Deep learning radar signal noise reduction method

Abstract

The invention discloses a radar signal noise reduction method for deep learning, and relates to the technical field of radar signal processing, and the method comprises the steps: converting a time domain radar signal into a two-dimensional time-frequency graph through short-time Fourier transform; frequency domain feature extraction is carried out on the two-dimensional time-frequency graph, and frequency domain feature representation is output through a DnCNN and a cascade CNN in sequence; performing time domain feature extraction on the time domain radar signal and outputting time domain feature representation; fusing the frequency domain features and the time domain features based on a multi-head attention mechanism to generate cross-domain joint features; and inputting the cross-domain joint feature into a residual shrinkage network for signal reconstruction, and outputting a denoised time domain signal. A time-frequency double-domain collaborative learning framework is constructed, and signal high-fidelity reconstruction in a complex noise environment is realized through deep fusion of time domain characteristics and a frequency domain structure distribution rule. According to the noise reduction method, an extremely low phase error and an extremely high feature retention rate can be kept in a strong noise environment.

Description

Technical Field

[0001] The present application relates to the field of radar signal processing technology, and in particular to a deep learning radar signal denoising method. Background Art

[0002] Radar signal noise reduction technology is a core preprocessing step in target detection and identification, and its performance directly impacts subsequent feature extraction, tracking and positioning, and imaging quality. In complex electromagnetic environments and diverse application scenarios, radar echoes are inevitably subject to interference from multiple sources, including internal system thermal noise, environmental clutter, man-made electromagnetic interference, and disturbances caused by multipath effects. Highly robust noise reduction technology is urgently needed to ensure signal quality.

[0003] Traditional signal processing schemes (such as wavelet threshold denoising and empirical mode decomposition) rely on manually designed feature rules and parameter adjustments, facing problems such as insufficient suppression of burst noise, modal aliasing, and high-frequency signal impairment. Their generalization capabilities decline sharply in unknown noise environments, and a conflict between noise suppression and signal distortion is common. While emerging deep learning methods have achieved breakthroughs in image denoising, direct application to radar signal processing fails to capture the dynamic characteristics of radar pulse trains due to the difficulty of modeling long-term temporal correlations with two-dimensional convolution kernels and the vanishing gradient defect of recursive networks. More critically, existing deep learning schemes ignore the physical nature of radar signals—the time-frequency spectrum contains complex phase information. Real-domain processing destroys phase continuity, resulting in the loss of target micro-motion features. Furthermore, the coherent nature of pulse Doppler radars requires strict phase consistency, but mainstream methods focus solely on amplitude-domain reconstruction, resulting in phase offsets in the inverse-transformed time-domain signal, severely impacting subsequent processing accuracy.

[0004] Therefore, how to simultaneously achieve the triple goals of noise suppression, phase protection, and structure preservation in a complex noise environment, break through the dual bottlenecks of poor generalization of traditional methods and physical mismatch of deep learning, and provide a high-fidelity preprocessing foundation for radar signal processing is a technical problem that needs to be solved urgently in this field. Summary of the Invention

[0005] In order to solve the above technical problems, this application proposes the following technical solutions: In a first aspect, an embodiment of the present application provides a deep learning radar signal noise reduction method, comprising: The time domain radar signal is converted into a two-dimensional time-frequency graph through short-time Fourier transform; Perform frequency domain feature extraction on the two-dimensional time-frequency graph, and output frequency domain feature representation by passing it through DnCNN and cascade CNN in sequence; Performing time domain feature extraction on the time domain radar signal and outputting a time domain feature representation; Based on the multi-head attention mechanism, the frequency domain features and the time domain features are fused to generate cross-domain joint features; The cross-domain joint features are input into the residual shrinkage network for signal reconstruction, and the denoised time domain signal is output.

[0006] In a possible implementation, converting the time-domain radar signal into a two-dimensional time-frequency graph through short-time Fourier transform includes: The total length is M Discrete time domain radar signal x [ m ] Divided into K overlapping data segments, each containing n sampling points, of which K=Mn ; For each data segment ( r =0,1,…, K −1) Execution n Pointwise discrete Fourier transform: , is a complex matrix; right A modulo operation is performed to obtain the two-dimensional time-frequency graph.

