A deep learning radar signal denoising method

Abstract

The application discloses a deep learning radar signal denoising method, and relates to the technical field of radar signal processing, comprising: converting a time domain radar signal into a two-dimensional time-frequency graph through short-time Fourier transform; performing frequency domain feature extraction on the two-dimensional time-frequency graph, sequentially passing through DnCNN and cascaded CNN, and outputting frequency domain feature representation; performing time domain feature extraction on the time domain radar signal to output time domain feature representation; fusing the frequency domain feature and the time domain feature based on a multi-head attention mechanism to generate cross-domain joint features; inputting the cross-domain joint features into a residual contraction network for signal reconstruction, and outputting denoised time domain signals. A time-frequency dual-domain collaborative learning framework is constructed, time domain characteristics and frequency domain structure distribution rules are deeply fused, and high-fidelity signal reconstruction under a complex noise environment is realized. The denoising method can maintain extremely low phase error and extremely high feature retention rate under a strong noise environment.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radar signal processing, in particular to a radar signal denoising method based on deep learning. BACKGROUND

[0002] As a core preprocessing link of target detection and recognition, the performance of radar signal denoising technology directly affects the quality of subsequent feature extraction, tracking positioning and imaging. In complex electromagnetic environment and diversified application scenarios, radar echoes are inevitably disturbed by multi-source noise, including system internal thermal noise, environmental clutter, artificial electromagnetic interference and disturbance caused by multipath effect, which urgently needs high-robustness denoising technology to guarantee signal quality.

[0003] Traditional signal processing schemes (such as wavelet threshold denoising and empirical mode decomposition) rely on manually designed feature rules and parameter adjustment, and face problems such as insufficient suppression of burst pulse noise, modal aliasing and damage to high-frequency signals. In unknown noise environment, the generalization ability decreases sharply, and there is a contradiction between noise suppression and signal distortion. Although the current emerging deep learning method has made breakthroughs in image denoising, it is difficult to model long-term correlation with two-dimensional convolution kernel, and there is a gradient vanishing defect in recurrent network, which leads to insufficient capture of dynamic characteristics of radar pulse sequence. More importantly, existing deep learning schemes ignore the physical nature of radar signals-the complex phase information contained in the time-frequency spectrum. Real number domain processing will destroy the phase continuity, causing the loss of target micro-motion characteristics. At the same time, the coherent characteristics of pulse Doppler radar require strict phase consistency, but the mainstream method only focuses on amplitude domain reconstruction, resulting in phase shift of time domain signal after inverse transformation, which seriously affects the accuracy of subsequent processing.

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

[0005] In order to solve the above technical problems, the present application provides the following technical solutions:

[0006] In a first aspect, the present application provides a radar signal denoising method based on deep learning, comprising:

[0007] Converting the time domain radar signal into a two-dimensional time-frequency graph through short-time Fourier transform;

[0008] Performing frequency domain feature extraction on the two-dimensional time-frequency graph, sequentially passing through DnCNN and cascaded CNN, and outputting frequency domain feature representation;

[0009] performing time domain feature extraction on the time domain radar signal to output a time domain feature representation;

[0010] generating a cross-domain joint feature based on the multi-head attention mechanism and the frequency domain feature and the time domain feature;

[0011] inputting the cross-domain joint feature into a residual contraction network to reconstruct the signal, and outputting a denoised time domain signal.

[0012] In a possible implementation, the converting the time domain radar signal into a two-dimensional time-frequency graph through short-time Fourier transform includes:

[0013] dividing a discrete time domain radar signal with a total length of M into x segments, each containing m sampling points, where K ; n K = M - n

[0014] performing a point discrete Fourier transform on each data segment r =0,1,…, K −1): n , is a complex matrix;

[0015] performing a modulo operation on to obtain the two-dimensional time-frequency graph.

