LPI radar modulation identification method and system based on dynamic wavelet frequency band enhancement module and deep residual shrinkage network, and computer equipment

Abstract

The invention discloses an LPI radar modulation identification method and system based on a dynamic wavelet frequency band enhancement module and a depth residual shrinkage network, and computer equipment, and belongs to the field of radar signal identification, and the method comprises the steps: 1, receiving an LPI radar signal; step 2, carrying out Choi-Williams distribution CWD time-frequency transformation on the received LPI radar signal, and generating a time-frequency TFI image; step 3, an LW-BERSNet model is established; and processing the received LPI radar signal through the established LW-BERSNet model, and outputting a modulation type classification result of the LPI radar signal. According to the invention, high-precision identification can be realized in complex electromagnetic environments with low signal-to-noise ratio, multipath fading effect, non-stationary noise coupling and the like.

Description

Technical Field

[0001] The present invention relates to the field of radar signal recognition, and more particularly to an LPI radar modulation recognition method, system and computer equipment based on a dynamic wavelet frequency band enhancement module and a deep residual shrinkage network. Background Art

[0002] Identifying radar signal modulation types is crucial for electronic countermeasures. Low Probability of Intercept (LPI) radars, as a typical representative of new radar systems, are increasingly becoming a focus of battlefield reconnaissance and counter-reconnaissance. Unlike traditional radar signals, LPI radars typically use complex modulation schemes to proactively reduce the probability of interception. For example, LPI radars' linear frequency modulation (LFM) signals disperse energy through wide-band sweeps, while Costas codes employ pseudo-random frequency hopping patterns, making it difficult for enemy receivers to effectively detect them using traditional pulse repetition period (PRI) matching or fixed parameter libraries. With the increasing intensity of battlefield electronic countermeasures, radar systems face a variety of complex electromagnetic environment challenges.

[0003] Multipath fading and noise coupling cause received signal distortion, especially in low signal-to-noise ratio conditions, where signal characteristics are often obscured or obscured by noise. In this environment, achieving high-precision radar signal modulation recognition despite the influence of multipath fading and noise becomes a key challenge in breaking through the battlefield's "electronic fog."

[0004] Traditional LPI radar signal modulation recognition methods primarily rely on manually designed feature extraction techniques, such as spectral correlation analysis, time-frequency distribution, and high-order statistics, combined with shallow classifiers such as decision trees and support vector machines to achieve signal recognition. These methods exploit the signal's cyclostationary properties, instantaneous parameters, or joint time-frequency features for classification, demonstrating some effectiveness in specific scenarios. However, these methods rely on researchers' expertise and experience, and their handcrafted features have limited generalization capabilities in dynamic electromagnetic environments and lack robustness under low signal-to-noise ratio conditions. For example, Thien Huynh-The noted that handcrafted features struggle to adapt to multipath fading and noise fluctuations in dynamic electromagnetic environments, resulting in a sharp decline in recognition performance. Furthermore, in the presence of colored noise, the skewed distribution of feature energy further exacerbates classification errors. These issues have prompted research towards end-to-end solutions based on deep learning to overcome the bottlenecks in feature representation and classification capabilities of traditional methods.

[0005] Therefore, how to provide an LPI radar modulation recognition method, system and computer equipment based on a dynamic wavelet frequency band enhancement module and a deep residual shrinkage network is a problem that needs to be solved urgently by those skilled in the art. Summary of the Invention

[0006] In view of this, the present invention provides an LPI radar modulation recognition method, system and computer equipment based on a dynamic wavelet frequency band enhancement module and a deep residual shrinkage network to solve the technical problems existing in the above-mentioned prior art.

[0007] In order to achieve the above object, the present invention provides the following technical solutions: A LPI radar modulation recognition method based on a dynamic wavelet frequency band enhancement module and a deep residual shrinkage network comprises the following steps: Step 1: Receive LPI radar signal; Step 2: Perform Choi-Williams distribution CWD time-frequency transform on the received LPI radar signal to generate a time-frequency TFI image; Step 3: Establish an LW-BERSNet model; process the received LPI radar signal through the established LW-BERSNet model and output the modulation type classification result of the LPI radar signal.

[0008] Preferably, the LPI radar signal received in step 1 is expressed as: ; in is the amplitude of the signal, is the gate function, is the pulse width, is the instantaneous frequency, is the initial phase, is the time phase function.

[0009] Preferably, the expression of CWD time-frequency transform in step 2 is: ; in, is the fuzzy function of the signal, defined as the signal in the time delay and frequency offset The related functions on It is an exponential kernel function that suppresses cross terms while retaining the main lobe energy focus.

[0010] Preferably, the step three: LW-BERSNet model includes: Feature extraction module, learnable wavelet band enhancement module LWBE, multi-band weight fusion module MBWF, deep residual shrinkage network DRSN, and classification module; Among them, the high-level features of the time-frequency TFI image are extracted by the feature extraction module; the high-level features are dynamically decomposed by the learnable wavelet band enhancement module LWBE to generate a multi-scale band feature map; the band feature map is cross-channel attention weighted fusion is performed by the multi-band weight fusion module MBWF; the fused features are input into the deep residual shrinkage network DRSN, and the noise is suppressed and the discriminative features are extracted by adaptive soft thresholding; the classification module adopts the channel-center joint loss function CC-Joint Loss to jointly optimize the cross entropy loss and the dynamic category center loss, and outputs the modulation type classification result of the LPI radar signal.

[0011] Preferably, the learnable wavelet band enhancement module LWBE performs discrete wavelet transform on the input signal using a learnable wavelet kernel, and the basis function of the learnable wavelet kernel is: , Where, Preset scale parameters; is the learnable parameter of the wavelet kernel and the preset scale parameter Together through back-propagation optimization, where When it is equal to 1, it is the standard Morlet wavelet kernel. When it is greater than 1, Follow As the frequency increases, the basis function has a higher time-frequency resolution in the low-frequency region. When it is less than 1, the ability to capture local features in high-frequency areas is enhanced.

[0012] Preferably, the cross-channel attention weighted fusion of the band feature maps is performed by the multi-band weight fusion module MBWF, and the specific steps include: Grouping the frequency band feature maps along the channel dimension; Average pooling is performed along the width and height directions to extract direction-sensitive statistics; The frequency band features are dynamically weighted and fused via a cross-channel attention weight matrix.

[0013] Preferably, the deep residual shrinkage network DRSN includes a dual-path attention mechanism, wherein: Main path: Generate channel attention weights through global average pooling and fully connected layers; Auxiliary path: Dynamically adjust the threshold strength through the scaling factor generation network; The fused dual-path output drives the soft thresholding operation to suppress redundant features.

