Low-interception probability radar signal enhancement method based on depth state space model

Abstract

The invention discloses a low-interception radar signal enhancement method based on a depth state space model. The method comprises the following steps: S1, obtaining a low-interception signal sequence data set; s2, constructing a low-interception probability radar signal enhancement model based on a deep state space model, and embedding the state space model into a deep neural network to capture signal long-time dependence; s3, constructing a loss function, and setting hyper-parameters of the network; s4, training a low-interception probability radar signal enhancement model based on the depth state space model; and S5, inputting the mixed signal containing the Gaussian white noise into the trained low-interception-probability radar signal enhancement model based on the depth state space model to obtain an enhanced low-interception-probability radar signal. According to the method, end-to-end enhancement can be carried out on the received low-interception-probability radar signals of various modulation types under the low signal-to-noise ratio from the time domain, noise is fully suppressed, and the original low-interception-probability radar signals are reconstructed.

Description

Technical Field

[0001] The invention belongs to the field of radar technology, and in particular relates to a low intercept probability radar signal enhancement method based on a deep state space model. Background Art

[0002] Non-cooperative low probability of intercept (LPI) radar signals have been widely used in modern radar systems due to their high duty cycle and large bandwidth. These characteristics can significantly reduce the peak power of radar signals, thereby effectively improving the stealth of radar systems. However, this low probability of intercept characteristic also brings severe challenges to the signal processing of the reconnaissance party. Reconnaissance receivers usually adopt a broadband receiving strategy, which can capture more signal information, but also leads to a large amount of Gaussian white noise in the intercepted signal. At this time, the low probability of intercept radar signal is often submerged in the noise, resulting in an extremely low signal-to-noise ratio (SNR). Low signal-to-noise ratio conditions seriously affect subsequent signal detection, identification and parameter estimation. Therefore, how to effectively enhance non-cooperative low probability of intercept radar signals in a low signal-to-noise ratio environment has become a key issue that needs to be urgently solved in the current radar signal processing field.

[0003] Traditional signal enhancement methods include Savitzky-Golay filtering, Wiener filtering, wavelet threshold denoising, and empirical mode decomposition. However, the performance of these methods is significantly reduced when processing non-stationary signals with low signal-to-noise ratio. In addition, traditional methods are usually based on local features, while low probability of intercept radar signals have long-term dependencies and global features, which are difficult to capture by traditional methods. Traditional methods usually require manual adjustment of parameters (such as filter order, threshold size, etc.) and lack adaptive capabilities. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a low probability of intercept radar signal enhancement method based on a deep state space model, which can perform end-to-end time domain signal enhancement on a received low probability of intercept radar signal under low signal-to-noise ratio conditions.

[0005] The objective of the present invention is achieved through the following technical solution: A method for enhancing a low probability of intercept radar signal based on a deep state space model comprises the following steps:

[0006] S1. Acquire low intercept signal sequence data set; including the following processes:

[0007] S11, setting a parameter range of a low probability of intercept radar signal, and obtaining a plurality of low probability of intercept radar signal sequences of different modulation modes as clean signal sequences; wherein the number of low probability of intercept radar signal sequences of each modulation mode is the same;

[0008] S12. Set the signal-to-noise ratio (SNR) range [SNR min , SNR max , SNR min and SNR max are respectively the upper and lower bounds of the SNR range, and the SNR change step size is set to ΔSNR; within the SNR range, Gaussian white noise at this SNR is generated every ΔSNR interval, and the Gaussian white noise is respectively superimposed on each clean signal sequence to obtain a mixed signal sequence;

[0009] S2. Construct a low probability of intercept radar signal enhancement model based on a deep state space model, and embed the state space model into a deep neural network to capture the long-term dependence of the signal; the process includes the following:

[0010] S21. Construct a feature extractor: The feature extractor includes a first linear layer, a first reshaping-attention-linear module, and a second reshaping-attention-linear module connected in sequence; the first reshaping-attention-linear module and the second reshaping-attention-linear module have the same structure and are composed of a reshaping layer, a channel attention layer, and a linear layer;

[0011] S22. Construct a signal reconstructor: The signal reconstructor includes a first convolutional-state space model module, a first linear-attention-reshaping module, a second convolutional-state space model block module, a second linear-attention-reshaping module, a third convolutional-state space model module, and a second linear layer connected in sequence; the first convolutional-state space model module is connected to the second reshaping-attention-linear module;

