving the performance of feature extraction-based identification methods and has high practical application value.

[0171] The above description is merely a preferred embodiment of the present invention, and the present invention should not be limited to the content disclosed in this embodiment and the accompanying drawings. Any equivalent or modified embodiments made without departing from the spirit of the present invention fall within the scope of protection of the present invention.

Claims

1. A radar active jamming identification method based on multi-domain features and decision trees, characterized in that, include: S1. In the multi-domain feature extraction stage, for the interference signal, extract time-domain skewness, time-domain kurtosis, normalized instantaneous amplitude absolute value standard deviation, normalized instantaneous frequency absolute value standard deviation, time-domain envelope undulation, and fast pulse modulation coefficients from the time domain; extract box dimension and information dimension from the fractal domain; extract frequency-domain skewness, frequency-domain kurtosis, frequency-domain envelope undulation, additive white Gaussian noise factor, carrier factor, spectral information entropy, spectral exponential entropy, and spectral norm entropy from the frequency domain; extract the energy proportion of low-frequency approximation coefficients, the energy proportion of high-frequency detail coefficients, wavelet energy spectrum entropy, and wavelet variance from the wavelet domain; and extract bispectral entropy, contour integral bispectral mean, contour integral bispectral variance, and bispectral waveform entropy from the bispectral domain to obtain the high-dimensional feature vector of each interference signal. S2. The multi-domain feature dataset construction phase completes the construction of the feature dataset, specifically as follows: S21. Take the high-dimensional feature vector of each interference signal in S1 as a data sample, and label all samples to obtain a labeled dataset. S22. Standardize the dataset in S21; S3. In the feature selection stage, the RF algorithm is used to select features from the multi-domain feature dataset in S2 to obtain the optimal feature subset. The dataset is then divided into training and test sets, specifically: S31, the RF algorithm obtains multiple samples through random resampling; The random resampling described in S31 specifically refers to: randomly selecting samples with replacement from the dataset. N One data point is used as a sample; S32. Construct a decision tree based on the samples in S31; S33, repeat S31 and S32 M Next, generate M decision trees to form a random forest; S34. Calculate the importance score of each feature in S2 in the random forest in S33, complete the feature selection, and obtain the optimal feature subset; The feature selection process involves calculating the importance score of each feature based on the Gini coefficient, sorting the features in descending order according to their importance scores, and eliminating features with low importance according to certain criteria. S35. Divide the optimal feature subset in S34 into a training set and a test set according to a certain ratio; Thus, from S31 to S34, the feature selection stage obtains the optimal feature subset and the training and test sets; S4. The XGBoost training phase completes the construction and training of the XGBoost classifier, specifically as follows: S41. Set the number of decision trees, decision tree depth, learning rate, and penalty term coefficient for the XGBoost classifier. and regularization term coefficient Thus, the initial XGBoost classifier is obtained; S42. Input the training set after feature selection in S3 into the initial XGBoost classifier. After training, the optimal XGBoost classifier is obtained. In the S5 and XGBoost classification stages, the test set after feature selection in S3 is input into the optimal XGBoost classifier, which outputs the active interference type to achieve the identification of radar active interference.