[0014] Preferably, the classification module adopts the channel-center joint loss function CC-Joint Loss to jointly optimize the cross entropy loss and the dynamic category center loss, and outputs the modulation type classification result of the LPI radar signal, including: The cross entropy loss drives model learning by minimizing the difference between the predicted probability and the true label: , in, For samples The true label, is the predicted probability, is the total number of categories; Standard center loss function: , in, For samples The eigenvector of for The current feature mean of is the batch size; Use the mean of the features of the same type in the current batch to replace the learnable parameters: , in Category in the current batch The number of samples, For category No. The feature vector of the samples, It is a class center of dynamic calculation; The standard center loss function Replaced with dynamic mean And introduce the normalization factor: , The loss for each class is divided by , divide the total loss by the number of categories , and finally get: , Finally, CC-Joint Loss is a weighted fusion of CE Loss and CC-Loss: , Where, is the cross entropy loss, is the dynamic category center loss, and λ is the balance coefficient.

[0015] On the other hand, the present invention also provides an LPI radar modulation recognition system based on a dynamic wavelet frequency band enhancement module and a deep residual shrinkage network, which is used to implement an LPI radar modulation recognition method based on a dynamic wavelet frequency band enhancement module and a deep residual shrinkage network, comprising: Receiving module: receives LPI radar signals; Processing module: performs Choi-Williams distribution CWD time-frequency transform on the received LPI radar signal to generate a time-frequency TFI image; Identification module: Establishes the LW-BERSNet model; processes the received LPI radar signal through the established LW-BERSNet model and outputs the modulation type classification result of the LPI radar signal.

[0016] On the other hand, the present invention also provides a computer device having a computer program stored thereon, which, when executed by a processor, implements the steps of an LPI radar modulation recognition method based on a dynamic wavelet frequency band enhancement module and a deep residual shrinkage network.

[0017] As can be seen from the above technical solutions, the present invention discloses a method, system, and computer device for LPI radar modulation recognition based on a dynamic wavelet band enhancement module and a deep residual shrinkage network. This method proposes a novel automatic identification scheme for LPI radar transmit signals, capable of achieving high-precision recognition in complex electromagnetic environments such as low signal-to-noise ratios, multipath fading, and non-stationary noise coupling. By introducing an adaptive wavelet band enhancement module, a deep residual shrinkage network, and a joint channel-center loss function, LW-BERSNet demonstrates excellent robustness and accuracy in radar signal modulation recognition tasks. The adaptive wavelet band enhancement module effectively captures the multi-scale time-frequency characteristics of the signal through a learnable wavelet kernel and multi-band weight fusion mechanism, enhancing signal characteristics. Simultaneously, the deep residual shrinkage network uses an adaptive soft thresholding mechanism to suppress background noise while preserving effective modulation characteristics, ensuring accurate signal recognition. Simulation results demonstrate that compared to existing technologies, the proposed automatic identification network can effectively improve the accuracy and robustness of radar signal recognition in complex electromagnetic countermeasure environments, particularly under conditions of colored noise and multipath fading. This method can meet the requirements of high-precision recognition and robustness of radar signals in dealing with actual electronic countermeasure scenarios, and provides a practical solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0019] Figure 1 Schematic diagram of the method flow of the present invention; Figure 2 Schematic diagram of complex multipath propagation environment; Figure 3 This is a structural diagram of the LW-BERSNet model; Figure 4 Schematic diagram of the structure of the learnable wavelet frequency band enhancement module; Figure 5 Schematic diagram of the process of learning wavelet kernel; Figure 6 This is the network structure diagram of MBWF; Figure 7 Schematic diagram of deep residual shrinkage network; Figure 8 Schematic diagram of the process of building a dataset; Figure 9 Schematic diagram of the impact of different environmental conditions on radar signals; Figure 10 Schematic diagram of TFIs for twelve LPI radar waveforms; Figure 11 Comparison chart of recognition accuracy of different methods in colored noise environment; Figure 12 Comparison of recognition accuracy of different methods in an environment with colored noise and multipath fading effect; Figure 13 Comparison chart of recognition accuracy for different time-frequency transformations; Figure 14 Observation diagram of the network training process; Figure 15 To visualize the clustering effect of LPI radar signal categories in different training sets and different loss functions; Figure 16 The bar graph shows the robustness of the recognition accuracy experiments under different environments. Figure 17 Figure 2 is a diagram of the confusion matrix of 12 radar signals in three test sets identified by the model when the signal-to-noise ratio is -10 dB; Figure 18 Schematic diagram of the recognition effect of twelve LPI radar signals under different signal-to-noise ratios. DETAILED DESCRIPTION

[0020] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention. Example 1:

[0021] See also Figure 1 As shown, an embodiment of the present invention discloses an LPI radar modulation recognition method based on a dynamic wavelet frequency band enhancement module and a deep residual shrinkage network, comprising the following steps: Step 1: Receive LPI radar signal; Step 2: Perform Choi-Williams distribution CWD time-frequency transform on the received LPI radar signal to generate a time-frequency TFI image; Step 3: Establish an LW-BERSNet model; process the received LPI radar signal through the established LW-BERSNet model and output the modulation type classification result of the LPI radar signal.

[0022] Specifically, the design of LPI radar systems requires careful consideration of the signal's time, frequency, and phase characteristics to achieve a low probability of intercept (PoI). To enhance the system's stealth and anti-interference capabilities, high-bandwidth and complex modulation techniques are often employed. For example, LFM signals offer superior temporal resolution, while Costas signals employ pseudo-random frequency agility, significantly reducing the probability of intercept. BPSK signals conceal signal energy through sudden phase jumps, but exhibit high spectral sidelobes. Furthermore, polyphase-coded signals can further reduce enemy detection capabilities through nonlinear frequency modulation.

[0023] In the LPI radar system, the received radar signal can be represented by the following mathematical model: in is the amplitude of the signal, is the gate function, is the pulse width, is the instantaneous frequency, is the initial phase, is the time phase function. and The modulation type is different in different modulation methods. and Different forms of RF are defined, the most common ones are linear frequency modulation, BPSK and polyphase coding.

[0024] The performance differences between different modulation schemes are primarily reflected in their time-frequency characteristics and engineering implementation complexity. To cover typical LPI radar signal scenarios, this embodiment selects 12 LPI radar signal modulation types, including BPSK, LFM, Costas, Frank, P1-P4, and T1-T4. The specific expression formulas for different radar signal modulation types are shown in Table 1.

[0025] Table 1 Expression formulas for different radar signal modulation types

[0026] In complex electromagnetic environments, LPI radar signal transmission faces a variety of non-ideal factors that degrade signal quality, including antenna thermal noise, circuit nonlinearity, multipath fading, and carrier frequency offset. These factors significantly reduce the signal-to-noise ratio and obscure modulation characteristics, posing a significant challenge to modulation recognition capabilities for low-power LPI signals. To simulate signal contamination in complex multipath electromagnetic environments, this example investigates Gaussian white noise, colored noise, multipath fading, and random carrier frequency interference.

