Radar working mode identification method based on high-resolution multi-scale time-frequency representation and visual Transform

Abstract

The invention relates to the technical field of radar signal processing, and discloses a radar working mode recognition method based on high-resolution multi-scale time-frequency representation and visual Transform, which comprises the following steps: carrying out improved wavelet transform on an acquired radar signal, and extracting time-frequency graph features of the signal from three different scales; forming a data set of a radar working mode recognition model; the method comprises the following steps: constructing a block embedding module, a block merging module and a BiFormer module based on a visual Transform model; the data set is divided into a training set, a verification set and a test set according to the proportion of 3: 1: 4, and a trained radar working mode recognition model is obtained; the model outputs a corresponding radar working mode recognition result according to the input time-frequency diagram characteristics; by adopting the WTMSST technology and through iterative optimization group delay estimation, the problem of energy diffusion existing when a traditional time frequency method analyzes a strong frequency change radar signal is effectively solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radar signal processing, and more particularly to a radar operating mode recognition method based on high-resolution multi-scale time-frequency representation and visual Transformer. BACKGROUND

[0002] With the rapid development of phased array radar technology, its flexible beam pointing, waveform modulation and multi-task processing capability greatly improve the adaptability and complexity of the radar system. Radar operating mode recognition is a key technology, which aims to accurately identify different operating modes of the radar through in-depth analysis of the radar signal. This technology not only requires extracting effective time-domain and frequency-domain features from the radar signal, but also needs to combine pattern recognition algorithms for in-depth learning and training to cope with the increasingly complex environment and high dynamic changes of the radar operating state.

[0003] The existing radar operating mode recognition method mainly faces the problem that the traditional time-frequency analysis method (such as STFT, CWT) has a serious energy diffusion phenomenon when processing complex radar pulse signals with strong frequency changes (such as linear frequency modulation, nonlinear frequency modulation, phase-coded transient), which leads to ambiguous time-frequency ridge lines and makes it difficult to accurately extract key modulation features. Most methods only extract features from a single time scale (such as within a pulse), making it difficult to fully capture the coordinated evolution characteristics of radar signals in three key scales: between pulse groups (mode switching), within pulse groups (pulse sequence regularity), and within pulses (fine modulation). Traditional machine learning or shallow neural network models are sensitive to changes in time-frequency features under low signal-to-noise ratio and complex electromagnetic environment interference, and have limited generalization ability, making it difficult to meet the requirements of recognition accuracy and robustness.

[0004] The time reassignment synchronous compression transform based on wavelet significantly improves the time-frequency energy concentration by fusing time reassignment and multiple synchronous compression strategies, and introducing group time delay estimation and iterative optimization mechanism, providing a new idea for complex radar signal preprocessing. However, applying it to multi-scale joint representation and driving high-performance recognition models is still a problem to be solved. SUMMARY

[0005] In order to overcome the above-mentioned defects of the prior art, the present application provides a radar operating mode recognition method based on high-resolution multi-scale time-frequency representation and visual Transformer to solve the problems existing in the above background art.

[0006] The present application provides the following technical solutions: a radar operating mode recognition method based on high-resolution multi-scale time-frequency representation and visual Transformer, comprising the following steps: Step one, perform improved wavelet transform on the acquired radar signal to extract time-frequency feature of the signal from three different scales of pulse group, pulse group and pulse. Step two, gray processing and size compression are performed on each scale time-frequency graph respectively to construct a three-channel time-frequency representation image, the time-frequency graph reflects the change rule of the signal in different time and frequency domain, and constitutes the data set of the radar working mode recognition model; Step three, a block embedding module, a block merging module and a BiFormer module in the visual Transformer model are constructed; Step four, the data set is divided into a training set, a validation set and a test set according to a ratio of 3:1:4, and the training data set is input into the visual Transformer model for training to obtain the trained radar working mode recognition model; Step five, the test set is input into the trained radar working mode recognition model, and the model outputs the corresponding radar working mode recognition result according to the input time-frequency graph feature.