[0016] In a possible implementation, the performing frequency domain feature extraction on the two-dimensional time-frequency graph includes sequentially passing the two-dimensional time-frequency graph through a DnCNN and a cascaded CNN to output a frequency domain feature representation, including:

[0017] inputting the two-dimensional time-frequency graph into the DnCNN, first performing 3*3 convolution to output a batch normalization and ReLU activation:

[0018]

[0019] wherein: is an activation function, is a batch normalization function, is a convolution function with a 3*3 convolution kernel;

[0020] then passing through l layer residual block structures, each residual block structure containing a 3*3 convolution calculation, a batch normalization calculation and a ReLU activation function, finally inputting and adding the output, represented as:

[0021] ​​​

[0022] wherein: is the output result of the l th residual block;

[0023] The output result is reduced from 64 channels to a single channel through a 1x1 convolution operation:

[0024]

[0025] The output result of the DnCNN is subjected to feature extraction by the CNN composed of a combination of multiple convolution kernels and pooling layers, the convolution kernel having a size of 5x1 in the time dimension and 1x3 in the frequency dimension, and the channel being expanded to The output result of each convolution-pooling combination is:

[0026]

[0027] wherein: is the output result of the kth convolution-pooling combination, is a pooling function;

[0028] The final transformation is completed through a fully connected layer: wherein: is a fully connected layer function.

[0029] In a possible implementation, the time-domain feature extraction on the time-domain radar signal outputs a time-domain feature representation, including:

[0030] The time-domain radar signal is simultaneously input into an LSTM network and a TCN network for double-path parallel processing;

[0031] The time-domain radar signal is processed by n LSTM units in the LSTM network to obtain wherein: is the final output result, is the unit state at each time;

[0032] The time-domain radar signal is subjected to dilated convolution and residual processing by multiple Block units in the TCN network, and the dilated factor is

[0033] The dilated convolution output is: wherein: is a dilated convolution function;

[0034] The dilated convolution output is normalized: wherein: is a weight normalization function;

[0035] A Dropout layer is added to prevent overfitting: , and finally residual connection is performed, wherein: is a random closed partial node function;

[0036] The output of the LSTM network and the TCN network is aggregated by an MLP network, and the MLP network is composed of multiple linear fully connected layers, and the output of each layer is

[0037]

[0038] wherein: is a linear fully connected layer function, and the output of the MLP is the time domain feature representation.

[0039] In a possible implementation, the multi-head attention mechanism is used to fuse the frequency domain features and the time domain features to generate cross-domain joint features, including:

[0040] The time domain features are used as dynamic query vectors, and the frequency domain features are used as key vectors and value vectors;

[0041] The multi-head attention mechanism is used to realize deep interaction guided by physical mechanisms, each time domain feature vector generates a group of query instructions, and a feature retrieval request is initiated to the frequency domain feature space;

[0042] First, the scaled dot product correlation between the time domain feature query vector and all frequency domain feature vectors is calculated to generate an original correlation score matrix:

[0043]

[0044] wherein: is an activation function, is a query vector, is a key vector, is the dimension of the key vector;

[0045] After the original correlation score matrix is normalized by the Softmax function, a probabilistic attention weight distribution is formed;

[0046] Then, the frequency domain value vectors are weighted and aggregated to capture the time-frequency feature correlation, and an attention matrix is output: wherein: is a key vector;

[0047] The outputs of all attention heads are combined to obtain: wherein: is a cross-domain joint feature, is a feature merging function.

[0048] In a possible implementation, the cross-domain joint feature is input into a residual contraction network for signal reconstruction, and a denoised time domain signal is output, including:

[0049] The residual shrinkage network processes the cross-domain joint features The feature preprocessing is performed by a wide convolution kernel to capture the dependence between features:

[0050]

[0051] Then, the noise reduction processing is performed by a plurality of residual shrinkage blocks to obtain a noise-reduced time-domain signal, wherein: is a 1-dimensional batch normalization function, is a 1-dimensional convolution function.

[0052] In a possible implementation, the noise reduction processing is performed by a plurality of residual shrinkage blocks to obtain a noise-reduced time-domain signal, including:

[0053] First, noise energy estimation is performed to calculate a noise intensity indicator:

[0054]

[0055] wherein: is an activation function;

[0056] The feature is adaptively filtered to implement soft thresholding, and the soft thresholding function is: ;

[0057] Finally, residual connection is performed: ;

[0058] After the processing of the plurality of residual shrinkage blocks, the final output time signal noise reduction result is: .

[0059] In a possible implementation, the method further includes: optimizing the network parameters by a joint loss function, the joint loss function being composed of a time-domain mean square error loss and a frequency-domain structural similarity loss.