[0027] AWGN is primarily caused by thermal noise, amplifier noise, and quantization noise in the receiver front end. Its instantaneous amplitude follows a Rayleigh distribution, while its phase follows a uniform distribution. AWGN's impact on the signal is primarily the introduction of random noise points into the time-frequency graph (TFIs), reducing the signal-to-noise ratio and thus obscuring valid signal features.

[0028] Colored noise is a significant noise source that affects radar signal reception quality, often introduced by non-ideal hardware or channel characteristics. Unlike additive white Gaussian noise, the power spectral density (PSD) of colored noise is not flat but rather frequency-dependent, with its energy distribution tilting with frequency, manifesting as an attenuation characteristic determined by the noise spectrum index. Common colored noise can be divided into three categories based on their spectral characteristics: pink noise, whose power spectral density is inversely proportional to frequency, has significantly higher energy in low-frequency components than in high-frequency components. It is widely found in low-frequency interference from electronic devices and environmental background noise. Brown noise exhibits a stronger low-frequency enhancement effect, with its power spectral density inversely proportional to the square of the frequency, and its energy decays more steeply with frequency than pink noise. Blue noise, on the other hand, exhibits the opposite characteristics of pink noise, with its power spectral density increasing with frequency. This high-frequency energy concentration can exacerbate spectral leakage in high-frequency modulated signals. The differences in the spectral characteristics of these colored noises directly impact the signal processing effectiveness of reconnaissance systems in different frequency bands.

[0029] Multipath fading is particularly detrimental to radar signals in complex propagation environments. During transmission, radar signals reach the receiver not only via a direct path but also through multiple reflected paths. Due to the varying propagation distances and environments of each reflection path, signals overlap at the receiver, resulting in amplitude fading and phase shifts. Multipath fading causes the time-frequency distribution of the received signal to spread, increasing signal complexity. The superposition of multiple propagation paths blurs the signal's modulation characteristics. This effect is particularly pronounced in complex multipath environments, particularly in urban areas, mountainous areas, and other environments with numerous reflective surfaces and obstacles. The accuracy of radar signal recognition and classification can be significantly reduced. Therefore, it is crucial to consider the impact of multipath fading when analyzing and identifying radar signals.

[0030] Under the effect of multipath fading, the received signal It can be represented as the superposition of multiple path signals with different delays and gains: in, is the number of multipath paths, For the The gain of the path, is the delay of the path, is the original transmitted signal.

[0031] The noise sources and multipath fading effects mentioned above are the main environmental factors that affect the accuracy of radar signal modulation recognition. Therefore, this requires the network model to maintain high classification performance even in scenarios containing such complex signals. To more accurately describe the radar signal reception process, the following signal types are defined: in, represents an ideal noise-free transmit signal. When the path index , represents a direct path, Indicates no delay; Indicates no Doppler shift; It is represented as the initial phase offset. The reflected path of the signal passes through the The paths for propagation, Indicates the The propagation delay of each path; represents the Doppler shift; Indicates phase offset. is the noise term, including Gaussian white noise and colored noise. Figure 2 Shown is the complex multipath propagation environment of radar signals.

[0032] In LPI radar signal modulation recognition, time-frequency analysis (TFA) is a key technology for extracting the features of complex modulated signals. TFA maps a one-dimensional time series signal into a two-dimensional time-frequency image (TFI). This intuitively displays the signal's instantaneous frequency variations and energy distribution, providing an important basis for feature extraction from complex modulated signals.

[0033] In scenarios with low signal-to-noise ratios and multipath fading, traditional linear time-frequency methods struggle to meet requirements due to energy leakage and cross-term interference. The short-time Fourier transform (STFT) uses a sliding window function to intercept signal segments and perform a Fourier transform. While computationally simple, it suffers from resolution issues caused by a fixed window length. Therefore, the STFT is only suitable for analyzing quasi-stationary signals that are stationary over a short time window. WVD, on the other hand, directly calculates time-frequency energy using the signal's autocorrelation function, offering optimal time-frequency resolution. However, cross-term interference is unavoidable, making it practically unusable for multi-component signals. By introducing a window function, CWD effectively suppresses the cross-term issue in WVD. By adjusting the shape of the window function, CWD can flexibly control the time-frequency resolution, thereby reducing the appearance of spurious frequency components.

[0034] CWD (Choi-Williams distribution) is a commonly used bilinear TFA method. Compared to other time-frequency analysis methods, CWD introduces an exponential kernel function to suppress cross-terms while maintaining high resolution, making it a preferred method for complex environments. The mathematical formula for CWD is as follows: in, is the fuzzy function of the signal, defined as the signal delay and frequency offset The related functions on It is an exponential kernel function that suppresses cross terms while retaining the main lobe energy focus.

[0035] In one embodiment, see Figure 3Figure 1 shows the overall architecture of the LW-BERSNet model. First, the input receives the time-frequency image (TFI) obtained through the CWD transform. Feature extraction then proceeds through three convolutional layers. Each convolutional kernel is 3×3 in size and combines batch normalization with a ReLU activation function to extract features from the original signal. Next, a max pooling operation is performed to extract high-level TFI features. These TFI features then enter the learnable wavelet band enhancement module (LWBE). This module combines the learnable wavelet kernel with the discrete wavelet transform (DWT) to obtain decomposed frequency bands and extract multi-scale time-frequency features of the signal. A multi-band attention fusion module weightedly fuses the features of different frequency bands. Finally, an inverse discrete wavelet transform (IDWT) is used to restore the frequency bands to highly discriminative time-frequency features. The backend of this network architecture is a deep residual contraction network consisting of four residual modules. Finally, after global average pooling and a fully connected layer, the final classification result is output, completing the modulation recognition task of LPI radar signals.

[0036] Specifically, the learnable wavelet band enhancement module (LWBE) uses the learnable wavelet kernel to perform discrete wavelet transform on the input signal and decompose the signal into multiple frequency bands. Then, the multi-band weight fusion module performs weighted fusion on the features of different frequency bands and optimizes the feature information of each frequency band using a learning mechanism. This learning mechanism automatically adjusts the feature weight of each frequency band through the network training process to enhance the information expression of important frequency bands while suppressing irrelevant or redundant frequency band features. Finally, the enhanced frequency bands are recombined into the original signal through the inverse discrete wavelet transform. The detailed structure is shown in Figure 2. Figure 4 The content of learning wavelet kernel and multi-band weight fusion module will be introduced in detail below.