[0007] Preferably, the radar signal obtained in the step one is subjected to improved wavelet transform, and the time-frequency graph features of the signal are extracted from three different scales of inter-pulse group, intra-pulse group and intra-pulse, and the specific process is as follows: The radar signal is represented in the form of a multi-component model based on the frequency domain eigenmode function, that is: ; wherein, represents the frequency domain of the radar signal; represents the signal amplitude, represents the component index; represents the total number of signal components; represents the imaginary unit; represents the phase; represents the angular frequency; The atom is modeled by a scaling factor and a translation factor , that is ; wherein, represents the mother wavelet function; The atom is the basic analysis unit of wavelet transform; the signal is: ; wherein, represents the wavelet transform coefficient; * is the conjugate complex representation; represents the conjugate complex of ; represents the square integrable function space; if the wavelet function is analytic, it is defined as a real window function modulated by , that is ; wherein, represents the center frequency; then​ ; When regular expression The expression takes into account additional phase shift At that time, the function definition of the improved wavelet transform is: ;in, This represents the local frequency parameter related to the position parameter b; set up And considering Passevar's theorem, we obtain Frequency domain form: ;in, Represents the frequency domain integral variable; express The conjugate of complex numbers; It is calculated using the following formula: ;in, and There is a conversion relationship between them, that is ;Right now: Therefore, we get: ;in, This represents the frequency domain integral variable.

[0008] Preferably, the scale map Described as: ;in, Indicates the area around the point The probability distribution function; therefore, The centroid of the lower signal is defined as: ; ; in, This represents the group delay estimate; This indicates the operation of taking the real part; Indicates that there is a window of ; Indicates that there is a window of .

[0009] Preferred, based on Time redistribution synchronous compression transform operator To define, that is: ;in, This indicates the result of synchronous compression transformation; Represents the Diclave function; The set of parameters representing non-zero wavelet coefficients; WTSST reduces the time scale factor from the point Convert to new point Furthermore, WTSST retains the ability to recover the original signal, that is: ;for ;Analyze the performance of WTSST under strong frequency variation group delay conditions;There exists a signal model whose phase is locally expanded using the second-order Taylor formula, i.e. , ; income Obtained using the following formula: ; According to Passevar's theorem, it can be rewritten as: ;in, Represents the frequency domain derivative of the signal; Representing scale The relevant frequency offset parameters; obtain The local group delay candidate is: ;in, , ;in, This represents the first derivative of the phase function; The second derivative of the phase function is represented. This represents the Taylor expansion coefficients.

[0010] Preferably, a fixed-point iteration strategy is introduced to compensate. and To address the error between them, the WTMSST technique is introduced and expressed as: ; ; ; in, That is equivalent to , Let be the number of iterations, such that ; analyze and The relationship between them will Substitution And by combining this with Fubini's theorem, we get: ;in, This represents the time integral variable.

[0011] Preferably, in step two, the time-frequency images at each scale are converted to grayscale and compressed to construct a three-channel time-frequency representation image. The time-frequency images constitute the dataset for radar operating mode recognition. The process is as follows: Grayscale processing normalizes each time-frequency distribution and maps it to a grayscale value range. : ;in, This represents the maximum value of the current distribution. This represents the minimum value of the current distribution. This represents the pixel value after grayscale processing; Represents time coordinates; Represents frequency coordinates; This represents the rounding function; Size compression resizes each grayscale image to a fixed size of 224×224, denoted as: The three-channel time-frequency representation construction uses grayscale images at three different scales as the RGB channels of a single image to generate a new three-channel time-frequency representation image. ; The final time-frequency representation is 224×224×3. Each time-frequency map is labeled according to its corresponding radar operating mode, generating a labeled sample. The processed time-frequency maps are classified according to radar operating modes to construct a time-frequency map dataset containing multiple operating modes.