[0012] The first convolutional-state space model module, the second convolutional-state space model module, and the third convolutional-state space model block have the same structure and are composed of eight cascaded convolutional-state space model blocks; the eight cascaded convolutional-state space model blocks have the same structure and are composed of channel division, parallel convolutional branches and state space model branches, and channel shuffling. Both the convolutional branch and the state space model branch are connected to the channel division, and the outputs of the convolutional branch and the state space model branch are connected to the channel shuffling after channel splicing;

[0013] The convolutional branch is composed of a 1×1 pointwise convolution, a 3×3 depthwise separable convolution, and a 1×1 pointwise convolution connected in sequence; the state space model branch is composed of two serial layers connected in sequence. The first serial layer is composed of a layer normalization, a state space model layer, a GeLU activation function, and a linear layer connected in sequence, and the input of the layer normalization is connected to the output of the linear layer for residual connection; the second serial layer is composed of a layer normalization, a linear layer, a GeLU activation function, and a linear layer, and the input of the layer normalization is connected to the output of the linear layer for residual connection;

[0014] S23. Construct skip connections: fuse the output of the second reshaping-attention-linear module and the output of the first convolutional-state space model module by element-wise addition, fuse the output of the first reshaping-attention-linear module and the output of the second convolutional-state space model module, and fuse the output of the first linear layer and the output of the third convolutional-state space model module;

[0015] S3. Construct the loss function of the low probability of intercept radar signal enhancement model based on the deep state space model, set the hyperparameters of the network, and initialize the network parameters;

[0016] S4. Use the mixed signal as the input of the low probability of intercept radar signal enhancement model based on the deep state space model, and train the low probability of intercept radar signal enhancement model based on the deep state space model;

[0017] S5. Input the mixed signal containing Gaussian white noise into the trained low probability of intercept radar signal enhancement model based on the deep state space model to obtain the enhanced low probability of intercept radar signal.

[0018] The beneficial effects of the present invention are as follows: Aiming at the problem that the signal enhancement performance of the traditional method for low probability of intercept radar signals under low signal-to-noise ratio degrades, the present invention constructs a low probability of intercept radar signal enhancement model based on the deep state space model, which combines the characteristics of dynamic system modeling and deep learning, and can accurately capture the dynamic characteristics and long-term dependencies of time series signals. The low probability of intercept radar signal features are extracted by the feature extractor, and the signal waveform of the low probability of intercept radar signal is restored by using the features. The present invention improves the enhancement performance of low probability of intercept radar signals under low signal-to-noise ratio; integrating the state space model into the deep learning framework not only helps to realize the modeling of global features, but also can significantly reduce the computational complexity, thereby improving the real-time performance and generalization ability of the enhancement model. This combination provides a new idea and solution for the low probability of intercept radar signal enhancement task in a low signal-to-noise ratio environment. Description of the Drawings

[0019] Figure 1 is the implementation flowchart of the present invention;

[0020] Figure 2 is the structure of the low probability of intercept radar signal enhancement model based on the deep state space model;

[0021] Figure 3 is the structure of the convolutional-state space model block;

[0022] Figure 4 is the enhancement effect of the model on the LFM signal when the signal-to-noise ratio is -10 dB;

[0023] Figure 5The enhancement effect of the model on Barker code signals when the signal-to-noise ratio is -10 dB;

[0024] Figure 6 The enhancement effect of the model on Costas signals when the signal-to-noise ratio is -10 dB. Detailed implementation manners

[0025] To enable those of ordinary skill in the art to better understand the technical solution of the present invention, the technical solution of the present application will be further described below in conjunction with the accompanying drawings and specific embodiments. This example mainly uses the scientific computing software MATLAB R2023a and Pycharm 2023.2.5 to conduct simulation experiments to verify the enhancement effect of low intercept probability radar signals.

[0026] As Figure 1 shown, a method for enhancing low intercept probability radar signals based on a deep state space model of the present invention includes the following steps:

[0027] S1. Obtain a low intercept signal sequence data set, including clean signals and mixed signals; and divide the data set into a training set, a validation set, and a test set; including the following processes:

[0028] S11. Set the parameter ranges of low intercept probability radar signals as shown in Table 1, with the sampling frequency f s being 20 MHz, and obtain low intercept probability radar signal sequences of three different modulation methods, namely LFM, Barker code, and Costas, as clean signal sequences; the length of each low intercept probability radar signal sequence is 10,000. The number of low intercept probability radar signal sequences of each modulation method is the same; to ensure the balance of training data, 500 clean signal sequences are generated for each modulation method under each signal-to-noise ratio condition.

