Low-interception radar signal detection-enhancement method based on lpi-de-gan

Abstract

This invention discloses a method for detecting and enhancing low probability of intercept (LPI) radar signals based on LPI-DE-GAN, comprising the following steps: S1, acquiring a LPI radar signal sequence and a 0 sequence to form a clean signal sequence; acquiring a noise and marine navigation signal sequence, and superimposing it with the clean signal sequence to obtain a mixed signal sequence; S2, constructing a label for the signal detection task; S3, constructing an LPI-DE-GAN model, including a generator and a discriminator; S32, constructing the discriminator; S4, constructing a loss function and training the LPI-DE-GAN model. This invention can accurately detect received LPI radar signals with multiple modulation types and mixed with large-amplitude fishing vessel navigation interference signals. After detecting the LPI radar signal, it performs end-to-end time-domain signal enhancement to suppress fishing vessel navigation signals and noise, and reconstructs the original LPI radar signal.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, and in particular relates to a low intercept radar signal detection and enhancement method based on LPI-DE-GAN. Background Technology

[0002] As a crucial component of electronic warfare, radar countermeasures play a key role in modern warfare and are one of the important means of achieving information superiority on the battlefield. Radar reconnaissance is the foundation of radar countermeasures. By intercepting enemy radar signals through radar reconnaissance, one can obtain parameters needed for electronic countermeasures, such as the type, purpose, and carrier of enemy radar, assess the threat level of enemy radar, understand the enemy's operational intentions, perceive the real-time battlefield situation, and provide an important basis for formulating effective countermeasure strategies.

[0003] Low Probability of Interception (LPI) radar signals are characterized by low peak power, large time-bandwidth product, frequency agility, and complex intra-pulse modulation methods. Therefore, LPI radar systems are widely used in modern warfare. Due to these characteristics, LPI radar signals are often submerged in noise and significant interference from ship navigation signals. Since the power of noise and interference is much greater than the power of the LPI radar signal, they form extremely weak signals, making them difficult for reconnaissance aircraft to detect.

[0004] Currently, common radar signal detection methods include matched filtering, time-domain energy detection, and frequency-domain energy detection. Matched filtering requires prior information about the target signal, making it unsuitable for non-cooperative radar signals with low probability of intercept. Time-domain and frequency-domain energy detection methods require observing noise and interference before the target signal arrives to determine the threshold, which necessitates extensive engineering experience and prior information about noise and interference. Furthermore, both energy-based detection methods perform poorly at low signal-to-noise ratios.

[0005] Under significant interference from marine navigation signals, non-cooperative low probability of intercept (LPI) radar signals are weak with low signal-to-interference-plus-noise ratio (SNR), and are often submerged in noise and interference. This causes a significant performance degradation in common radar signal detection methods. Therefore, it is urgent to research methods that can accurately detect and effectively enhance low SNR LPI radar signals under significant marine navigation signal interference, laying the foundation for subsequent signal processing procedures such as modulation scheme identification and parameter estimation. Summary of the Invention

[0006] This invention provides a low probability of intercept (LPI) radar signal detection and enhancement method based on LPI-DE-GAN, which can accurately detect low probability of intercept radar signals with multiple modulation types and mixed with large-amplitude fishing vessel navigation interference signals. After detecting the low probability of intercept radar signal, it performs end-to-end time domain signal enhancement to suppress fishing vessel navigation signals and noise, and reconstruct the original low probability of intercept radar signal.

[0007] The objective of this invention is achieved through the following technical solution: a low-interception radar signal detection and enhancement method based on LPI-DE-GAN, comprising the following steps:

[0008] S1. Obtain multiple low probability of intercept (LPI) radar signal sequences with different modulations, and obtain a 0 sequence with the same total length as the LPI radar signal sequence. Then, combine the LPI signal and 0 sequence samples to form a clean signal sequence. Next, obtain noise and marine navigation signal sequences, and superimpose them with the clean signal sequence to obtain a mixed signal sequence.