2. The radar active interference identification method according to claim 1, characterized in that, The extraction of time-domain skewness, time-domain kurtosis, normalized instantaneous amplitude absolute standard deviation, normalized instantaneous frequency absolute standard deviation, time-domain envelope ripple, and fast pulse modulation coefficients from the time domain specifically includes: The extraction of time-domain skewness from the time domain specifically involves: calculating the mean and standard deviation of the time-domain interference signal, subtracting the mean from the time-domain interference signal, dividing by the standard deviation, and then taking the mean of the third power to obtain the time-domain skewness. The extraction of time-domain kurtosis from the time domain specifically involves: calculating the mean and standard deviation of the time-domain interference signal, subtracting the mean from the time-domain interference signal, dividing by the standard deviation, and then taking the mean of the fourth power to obtain the time-domain kurtosis. The extraction of the standard deviation of the normalized instantaneous amplitude absolute value from the time domain is specifically as follows: based on the analytical expression of the time-domain interference signal obtained by Hilbert transform, the instantaneous amplitude is further calculated and the zero-center normalized instantaneous amplitude is calculated to obtain the standard deviation of the normalized instantaneous amplitude absolute value. The step of extracting the normalized instantaneous frequency absolute standard deviation from the time domain specifically involves: extracting the instantaneous frequency of the interference signal and normalizing it to obtain the normalized instantaneous frequency absolute standard deviation. The extraction of time-domain envelope variability from the time domain specifically involves: obtaining the signal analytical expression based on the Hilbert transform; the sum of the squares of the real part and the squares of the imaginary part of the signal analytical expression is the instantaneous envelope sum of squares; and further obtaining the time-domain envelope variability based on the ratio of the variance to the square of the mean of the instantaneous envelope sum of squares. The extraction of fast intra-pulse modulation coefficients from the time domain specifically involves: calculating the autocorrelation function of the interference signal, taking the autocorrelation function values ​​of equally spaced sampling points of the interference signal, and calculating the fast intra-pulse modulation coefficients according to the definition of fast intra-pulse modulation coefficients.

3. The radar active interference identification method according to claim 1, characterized in that, The extraction of box dimension and information dimension from the fractal domain specifically includes: The extraction of box dimension from the fractal domain specifically involves: performing spatial measurement on the temporal interference signal, selecting an appropriate box length, and ensuring that multiple boxes cover the entire interference signal to calculate the box dimension. The extraction of information dimension from the fractal domain specifically involves: performing forward differencing on the interference signal to obtain the reconstructed signal, calculating the probability that the reconstructed signal falls into each box, and obtaining the information dimension using the Shannon information entropy formula.

4. The radar active interference identification method according to claim 1, characterized in that, To extract features from the frequency domain, firstly, a Fast Fourier Transform is performed on the interference signal to obtain the signal spectrum and signal power spectrum, which are then normalized. Then, frequency domain skewness, kurtosis, envelope ripple, additive white Gaussian noise factor, carrier factor, spectral information entropy, spectral exponential entropy, and spectral norm entropy are extracted from the frequency domain. Specifically, these include: The extraction of frequency domain skewness from the frequency domain specifically involves: calculating the mean and standard deviation of the signal power spectrum, subtracting the mean from the signal power spectrum and dividing by the standard deviation, then taking the mean of the third power to obtain the frequency domain skewness. The extraction of frequency domain kurtosis from the frequency domain specifically involves: calculating the mean and standard deviation of the signal power spectrum, subtracting the mean from the signal power spectrum and dividing by the standard deviation, then taking the mean to the power of 4 to obtain the frequency domain kurtosis. The extraction of frequency domain envelope undulation from the frequency domain specifically involves: obtaining the analytical expression of the signal power spectrum based on the Hilbert transform; the sum of the squares of the real part and the squares of the imaginary part of the analytical expression of the signal power spectrum is the instantaneous envelope sum of squares; and further obtaining the frequency domain envelope undulation based on the ratio of the variance to the square of the mean of the instantaneous envelope sum of squares. The extraction of additive white Gaussian noise factor from the frequency domain specifically involves: first, calculating the mean of the signal power spectrum. Secondly, calculate the power spectrum of the signal that is greater than the mean. Partial mean Then calculate the signal power spectrum greater than Partial mean Finally, two additive white Gaussian noise factors were obtained: and Difference divided by as well as and Difference divided by ; The process of extracting the carrier factor from the frequency domain specifically involves: calculating the maximum and second-largest values ​​of the signal spectrum, and then taking the ratio of the maximum and second-largest values ​​to obtain the carrier factor; The extraction of spectral information entropy from the frequency domain is specifically achieved by calculating the probability value of each frequency resolution unit in the signal spectrum and then obtaining the spectral information entropy according to the Shannon information entropy formula. The extraction of spectral exponential entropy from the frequency domain is specifically achieved by calculating the probability value of each frequency resolution unit in the signal spectrum and then obtaining the spectral exponential entropy according to the exponential entropy formula. The extraction of spectral norm entropy from the frequency domain is specifically achieved by calculating the signal spectrum. p The spectral norm entropy is obtained by exponentiation and summation.