[0037] Specifically, the generation of learnable wavelet kernels includes:

[0038] First, initialize the learnable wavelet kernel (LWK). The scale and fractional order modulation parameters of each wavelet kernel are learnable parameters, and their initial values ​​are set to 1.0. The purpose of the learnable wavelet kernel is to dynamically adjust its frequency band distribution according to the time-frequency characteristics of the input signal, thereby optimizing the decomposition of the signal in the time-frequency domain. Through the gradient descent method, the model automatically adjusts the scale parameters and fractional order modulation parameters of the wavelet kernel according to the input time-frequency graph, so that the wavelet kernel can match the time-frequency characteristics of different signals, thereby improving the effect of signal feature extraction. The basis function of traditional wavelet transform, taking the Morlet wavelet kernel as an example, usually relies on the preset scale parameter With fixed frequency modulation , its linear frequency scaling is difficult to capture the rapidly changing local features in non-stationary signals. The basis function is defined as: The resolution of this type of basis function in the time-frequency plane is limited by linear frequency scaling, making it difficult to adapt to the local characteristics of non-stationary signals. To this end, a learnable fractional-order wavelet kernel is introduced. By introducing fractional-order parameters Reconstruct the basis function to dynamically adjust the frequency modulation characteristics of the basis function: in, is the learnable parameter of the wavelet kernel, and the scale parameter Together through back propagation optimization. When it is equal to 1, it is the standard Morlet wavelet kernel. When it is greater than 1, Follow As the frequency increases, the basis function has a higher time-frequency resolution in the low-frequency region. When it is less than 1, the ability to capture local features in high-frequency areas is enhanced. This wavelet kernel is used for convolution of the time-frequency graph to decompose the signal at multiple scales to obtain characteristic frequency bands in different frequency ranges. The parameter gradient is driven by the downstream task loss, and its partial derivative can be decomposed into: in is the loss function. It is passed to the shallow layer of the network through the chain rule to achieve end-to-end optimization. In addition, the gradient is obtained by back propagation of the network and depends on the gradient back propagation of the subsequent layer. The scale parameter of the wavelet kernel is updated during the training process of the gradient descent method. It will be optimized according to the time-frequency characteristics of the signal. This will enable the wavelet kernel to more accurately match the time-frequency characteristics of the input signal. Parameters are used to extract the time-frequency subband features of the signal. Each set of parameters corresponds to a basis function , decompose the input signal into different frequency bands through convolution operation, Figure 5 The end-to-end optimization process of the learnable wavelet kernel is shown in the figure. Is the learning rate. The signal is mapped to multiple frequency band feature maps through convolution operation. , For the input time-frequency graph features, generate Multi-scale frequency band feature maps .

[0039] Specifically, after obtaining multi-scale frequency band feature maps, these feature maps reflect the multi-level information of the signal in the time-frequency domain. To more effectively fuse these multi-scale features, the Multi-Band Weighted Fusion module (MBWF) is introduced. This model incorporates the cross-spatial learning concept of the efficient multi-scale attention algorithm to establish dependencies between different frequency bands. The MBWF module dynamically adjusts the weights of each frequency band feature map through adaptive weighting, allocating appropriate attention between different frequency bands, thereby enhancing the learning of key features and suppressing the interference of redundant information.

[0040] Specifically, the MBWF module consists of three parts: group channel decoupling, direction-sensitive statistics extraction, and cross-channel attention generation. The input is the K frequency band feature maps generated by wavelet decomposition. , K=4 in this study. These frequency band features capture the time-frequency information of the signal in different frequency bands and are spliced ​​into a tensor along the channel dimension .

[0041] First, the module groups the concatenated feature tensors, dividing the channels into G groups, where G = K. Each group corresponds to an independent frequency band, and generates the corresponding grouped feature tensor. This process ensures the independence of each frequency band and avoids feature confusion between bands.

[0042] Next, the MBWF module performs pooling operations along the width and height dimensions to extract direction-sensitive statistics, representing the signal's temporal accumulation and frequency energy concentration, respectively. These direction-sensitive statistics are then convolved to generate joint directional features. This process helps the model capture the signal's directional information.

[0043] Finally, the directional statistics are multiplied element-by-element with the original features, and a preliminary attention map is generated through group normalization and convolution. Adaptive average pooling is used to compress the spatial dimension, and cross-channel correlation is calculated through matrix multiplication to generate an inter-band weight matrix. The Sigmoid function is used to map the weights to the [0,1] interval, dynamically weighting the original features and outputting the enhanced features. The network structure diagram of MBWF is shown in the figure below. Figure 6 shown.

[0044] The Deep Residual Shrinkage Network (DRSN) combines the advantages of residual networks and shrinkage networks. Residual connections introduce short-circuit paths, enabling efficient gradient propagation and addressing the vanishing gradient problem. The shrinkage mechanism automatically shrinks irrelevant features to zero, reducing the impact of redundant information. This paper introduces the Deep Residual Shrinkage Network framework for the first time, addressing the challenges of radar signal processing with nonstationary noise and complex time-varying spectra.

[0045] In the radar modulation signal classification task, the residual jump connection of DRSN can effectively alleviate the gradient disappearance problem. Figure 7 The basic structure of the deep residual contraction network is shown. The deep residual contraction network is a variant of the ResNet network. The contraction module consists of two paths: feature channel attention and adaptive scaling factor. After extracting channel-level statistical features through a global average pooling layer (GAP), the main attention path uses a fully connected-ReLU-fully connected structure to generate initial attention weights. The auxiliary path uses an independent scaling factor generation network to generate dynamic adjustment coefficients in the range [0, 1] to adaptively adjust the threshold strength. The weights output by the two paths are fused through element-by-element multiplication, ultimately driving the soft thresholding operation. This dual-path design enables the model to simultaneously capture long-range dependencies between feature channels and local noise intensity variations.

[0046] The cross-entropy loss function is commonly used in previous classification problems. However, in the LPI radar signal modulation recognition task, especially in low signal-to-noise ratio (SNR) environments, a single cross-entropy loss fails to constrain the feature space distribution, leading to divergence of intra-class features and decreased inter-class discrimination for different modulation signals. Therefore, a Channel-Center Joint Loss (CC-Joint Loss) is proposed to jointly optimize classification probability and feature space compactness, improving the model's robustness and classification performance under low SNR conditions.

[0047] The CC-Joint Loss consists of a cross-entropy loss and a class center loss. On the one hand, the CE loss ensures the model's ability to distinguish different modulation types; on the other hand, the CC-Loss forces similar samples to cluster in the feature space, suppressing distribution shifts caused by noise.