[0009] S2. Slice the clean signal sequence and the mixed signal sequence, and construct the labels for the signal detection task; combine the sliced ​​mixed signal sequence and the clean signal sequence, along with the labels for the signal detection task, to form a dataset;

[0010] S3. Construct an LPI-DE-GAN model for the detection and enhancement of low-intercept radar signals; this model includes a generator G and a discriminator D; the process includes the following steps:

[0011] S31. Constructing Generator G: Generator G consists of an encoder, a decoder, and a signal detector;

[0012] The encoder consists of 11 sequentially connected convolutional layers, each using the PReLU activation function; the mixed signal s noisy The encoder compresses the noise into an encoded vector c. Then, a random noise vector z with the same size as c and conforming to a Gaussian distribution is selected. The encoded vector c and the noise vector z are concatenated and used as the input of the decoder.

[0013] The decoder consists of 11 transposed convolutional layers connected in sequence; except for the last transposed convolutional layer, the remaining transposed convolutional layers use the PReLU activation function; the first to Nth convolutional layers of the encoder are connected to the first to Nth transposed convolutional layers of the decoder in a skip connection, where N is the number of convolutional layers / transposed convolutional layers.

[0014] The decoder generates the enhanced signal G(z,s) based on the concatenated vector of the encoded vector c and the noise vector z. noisy );

[0015] The signal detector consists of a Flatten layer and four fully connected layers connected sequentially. Except for the last fully connected layer, the remaining fully connected layers use the ReLU activation function and employ Dropout to prevent overfitting. The last fully connected layer uses the Sigmoid activation function. The signal detector weights and integrates different features of the low-intercept radar signal contained in the encoded vector c, using the integrated features as the basis for signal detection and inputting them into the Sigmoid activation function, outputting a test statistic T. Net ∈[0,1];

[0016] S32. Construct discriminator D, which is a binary classifier used to distinguish the input signal. Discriminator D identifies the enhanced signal generated by generator G as false and the clean signal as true, and feeds back the result of the discrimination to generator G.

[0017] Discriminator D uses 11 convolutional layers to perform convolution operations on the data, and introduces a batch normalization layer and a LeakyReLU activation function after each convolutional layer; then the features extracted by the convolutional layers are used to make a judgment through a fully connected layer and a Softmax activation function.

[0018] S4. Construct the loss function of the LPI-DE-GAN model, set the hyperparameters of the network, initialize the LPI-DE-GAN parameters, and train the LPI-DE-GAN model.

[0019] The beneficial effects of this invention are as follows: This invention proposes a low probability of intercept (LPI) radar signal detection and enhancement method based on LPI-DE-GAN. Addressing the performance degradation of traditional methods due to the low signal-to-interference-plus-noise ratio (SNR) of LPI radar signals under conditions of significant marine navigation signal interference, this invention constructs an LPI-DE-GAN model. Through the adversarial interaction between the generator and discriminator, the model can accurately detect and enhance LPI radar signals in complex electromagnetic environments. Joint optimization of signal enhancement and detection tasks during network model training improves the network model's efficiency. During inference, the LPI-DE-GAN model directly detects the received mixed signal. If the test statistic is higher than a threshold, signal enhancement is performed; otherwise, the task terminates. Compared to the traditional method of filtering the received mixed signal for noise and interference before detection, the end-to-end detection process proposed in this invention saves resources. This invention improves the detection and enhancement performance of low probability of intercept (LPI) radar signals under low SNR conditions, has strong generalization ability, and can be implemented in engineering. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0021] Figure 2The reasoning process of LPI-DE-GAN;

[0022] Figure 3 The generator structure for LPI-DE-GAN;

[0023] Figure 4 Discriminator structure for LPI-DE-GAN

[0024] Figure 5 This is a line graph showing the detection probability of the present invention under different signal-to-interference-plus-noise ratios;

[0025] Figure 6 This is a line graph showing the false alarm probability of the present invention under different signal-to-interference-plus-noise ratios;

[0026] Figure 7 This is a diagram showing the enhancement results of the present invention for low intercept probability signals at a signal-to-interference-plus-noise ratio of -20dB. Detailed Implementation

[0027] To enable those skilled in the art to better understand the technical solution of this invention, the technical solution of this application is further described below in conjunction with the accompanying drawings and specific embodiments. This example mainly utilizes the scientific computing software MATLAB R2023a and PyCharm 2023.2.5 for simulation experiments to verify its signal enhancement and detection effects.