[0012] Preferably, in step three, a visual Transformer-based model is obtained by constructing a block embedding, block merging, and BiFormer module for the input time-frequency graph. Divide it into blocks according to the block size P×P. Each of the following sub-blocks is mapped to a D-dimensional embedding vector via linear projection: , ;in, For learnable projection matrices, Indicates sub-block vectorization operation; Represents the bias vector; Indicates a sub-block index; Indicates the first Embedded vectors; Indicates the total number of sub-blocks; Indicates the first One input sub-block; For the Feature map of layer Merge into 2×2 domains Each superblock generates high-dimensional features through channel concatenation and linear transformation: Among them, the first The output feature dimension of the layer is , Represents a linear transformation operation; Indicates a channel splicing operation; Indicates the range of row indexes; Indicates the range of column indexes; Indicates column index variable; This represents a 2×2 neighborhood feature block in the first layer; The overall structure of the BiFormer module can be formally represented as follows: ;in, This represents the output feature map after pooling; Indicates the input feature map; Indicates the convolution operation; Indicates a depthwise convolution operation; Indicates adaptive global pooling; This indicates a two-level routing attention mechanism; Representation layer normalization; The formula for adaptive global pooling is expressed as: .

[0013] Preferably, in step four, the dataset is divided into training set, validation set and test set in a ratio of 3:1:4, and the training dataset is input into the visual Transformer model for training to obtain the trained model.

[0014] Preferably, in step five, the test set is input into the trained working mode recognition model, and the model will output the corresponding radar working mode recognition result based on the input time-frequency map features.

[0015] The technical effects and advantages of this invention are as follows: This invention, by employing WTMSST technology, effectively solves the energy diffusion problem existing in the analysis of radar signals with strong frequency variations by traditional time-frequency methods through iterative optimization of group delay estimation. It obtains a time-frequency map with accurate focus and clear contours, laying a high-quality underlying feature foundation for identification.

[0016] This invention employs a three-channel time-frequency representation framework to fuse and encode time-frequency information from three key scales—inter-pulse group (macroscopic mode), intra-pulse group (mesoscopic correlation), and intra-pulse (microscopic modulation)—into a single color image (RGB channels). This representation inherently incorporates the multi-layered spatiotemporal evolution characteristics of radar signals, providing a more comprehensive and richer basis for identification.

[0017] This invention constructs a recognition model based on visual Transformer, which significantly reduces computational complexity through efficient block processing and hierarchical feature fusion. The two-level routing attention mechanism can dynamically focus on the most discriminative time-frequency region, effectively eliminating the influence of noise and interference. Attached Figure Description

[0018] Fig. 1 This is a flowchart of the radar operating mode recognition method based on high-resolution multi-scale time-frequency representation and visual Transformer of the present invention.

[0019] Fig. 2 This is a schematic diagram of the multi-scale three-channel time-frequency characterization framework based on WTMSST of the present invention.

[0020] Fig. 3 This is a schematic diagram of the visual Transformer-based recognition model framework of the present invention.

[0021] Fig. 4 This is a graph comparing the recognition accuracy of the present invention with other methods at different signal-to-noise ratios. Detailed Implementation

[0022] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. In addition, the forms of the various structures described in the following embodiments are merely illustrative. The radar working mode recognition method based on high-resolution multi-scale time-frequency representation and visual Transformer involved in the present invention is not limited to the structures described in the following embodiments. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] like Figs. 1 to 4 As shown, this invention provides a radar operating mode recognition method based on high-resolution multi-scale time-frequency representation and visual Transformer, comprising the following steps: Step 1: Perform improved wavelet transform on the acquired radar signal to extract the time-frequency characteristics of the signal at three different scales: between pulse groups, within pulse groups, and within pulses. Step 2: Perform grayscale processing and size compression on the time-frequency maps at each scale to construct a three-channel time-frequency representation image. The time-frequency maps reflect the variation of the signal in different time and frequency domains, thus forming the dataset for the radar working mode recognition model. Step 3: Construct the block embedding module, block merging module, and BiFormer module based on the visual Transformer model; Step 4: Divide the dataset into training set, validation set and test set in a ratio of 3:1:4, and input the training dataset into the visual Transformer model for training to obtain the trained radar working mode recognition model. Step 5: Input the test set into the trained radar operating mode recognition model. The model outputs the corresponding radar operating mode recognition result based on the input time-frequency map features.