[0048] The cross entropy loss drives model learning by minimizing the difference between the predicted probability and the true label: in, For samples The true label, is the predicted probability, is the total number of categories, which is 12 in this task. The category center loss is designed to enhance the discriminability of the feature space and constrain similar features to move closer to the dynamically updated category center. The standard center loss function is: in, For samples The eigenvector of for The current feature mean of is the batch size. To avoid explicitly maintaining the class center parameters, a sliding average is used to dynamically update the class center. The learnable parameters are replaced by the mean of the features of the same class in the current batch.

[0049] in Category in the current batch The number of samples, For category No. The feature vector of the samples, is the class center calculated dynamically. Replaced with dynamic mean And introduce the normalization factor: The loss for each class is divided by , divide the total loss by the number of categories , and finally get: Finally, CC-Joint Loss is a weighted fusion of CE Loss and CC-Loss: Where, is the cross entropy loss, is the dynamic category center loss, and λ is the balance coefficient.

[0050] On the other hand, the present invention also provides an LPI radar modulation recognition system based on a dynamic wavelet frequency band enhancement module and a deep residual shrinkage network, which is used to implement an LPI radar modulation recognition method based on a dynamic wavelet frequency band enhancement module and a deep residual shrinkage network, comprising: Receiving module: receives LPI radar signals; Processing module: performs Choi-Williams distribution CWD time-frequency transform on the received LPI radar signal to generate a time-frequency TFI image; Identification module: Establishes the LW-BERSNet model; processes the received LPI radar signal through the established LW-BERSNet model and outputs the modulation type classification result of the LPI radar signal.

[0051] On the other hand, the present invention also provides a computer device having a computer program stored thereon, which, when executed by a processor, implements the steps of an LPI radar modulation recognition method based on a dynamic wavelet frequency band enhancement module and a deep residual shrinkage network. Example 2:

[0052] The experiments in this study involve the classification and recognition of 12 different LPI radar signal modulation types, among which the parameter settings of different signals are shown in Table 2, where the signal sampling rate Hz. The modulation parameters of each signal are randomly selected from a predetermined range of values ​​to simulate the variable electromagnetic environment that may be encountered in reality. The signal-to-noise ratio (SNR) ranges from -14 to 4dB, with a step size of 2dB. 18,000 pulses are randomly generated for each signal-to-noise ratio, and then the pulse signal is preprocessed by CWD to generate TFI. In the data set division, each signal type in the training set contains 1,100 pulses, while each signal type in the validation set contains 500 pulses. It is assumed that each TFI contains one and only one signal object. Under the same conditions, 100 samples of each type are generated for the test set. To ensure data consistency, all TFIs are adjusted to .

[0053] Table 2 Different signal parameter settings

[0054] like Figure 8 As shown, the dataset is designed for LPI radar signal recognition in complex electromagnetic environments, focusing on simulating the coupled colored noise and multipath fading effects found in real battlefields to enhance the model's generalization and noise robustness. Composite signal samples are generated by signal superposition to account for the colored noise and multipath fading effects of these radar signals. First, a time-frequency transform is performed on the composite signal to generate time-frequency images (TFIs). Second, the generated TFIs are grayscaled and zero-mean normalized to convert the RGB three-channel images into single-channel grayscale images to reduce data dimensionality. Finally, normalization is performed to eliminate illumination variations, accelerating model convergence.

[0055] In a multipath propagation environment, signals travel through different paths to the receiver. Parameters such as delay, gain, and signal-to-noise ratio (SNR) of these paths affect the final received signal. To simulate the effects of multipath fading, the present invention designed signal paths as shown in Table 3, each with different delays and gains. Furthermore, to more clearly distinguish experimental conditions, the SNR mentioned in this invention only represents the noise level and does not include the impact of multipath fading.

[0056] Table 3 Multipath effect simulation parameters

[0057] Taking LFM as an example, Figure 9 The time domain and time-frequency characteristics of radar signals are respectively demonstrated when colored noise, multipath fading effects, and the two exist simultaneously. Figure 9Part (a) shows the time domain waveform of the original LFM signal, and Figure 9 Part (e) shows the time-frequency diagram of the signal without noise as a reference. In order to simulate the influence of complex electromagnetic environment, Figure 9 The LFM signal performance under different conditions is also shown in Figure 9 (b) and Figure 9 (f) shows the time domain signal and time-frequency diagram of the LFM signal after adding the multipath fading effect. The frequency components of the signal are affected by multiple reflection paths. Figure 9 (c) and Figure 9 (g) shows the effect of colored noise on the LFM signal. After the noise is introduced, the frequency components of the signal are offset and blurred, affecting the clarity of the signal. Figure 9 (d) and Figure 9 (h) shows the coupling scenario of colored noise and multipath fading effects. In this case, the time-frequency characteristics of the LFM signal become more complex, the frequency components change significantly, and the features are blurred to varying degrees. Especially under low signal-to-noise ratio conditions, the signal recognition is significantly reduced.

[0058] Figure 10 CWD time-frequency plots are presented for 12 LPI radar modulation signals, including linear frequency modulation, Costas code, BPSK, and polyphase coding (Frank, P1-P4, and T1-T4). CWD's high-resolution time-frequency plots clearly demonstrate the characteristic differences between different modulation types. These plots intuitively demonstrate CWD's ability to preserve key signal features.

[0059] In LW-BERSNet training, Adam was used as the loss function optimizer. The initial learning rate was 0.01, the training batch size was 64, and the total number of iterations was 100. To optimize the training process, a cosine annealing learning rate decay strategy was introduced, in which the learning rate gradually decays from the initial value to a minimum value, preventing overly rapid convergence and improving model accuracy. Furthermore, to enhance the model's generalization capabilities, data augmentation techniques were employed to ensure the model's adaptability to a variety of input modes. All networks were implemented in PyCharm using PyTorch 2.1.0 and CUDA 12.1. The computer configuration was a 25-core Xeon Platinum 8481C processor and a 32GB vGPU.

[0060] Specifically, comparative experiments:

[0061] (1) Performance comparison of different classification methods Here, we verify the overall recognition performance of the LW-BERSNet model for 12 radar emission signals through simulation and compare it with three other radar emission signal recognition methods from the CWD+LPI-Net paper, the LDC-Unet paper, the VMD-LMD-WT+CNN paper, and the Hybrid Attention+SFA+DCNN paper.