[0029] Table 1

[0030]

[0031]

[0032] In the above table, cpp represents the phase modulation count; U(·) represents the uniform distribution, and {·} represents randomly taking values from the given data.

[0033] S12. Set the signal-to-noise ratio SNR range [SNR min , SNR max , where SNR min and SNR max are respectively the upper and lower bounds of the signal-to-noise ratio range, and the signal-to-noise ratio change step size is set to ΔSNR. In this embodiment, SNR min is set to -20 dB, and SNR maxis 0 dB, and ΔSNR is set to 2 dB; within the SNR range, Gaussian white noise at this SNR is generated every ΔSNR; the Gaussian white noise generated at each SNR is respectively superimposed one by one with 500 clean signal sequences of the three modulation methods generated in S11 to obtain 500 mixed signal sequences;

[0034] S13. Divide the obtained signal sequences into a training set, a validation set, and a test set according to a ratio of 8:1:1. The training set and the validation set are used to train the model, and the test set is used to verify the model effect.

[0035] S2. Construct a low probability of intercept radar signal enhancement model based on a deep state space model, embed the state space model into a deep neural network to capture the long-term dependence of the signal, and its structure is as Figure 2 shown; including the following processes:

[0036] S21. Construct a feature extractor: The feature extractor includes a first linear layer, a first reshaping-attention-linear module, and a second reshaping-attention-linear module connected in sequence; the first reshaping-attention-linear module and the second reshaping-attention-linear module have the same structure and are composed of a reshaping layer, a channel attention layer, and a linear layer;

[0037] S22. Construct a signal reconstructor: The signal reconstructor includes a first convolutional-state space model module, a first linear-attention-reshaping module, a second convolutional-state space model block module, a second linear-attention-reshaping module, a third convolutional-state space model module, and a second linear layer connected in sequence; the first convolutional-state space model module is connected to the second reshaping-attention-linear module;

[0038] The first convolutional-state space model module, the second convolutional-state space model module, and the third convolutional-state space model block have the same structure and are composed of eight cascaded convolutional-state space model blocks; the eight cascaded convolutional-state space model blocks have the same structure, as Figure 3 shown, and are composed of channel division, parallel convolutional branches and state space model branches, and channel shuffling. Both the convolutional branch and the state space model branch are connected to the channel division. The outputs of the convolutional branch and the state space model branch are connected to the channel shuffling after channel splicing;

[0039] The convolutional branch consists of a sequential connection of a 1×1 pointwise convolution, a 3×3 depthwise separable convolution, and a 1×1 pointwise convolution; the state space model branch consists of a sequential connection of two serial layers. The first serial layer consists of a sequential connection of layer normalization, a state space model layer, a GeLU activation function, and a linear layer, with a residual connection between the input of the layer normalization and the output of the linear layer. The second serial layer consists of a sequential connection of layer normalization, a linear layer, a GeLU activation function, and a linear layer, with a residual connection between the input of the layer normalization and the output of the linear layer.

[0040] S23. Construct a skip connection: The skip connection fuses the output of the reshaping-attention-linear module in the feature extractor and the output of the convolution-state space model module in the signal reconstructor by element-wise addition. Specifically, it fuses the output of the second reshaping-attention-linear module and the output of the first convolution-state space model module, the output of the first reshaping-attention-linear module and the output of the second convolution-state space model module, and the output of the first linear layer and the output of the third convolution-state space model module by element-wise addition.

[0041] S3. Construct the loss function of the low probability of intercept radar signal enhancement model based on the deep state space model, set the hyperparameters of the network, and initialize the network parameters. The process includes the following:

[0042] S31. Construct the loss function of the low probability of intercept radar signal enhancement model based on the deep state space model, that is, the loss function of the signal enhancement task, and its expression is:

[0043]

[0044] In the formula, s enhanced represents the enhanced signal output by the low probability of intercept radar signal enhancement model based on the deep state space model, s clean represents the clean signal, and N represents the number of samples.