[0007] In a possible implementation, extracting frequency domain features from the two-dimensional time-frequency graph and outputting frequency domain feature representation by sequentially passing through DnCNN and cascaded CNN include: The two-dimensional time-frequency map is input into the DnCNN, and a 3×3 convolution is first performed on the output, followed by batch normalization and ReLU activation: in: is the activation function, is the batch normalization function, is the convolution function with a convolution kernel of 3×3; Then pass l Layer residual block structure, each residual block structure contains a 3×3 convolution calculation, a batch normalization calculation and a ReLU activation function, and finally the input and output are added, expressed as: in: For the l The residual block outputs the result; The output is then reduced to a single channel through a 1×1 convolution operation: The output of DnCNN is subjected to feature extraction by the CNN, which is composed of a combination of multiple convolution kernels and pooling layers. The convolution kernel size in the time dimension is 5×1, the frequency dimension size is 1×3, and the channel expansion is , the output of each convolution pooling combination is: in: is the output result of the kth convolution pooling combination, is the pooling function; Finally, the final transformation is completed through the fully connected layer: ,in: is the fully connected layer function.

[0008] In a possible implementation, extracting time domain features from the time domain radar signal and outputting a time domain feature representation includes: The time domain radar signal is simultaneously input into the LSTM network and the TCN network for dual-path parallel processing; The time domain radar signal is processed by n LSTM units in the LSTM network. , where: For the final output, is the unit state at each moment; The time domain radar signal undergoes dilation convolution and residual processing in the TCN network through multiple Block units. The dilation factor in the kth layer is The output of the dilated convolution is: ,in: is the dilated convolution function; Normalize the dilated convolution output: ,in: is the weight normalization function; Add Dropout layer to prevent overfitting: , and finally perform residual connection, where: To randomly close some node functions; The output of the LSTM network and the TCN network is aggregated through the MLP network. The MLP network consists of multiple linear fully connected layers, and the output of each layer is in: It is a linear fully connected layer function, and the output of MLP is the time domain feature representation.

[0009] In one possible implementation, the fusing of the frequency domain features and the time domain features based on the multi-head attention mechanism to generate cross-domain joint features includes: The time domain features are used as dynamic query vectors, and the frequency domain features serve as both key vectors and value vectors; Through the multi-head attention mechanism, deep interaction guided by physical mechanisms is achieved. Each time-domain feature vector generates a set of query instructions and initiates feature retrieval requests in the frequency-domain feature space. First, the scaled dot product correlation between the time domain feature query vector and all frequency domain feature vectors is calculated to generate the original correlation score matrix: in: is the activation function, is the query vector, is the key vector, is the dimension of the key vector; The original relevance score matrix is ​​normalized by the Softmax function to form a probabilistic attention weight distribution; Then the frequency domain value vector is weighted and aggregated to capture the time-frequency feature association and output the attention matrix: ,in: is the key vector; Combining the outputs of all attention heads yields: ,in: is a cross-domain joint feature. is the feature merging function.

[0010] In a possible implementation, inputting the cross-domain joint features into a residual shrinkage network for signal reconstruction and outputting a denoised time domain signal includes: The residual shrinkage network is used to combine the cross-domain features Perform feature preprocessing and capture the dependencies between features through wide convolution kernels: Then, the noise reduction process is performed through multiple residual shrinkage blocks to obtain the denoised time domain signal, where: is the 1-dimensional batch normalization function, is a 1-dimensional convolution function.

[0011] In a possible implementation, the step of performing noise reduction processing on the plurality of residual shrinkage blocks to obtain a noise-reduced time domain signal includes: First, estimate the noise energy and calculate the noise intensity index: in: is the activation function; Adaptively filter the features to achieve soft thresholding. The soft thresholding function is: ; Finally, perform residual connection: ; After processing by multiple residual shrinkage blocks, the final output of the time signal denoising result is: .

[0012] In a possible implementation, the method further includes optimizing network parameters through a joint loss function, where the joint loss function is composed of a weighted combination of a time domain mean square error loss and a frequency domain structural similarity loss.