[0024] In this embodiment, it should be specifically explained that in step one, the acquired radar signal is subjected to improved wavelet transform to extract the time-frequency map features of the signal at three different scales: between pulse groups, within pulse groups, and within pulses. The specific process is as follows: The radar signal is represented in a multi-component form by modeling the frequency domain eigenmode functions, namely: ;in, Represents the frequency domain of radar signals; Indicates signal amplitude. Indicates component index; Indicates the total number of signal components; Represents the imaginary unit; Indicates phase; Indicates angular frequency; Traditional linear time-frequency analysis methods will analyze the signal. With waveform dictionary Connecting them, among them, This represents the waveform functions in the waveform dictionary; Represents a set of multiple index parameters; The domain of the parameter set is defined; the waveform dictionary consists of a series of waveform functions with certain time-frequency positioning capabilities, i.e. ;in, This indicates the time-frequency analysis results; The time parameter is represented; the inner product results show that the position and size of the Heisenberg box depend on the time-frequency center and The span, when the frequency index is in When the frequency changes, the Heisenberg box covers the entire time-frequency plane. Represents the set of real numbers; Atoms are proportional to factors Translation factor Modeling, i.e. ;in, Represents the mother wavelet function; Atoms are the basic analytical units of wavelet transform; signals of for: ;in, Represents wavelet transform coefficients; * denotes conjugate complex number representation; express The conjugate of complex numbers; Let represent the space of square-integrable functions; assuming the wavelet function is analytic, it means it can be defined as [equation missing]. Modulated real window function ,Right now ;in, Representing the center frequency; then we have: ; When regular expression The expression takes into account additional phase shift At that time, the function definition of the improved wavelet transform is: ;in, This represents the frequency modulation parameter associated with the position parameter b; set up And considering Passevar's theorem, we obtain Frequency domain form: ;in, Represents the frequency domain integral variable; express The conjugate of complex numbers; It is calculated using the following formula: ;in, and There is a conversion relationship between them, that is ;Right now: Therefore, we get: ;in, Represents the frequency domain integral variable; Considering The severe energy diffusion phenomenon necessitates further exploration of energy distribution patterns. According to Plancherel's theorem... scale map It can be described as: ;in, Indicates the area around the point The probability distribution function; therefore, The centroid of the lower signal can be defined as: ; ; in, This represents the group delay estimate; This indicates the operation of taking the real part; Indicates that there is a window of ; Indicates that there is a window of ; In order to improve Energy is concentrated and reconstruction capability is maintained. Considering post-processing strategies along the time direction, therefore, based on Time-redistribution synchronous compression transformation can be used with operators To define, that is: ;in, This indicates the result of synchronous compression transformation; Represents the Diclave function; The set of parameters representing non-zero wavelet coefficients; The essence of WTSST is a cumulative process, which involves changing the time scale coefficient from point to point. Convert to new point Furthermore, WTSST retains the ability to recover the original signal, that is: ;for If the selected window satisfies the time band constraint, the time-frequency distribution of the non-zero coefficients of WTSST is concentrated in a narrow band near the trajectory. WTSST is indeed a reliable tool for processing weak frequency-varying signals. However, radar pulse signals usually exhibit more complex modulation patterns, which may cause WTSST to lose its resolution. Therefore, we need to analyze the performance of WTSST under the condition of strong frequency-varying group delay. Consider a signal model whose phase can be locally expanded using the second-order Taylor formula, i.e. , ; income It can be obtained using the following formula: ; According to Passevar's theorem, it can be rewritten as: ;in, This indicates that the signal frequency domain is affected; Representing scale The relevant frequency offset parameters can be obtained. The local group delay candidate is: ;in, , ;in, This represents the first derivative of the phase function; The second derivative of the phase function is represented. Represents the Taylor expansion coefficients; To facilitate observation of the error of the group delay estimator, a Gaussian window is selected. To specify the equation, i.e. Furthermore, a fixed-point iteration strategy is introduced to compensate. and The error between them is therefore addressed by introducing the WTMSST technique, which is expressed as: ; ; ; in, That is equivalent to , Let be the number of iterations, such that ; In order to obtain patterns through multiple iterations, analysis is necessary. and The relationship between them will Substitution And by combining this with Fubini's theorem, we get: ;in, Represents the time integral variable; The above formula shows The iterative operation is equivalent to compressing the WT coefficients into the newly generated group delay candidate. In this process, if the iterative steps continue, the group delay candidate can always be updated, further introducing... To replace the original group delay candidate in WTSST The expression for obtaining WTMSST is: ; can Described as: ; When the number of iterations is large enough, new group delay candidates will emerge. and The error between them may be close to 0, that is This means the new operator is... It is better suited for processing signals with strong frequency variations. In addition, WTMSST can accurately locate energy ridges, i.e.: ; Furthermore, WTMSST not only improves the resolution of WTSST, but also retains its reconstruction capabilities, namely: .