[0062] Wangkui Jiang et al. used SPWVD for time-frequency analysis and combined it with a DCNN for waveform recognition. The preprocessing stage employed an LDC-Unet network, which reduced noise interference and enhanced time-frequency image features through a locally densely connected structure. Thien Huynh-The designed LPI-Net, a deep convolutional neural network (CNN), combined with the Choi-Williams distribution CWD-TFA technique for automated identification of low-probability intercept radar waveforms. Through multiple cascaded processing modules, it learned highly discriminative features from time-frequency images. Mengting Jiang et al. designed a network that combined a multi-layer decomposition denoising method (VMD-LMD-WT) with an improved convolutional neural network for radar signal modulation recognition under low signal-to-noise ratio (SNR) conditions. Multi-layer denoising effectively improved signal quality, while the improved CNN enhanced signal feature extraction and classification performance. Yuanpu Guo's team proposed a convolutional neural network approach based on a hybrid attention mechanism and skip feature aggregation (SFA). By introducing time-frequency self-attention modeling and a multi-layer feature fusion strategy, it improved the recognition accuracy of radar signals in complex electromagnetic environments.

[0063] like Figure 11Experiments show that LW-BERSNET significantly outperforms other methods in low signal-to-noise ratio (SNR) scenarios (SNR ≤ -6 dB). In a colored noise environment with an SNR of -10 dB, its recognition accuracy improves by 9.51%, 3.1%, 17.8%, and 6.4% compared to Hybrid Attention + SFA + DCNN, LDC-Unet, CWD + LPI-Net, and VMD-LMD-WT + CNN, respectively. This demonstrates the synergistic suppression capability of the dynamic wavelet kernel and multi-band weight fusion module for time-frequency aliasing noise. Compared to a network model without the LWBE module, the LW-BERSNet model demonstrates the importance of its modular design in signal recognition accuracy. Specifically, the model's accuracy decreases significantly after removing the LWBE module, demonstrating its importance in the model. It is worth noting that as the SNR decreases to the extreme condition of SNR=-14 dB, the performance degradation of the model in the scenario of colored noise superimposed multipath fading effect is significantly smaller than that of other methods, highlighting its robustness advantage achieved through frequency band adaptation and direction-sensitive feature enhancement.

[0064] The comparative experimental results in the environment of colored noise superimposed multipath fading effect are as follows: Figure 12 The results further demonstrate the robustness and high recognition capabilities of the LW-BERSNet model. Despite the increased complexity of signal recognition due to multipath fading, the LW-BERSNet model maintains a high accuracy, significantly outperforming other compared methods. In scenarios with colored noise and multipath fading, its accuracy improves by 4.9%-15.5% compared to the comparison methods. In contrast, the CWD+LPI-Net and VMD-LMD-WT + CNN models perform poorly when processing signals coupled with multipath fading, especially under low SNR conditions, where accuracy fluctuates significantly.

[0065] In order to verify the impact of different time-frequency analysis methods on the accuracy and select the most appropriate time-frequency analysis method, data sets based on three time-frequency analysis methods, namely CWD, WVD and STFT, were designed respectively. Figure 13The average accuracy performance of the three methods under different signal-to-noise ratio conditions is shown in the figure. In this experiment, STFT adopted a Kaiser window with a window length of 128, an overlap rate of 50%, and an FFT point number of 1024; the WVD frequency resolution was set to 1024. CWD performed more stably at low SNRs, which shows that the CWD method has good robustness in low signal-to-noise ratio environments. The classification accuracy of WVD and STFT at low SNRs increases slowly, but as the SNR increases, their accuracy gradually improves and eventually tends to similar values. Compared with the other two methods, the CWD method has obvious advantages in low SNR environments, and its performance at high SNRs is also more stable. The network used in this embodiment is the LW-BERSNet model provided by the present invention.

[0066] To analyze the differences between the model's cross-entropy loss function and CC-Joint Loss, the LW-BERSNet model was trained on a dataset of 12 LPI radar signals using the two different loss functions. The colored noise dataset used in this experiment had a signal-to-noise ratio of -8dB. Figure 14 The figure shows the model training progress over 100 training cycles. To more intuitively demonstrate the impact of the joint loss on model optimization, the training results of the two loss functions are compared on a colored noise dataset. It can be seen that the CC-Joint Loss exhibits significantly better convergence stability than the traditional cross-entropy loss. Its loss curve decreases smoothly without significant abnormal fluctuations, while the cross-entropy loss exhibits intermittent and violent fluctuations mid-training, indicating its sensitivity to noise and limited generalization robustness.

[0067] In terms of classification performance, the CC-Joint Loss-based model consistently achieved higher accuracy than the cross-entropy-based model, particularly in the presence of noise. The CC-Joint Loss model steadily converged to a high accuracy in the later stages of training, while the CC-Joint Loss model experienced significant fluctuations and declines in accuracy due to a sudden increase in loss. This experiment demonstrated that the CC-Joint Loss, by combining intra-class variance constraints with the classification loss, effectively suppressed feature space divergence, enhancing the model's robustness in complex electromagnetic interference environments while maintaining training stability.

[0068] Figure 15 (a) shows the signal classification results trained with the LW-BERSNet model and CC-Joint Loss function under the condition of SNR of -12dB, while Figure 15(b) shows the signal classification results trained using the cross-entropy loss function under the same conditions. As can be seen from the figure, compared with the model using the cross-entropy loss function, the LW-BERSNet model using CC-JointLoss can better cluster different types of signals, clearly distinguishing between signal categories, and the signal clusters are more compact with no significant overlap, demonstrating strong robustness. In contrast, the model using the cross-entropy loss function performs poorly at low signal-to-noise ratios, with blurred boundaries between categories and significant overlap between signals.

[0069] Figure 15 (c) and Figure 15 Figure (d) shows the signal classification results of the LW-BERSNet model with the learnable wavelet band enhancement module frozen under an SNR of -12dB. As can be seen from the aforementioned experimental results, after freezing this module, the clustering effect decreases to a certain extent, and the separation between signal categories becomes less obvious than before. This phenomenon indicates that the learnable wavelet band enhancement module suppresses the negative impact of noise on signal recognition and classification. Therefore, it can be concluded that the presence of the learnable wavelet band enhancement module effectively improves the model's noise resistance, especially when facing low signal-to-noise ratios, and can improve the stability and robustness of signal recognition.

[0070] In order to verify the robustness of the model in a complex electromagnetic environment, the present invention designed a multi-scenario noise experiment, including colored noise, and colored noise superimposed on three paths and five paths of multipath fading effects, corresponding to Scenario 1 and Scenario 2 in Table 3 respectively. The experiment set the signal-to-noise ratio conditions of -8 dB, -10 dB, and -12 dB respectively, and tested the model performance in these three scenarios. The experimental results are shown in Figure 3. Figure 16 As shown in the figure, the proposed LW-BERSNet architecture maintains good performance in scenarios with increasing environmental complexity. In a basic colored noise environment, the model's recognition accuracy demonstrates excellent performance. Although model performance declines with increasing multipath fading and decreasing signal-to-noise ratio, it maintains high recognition accuracy in scenarios of varying complexity. Further analysis shows that the model dynamically generates parameters that adapt to frequency band characteristics and combines direction-sensitive attention to enhance the discriminability of spatial features, thereby achieving a balanced optimization of robustness, generalization, and computational efficiency in multi-source coupling scenarios. Further analysis shows that the model dynamically generates adaptive parameters to optimize frequency band characteristics in different environments. At the same time, the combination of a direction-sensitive attention mechanism enhances the discriminability of spatial features, allowing the model to maintain high robustness in complex environments.