[0013] In one possible implementation, optimizing network parameters by using a joint loss function includes: Calculate the time domain mean square error MSE to obtain the denoised time domain signal and the real signal , both are discrete sequences of length N; Compute the squared error point by point: ; Find the mean error across all time points: ; Calculate the time-frequency spectrum after noise reduction and real time spectrum , and normalize it to the interval [0,1]: Define the local calculation window and traverse each position in the time-frequency plane , calculate the mean within the window: in: is the weight of each position, i, j are the traversal numbers; Calculate the variance within the window: Calculate the covariance: Calculate the local SSIM value: in: , is the stability constant, is the variance of the true value, is the covariance of the true value; Calculate the global average SSIM: Where: T is the time length, F is the frequency length; Calculate SSIM loss: Finally, the joint loss is weighted summed: in: and It is an adjustable hyperparameter used to balance the priority of waveform fidelity and time-frequency structure preservation. , late training .

[0014] In this application, a dual-domain collaborative learning framework is constructed to achieve high-fidelity signal reconstruction in complex noise environments by deeply integrating time-domain characteristics with frequency-domain structural distribution patterns. This noise reduction method can maintain extremely low phase error and high feature retention in strong noise environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 A flowchart of a deep learning radar signal noise reduction method provided in an embodiment of the present application; Figure 2 A schematic diagram of the frequency domain feature extraction process provided in an embodiment of the present application; Figure 3 A schematic diagram of the time domain feature extraction process provided in an embodiment of the present application; Figure 4 A schematic diagram of a residual link module provided in an embodiment of the present application; Figure 5 A schematic diagram of the time-frequency feature fusion process provided in an embodiment of the present application; Figure 6 Schematic diagram of time signal reconstruction provided in an embodiment of the present application Figure 7 Schematic diagram of the residual shrinkage block provided in the embodiment of the present application DETAILED DESCRIPTION The present invention will be described below with reference to the accompanying drawings and specific implementation methods.

[0016] See also Figure 1 The radar signal denoising method based on deep learning provided in this embodiment includes: S101, converting the time domain radar signal into a two-dimensional time-frequency graph through short-time Fourier transform.

[0017] like Figure 2 As shown, this step mainly extracts the frequency domain features of the signal, and the total length is M Discrete time series signal x [ m ] , m =0,1,…, M −1, divided into K overlapping data segments, each containing n sampling points, of which K=Mn .

[0018] For each data segment , r =0,1,…, K −1, execute n Point discrete Fourier transform DFT: , is a complex matrix, A modulo operation is performed to obtain the two-dimensional time-frequency graph.

[0019] Converting a one-dimensional time-domain signal into a two-dimensional time-frequency image can simultaneously display the signal's time-varying characteristics and spectral features. Using the Short-Time Fourier Transform as the foundational tool for time-frequency analysis, this method uses a sliding window approach to achieve time-frequency localization analysis of the signal, simultaneously displaying the signal's changing characteristics in both time and frequency dimensions.

[0020] S102, extracting frequency domain features from the two-dimensional time-frequency graph, and outputting frequency domain feature representation by sequentially passing through a denoising convolutional neural network DnCNN and a cascaded convolutional neural network CNN.

[0021] The two-dimensional time-frequency map is input into the DnCNN, and a 3×3 convolution (channel 1→64) is first performed, and the output is batch normalized and ReLU activated: in: is the activation function, is the batch normalization function, is the convolution function with a convolution kernel of 3×3; Then pass l Layer residual block structure, each block contains a 3×3 convolution (channel 64→64) calculation, a batch normalization calculation, and a ReLU activation function. Finally, the input and output are added, which can be expressed as: in: For the l The residual block outputs the result.

[0022] The output result undergoes a 1×1 convolution operation to reduce the 64 channels to a single channel: The output of DnCNN is subjected to a CNN for feature extraction. CNN consists of a combination of multiple convolution and pooling layers. The convolution kernel size is 5×1 in the time dimension and 1×3 in the frequency dimension. The channel expansion is , the output of each convolution pooling combination is: in: is the output result of the kth convolution pooling combination, is the pooling function.

[0023] Finally, the final transformation is completed through the fully connected layer: ,in: is the fully connected layer function.

[0024] This example uses a hybrid architecture combining DnCNN and CNN in the frequency domain feature extraction network design. DnCNN is known for its excellent noise modeling capabilities, making it particularly well-suited for processing random noise components in time-frequency images. This network consists of multiple convolutional layers and employs a residual learning strategy, effectively separating the feature representations of signal and noise.