[0045] S32. Set the hyperparameters of the low probability of intercept radar signal enhancement model based on the deep state space model. Its Batch Size is set to 32, Epoch is set to 200, the optimizer is selected as AdamW, and the learning rate is set to 0.001. Use Kaiming initialization to initialize the model weights.

[0046] S4. Use the mixed signals of the training set and the validation set as the input of the low probability of intercept radar signal enhancement model based on the deep state space model, and train the low probability of intercept radar signal enhancement model based on the deep state space model. The process includes the following sub-steps:

[0047] S41. Train the feature extractor: First, use the mixed signals The input is fed into the first linear layer for dimensionality increase to extract its high-dimensional features, obtaining a first feature map with 128 channels; then it is input into the first reshaping-attention-linear module, as Figure 4 shown. The dimensionality of the feature map is adjusted through reshaping, and then the inter-channel attention mechanism is used to enable the model to focus on the features beneficial to the signal enhancement task. Finally, a linear layer is used to perform dimensionality transformation on the feature map to obtain a second feature map

[0048] The dimensionality transformation in the reshaping-attention-linear module for the feature map is expressed as:

[0049]

[0050] where T and C respectively represent the length and the number of channels of the input feature map, p is the downsampling factor, and q is the expansion factor. In this embodiment, p = 4 and q = 2.

[0051] The inter-channel attention is applied to an input feature map Specifically, average pooling is performed on the time dimension of each channel of the feature map to squeeze it into a real number z c , where c = 1,..., C, and the process is as follows:

[0052]

[0053] where F c (t) represents the value of the c-th channel of F at the t-th position in the time dimension.

[0054] After the above operations, the feature map is transformed into Then, a fully connected layer is used to reduce the dimensionality of z to obtain where d represents the dimensionality reduction factor. In this embodiment, d = 4. The process can be expressed as:

[0055] z' = ReLU(W 1 z + b 1 )

[0056] where is the weight matrix; is the bias; ReLU(·) represents the ReLU activation function. Then, the dimensionality of z' is increased to obtain the channel weights The process is similar to the above dimensionality reduction and is also achieved through a fully connected layer. Then, the Sigmoid function is used to activate the feature map, and the process is as follows:

[0057] z” = Sigmoid(W 2 z' + b 2 )

[0058] where is the weight matrix; is the bias; Sigmoid(·) represents the Sigmoid activation function. Through the above operations, the C values in z are compressed into the range [0, 1], and these values represent the relative importance degrees of their corresponding channels. Finally, the channel weight z” is weighted onto the feature map:

[0059] F c' = z c ”F c

[0060] where F c' represents the value in the time dimension of the c-th channel of the feature vector focused by channel attention, z c ” represents the c-th channel weight, and F c represents the feature map of the c-th channel. After weighting each channel, the final feature map is used as the second feature map F 2 .

[0061] After obtaining the second feature map F 2 , the second feature map is input into the second reshaping-attention-linear module to obtain the third feature map

[0062] S42. Training signal reconstructor: First, input the third feature map into the first convolutional-state space model module, which contains eight cascaded convolutional-state space model blocks. Each convolutional-state space model block divides the input feature map into channels, and then the two feature maps after channel division are respectively input into the convolutional branch and the state space model branch to obtain the results of the corresponding two branches. Then, the results of the two branches are merged in the channel dimension and then channel shuffled. After passing through the first convolutional-state space model module, the fourth feature map is obtained.

[0063] The specific operations in the state space model branch are as follows: First, input the feature map into the first serial layer, as Figure 3 shown. The input feature map passes through layer normalization (Layer Normalization, LN), the state space model layer, the GeLU activation function, and the linear layer, and then is added to the input feature map. Then, the result is input into the second serial layer, and the second row layer contains normalization, the linear layer, the GeLU activation function, and the linear layer. The specific operations of the state space model layer are as follows: The state space model maps the one-dimensional continuous time series u(t) to y(t), and the process is as follows:

[0064]

[0065] y(t) = Cx(t)

[0066] where \(A\in R\) N×N is the evolution parameter matrix, \(B\in R\) N×1 , \(C\in R\) 1×N is the projection parameter matrix, \(x(t)\) is the hidden state, denotes the derivative of \(x(t)\). Since the input to the state space model layer is a discrete sequence, the state space model layer discretizes the above process using the time scale \(\Delta\) parameter:

[0067]

[0068] y k \(= Cx\) k

[0069]

[0070] where \(k = 0, 1, 2, \cdots, L\), \(L\) represents the sequence length, \(\exp(\cdot)\) is the matrix exponential, and \(I\) is the identity matrix. It can be found from the above formula that the output \(y=(y 0 ,y 1 ,\cdots,y L-1 ) of the state space model layer can be represented by global convolution:

[0071]

[0072] where \(u=(u 0 ,u 1 ,\cdots,u L-1 ) is the input sequence, is the global convolution kernel.