[0060] In a possible implementation, the network parameters are optimized by the joint loss function, including:

[0061] The time-domain mean square error (MSE) is calculated to obtain a noise-reduced time-domain signal and a real signal , both of which are discrete sequences with a length of N;

[0062] The error square is calculated point by point: ;

[0063] The average error of all time points is calculated: ;

[0064] The noise-reduced time-frequency spectrum is calculated, and a real time-frequency spectrum and normalized to the interval [0, 1]:

[0065]

[0066]

[0067] Define local computation window, iterate over each position in the time-frequency plane Compute mean within the window:

[0068]

[0069] where: is the weight for each position, i, j are the iteration indices;

[0070] Compute variance within the window:

[0071]

[0072] Compute covariance:

[0073]

[0074] Compute local SSIM value:

[0075]

[0076] where: , is a stability constant, is the variance of the ground truth, is the covariance of the ground truth;

[0077] Compute global average SSIM:

[0078]

[0079] where: T is the length of time, F is the length of frequency;

[0080] Compute SSIM loss:

[0081]

[0082] Finally, sum the joint loss with weights:

[0083]

[0084] where: and are adjustable hyperparameters to balance the priority of waveform fidelity and time-frequency structure preservation, at the beginning of training , at the end of training .

[0085] In the embodiment of the present application, a time-frequency dual-domain collaborative learning framework is constructed, and through deeply fusing time domain characteristics and frequency domain structure distribution rules, high-fidelity reconstruction of signals in a complex noise environment is realized. The noise reduction method can maintain extremely low phase error and extremely high feature retention rate in a strong noise environment. BRIEF DESCRIPTION OF DRAWINGS

[0086] Figure 1 A flowchart of a deep learning radar signal noise reduction method provided by the embodiment of the present application is shown in the figure.

[0087] Figure 2 A frequency domain feature extraction flowchart provided by the embodiment of the present application is shown in the figure.

[0088] Figure 3 A time domain feature extraction flowchart provided by the embodiment of the present application is shown in the figure.

[0089] Figure 4 A schematic diagram of a residual link module provided by the embodiment of the present application is shown in the figure.

[0090] Figure 5 A schematic diagram of a time-frequency feature fusion flow provided by the embodiment of the present application is shown in the figure.

[0091] Figure 6 A schematic diagram of a time signal reconstruction provided by the embodiment of the present application is shown in the figure

[0092] Figure 7 A schematic diagram of a residual shrinkage block provided by the embodiment of the present application is shown in the figure DETAILED DESCRIPTION

[0093] The present scheme will be described below in combination with the accompanying drawings and specific embodiments.

[0094] Referring to Figure 1 , the deep learning radar signal noise reduction method provided by the embodiment includes:

[0095] S101, converting a time domain radar signal into a two-dimensional time-frequency graph through short-time Fourier transform.

[0096] As shown in Figure 2 , this step mainly extracts frequency domain features of the signal, and a discrete time sequence signal M [ x ], m =0,1,…, m −1, is divided into M overlapping data segments, each containing K sampling points, where n . K = M - n

[0097] For each data segment ,​r =0,1,…, K −1, execute n point discrete Fourier transform DFT: , is a complex matrix, and the modulo operation is performed on to obtain the two-dimensional time-frequency diagram.

[0098] Converting a one-dimensional time-domain signal into a two-dimensional time-frequency image, this representation can simultaneously exhibit the time-varying characteristics and spectral characteristics of the signal. The short-time Fourier transform is used as the basic tool for time-frequency analysis, and the time-frequency localization analysis of the signal is realized through the sliding window method, which can simultaneously exhibit the change characteristics of the signal in the time and frequency dimensions.

[0099] S102, frequency domain feature extraction is performed on the two-dimensional time-frequency diagram, and a denoising convolutional neural network DnCNN and a cascaded convolutional neural network CNN are sequentially passed through to output a frequency domain feature representation.