5. The radar active interference identification method according to claim 1, characterized in that, Feature extraction is performed in the wavelet domain first, and the interference signal is then analyzed. J Layer wavelet decomposition yields the signal in J The low-frequency approximation coefficients and high-frequency detail coefficients are decomposed at each scale, and the total signal energy, the energy of the low-frequency approximation coefficients, and the energy of the high-frequency detail coefficients are calculated separately. Then, the energy proportions of the low-frequency approximation coefficients, the energy proportions of the high-frequency detail coefficients, the wavelet energy spectral entropy, and the wavelet variance are extracted, specifically including: The extraction of the energy proportion of low-frequency approximation coefficients from the wavelet domain is specifically as follows: based on J The energy ratio of the low-frequency approximation coefficients to the total energy after layer wavelet decomposition is used to calculate the energy proportion of the low-frequency approximation coefficients. The extraction of high-frequency detail coefficient energy proportions from the wavelet domain specifically involves: based on... J The ratio of the energy of the high-frequency detail coefficients to the total energy after layer wavelet decomposition is used to calculate the energy proportion of the high-frequency detail coefficients. The extraction of wavelet energy spectrum entropy from the wavelet domain specifically involves: calculating the ratio of the energy of the low-frequency approximation coefficients and high-frequency detail coefficients under each scale decomposition to the total signal energy, using it as a probability value, and obtaining the wavelet energy spectrum entropy according to the Shannon information entropy formula; The extraction of wavelet variance from the wavelet domain specifically involves calculating the variance of the low-frequency approximation coefficients and the high-frequency detail coefficients after wavelet decomposition.

6. The radar active interference identification method according to claim 1, characterized in that, To extract features from the bispectral domain, the interference signal is first zero-mean normalized to obtain the bispectral matrix. Then, the bispectral entropy, mean of the contour integral bispectral matrix, variance of the contour integral bispectral matrix, and bispectral waveform entropy are extracted, specifically including: The extraction of bispectral entropy specifically involves: calculating the energy of the bispectral matrix, taking the ratio of the absolute value of a point in the bispectral matrix to the energy as the probability, and then obtaining the bispectral energy entropy, i.e., the bispectral entropy, according to the Shannon information entropy formula. The extraction of the mean value of the contour integral bispectral from the bispectral domain is specifically as follows: take multiple squares centered at the origin in the bispectral matrix as integration paths, calculate the contour integral bispectral sequence, and then calculate its mean value to obtain the mean value of the contour integral bispectral. The extraction of the bispectral variance of the contour integral from the bispectral domain is specifically achieved by calculating the variance of the bispectral sequence of the contour integral. The extraction of bispectral waveform entropy from the bispectral domain specifically involves: calculating the sum of integrals for all integration paths, using the ratio of the integral of each integration path to the sum of integrals as a probability, and then obtaining the bispectral waveform entropy according to the Shannon information entropy formula. The extracted time-domain skewness, time-domain kurtosis, normalized instantaneous amplitude absolute standard deviation, normalized instantaneous frequency absolute standard deviation, time-domain envelope ripple, fast pulse modulation coefficient, box dimension, information dimension, frequency-domain skewness, frequency-domain kurtosis, frequency-domain envelope ripple, additive white Gaussian noise factor, carrier factor, spectral information entropy, spectral exponential entropy, spectral norm entropy, low-frequency approximation coefficient energy proportion, high-frequency detail coefficient energy proportion, wavelet energy spectrum entropy, wavelet variance, bispectral entropy, bispectral domain extracted contour integral bispectral mean, contour integral bispectral variance, and bispectral waveform entropy are merged to form a high-dimensional feature vector for each interference signal.

7. The radar active interference identification method according to claim 1, characterized in that, The labeling described in S21 specifically involves using positive integers. n The labels represent different types of interference, and are used as the last dimension of each high-dimensional feature vector.

8. The radar active interference identification method according to claim 1, characterized in that, The construction of the decision tree described in S32 specifically involves: randomly selecting without repetition. k The decision tree is constructed by selecting the optimal feature based on the minimum Gini coefficient criterion and splitting the tree when all samples of a node belong to the same class.

Images