[0025] In this embodiment, it should be specifically explained that in step two, the time-frequency images at each scale are processed by grayscale conversion and size compression to construct a three-channel time-frequency representation image. These time-frequency images constitute the dataset for radar operating mode recognition. The process is as follows: Grayscale processing involves normalizing each time-frequency distribution and mapping it to a grayscale value range. : ;in, This represents the maximum value of the current distribution. This represents the minimum value of the current distribution. This represents the pixel value after grayscale processing; Represents time coordinates; Represents frequency coordinates; This represents the rounding function; Size compression involves resizing each grayscale image to a fixed size of 224×224, denoted as: The three-channel time-frequency representation is constructed by using grayscale images at three different scales as the RGB channels of a single image to generate a new three-channel time-frequency representation image. ; The final result is a time-frequency representation of size 224×224×3. Each time-frequency map is labeled according to its corresponding radar operating mode, generating a labeled sample. The processed time-frequency maps are classified according to radar operating modes to construct a time-frequency map dataset containing multiple operating modes.

[0026] In this embodiment, it should be specifically explained that the process of obtaining the visual Transformer-based model in step three through block embedding, block merging, and the BiFormer module is as follows: To discretize the continuous time-frequency graph into a serialized feature suitable for Transformer processing while preserving local time-frequency structure information, a patch embedding (PE) strategy is introduced for the input time-frequency graph. Divide it into blocks according to the block size P×P. Each of the following sub-blocks is mapped to a D-dimensional embedding vector via linear projection: , ;in, For learnable projection matrices, Indicates sub-block vectorization operation; Represents the bias vector; Indicates a sub-block index; Indicates the first Embedded vectors; Indicates the total number of sub-blocks; Indicates the first One input block; The role of block embedding is to capture the energy distribution characteristics of adjacent regions in the time-frequency map through block operations, and to simplify the quadratic complexity of pixel-level attention to the linear complexity of inter-block attention. Moreover, this operation supports multi-scale block strategies to adapt to different radar time-frequency representation resolution requirements.