[0100] The two-dimensional time-frequency diagram is input into the DnCNN, and first a 3×3 convolution (channel 1→64) is performed, and the output is batch normalized and ReLU activated:

[0101]

[0102] wherein: is an activation function, is a batch normalization function, is a convolution function with a 3×3 convolution kernel;

[0103] Then pass through 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, and finally the input and output are added, which can be represented as:

[0104]

[0105] wherein: is the output result of the i-th residual block. l

[0106] The output result is subjected to a 1×1 convolution operation to reduce the 64 channels to a single channel:

[0107]

[0108] The output result of the DnCNN is subjected to a CNN for feature extraction, and the CNN is composed of a combination of multiple convolution and pooling layers, the convolution kernel has a size of 5×1 in the time dimension and 1×3 in the frequency dimension, and the channel is expanded to The output result of each convolution and pooling combination is:​

[0109]

[0110] wherein: is the kth convolutional pooling combination output result, is a pooling function.

[0111] Finally, the final transformation is completed through a fully connected layer: wherein: is a fully connected layer function.

[0112] In the design of the frequency domain feature extraction network, the embodiment adopts a hybrid architecture combining DnCNN and CNN. DnCNN is known for its excellent noise modeling capability, and is particularly suitable for processing random noise components in time-frequency images. The network is composed of multiple convolutional layers, adopts a residual learning strategy, and can effectively separate the feature representations of signals and noise.

[0113] In order to enhance the network's understanding of the structure of the frequency domain, a dedicated feature refining CNN is cascaded after the DnCNN. This network adopts an asymmetric convolution kernel design, which is specifically optimized for the different characteristics of time-frequency images in the time and frequency dimensions. Through this combined design, the network can represent both local details and global structural features of the frequency domain, and has an implicit connection with the phase change rate.

[0114] S103, performing time domain feature extraction on the time domain radar signal to output a time domain feature representation.

[0115] As shown in Figure 3 , in the embodiment, the time domain radar signal is simultaneously input into the LSTM network and the TCN network for double-path parallel processing.

[0116] The time series of length n (t=0,1,…,n) is processed by n LSTM units to obtain:

[0117]

[0118] In the formula, is the final output result, is the unit state at each time.

[0119] The other time series is processed by the TCN network. The TCN network is composed of multiple Block units, and the structure of each Block is as shown in Figure 4 . In the Block, mainly dilated convolution and residual processing are performed, and in the k layer, the dilation factor is , to expand the receptive field, dilated convolution output: , wherein: is a dilated convolution function.

[0120] The dilated convolution output is normalized: , to prevent overfitting, a Dropout layer is added, , and finally a residual connection is made, wherein: is a weight normalization function, is a random part node function.

[0121] The LSTM and TCN two-way outputs are aggregated through an MLP network, which is composed of multiple linear fully connected layers, and the output of each layer is

[0122]

[0123] , wherein: is a linear fully connected layer function, and the output of the MLP is the time domain feature representation.

[0124] In this embodiment, the time domain deep feature extraction adopts a dual-path parallel processing architecture, which realizes comprehensive extraction of different time scale features by combining the advantages of LSTM and TCN. The time series signal is simultaneously sent into the LSTM and TCN two parallel processing networks.

[0125] LSTM is used to capture long-term dependencies in the signal, and the network adopts a three-layer stacked structure, which can effectively identify and remember signal patterns across multiple pulse repetition periods through the gating mechanism. The TCN network focuses on extracting local time sequence features of the signal, and the network adopts a dilated causal convolution structure, which combines multiple dilation factors (1, 2, 4, 8) to construct a time sequence feature extractor with a large receptive field. Batch normalization and ReLU activation functions are connected after each convolution layer to ensure stable training of the network.

[0126] The feature fusion process of the two networks is realized through a three-layer fully connected network, which not only completes the unified mapping of feature dimensions, but also realizes intelligent weighted combination of different time scale features. The first layer of fully connected network preliminarily mixes the features of LSTM and TCN, the second layer extracts high-order feature interaction information, and the last layer outputs the time domain feature representation.

[0127] S104, based on the multi-head attention mechanism, the frequency domain features and the time domain features are fused to generate cross-domain joint features.

[0128] After obtaining the time domain features and the frequency domain features, the features of the two channels are fused through the multi-head attention mechanism, as shown in Figure 5 The time domain features and the frequency domain features obtained in the front are both 1xn the number of heads of multi-head attention is n .

[0129] In this embodiment, the time domain features are taken as dynamic query vectors, and the frequency domain features act as key vectors and value vectors at the same time. The physical mechanism guided deep interaction is realized through the multi-head attention mechanism. Each time domain feature vector generates a set of query instructions to initiate a "feature retrieval" request to the frequency domain feature space.