[0025] To enhance the network's understanding of frequency-domain structure, a dedicated feature-refining CNN is cascaded after the DnCNN. This network employs asymmetric convolutional kernels specifically optimized for the distinct characteristics of time-frequency images in both the time and frequency dimensions. This combined design enables the network to simultaneously characterize both local details and global structural features in the frequency domain, implicitly linking them to the rate of phase change.

[0026] S103: Perform time domain feature extraction on the time domain radar signal to output a time domain feature representation.

[0027] like Figure 3 As shown, in this embodiment, the time domain radar signal is simultaneously input into the LSTM network and the TCN network for dual-path parallel processing.

[0028] A time series of length n (t=0,1,…,n), after n LSTM units are processed to obtain: In the formula For the final output, is the unit state at each moment.

[0029] Another time series After processing by TCN network, TCN network consists of multiple Block units, and the structure of each Block is as follows Figure 4 As shown, the main processing steps in Block are dilation convolution and residual processing. k Layer expansion factor for , to expand the receptive field and dilate the convolution output: ,in: is the dilated convolution function.

[0030] Normalize the dilated convolution output: , in order to prevent overfitting, a Dropout layer is added. , and finally perform residual connection, where: is the weight normalization function, To randomly close some node functions.

[0031] The outputs of LSTM and TCN are aggregated through the MLP network. The MLP consists of multiple linear fully connected layers, and the output of each layer is in: It is a linear fully connected layer function, and the output of MLP is the time domain feature representation.

[0032] In this embodiment, time-domain deep feature extraction uses a dual-path parallel processing architecture, combining the advantages of LSTM and TCN to achieve comprehensive extraction of features at different time scales. The time series signal is simultaneously fed into two parallel processing networks, LSTM and TCN.

[0033] LSTM is used to capture long-term dependencies in signals. The network utilizes a three-layer stacked structure and, through a gating mechanism, can effectively identify and memorize signal patterns spanning multiple pulse repetition periods. The TCN network focuses on extracting local temporal features of the signal. This network utilizes a dilated causal convolutional architecture, combining multiple dilation factors (1, 2, 4, and 8) to construct a temporal feature extractor with a large receptive field. Each convolutional layer is followed by batch normalization and a ReLU activation function to ensure stable network training.

[0034] The feature fusion process extracted by the two networks is achieved through a three-layer fully connected network. This network not only achieves a unified mapping of feature dimensions but also implements an intelligent weighted combination of features at different time scales. The first layer of the fully connected network initially blends the features of the LSTM and TCN. The second layer extracts high-order feature interactions, and the final layer outputs a time-domain feature representation.

[0035] S104, fusing the frequency domain features and the time domain features based on a multi-head attention mechanism to generate a cross-domain joint feature.

[0036] After obtaining the time domain features and frequency domain features, the features of the two channels are fused through the multi-head attention mechanism, such as Figure 5 As shown. The time domain features and frequency domain features obtained above are both 1× n Therefore, the number of heads of multi-head attention is n .

[0037] In this embodiment, time-domain features are used as dynamic query vectors, while frequency-domain features serve as both key and value vectors. A multi-head attention mechanism is used to achieve deep interaction guided by physical mechanisms. Each time-domain feature vector generates a set of query instructions, initiating a "feature retrieval" request in the frequency-domain feature space.

[0038] First, calculate the scaled dot product correlation between the time domain feature query vector and all frequency domain feature vectors: in: is the activation function, is the query vector, is the key vector, is the dimension of the key vector.

[0039] Generate a raw correlation score matrix. This score matrix is ​​normalized by the Softmax function to form a probabilistic attention weight distribution. These weights quantify the strength of the physical correlation between the time domain dynamic behavior at a specific moment and the specific frequency band structure. Then, the frequency domain value vector is weighted and aggregated to capture the time-frequency feature correlation, and the output is the attention matrix: Combine the outputs of all attention heads: in: is the key vector, is a cross-domain joint feature. is the feature merging function.

[0040] In this embodiment, features extracted from the time and frequency domains are deeply integrated to establish intrinsic correlations between the time and frequency features, thereby forming a more expressive joint feature. This time-frequency feature fusion is implemented using a multi-head attention mechanism, which divides the fusion space into multiple attention heads, each of which independently calculates the correlation between the time and frequency features.