[0028] like Figure 1 As shown, the present invention provides a low-intercept radar signal detection-enhancement method based on LPI-DE (D stands for Detection, E stands for Enhancement)-GAN (Generative Adversarial Network), comprising the following steps:

[0029] S1. Acquire multiple low probability of intercept (LPI) radar signal sequences with different modulations, and acquire a 0 sequence with the same total length as the LPI radar signal sequence. Then, combine the LPI signal and 0 sequence samples to form a clean signal sequence, and use the clean signal sequence as a signal enhancement label. Next, acquire noise (Gaussian white noise in the environment) and marine navigation signal sequences, and superimpose them with the clean signal sequence to obtain a mixed signal sequence. The process includes the following steps:

[0030] S11. Set the parameter range of the low probability of intercept (LPI) radar signal pulse and acquire LPI radar signal sequences with various modulation schemes. The parameter range used in this embodiment is shown in Table 1. In this embodiment, the sampling frequency is set to 50MHz, and LPI radar signal sequences with four different modulation schemes (LFM, Bark, Frank, and Costas) are acquired. The length of each LPI radar signal sequence is L. Obtain the 0 sequence with the same total length as the multiple LPI radar signal sequences as the comparison sample signal sequence when there is no signal. Combine all the LPI signals and 0 sequence samples to form a clean signal sequence. Where 8L is the length of the clean signal sequence, and 2 indicates that the signal contains two dimensions: real and imaginary.

[0031] Table 1

[0032]

[0033] S12. Set the signal-to-interference-plus-noise ratio (SINR) range to [SINR]. min SINR max SINR min and SINR max These are the upper and lower bounds of the signal-to-interference-plus-noise ratio (SINR) range, respectively. In this embodiment, SINR is set as... min -20dB, SINR max The signal-to-interference-plus-noise ratio (SINR) is set to 0 dB; the SINR variation step size ΔSINR is set to 2 dB; within the SINR range, noise and marine navigation signals at that SINR are generated at each interval ΔSINR. The noise and marine navigation signals are then superimposed with the clean signal to obtain a mixed signal sequence.

[0034] S2. Slice the clean signal sequence and the mixed signal sequence, and construct labels for the signal detection task; combine the sliced ​​mixed signal sequence and the clean signal sequence, along with the labels for the signal detection task, to form a dataset; and divide the dataset into a training set, a validation set, and a test set; including the following steps:

[0035] S21. Set the window length w and step size s. In this embodiment, the window length w is set to 32768 and the step size s is set to 16384. Use the set window length and step size to adjust S. noisy and S clean Slice the signal to obtain n mixed signal sample blocks. and n clean signal sample blocks The mixed signal sequence and the signal enhancement task label were used as inputs to LPI-DE-GAN, respectively.

[0036] S22. Obtain "0" or "1" as the tag for low probability of intercept radar signal detection missions; all tags y iThis constitutes the signal detection tag sequence y;

[0037]

[0038] When the mixed signal input to the network model contains one of the multiple low probability of intercept radar signals in step S1, y i Select "1"; otherwise, y i Take "0";

[0039] S23. Divide the obtained sample blocks and labels into training set, validation set and test set in a ratio of 8:1:1. The training set and validation set are used for subsequent training of LPI-DE-GAN model, and the test set is used to test the model performance.

[0040] S3. Construct an LPI-DE-GAN model for the detection and enhancement of low-intercept radar signals; this model includes a generator G and a discriminator D, the principle of which is as follows: Figure 2 As shown; including the following processes:

[0041] S31. Constructing the generator G: The generator G consists of an encoder, a decoder, and a signal detector, and its structure is as follows: Figure 3 As shown;

[0042] The encoder consists of 11 sequentially connected convolutional layers, each using the PReLU activation function, with a kernel size of 32 and a stride of 2. The mixed signal s noisy The encoder compresses the noise vector into an encoded vector c with a size of 16×1024. Then, a random noise vector z with the same size as c and conforming to a Gaussian distribution is selected. The encoded vector c and the noise vector z are concatenated and used as the input of the decoder.

[0043] The decoder consists of 11 transposed convolutional layers connected in sequence; except for the last transposed convolutional layer, the remaining transposed convolutional layers use the PReLU activation function; the deconvolution kernel size of each transposed convolutional layer is 32, and the stride is 2; the first to Nth convolutional layers of the encoder are connected to the first to Nth transposed convolutional layers of the decoder in a skip connection, where N is the number of convolutional layers / transposed convolutional layers; Figure 3 In this diagram, the convolutional layers from bottom to top (from input to output) are denoted as conv1 to conv11, and the transposed convolutional layers from bottom to top (from input to output) are denoted as deconv11 to deconv1. conv1 and deconv1 are skipped connections, conv2 and deconv2 are skipped connections, and so on...