[0073] Add the feature map output by the first convolution-state space model module and the third feature map through skip connection, then input it into the first linear-attention-reshape module, use the linear layer to perform dimensional transformation on the feature map, then use the inter-channel attention mechanism to make the model focus on the features beneficial to the signal enhancement task, and finally adjust the dimension of the feature map through reshape. Finally, use the linear layer to perform dimensional transformation on the feature map to obtain the fifth feature map; the dimensional transformation of the feature map in the linear-attention-reshape module is expressed as:

[0074]

[0075] where \(u\) is the upsampling factor. In this embodiment, \(u = 4\), and the setting of \(q\) is the same as that in the reshape-attention-linear module in the feature extractor.

[0076] Then, the feature map passes through the second convolution-state space model module, skip connection, second linear-attention-reshape module, third convolution-state space model module, skip connection, and second linear layer to obtain the enhanced low probability of intercept radar signal

[0077] S43, calculating the loss function value of the low probability of intercept radar signal enhancement model based on the deep state space model; updating the parameters of the low probability of intercept radar signal enhancement model based on the deep state space model according to the loss function value through the back propagation algorithm; repeating the above process until the loss function converges.

[0078] S5. Inputting the mixed signal containing Gaussian white noise into the trained low probability of intercept radar signal enhancement model based on the deep state space model to obtain an enhanced low probability of intercept radar signal.

[0079] In this embodiment, the mixed signal in the test set is input into a trained low probability of intercept radar signal enhancement model based on a deep state space model. Figures 4 to 6 The enhancement effects of the model on LFM, Barker code, and Costas signals when the signal-to-noise ratio is -10dB are shown respectively. It can be seen from the figure that when the signal-to-noise ratio is as low as -10dB, the low probability of intercept radar signal enhancement model based on the deep state space model can effectively enhance the low probability of intercept radar signal, the Gaussian white noise in the mixed signal is fully suppressed, and the enhanced signal waveform output by the model is similar to the clean signal.

[0080] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A low probability of intercept radar signal enhancement method based on a deep state space model, characterized in that: The following steps are involved: S1. Acquire low intercept signal sequence data set; The process includes: S11, setting a parameter range of a low probability of intercept radar signal, and obtaining a plurality of low probability of intercept radar signal sequences of different modulation modes as clean signal sequences; wherein the number of low probability of intercept radar signal sequences of each modulation mode is the same; S12, set the signal-to-noise ratio SNR range [SNR min ,SNR max ], SNR min and SNR max are the upper and lower bounds of the signal-to-noise ratio range, respectively. The signal-to-noise ratio change step is set to ΔSNR. Within the SNR range, Gaussian white noise under the signal-to-noise ratio is generated at each interval ΔSNR. The Gaussian white noise is superimposed on each clean signal sequence to obtain a mixed signal sequence. S2. Build a low probability of intercept radar signal enhancement model based on a deep state space model, embed the state space model into a deep neural network to capture the long-term dependency of the signal; including the following processes: S21. Construct a feature extractor: The feature extractor includes a first linear layer, a first reshaping-attention-linear module, and a second reshaping-attention-linear module connected in sequence; the first reshaping-attention-linear module and the second reshaping-attention-linear module have the same structure, and are composed of a reshaping layer, a channel attention layer, and a linear layer; S22, constructing a signal reconstructor: the signal reconstructor includes a first convolution-state space model module, a first linear-attention-reshaping module, a second convolution-state space model block module, a second linear-attention-reshaping module, a third convolution-state space model module, and a second linear layer connected in sequence; the first convolution-state space model module is connected to the second reshaping-attention-linear module; The first convolution-state space model module, the second convolution-state space model module, and the third convolution-state space model block have the same structure, which is composed of eight convolution-state space model blocks connected in series; the eight convolution-state space model blocks connected in series have the same structure, which is composed of channel division, parallel convolution branches and state space model branches, and channel shuffling, and the convolution branches and state space model branches are both connected to the channel division, and the outputs of the convolution branches and the state space model branches are connected to the channel shuffling after channel splicing; The convolution branch is composed of 1×1 point-by-point convolution, 3×3 depth-separable convolution, and 1×1 point-by-point convolution in sequence; the state-space model branch is composed of two serial layers in sequence, the first serial layer is composed of sequential layer normalization, state-space model layer, GeLU activation function, and linear layer connection, and the input of the layer normalization is residually connected to the output of the linear layer; the second serial layer is composed of sequential layer normalization, linear layer, GeLU activation function, and linear layer, and the input of the layer normalization is residually connected to the output of the linear layer; S23, constructing a jump connection: fusing the output of the second reshape-attention-linear module and the output of the first convolution-state space model module by element-wise addition, fusing the output of the first reshape-attention-linear module and the output of the second convolution-state space model module, and fusing the output of the first linear layer and the output of the third convolution-state space model module; S3. Construct the loss function of the low probability of intercept radar signal enhancement model based on the deep state space model, set the network's hyperparameters, and initialize the network parameters; S4, using the mixed signal as an input of a low probability of intercept radar signal enhancement model based on a deep state space model, and training the low probability of intercept radar signal enhancement model based on a deep state space model; S5. Inputting the mixed signal containing Gaussian white noise into the trained low probability of intercept radar signal enhancement model based on the deep state space model to obtain an enhanced low probability of intercept radar signal.