[0071] In order to further intuitively display the detailed recognition results in different scenarios, Figure 17The figure shows the confusion matrices of 12 radar signals from three test sets identified by the model at a signal-to-noise ratio of -10dB. As shown, although multipath fading causes some degradation in recognition accuracy, the LW-BERSNet network maintains a high recognition accuracy. In the presence of colored noise, the model achieves near-perfect recognition rates for most signals, such as BPSK, Costas, and LFM, demonstrating its robustness to underlying noise. When multipath fading is introduced, although the recognition rate of some phase-sensitive signals (such as P3 and T2) decreases due to delay spread, the overall model accuracy remains stable at 93% (colored noise + Scenario 1) and 91.08% (colored noise + Scenario 2). Notably, the model maintains a recognition rate of >95% for constant envelope signals (such as BPSK and Frank) and wideband signals (such as LFM) under multipath fading, demonstrating that the dynamic wavelet kernel's frequency band adaptation and the multi-band weight fusion module effectively suppress time-frequency aliasing caused by multipath fading. Furthermore, in extremely complex scenarios, such as the presence of colored noise and Scenario 2, the model's recognition accuracy for highly complex coded signals (such as T3 and P1) remains unchanged, further validating the enhanced feature discriminability of the learnable wavelet frequency band enhancement module. This experiment demonstrates the technical advantages of the proposed method in complex electromagnetic countermeasure scenarios from the perspective of signal type.

[0072] Figure 18 The recognition accuracy of 12 LPI radar signals at various signal-to-noise ratios (SNRs) is shown. Experiments demonstrate that the proposed model exhibits significant advantages in extremely low SNRs (SNRs ≤ -10 dB) and in scenarios where multipath fading and noise are coupled. When the SNR is ≥ 0 dB, the model achieves near 100% recognition accuracy for all signal classes, demonstrating its high reliability in conventional noise environments. As the SNR decreases to -10 dB, the model's overall accuracy remains stable at 93% in the presence of colored noise and Scenario 1, significantly outperforming the 91.92% accuracy achieved without the learnable wavelet band enhancement module. Notably, under the extreme condition of -14 dB SNR, the model maintains a recognition accuracy exceeding 75% for constant envelope signals (such as BPSK and Frank) and wideband signals (such as LFM), while the performance degradation for phase-sensitive signals (such as P3 and T2) is manageable, at approximately 50%. This demonstrates that the dynamic wavelet kernel and multi-band weight fusion module effectively suppress feature blurring caused by multipath fading. This result highlights the model's strong adaptability and generalization capabilities in complex electromagnetic confrontation scenarios.

[0073] Furthermore, experiments demonstrating the technical necessity of the LWBE module showed that removing it significantly degraded the model's performance in scenarios with low signal-to-noise ratios and multipath fading. In the Scenario 1 scenario with colored noise and an SNR of -10 dB, the accuracy after removing the LWBE module decreased by 4.3% compared to the intact model, and the recognition rate for phase-sensitive signals (such as P3 and T2) dropped by over 15%. Further analysis revealed that the LWBE module significantly improved the model's ability to suppress time-varying noise and signal fluctuations through dynamic band weighting and direction-sensitive feature enhancement. In the presence of colored noise at an SNR of -14 dB and Scenario 1, the full model achieved a 12%-20% improvement in recognition accuracy for highly complex coded signals (such as T3 and P1) compared to when the LWBE module was removed. This validates its core mechanism for signal feature enhancement through band-spatial co-optimization. Furthermore, in-depth analysis revealed that, in the presence of colored noise at an SNR of -14 dB and Scenario 1, the full model achieved an 8.2% improvement in recognition accuracy for wideband signals (such as LFM) and a 12.1% improvement in recognition accuracy for highly complex coded signals (such as T3) compared to when the LWBE module was removed. This experiment confirms the irreplaceable role of LWBE in noise robustness, feature discrimination, and stability in extreme scenarios.

[0074] In order to comprehensively evaluate the impact of network architecture optimization on model robustness, this paper designed a systematic ablation experiment. By gradually removing the learnable wavelet kernel mechanism (LWK), the multi-band weight fusion module (MBWF) and the learnable wavelet band enhancement module (LWBE), the model performance was tested in two complex electromagnetic environments: colored noise and colored noise plus multipath fading effects. The signal-to-noise ratio was set to -10 dB. Among them, the design of removing the learnable wavelet kernel mechanism is to set fixed parameters ; . The experimental results show that the complete network shows significant advantages in both scenarios: compared with the variant without dynamic parameter generation, its recognition accuracy is improved, verifying the role of the dynamic wavelet kernel in noise adaptation; after removing the multi-band weight fusion module, the performance degradation of the model in the colored noise plus multipath fading scenario is particularly obvious, indicating that the multi-band weight fusion module has a collaborative optimization effect in complex environments. In addition, the performance stability of the complete model in the colored noise plus multipath fading effect scenario far exceeds that of other variants. As shown in Table 4, this experiment verified the contribution of each module of the designed network to the performance in a complex electromagnetic environment through ablation experiments.

[0075] Table 4 Recognition accuracy ablation experiments under different datasets

[0076] Through the above technical solutions, it can be seen that the present invention discloses a method, system and computer equipment for LPI radar modulation recognition based on a dynamic wavelet band enhancement module and a deep residual shrinkage network. Specifically, a deep learning method combining adaptive wavelet decomposition, a multi-band attention fusion mechanism and a deep residual shrinkage network is proposed, which can learn the wavelet band enhancement residual shrinkage network (LW-BERSNet). This method effectively copes with the LPI radar signal recognition and classification tasks in multipath fading and colored noise scenarios by dynamically optimizing the multi-scale frequency band characteristics of the signal, including the recognition and classification tasks of twelve types of LPI radar signals, including BPSK, LFM, Costas, five polyphase codes (such as Frank, P1, P2, P3 and P4) and four polytime codes (such as T1, T2, T3 and T4). Compared with traditional methods and existing deep learning models, the present invention has significant advantages in the following aspects: 1. A framework for LPI radar signal recognition is proposed: This framework aims to address the low recognition performance of existing methods in complex scenarios coupled with colored noise and multipath fading effects.