[0044] The decoder generates the enhanced signal G(z,s) based on the concatenated vector of the encoded vector c and the noise vector z. noisy );

[0045] The signal detector consists of a Flatten layer and four fully connected layers connected sequentially. Except for the last fully connected layer, the remaining fully connected layers use the ReLU activation function and employ Dropout to prevent overfitting; the last fully connected layer uses the Sigmoid activation function. The signal detector weights and integrates different features of the low-intercept radar signal contained in the encoded vector c, uses the integrated features as the basis for signal detection and inputs them into the Sigmoid activation function, outputting a test statistic T. Net ∈[0,1]. When the test statistic is higher than the preset threshold τ Net When a low probability of intercept (LPI) radar signal is detected, an enhanced signal is generated using the model constructed in this invention to reconstruct the LPI radar signal, thereby suppressing noise and interference with marine navigation signals. When the test statistic is below the threshold τ... Net If the input mixed signal sequence does not contain low probability of intercept radar signals, the mixed signal is discarded, and the next set of input signals is processed.

[0046] S32. Construct discriminator D, which is a binary classifier with the following structure: Figure 4 As shown; the discriminator is used to discriminate the input signal. The input signal consists of an enhanced signal and a clean signal; the former is the enhanced signal generated by the generator, which includes the enhanced low probability of intercept (LPI) radar signal and the enhanced 0 sequence (still close to 0); the latter, the clean signal, includes the LPI radar signal and the 0 sequence; the clean signal is also used as a tag.

[0047] The discriminator D identifies the enhanced signal generated by the generator G as false and the clean signal as true, and feeds back the results of the identification to the generator G, so that the generator G can adjust its own weights to improve the signal enhancement capability.

[0048] When an augmented signal is input (at the very beginning of training), the discriminator identifies it as false; when a labeled signal is input, the discriminator identifies it as true. In simpler terms, the discriminator forces the generator to produce a higher-quality low-probability-of-interception (LPI) radar signal, meaning the generated augmented image becomes increasingly closer to the LPI radar signal.

[0049] Discriminator D uses 11 convolutional layers to perform convolution operations on the data, and introduces a batch normalization layer and a LeakyReLU activation function after each convolutional layer; then the features extracted by the convolutional layers are used to make a judgment through a fully connected layer and a Softmax activation function.

[0050] The discriminator D provides feedback on the quality of the enhanced signal during training, enabling the generator G to produce a higher-quality enhanced signal and improve its signal enhancement capability. After training, the generator G is used to enhance and detect the signal to be identified, and the discriminator D can be removed.

[0051] S4. Construct the loss function for the LPI-DE-GAN model, set the network's hyperparameters, initialize the LPI-DE-GAN parameters, and train the LPI-DE-GAN model using the training and validation sets; this includes the following steps:

[0052] S41. Construct the loss functions for the LPI-DE-GAN generator and discriminator; the LPI-DE-GAN generator needs to detect and enhance LPI radar signals submerged in noise and marine navigation signals. Therefore, the generator's loss function must include the loss functions for both signal detection and enhancement tasks. The generator's target loss function is:

[0053]

[0054] In the formula, V Detect (G) and V Enhance (G) represents the loss function for the signal detection task and the signal enhancement task, respectively, and α and β represent the weights in the signal detection task and the signal enhancement task, respectively; p represents the average of the input, i.e., the expectation; z represents the sample obtained from random noise; p z (z) refers to the probability distribution of the input noise z; s noisy Indicates a mixed signal, p data (s noisy ) is a mixed signal s noisy The probability distribution of s; clean Let represent a clean signal, |||||2 represent the L2 loss, and λ be a hyperparameter controlling the L2 loss. The test statistic T represents the output of the detector. Net The value of y i The detection label takes a value of 0 or 1, M represents the number of samples, and μ is a hyperparameter controlling the loss of the detection task; D(G(z,s) noisy ),s noisy ) represents the output of the discriminator D, and the input of the discriminator is the enhancement signal G(z,s). noisy ) and noise signal s noisy The output is either 1 or 0, G(z,s) noisy If it is closer to the true signal, then D(G(z,s)) noisy ),s noisy If the first term approaches 1, then the first term approaches 0, and the loss will be smaller.