[0130] First, calculate the scaled dot product correlation between the time domain feature query vector and all frequency domain feature vectors:

[0131]

[0132] wherein: is an activation function, is a query vector, is a key vector, is the dimension of the key vector.

[0133] Generate the original correlation score matrix. After normalization by the Softmax function, the score matrix forms a probabilistic attention weight distribution. These weights quantify the physical correlation strength between the time domain dynamic behavior at a certain time and the specific frequency band structure. Then, the weighted aggregation of the frequency domain value vector captures the time-frequency feature correlation, and outputs the attention matrix:

[0134]

[0135] Merge the outputs of all attention heads:

[0136]

[0137] wherein: is a key vector, is a cross-domain joint feature, is a feature merging function.

[0138] In this embodiment, the features extracted from the time domain channel and the frequency domain channel are deeply integrated to establish the internal correlation between time-frequency features, thereby forming a more representative joint feature. The multi-head attention mechanism is used for time-frequency feature fusion, and the fusion space is divided into multiple attention heads, each of which independently calculates the correlation between time-frequency features.

[0139] In the calculation process, query, key and value vectors are first generated through linear transformation, and then attention weights are calculated. These weights reflect the importance relationship between features at different time-frequency positions, and can adaptively focus on key information areas. The attention matrix constructed by the multi-head attention mechanism is essentially a correlation strength distribution map between time domain dynamic features and frequency domain structure features.

[0140] The matrix accurately quantifies the correlation strength between each time-domain time node and a specific frequency-domain unit through the normalized weight value: when a certain time-domain transient pulse and a specific frequency band structure have a physical coupling relationship, the attention weight of the corresponding position will be significantly enhanced; on the contrary, the weight of the noise dominant area is suppressed to a very low level. This dynamically generated weight distribution essentially builds a geometric mapping relationship between the dynamic evolution of the time-domain waveform and the energy distribution of the frequency domain, providing a key structure preservation prior for subsequent reconstruction.

[0141] After the attention calculation is completed, the outputs of each head are spliced and linearly transformed to form the preliminary fusion features. This process fully retains the dynamic evolution information of the time-domain features and the structural distribution information of the frequency-domain features, indirectly learning the phase-related time sequence dynamics. In order to balance the relationship between time-domain and frequency-domain constraints, an adaptive weight adjustment strategy is adopted. In different stages of network training, the weight proportion of the two constraints is dynamically adjusted according to the current learning state. In the early stage of training, more emphasis is placed on time-domain constraints to ensure the basic waveform characteristics of the signal; as the training progresses, the frequency-domain constraint is gradually strengthened to optimize the ability to maintain frequency-domain details. This dynamic adjustment strategy enables the network to sequentially and progressively learn the optimal noise reduction mapping.

[0142] S105, inputting the cross-domain joint features into a residual contraction network for signal reconstruction, and outputting a time-domain signal after noise reduction.

[0143] Referring to Figure 6 , the residual contraction network performs feature preprocessing on the cross-domain joint features , and captures the dependencies between features through a wide convolution kernel:

[0144]

[0145] Then, a plurality of residual contraction blocks are used for noise reduction processing to obtain a time-domain signal after noise reduction, wherein: is a 1-dimensional batch normalization function, is a 1-dimensional convolution function.

[0146] As shown in Figure 7 , the processing process of each residual contraction block is as follows:

[0147] First, noise energy estimation is performed to calculate the noise intensity index:

[0148]

[0149] wherein: is an activation function.

[0150] The feature is adaptively filtered to realize soft thresholding, and the soft thresholding function is:

[0151]

[0152] Finally, the residual connection is made:

[0153]

[0154] After multiple residual block processing, the final output of the time signal denoising result is:

[0155]

[0156] In this embodiment, a wide kernel convolution layer is used to capture the dependency between the 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 the features, laying a foundation for subsequent signal reconstruction.

[0157] Subsequently, multiple layers of residual shrinkage blocks are stacked to further enhance the feature expression ability and suppress noise interference. Each residual shrinkage block includes a noise energy estimation module that dynamically calculates a soft threshold parameter based on global feature statistics. Based on the calculated soft threshold, a Wiener-like filtering operation is performed in the feature space, effectively suppressing noise while preserving and enhancing the effective components in the signal, thereby improving the signal-to-noise ratio and feature fidelity.