[0041] During the computation process, a linear transformation is first performed to generate query, key, and value vectors. Attention weights are then calculated. These weights reflect the importance of features at different time-frequency locations, enabling adaptive focus on key information areas. The attention matrix constructed by the multi-head attention mechanism is essentially a distribution of the correlation strength between dynamic features in the time domain and structural features in the frequency domain.

[0042] This matrix, through normalized weight values, precisely quantifies the strength of the correlation between each time-domain node and a specific frequency-domain unit: when a time-domain transient pulse is physically coupled to a specific frequency band structure, the attention weight at that location is significantly enhanced; conversely, the weight of noise-dominated regions is suppressed to an extremely low level. This dynamically generated weight distribution essentially establishes a geometric mapping between the dynamics of the time-domain waveform and the energy distribution in the frequency domain, providing a critical structure-preserving prior for subsequent reconstruction.

[0043] After the attention calculation is completed, the outputs of each head are concatenated and linearly transformed to form a preliminary fusion feature. This process fully preserves the dynamic evolution information of time domain features and the structural distribution information of frequency domain features, indirectly learning the phase-related temporal dynamics. To balance the relationship between time domain and frequency domain constraints, an adaptive weight adjustment strategy is adopted. At different stages of network training, the weight ratio of the two constraints is dynamically adjusted according to the current learning state. In the early stages of training, more emphasis is placed on time domain constraints to ensure the basic waveform characteristics of the signal. As training progresses, frequency domain constraints are gradually strengthened to optimize the ability to preserve frequency domain details. This dynamic adjustment strategy enables the network to gradually learn the optimal denoising mapping.

[0044] S105: Input the cross-domain joint features into a residual shrinkage network to reconstruct the signal and output a denoised time domain signal.

[0045] See also Figure 6 , the residual shrinkage network is used to combine the cross-domain features Perform feature preprocessing and capture the dependencies between features through wide convolution kernels: Then, the noise reduction process is performed through multiple residual shrinkage blocks to obtain the denoised time domain signal, where: is the 1-dimensional batch normalization function, is a 1-dimensional convolution function.

[0046] like Figure 7 As shown, the processing process of each residual shrinkage block is: First, estimate the noise energy and calculate the noise intensity index: in: is the activation function.

[0047] Adaptively filter the features to achieve soft thresholding. The soft thresholding function is: Finally, perform residual connection: After processing by multiple residual blocks, the final output of the temporal signal denoising result is: In this embodiment, a wide-kernel convolutional layer is used to capture the dependencies between fused features, thereby generating an initial feature map. This initial feature map not only preserves the feature structure of the original input but also preliminarily integrates the dynamic information between features, laying the foundation for subsequent signal reconstruction.

[0048] Subsequently, multiple layers of residual shrinkage blocks are stacked to further enhance feature expression and suppress noise interference. Each residual shrinkage block includes a noise energy estimation module, which dynamically calculates soft threshold parameters using global feature statistics. Based on the calculated soft threshold, a Wiener-like filtering operation is performed in the feature space to effectively suppress noise while preserving and enhancing the effective components of the signal, thereby improving the signal-to-noise ratio and feature fidelity.

[0049] Finally, the original input is added to the thresholded features through the residual path. The residual connection mechanism can maintain the linear relationship of the feature map, reduce phase distortion to a certain extent, and ensure that key pulses or feature edges are not overly weakened by the filtering operation in low signal-to-noise ratio scenarios, thereby maintaining the integrity of the structure and key details to form the final output signal.

[0050] The loss function is designed by jointly optimizing the time domain error and frequency domain structural similarity, where the time domain mean square error ensures waveform consistency; the frequency domain SSIM loss constrains the local structural similarity of the time spectrum.

[0051] First, calculate the time domain mean square error (MSE) to obtain the denoised time domain signal and real clean signal , both are discrete sequences of length N, and the square error is calculated point by point: Find the mean error across all time points: This loss forces the reconstructed signal to be consistent with the true signal in time domain waveform.

[0052] Then, calculate the denoised time spectrum and real time spectrum , and normalize it to the interval [0,1]: Define the local calculation window and traverse each position in the time-frequency plane , calculate the mean within the window: in: is the weight of each position, i, j are the traversal numbers.