[0027] To perform continuous spatial downsampling and channel expansion of feature maps in deep networks, a pyramid-structured layer-by-layer block merging method is used to achieve cross-scale feature fusion through spatial compression. For the first layer... Feature map of layer Merge into 2×2 domains Each superblock generates high-dimensional features through channel concatenation and linear transformation: Among them, the first The output feature dimension of the layer is , Represents a linear transformation operation; Indicates a channel splicing operation; Indicates the range of row indexes; Indicates the range of column indexes; Indicates column index variable; This represents a 2×2 neighborhood feature block in the first layer; The significance of block merging lies in gradually expanding the time-frequency range of feature coverage through hierarchical downsampling, enabling deep networks to capture mode transfer between pulse groups, shallow networks to analyze modulation details within pulses, and reducing sequence length as depth increases, thus balancing attention computational overhead.

[0028] The overall structure of the BiFormer module can be formally represented as follows: ;in, This represents the output feature map after pooling; Indicates the input feature map; Indicates the convolution operation; Indicates a depthwise convolution operation; Indicates adaptive global pooling; This indicates a two-level routing attention mechanism; Representation layer normalization; Adaptive Global Pooling (AGP) is a pooling method used to transform input feature maps of different sizes into outputs of a fixed size. Unlike traditional global pooling, AGP automatically adjusts the pooling operation parameters based on the size of the input feature map, thus working effectively on inputs of different sizes. In this way, BiFormer can adapt to different input sizes without losing important spatial information. The formula for adaptive global pooling can be expressed as: In the BiFormer module, AGP is used to reduce computational complexity while preserving global information of the input feature map, and it plays a crucial role in the extraction of multi-scale features.

[0029] Depthwise separable convolution is an efficient convolution computation method in convolutional neural networks. Traditional convolution performs computation between each input and output channel, while depthwise separable convolution divides the convolution operation into two steps: first, channel-wise convolution (depthwise convolution), and then pointwise convolution between output channels (1×1 convolution). This method significantly reduces computational cost, making the model more efficient.

[0030] Depthwise separable convolution first performs a depthwise convolution operation, followed by a pointwise convolution operation. The formula is expressed as: ;in, This represents a pointwise convolution operation. By decomposing the operation in this way, the computational cost of convolution is reduced, making the model computation more efficient. In BiFormer, depthwise separable convolution effectively reduces computational complexity while maintaining the richness of feature representation when used for feature extraction.

[0031] Residual connections help mitigate the vanishing gradient problem in deep networks by directly adding input to output. Specifically, in the BiFormer module, residual connections allow features from previous layers to be directly passed to subsequent layers, thereby accelerating the training process and improving model performance. It enhances the network's expressive power and ensures that information is not lost between layers.

[0032] Layer normalization is a commonly used normalization method, primarily used in deep learning to improve training stability. Unlike batch normalization, layer normalization operates on a per-sample basis, making it suitable for mini-batch and dynamic input scenarios. Layer normalization effectively mitigates training instability caused by variations in activation value distribution. In the BiFormer module, layer normalization ensures the stability of the mean and variance of the input features at each layer, thereby improving model training efficiency.

[0033] A multilayer perceptron (MLP) is a feedforward neural network containing multiple hidden layers, typically used to learn nonlinear mappings. In BiFormer, the MLP is used to perform higher-level nonlinear combinations of extracted features. Through the combination of multiple neuron layers, it enables the model to capture more complex data patterns.

[0034] The output of a multilayer perceptron can be expressed by the following formula: ;in, This represents the output after processing by the multilayer perceptron. and Represents the weight matrix; Represents input features; and Indicates the bias term. This represents the activation function, through multiple layers of nonlinear transformations, enabling the model to capture complex patterns.

[0035] In this embodiment, it should be specifically noted that in step four, the dataset is divided into training set, validation set and test set in a ratio of 3:1:4, and the training dataset is input into the visual Transformer model for training to obtain the trained model.

[0036] In step five, the test set is input into the trained working mode recognition model, and the model will output the corresponding radar working mode recognition result based on the input time-frequency map features.