[0158] Finally, the original input is added to the threshold-processed features through the residual path. The residual connection mechanism can maintain the linear relationship of the feature map, to some extent, reduce phase distortion, ensure that key pulses or feature edges are not excessively weakened by filtering operations in low signal-to-noise ratio scenarios, thereby maintaining the integrity of the structure and key details, and forming the final output signal.

[0159] The loss function is designed by jointly optimizing the time domain error and the 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-frequency spectrum.

[0160] First, calculate the time domain mean square error (MSE) to obtain the time domain signal after denoising and the real clean signal , both of which are discrete sequences of length N, and the error square is calculated point by point:

[0161]

[0162] Find the average error of all time points:

[0163]

[0164] This loss forces the reconstructed signal to be consistent with the real signal in the time domain waveform.

[0165] Then, the denoised time-frequency spectrum and the real time-frequency spectrum are normalized to the interval [0, 1]:

[0166]

[0167]

[0168] The local calculation window is defined, and each position of the time-frequency plane is traversed The mean value in the calculation window is calculated:

[0169]

[0170] wherein: is the weight value of each position, i, j is the traversal serial number.

[0171] The variance in the calculation window is calculated:

[0172]

[0173] The covariance is calculated:

[0174]

[0175] The local SSIM value is calculated:

[0176]

[0177] wherein , is the stability constant, is the variance of the real value, is the covariance of the real value.

[0178] The global average SSIM is calculated:

[0179]

[0180] wherein: T is the time length, and F is the frequency length.

[0181] The SSIM loss is calculated:

[0182]

[0183] The loss maintains the local structural similarity of the time-frequency spectrum and protects key features such as target micro-Doppler.

[0184] Finally, the joint loss is weighted and summed:

[0185]

[0186] where a and b are adjustable hyperparameters to balance the priority between waveform fidelity and time-frequency structure preservation, at the early stage of training , at the late stage of training .

[0187] The loss function is designed to ensure that the denoising result meets the physical characteristics of the radar signal. The loss function constrains the network training from two dimensions of time domain and frequency domain, which not only guarantees the accuracy of the denoised signal in the waveform level, but also maintains the structural integrity of the frequency domain features.

[0188] In order to make the denoised signal consistent with the original signal in the overall waveform, the matching degree of the radar signal waveform is taken as the time domain loss function. Through this constraint method, the denoising mapping learned by the network can better maintain the time domain characteristics of the radar signal. The structural similarity measure is used in the frequency domain loss function to evaluate the matching degree of the frequency domain features before and after denoising. This measure can better capture the local correlation of the frequency domain structure.

[0189] In the embodiments of the present application, "at least one" means one or more, and "multiple" means two or more. The "and / or" describes the association relationship between the associated objects, which means that there can be three kinds of relationships, for example, A and / or B, which can represent the existence of A alone, the existence of A and B at the same time, and the existence of B alone. Wherein A, B can be singular or plural. The character " / " generally represents that the associated objects before and after are a kind of "or" relationship. "At least one of the following" and the like means any combination of these items, including any combination of single or multiple items. For example, at least one of a, b and c can represent: a, b, c, a-b, a-c, b-c, or a-b-c, where a, b, c can be single or multiple.

[0190] The above is only a specific embodiment of the present application, and any skilled person in the art can easily think of changes or replacements within the technical scope disclosed in the present application, which should be covered within the protection scope of the present application. The protection scope of the present application should be subject to the protection scope 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 diagram through short-time Fourier transform, including: 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 Performing a modulo operation to obtain the two-dimensional time-frequency graph; The two-dimensional time-frequency graph is subjected to frequency domain feature extraction, and the frequency domain feature representation is outputted by sequentially passing through DnCNN and cascade CNN, including: 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; 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 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.

3. 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.

4. The radar signal denoising method based on deep learning according to claim 3, wherein: 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.

5. The radar signal denoising method based on deep learning according to claim 4, 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: .

6. The radar signal denoising method based on deep learning according to any one of claims 1 to 5, 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.

7. The radar signal denoising method based on deep learning according to claim 6, 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: Compute 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 weighted sum of the joint losses is: 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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