[0053] Calculate the variance within the window: Calculate the covariance: Calculate the local SSIM value: in , is the stability constant, is the variance of the true value, is the covariance of the true value.

[0054] Calculate the global average SSIM: Where: T is the time length, F is the frequency length.

[0055] Calculate SSIM loss: This loss maintains the local structural similarity of the time-frequency spectrum and protects key features such as the target micro-Doppler.

[0056] Finally, the joint loss is weighted summed: Among them, α and β are adjustable hyperparameters used to balance the priority of waveform fidelity and time-frequency structure preservation. , late training .

[0057] A loss function is designed to ensure that the denoising result conforms to the physical characteristics of the radar signal. The loss function constrains network training in both the time domain and the frequency domain, ensuring the accuracy of the denoised signal at the waveform level while maintaining the structural integrity of the frequency domain features.

[0058] To ensure that the overall waveform of the denoised signal remains consistent with the original signal, the matching degree of the radar signal waveform is used as a time-domain loss function. Through this constraint, the denoising mapping learned by the network can better preserve the time-domain characteristics of the radar signal. The frequency-domain loss function uses a structural similarity metric to evaluate the matching degree of frequency-domain features before and after denoising. This metric can better capture the local correlation of frequency-domain structures.

[0059] In the embodiments of the present application, "at least one" refers to one or more, and "more" refers to two or more. "And / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B can represent the existence of A alone, the existence of A and B at the same time, and the existence of B alone. Among them, A and B can be singular or plural. The character " / " generally indicates that the previous and next associated objects are in an "or" relationship. "At least one of the following" and similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one of a, b and c can be represented by: a, b, c, ab, ac, bc, or abc, where a, b, c can be single or multiple.

[0060] The above description is merely a specific embodiment of the present application. Any person skilled in the art may easily conceive of variations or substitutions within the technical scope disclosed in this application, and such variations or substitutions shall be within the scope of protection of this application. The scope of protection of this application shall be subject to the scope of protection of the claims.

Claims

1. A deep learning radar signal denoising method, characterized in that: include: The time domain radar signal is converted into a two-dimensional time-frequency graph through short-time Fourier transform; Perform frequency domain feature extraction on the two-dimensional time-frequency graph, and output frequency domain feature representation by passing it through DnCNN and cascade CNN in sequence; Performing time domain feature extraction on the time domain radar signal and outputting a time domain feature representation; Based on the multi-head attention mechanism, the frequency domain features and the time domain features are fused to generate cross-domain joint features; The cross-domain joint features are input into the residual shrinkage network for signal reconstruction, and the denoised time domain signal is output.

2. The radar signal denoising method based on deep learning according to claim 1, characterized in that: The converting of the time domain radar signal into a two-dimensional time-frequency graph by short-time Fourier transform comprises: The total length is M Discrete time domain radar signal x [ m ] , m =0,1,…, M −1, divided into K overlapping data segments, each containing n sampling points, of which K=Mn ; For each data segment , r =0,1,…, K −1, execute n Pointwise discrete Fourier transform: , is a complex matrix; right A modulo operation is performed to obtain the two-dimensional time-frequency graph.

3. The radar signal denoising method based on deep learning according to claim 2, characterized in that: The extracting frequency domain features from the two-dimensional time-frequency graph and outputting frequency domain feature representation by sequentially passing through DnCNN and cascade CNN include: The two-dimensional time-frequency diagram The DnCNN is input and first performs a 3×3 convolution and the output is batch normalized with ReLU activation: in: is the activation function, is the batch normalization function, is the convolution function with a convolution kernel of 3×3; Then pass l Layer residual block structure, each residual block structure contains a 3×3 convolution calculation, a batch normalization calculation and a ReLU activation function, and finally the input and output are added, expressed as: in: For the l The residual block outputs the result; The output is then reduced to a single channel through a 1×1 convolution operation: The output of DnCNN is subjected to feature extraction by the CNN, which is composed of a combination of multiple convolution kernels and pooling layers. The convolution kernel size in the time dimension is 5×1, the frequency dimension size is 1×3, and the channel expansion is , the output of each convolution pooling combination is: in: is the output result of the kth convolution pooling combination, is the pooling function; Finally, the final transformation is completed through the fully connected layer: ,in: is the fully connected layer function.