[0037] This invention performs an improved wavelet transform on acquired radar signals to obtain three-scale time-frequency image data. This data is then grayscaled and stitched together by channel to form a multi-channel time-frequency representation image. These images constitute a dataset for radar operating mode recognition. The training set from this dataset is then input into a visual Transformer-based model for training, resulting in a trained recognition model. Finally, the test set from the dataset is used as input to the recognition model, which identifies the radar operating mode at the current moment based on the visual Transformer model and outputs the result.

[0038] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0039] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A radar operating mode recognition method based on high-resolution multi-scale time-frequency representation and visual Transformer, characterized in that: Includes the following steps: Step 1: Perform improved wavelet transform on the acquired radar signal to extract the time-frequency characteristics of the signal at three different scales: between pulse groups, within pulse groups, and within pulses. Step 2: Perform grayscale processing and size compression on the time-frequency maps at each scale to construct a three-channel time-frequency representation image. The time-frequency maps reflect the variation of the signal in different time and frequency domains, forming the dataset for the radar working mode recognition model. Step 3: Construct the block embedding module, block merging module, and BiFormer module based on the visual Transformer model; Step 4: Divide the dataset into training set, validation set and test set in a ratio of 3:1:4, and input the training dataset into the visual Transformer model for training to obtain the trained radar working mode recognition model. Step 5: Input the test set into the trained radar operating mode recognition model. The model outputs the corresponding radar operating mode recognition result based on the input time-frequency map features.

2. The radar operating mode recognition method based on high-resolution multi-scale time-frequency representation and visual Transformer according to claim 1, characterized in that: In step one, the acquired radar signal undergoes an improved wavelet transform to extract time-frequency features from three different scales: inter-pulse group, intra-pulse, and intra-pulse. The specific process is as follows: The radar signal is represented in a multi-component form by modeling the frequency domain eigenmode functions, namely: ;in, Represents the frequency domain of radar signals; Indicates signal amplitude. Indicates component index; Indicates the total number of signal components; Represents the imaginary unit; Indicates phase; Indicates angular frequency; Atoms are proportional to factors Translation factor Modeling, i.e. ;in, Represents the mother wavelet function; Atoms are the basic analytical units of wavelet transform; signals of for: ;in, Represents wavelet transform coefficients; * denotes conjugate complex number representation; express The conjugate of complex numbers; Let represent the space of square-integrable functions; if the wavelet function is analytic, then it is defined as [the space of square-integrable functions]. Modulated real window function ,Right now ;in, Representing the center frequency; then we have: ； When regular expression The expression takes into account additional phase shift At that time, the function definition of the improved wavelet transform is: ;in, This represents the local frequency parameter related to the position parameter b; set up And considering Passevar's theorem, we obtain Frequency domain form: ;in, Represents the frequency domain integral variable; express The conjugate of complex numbers; It is calculated using the following formula: ;in, and There is a conversion relationship between them, that is ;Right now: Therefore, we get: ;in, This represents the frequency domain integral variable.

3. The radar operating mode recognition method based on high-resolution multi-scale time-frequency representation and visual Transformer according to claim 2, characterized in that: The scale map Described as: ;in, Indicates the area around the point The probability distribution function; The centroid of the lower signal is defined as: ； ； in, This represents the group delay estimate; This indicates the operation of taking the real part; Indicates that there is a window of ; Indicates that there is a window of .

4. The radar operating mode recognition method based on high-resolution multi-scale time-frequency representation and visual Transformer according to claim 3, characterized in that: based on Time redistribution synchronous compression transform operator To define, that is: ;in, This indicates the result of synchronous compression transformation; Represents the Diclave function; The set of parameters representing non-zero wavelet coefficients; WTSST reduces the time scale factor from the point Convert to new point Furthermore, WTSST retains the ability to recover the original signal, that is: ;for ;Analyze the performance of WTSST under strong frequency variation group delay conditions;There exists a signal model whose phase is locally expanded using the second-order Taylor formula, i.e. , ; the result Obtained using the following formula: ; According to Passevar's theorem, it can be rewritten as: ;in, Represents the frequency domain derivative of the signal; Representing scale The relevant frequency offset parameters; obtain The local group delay candidate is: ;in, , ;in, This represents the first derivative of the phase function; The second derivative of the phase function is represented. This represents the Taylor expansion coefficients.