[0055] The objective loss function of the discriminator is:

[0056]

[0057] S42. Set the hyperparameters of LPI-DE-GAN and initialize the model weights; set the RMSprop optimizer as the optimizer for both the generator and discriminator, with an initial learning rate of 0.001, a batch size of 16, a maximum number of iterations of 250, α and β set to 1, λ to 10, μ to 100, and a dropout rate of 0.5; initialize the LPI-DE-GAN weights using Xavier.

[0058] S43. The LPI-DE-GAN model is trained using training and validation set data. The loss function values ​​of the LPI-DE-GAN generator and discriminator are calculated by forward propagation. Then, the parameters of the network model are updated by backpropagation algorithm. This process is repeated until the predetermined maximum number of iterations is reached. At the same time, the RMSprop optimizer is used to reduce the loss function value during the training process, so that the distribution of the generated enhanced signal gradually approaches the distribution of the real LPI radar signal, thereby realizing the detection and enhancement of low probability of intercept radar signals in the background of large-amplitude marine navigation signals.

[0059] S5. The trained LPI-DE-GAN model is used for the detection and enhancement of mixed signals; the detector outputs the test statistic T in the generator. Net The detection threshold τ of the generator. Net Set to 0.5 when the test statistic T Net Above the threshold τ Net Low probability of intercept (LPI) radar signals are detected and reconstructed, suppressing noise and shipborne interference signals; when the test statistic is below the threshold τ... Net If the input mixed signal sequence does not contain low probability of intercept radar signals, then it is assumed that there are no low probability of intercept radar signals.

[0060] In this embodiment, in addition to the test set data, a low signal-to-noise ratio (SNR) and low probability of intercept (PRI) radar signal that was not used in the training is also included. The SNR range of the signal used in the test is -40 to 0 dB. Net When the value is 0.5, the changes in detection probability and false alarm probability are as follows: Figure 5 and Figure 6 As shown. After detecting the low probability of intercept (LPI) radar signal, LPI-DE-GAN suppresses noise and marine interference signals, enhances the original LPI radar signal, and reconstructs its time-domain waveform. Figure 7 The signal-to-interference-plus-noise ratio (SINR) is -20dB, consisting of a mixed signal, a clean low probability of intercept (LPI) radar signal, and an enhanced signal.

[0061] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A low-intercept radar signal detection and enhancement method based on LPI-DE-GAN, characterized in that, Includes the following steps: S1. Obtain multiple low probability of intercept (LPI) radar signal sequences with different modulations, and obtain a 0 sequence with the same total length as the LPI radar signal sequence. Then, combine the LPI signal and 0 sequence samples to form a clean signal sequence. Next, obtain noise and marine navigation signal sequences, and superimpose them with the clean signal sequence to obtain a mixed signal sequence. S2. Slice the clean signal sequence and the mixed signal sequence, and construct the labels for the signal detection task; combine the sliced ​​mixed signal sequence and the clean signal sequence, along with the labels for the signal detection task, to form a dataset; S3. Construct an LPI-DE-GAN model for the detection and enhancement of low-intercept radar signals; this model includes a generator G and a discriminator D. The process includes the following steps: S31. Constructing Generator G: Generator G consists of an encoder, a decoder, and a signal detector; The encoder is composed of 11 convolutional layers in sequence, and PReLU activation function is used in each convolutional layer; the mixed signal s noisy The encoder is compressed into an encoding vector c, and then a random noise vector z of the same size as c and conforming to Gaussian distribution is selected, the encoding vector c is spliced with the noise vector z as the input of the decoder; The decoder consists of 11 transposed convolutional layers connected in sequence; except for the last transposed convolutional layer, the remaining transposed convolutional layers use the PReLU activation function; the first to Nth convolutional layers of the encoder are connected to the first to Nth transposed convolutional layers of the decoder in a skip connection, where N is the number of convolutional layers / transposed convolutional layers. The decoder generates the enhanced signal G(z,s noisy ) based on a concatenated vector of the encoding vector c and the noise vector z. The signal detector consists of a Flatten layer and four fully connected layers connected sequentially. Except for the last fully connected layer, the remaining fully connected layers use the ReLU activation function and employ Dropout technology to prevent overfitting; the last fully connected layer uses the Sigmoid activation function. The signal detector inputs the integrated features into a Sigmoid activation function as signal detection basis, and outputs a test statistic T Net ∈[0,1] When the test statistic is higher than a preset threshold τ Net , it is judged that a low probability of intercept radar signal is detected, an enhanced signal is generated through a model, and reconstruction of the low probability of intercept radar signal is realized; when the test statistic is lower than the threshold τ Net , it is considered that there is no low probability of intercept radar signal in the input mixed signal sequence, and the signal is discarded. S32. Construct discriminator D, which is a binary classifier used to distinguish the input signal. Discriminator D identifies the enhanced signal generated by generator G as false and the clean signal as true, and feeds back the result of the discrimination to generator G. Discriminator D uses 11 convolutional layers to perform convolution operations on the data, and introduces a batch normalization layer and LeakyReLU activation function after each convolutional layer; then the features extracted by the convolutional layers are used for judgment through fully connected layers and Softmax activation function; S4. Construct the loss function of the LPI-DE-GAN model, set the hyperparameters of the network, initialize the LPI-DE-GAN parameters, and train the LPI-DE-GAN model.