4. The radar signal denoising method based on deep learning according to claim 1, wherein: The extracting time domain features from the time domain radar signal and outputting a time domain feature representation includes: The time domain radar signal is simultaneously input into the LSTM network and the TCN network for dual-path parallel processing; The time domain radar signal is processed by n LSTM units in the LSTM network. , where: For the final output, is the unit state at each moment; The time domain radar signal is subjected to dilated convolution and residual processing in the TCN network through multiple Block units, and the dilation factor in the kth layer is for The output of the dilated convolution is: ,in: is the dilated convolution function; Normalize the dilated convolution output: ,in: is the weight normalization function; Add Dropout layer to prevent overfitting: , and finally perform residual connection, where: To randomly close some node functions; The outputs of the LSTM network and the TCN network are aggregated through the multi-layer perceptron (MLP) network. The MLP network consists of multiple linear fully connected layers, and the output of each layer is: in: It is a linear fully connected layer function, and the output of MLP is the time domain feature representation.

5. The radar signal denoising method based on deep learning according to claim 1, wherein: The method of fusing the frequency domain features and the time domain features based on the multi-head attention mechanism to generate cross-domain joint features includes: The time domain features are used as dynamic query vectors, and the frequency domain features serve as both key vectors and value vectors; Through the multi-head attention mechanism, deep interaction guided by physical mechanisms is achieved. Each time-domain feature vector generates a set of query instructions and initiates feature retrieval requests in the frequency-domain feature space. First, the scaled dot product correlation between the time domain feature query vector and all frequency domain feature vectors is calculated to generate the original correlation score matrix: in: is the activation function, is the query vector, is the key vector, is the dimension of the key vector; The original relevance score matrix is ​​normalized by the Softmax function to form a probabilistic attention weight distribution; Then the frequency domain value vector is weighted and aggregated to capture the time-frequency feature association and output the attention matrix: ,in: is the key vector; Combining the outputs of all attention heads yields: ,in: is a cross-domain joint feature. is the feature merging function.

6. The radar signal denoising method based on deep learning according to claim 5, characterized in that: Inputting the cross-domain joint features into the residual shrinkage network to reconstruct the signal and output the denoised time domain signal, including: The residual shrinkage network is used to combine the cross-domain features Perform feature preprocessing and capture the dependencies between features through wide convolution kernels: Then, the noise reduction process is performed through multiple residual shrinkage blocks to obtain the denoised time domain signal, where: is the 1-dimensional batch normalization function, is a 1-dimensional convolution function.

7. The radar signal denoising method based on deep learning according to claim 6, characterized in that: The noise reduction process is then performed through multiple residual shrinkage blocks to obtain a noise-reduced time domain signal, including: First, estimate the noise energy and calculate the noise intensity index: in: is the activation function; Adaptively filter the features to achieve soft thresholding. The soft thresholding function is: ; Finally, perform residual connection: ; After processing by multiple residual shrinkage blocks, the final output of the time signal denoising result is: .

8. The radar signal denoising method based on deep learning according to any one of claims 1 to 7, characterized in that: Also includes: The network parameters are optimized by a joint loss function consisting of a weighted mean square error loss in the time domain and a structural similarity loss in the frequency domain.

9. The radar signal denoising method based on deep learning according to claim 8, characterized in that: The network parameters are optimized by the joint loss function, including: Calculate the time domain mean square error MSE to obtain the denoised time domain signal and the real signal , both are discrete sequences of length N; Compute the squared error point by point: , ; Find the mean error across all time points: ; Calculate the time-frequency spectrum after noise reduction and real time spectrum , and normalize it to the interval [0,1]: Define the local calculation window and traverse each position in the time-frequency plane , calculate the mean within the window: in: is the weight of each position, i, j are the traversal numbers; Calculate the variance within the window: Calculate the covariance: Calculate the local SSIM value: in: , is the stability constant, is the variance of the true value, is the covariance of the true value; Calculate the global average SSIM: Where: T is the time length, F is the frequency length; Calculate SSIM loss: Finally, the joint loss is weighted summed: in: and It is an adjustable hyperparameter used to balance the priority of waveform fidelity and time-frequency structure preservation. , late training .

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