[0077] 2. A learnable wavelet frequency band enhancement module is proposed: This module dynamically optimizes frequency band decomposition parameters using a learnable wavelet kernel to effectively capture the multi-scale frequency band characteristics of the signal. A multi-band weighted fusion module is introduced to group and decouple frequency band characteristics, extract time-frequency statistics using row-column average pooling, and dynamically enhance key frequency bands using cross-channel attention weights. This module improves the representation of complex modulated signals through adaptive frequency band partitioning and direction-sensitive weighting.

[0078] 3. We propose a deep residual shrinkage network that combines a channel-center composite loss function. This network incorporates a deep residual shrinkage module into its backbone architecture. A channel-attention mechanism dynamically generates local adaptive thresholds related to the signal's time-frequency energy, thereby suppressing background noise. By jointly optimizing the cross-entropy loss and the dynamic class center loss, the network constrains similar features to converge toward the class center updated by a sliding average, while also increasing the feature distance between different classes and enhancing inter-class discrimination.

[0079] As for the system device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the description of the method part.

[0080] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0081] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A LPI radar modulation recognition method based on dynamic wavelet band enhancement module and deep residual shrinkage network, characterized in that: The following steps are involved: Step 1: Receive LPI radar signal; Step 2: Perform Choi-Williams distribution CWD time-frequency transform on the received LPI radar signal to generate a time-frequency TFI image; Step 3: Establish an LW-BERSNet model; process the received LPI radar signal through the established LW-BERSNet model and output the modulation type classification result of the LPI radar signal.

2. The LPI radar modulation recognition method based on dynamic wavelet frequency band enhancement module and deep residual shrinkage network according to claim 1 is characterized in that: The LPI radar signal received in step 1 is expressed as: ， in is the amplitude of the signal, is the gate function, is the pulse width, is the instantaneous frequency, is the initial phase, is the time phase function.

3. The LPI radar modulation recognition method based on dynamic wavelet frequency band enhancement module and deep residual shrinkage network according to claim 1 is characterized in that: The expression of CWD time-frequency transform in step 2 is: ； in, is the fuzzy function of the signal, defined as the signal delay and frequency offset The related functions on It is an exponential kernel function that suppresses cross terms while retaining the main lobe energy focus.

4. The LPI radar modulation recognition method based on dynamic wavelet frequency band enhancement module and deep residual shrinkage network according to claim 1 is characterized in that: Step 3: LW-BERSNet model, including: Feature extraction module, learnable wavelet band enhancement module LWBE, multi-band weight fusion module MBWF, deep residual shrinkage network DRSN, and classification module; Among them, the high-level features of the time-frequency TFI image are extracted by the feature extraction module; the high-level features are dynamically decomposed by the learnable wavelet band enhancement module LWBE to generate a multi-scale band feature map; the band feature map is cross-channel attention weighted fusion is performed by the multi-band weight fusion module MBWF; the fused features are input into the deep residual shrinkage network DRSN, and the noise is suppressed and the discriminative features are extracted by adaptive soft thresholding; the classification module adopts the channel-center joint loss function CC-Joint Loss to jointly optimize the cross entropy loss and the dynamic category center loss, and outputs the modulation type classification result of the LPI radar signal.

5. The LPI radar modulation recognition method based on dynamic wavelet frequency band enhancement module and deep residual shrinkage network according to claim 4 is characterized in that: The learnable wavelet band enhancement module LWBE uses a learnable wavelet kernel to perform discrete wavelet transform on the input signal. The basis function of the learnable wavelet kernel is: ； Where, Preset scale parameters; is the learnable parameter of the wavelet kernel and the preset scale parameter Together through back-propagation optimization, where When it is equal to 1, it is the standard Morlet wavelet kernel. When it is greater than 1, Follow As the frequency increases, the basis function has a higher time-frequency resolution in the low-frequency region. When it is less than 1, the ability to capture local features in high-frequency areas is enhanced.

6. The LPI radar modulation recognition method based on dynamic wavelet frequency band enhancement module and deep residual shrinkage network according to claim 4 is characterized in that: The multi-band weight fusion module MBWF is used to perform cross-channel attention weighted fusion on the band feature map, and the specific steps include: Grouping the frequency band feature maps along the channel dimension; Average pooling is performed along the width and height directions to extract direction-sensitive statistics; The frequency band features are dynamically weighted and fused via a cross-channel attention weight matrix.

7. The LPI radar modulation recognition method based on dynamic wavelet frequency band enhancement module and deep residual shrinkage network according to claim 4 is characterized in that: The deep residual shrinkage network DRSN includes a dual-path attention mechanism, where: Main path: Generate channel attention weights through global average pooling and fully connected layers; Auxiliary path: Dynamically adjust the threshold strength through the scaling factor generation network; The fused dual-path output drives the soft thresholding operation to suppress redundant features.

8. The LPI radar modulation recognition method based on dynamic wavelet frequency band enhancement module and deep residual shrinkage network according to claim 4 is characterized in that: The classification module uses the channel-center joint loss function CC-JointLoss to jointly optimize the cross entropy loss and the dynamic category center loss, and outputs the modulation type classification results of the LPI radar signal, including: The cross entropy loss drives model learning by minimizing the difference between the predicted probability and the true label: ， in, For samples The true label, is the predicted probability, is the total number of categories; Standard center loss function: ， in, For samples The eigenvector of for The current feature mean of is the batch size; Use the mean of the features of the same type in the current batch to replace the learnable parameters: ， in Category in the current batch The number of samples, For category No. The feature vector of the samples, It is a class center of dynamic calculation; The standard center loss function Replaced with dynamic mean And introduce the normalization factor: ， The loss for each class is divided by , divide the total loss by the number of categories , and finally get: ， Finally, CC-Joint Loss is a weighted fusion of CE Loss and CC-Loss: ； Where, is the cross entropy loss, is the dynamic category center loss, and λ is the balance coefficient.

9. An LPI radar modulation recognition system based on a dynamic wavelet frequency band enhancement module and a deep residual shrinkage network, used to implement the LPI radar modulation recognition method based on a dynamic wavelet frequency band enhancement module and a deep residual shrinkage network according to any one of claims 1 to 8, characterized in that: include: Receiving module: receives LPI radar signals; Processing module: performs Choi-Williams distribution CWD time-frequency transform on the received LPI radar signal to generate a time-frequency TFI image; Identification module: Establishes the LW-BERSNet model; processes the received LPI radar signal through the established LW-BERSNet model and outputs the modulation type classification result of the LPI radar signal.

10. A computer device, characterized in that: A computer program is stored on the computer device, and when the computer program is executed by the processor, the steps of the LPI radar modulation recognition method based on a dynamic wavelet frequency band enhancement module and a deep residual shrinkage network as described in any one of claims 1 to 8 are implemented.

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