2. The low intercept radar signal detection and enhancement method based on LPI-DE-GAN according to claim 1, characterized in that, Step S1 includes the following process: S11. Set the parameter range of low probability of intercept (LPI) radar signal pulses, and obtain multiple LPI radar signal sequences with different modulation methods; obtain a 0 sequence with the same total length as the multiple LPI radar signal sequences as a comparison sample signal sequence when there is no signal; combine all LPI signals and 0 sequence samples to form a clean signal sequence. S12, set the signal-to-interference-and-noise ratio SINR range as [SINR min , SINR max ], SINR min and SINR max are the upper and lower bounds of the signal-to-interference-and-noise ratio range respectively; the signal-to-interference-and-noise ratio change step is ΔSINR; within the SINR range, noise and marine navigation signals under the signal-to-interference-and-noise ratio are generated every ΔSINR, and the noise and marine navigation signals are superimposed with the clean signal to obtain a mixed signal sequence.

3. The low intercept radar signal detection and enhancement method based on LPI-DE-GAN according to claim 1, characterized in that, Step S2 includes the following process: S21. Set the window length w and step size s, and use the set window length and step size to adjust S. noisy and S clean Slicing is performed to obtain n mixed signal sample blocks s noisy and n clean signal sample blocks s clean These are the mixed signal sequence and the signal enhancement task label, respectively, used as inputs to LPI-DE-GAN; S22. Obtain "0" or "1" as tags for low probability of intercept radar signal detection tasks; all tags y i This constitutes the signal detection tag sequence y; When the mixed signal input to the network model contains one of the multiple low probability of intercept radar signals in step S1, y i Select "1"; otherwise, y i Take "0".

4. The low intercept radar signal detection and enhancement method based on LPI-DE-GAN according to claim 1, characterized in that, Step S4 includes the following process: S41. Construct the loss functions for the LPI-DE-GAN generator and discriminator; The loss function of the generator is: In the formula, V Detect (G) and V Enhance (G) represents the loss function for the signal detection task and the signal enhancement task, respectively, and α and β represent the weights in the signal detection task and the signal enhancement task, respectively; p represents the average of the input; z represents a sample obtained from random noise; p z (z) refers to the probability distribution of the input noise z; s noisy Indicates a mixed signal, p data (s noisy ) is a mixed signal s noisy The probability distribution of s; clean Let represent a clean signal, |||||2 represent the L2 loss, and λ be a hyperparameter controlling the L2 loss. The test statistic T represents the output of the detector. Net The value of y i The detection label takes a value of 0 or 1, M represents the number of samples, and μ is a hyperparameter controlling the loss of the detection task; D(G(z,s) noisy ),s noisy ) represents the output of discriminator D; The objective loss function of the discriminator is: S42. Set the hyperparameters of LPI-DE-GAN and initialize the model weights; S43. Train the LPI-DE-GAN model, perform forward propagation to calculate the loss function values ​​of the LPI-DE-GAN generator and discriminator, and then update the parameters of the network model through the backpropagation algorithm. Repeat this process until the predetermined maximum number of iterations is reached.

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