5. The radar operating mode recognition method based on high-resolution multi-scale time-frequency representation and visual Transformer according to claim 4, characterized in that: Introducing a fixed-point iterative strategy to compensate and To address the error between them, the WTMSST technique is introduced and expressed as: ； ； ； in, That is equivalent to , Let be the number of iterations, such that ; analyze and The relationship between them will Substitution And by combining this with Fubini's theorem, we get: ;in, This represents the time integral variable.

6. The radar operating mode recognition method based on high-resolution multi-scale time-frequency representation and visual Transformer according to claim 5, characterized in that: In step two, the time-frequency images at each scale are converted to grayscale and compressed to construct a three-channel time-frequency representation image. The time-frequency images constitute the dataset for radar operating mode recognition. The process is as follows: Grayscale processing normalizes each time-frequency distribution and maps it to a grayscale value range. : ;in, This represents the maximum value of the current distribution. This represents the minimum value of the current distribution. This represents the pixel value after grayscale processing; Represents the time coordinate; Represents frequency coordinates; This represents the rounding function; Size compression resizes each grayscale image to a fixed size of 224×224, denoted as: The three-channel time-frequency representation construction uses grayscale images at three different scales as the RGB channels of a single image to generate a new three-channel time-frequency representation image. ； The final time-frequency representation is 224×224×3. Each time-frequency map is labeled according to its corresponding radar operating mode, generating a labeled sample. The processed time-frequency maps are classified according to radar operating modes to construct a time-frequency map dataset containing multiple operating modes.

7. The radar operating mode recognition method based on high-resolution multi-scale time-frequency representation and visual Transformer according to claim 6, characterized in that: In step three, a visual Transformer-based model is obtained by constructing a block embedding, block merging, and BiFormer module for the input time-frequency graph. Divide it into blocks according to the block size P×P. Each of the following sub-blocks is mapped to a D-dimensional embedding vector via linear projection: , ;in, For learnable projection matrices, Indicates sub-block vectorization operation; Represents the bias vector; Indicates a sub-block index; Indicates the first Embedded vectors; Indicates the total number of sub-blocks; Indicates the first One input sub-block; For the Feature map of layer Merge into 2×2 domains Each superblock generates high-dimensional features through channel concatenation and linear transformation: Among them, the first The output feature dimension of the layer is , Represents a linear transformation operation; Indicates a channel splicing operation; Indicates the range of row indexes; Indicates the range of column indexes; Indicates column index variable; This represents a 2×2 neighborhood feature block in the first layer; The overall structure of the BiFormer module can be formally represented as follows: ;in, This represents the output feature map after pooling; Indicates the input feature map; Indicates the convolution operation; Indicates a depthwise convolution operation; Indicates adaptive global pooling; This indicates a two-level routing attention mechanism; Representation layer normalization; The formula for adaptive global pooling is expressed as: 。 8. The radar operating mode recognition method based on high-resolution multi-scale time-frequency representation and visual Transformer according to claim 7, characterized in that: In step four, the dataset is divided into training, validation, and test sets in a ratio of 3:1:4, and the training dataset is input into the visual Transformer model for training to obtain the trained model.

9. The radar operating mode recognition method based on high-resolution multi-scale time-frequency representation and visual Transformer according to claim 8, characterized in that: In step five, the test set is input into the trained working mode recognition model, and the model will output the corresponding radar working mode recognition result based on the input time-frequency map features.

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