2. The method for enhancing low probability of intercept radar signals based on a deep state space model according to claim 1, characterized in that: The step S3 includes the following process: S31. Construct the loss function of the low probability of intercept radar signal enhancement model based on the deep state space model, that is, the loss function of the signal enhancement task, which is expressed as: In the formula, s enhanced represents the enhanced signal output by the low probability of intercept radar signal enhancement model based on the deep state space model, s clean represents a clean signal, and N represents the number of samples; S32. Set hyperparameters of a low probability of intercept radar signal enhancement model based on a deep state space model, and initialize model weights.

3. The method for enhancing low probability of intercept radar signals based on a deep state space model according to claim 1, characterized in that: Step S4 includes: S41, training feature extractor: first, the mixed signal is input into the first linear layer for dimension increase to obtain the first feature map; then it is input into the first reshape-attention-linear module, the dimension of the feature map is adjusted by reshape, and then the inter-channel attention mechanism is used to make the model focus on the features that are beneficial to the signal enhancement task, and finally the linear layer is used to transform the dimension of the feature map to obtain the second feature map; the dimension transformation in the feature map reshape-attention-linear module is expressed as: Among them, T and C represent the length and number of channels of the input feature map respectively, p is the downsampling factor, and q is the expansion factor; then the second feature map is input into the second reshape-attention-linear module to obtain the third feature map; S42, training signal reconstructor: first, the third feature map is input into the first convolution-state space model module, which includes eight convolution-state space model blocks connected in series, each convolution-state space model block performs channel division on the input feature map, and then the two feature maps after channel division are respectively input into the convolution branch and the state space model branch to obtain the results of the corresponding two branches, and then the results of the two branches are merged in the channel dimension, and then the channels are shuffled, and after passing through the first convolution-state space model module, the fourth feature map is obtained; then it is added to the third feature map through a jump connection, and then input into the first linear-attention-reshaping module, and the linear layer is used to transform the dimension of the feature map, and then the inter-channel attention mechanism is used to make the model focus on the features that are beneficial to the signal enhancement task, and finally the feature map dimension is adjusted by reshaping, and finally the linear layer is used to transform the dimension of the feature map to obtain the fifth feature map; the dimensional transformation of the feature map in the linear-attention-reshaping module is expressed as: Where u is the upsampling factor; Then, it is passed through the second convolution-state space model module, the skip connection, the second linear-attention-reshape module, the third convolution-state space model module, the skip connection, and the second linear layer to obtain an enhanced low probability of intercept radar signal; S43, calculating the loss function value of the low probability of intercept radar signal enhancement model based on the deep state space model; updating the parameters of the low probability of intercept radar signal enhancement model based on the deep state space model according to the loss function value through the back propagation algorithm; repeating the above process until the loss function converges.

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