LMSST and DCNN-based radar signal intra-pulse modulation recognition method

Abstract

The application discloses a radar signal intra-pulse modulation recognition method based on LMSST and DCNN. The application estimates the instantaneous frequency based on a ridge extraction algorithm by adopting an LMSST time-frequency distribution, and detects the local maximum value of a time-frequency spectrum in a frequency direction, so that the energy aggregation is improved, and the time-frequency representation characteristics under different modulations are significantly improved. Meanwhile, the deep cascaded convolutional neural network improves the multi-scale resolution of the convolutional neural network, can solve the problems of weak learning ability, low generalization ability and poor clustering effect of the deep model, so that the accuracy of LPI radar signal modulation recognition is improved, automatic classification of radar modulation waveforms is realized, the workload of electronic reconnaissance professionals is reduced, and subsequent situation and threat estimation is facilitated.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing, and in particular, it is a radar signal intra-pulse modulation recognition method based on LMSST and DCNN. Background Technology

[0002] Radar signal classification and recognition play a crucial role in electronic warfare, electronic reconnaissance, and spectrum management. With the development of modern electronic equipment, research on radar systems is constantly deepening, and more modulation types are being applied to radar signals. Therefore, improving the accuracy of intra-pulse modulation discrimination of radar signals is of great significance, whether for identifying enemy jamming signals and radar countermeasures in the military field or for monitoring and measurement in the civilian field. The modern radio environment is increasingly harsh, the signal-to-noise ratio (SNR) of radar signals is constantly decreasing, and it is difficult to collect battlefield radar signal samples. Therefore, improving the classification and recognition rate of radar signals under low SNR and small sample conditions is becoming increasingly important.

[0003] Intra-pulse modulation classification and recognition technology for radar signals mainly consists of two steps: feature extraction and classification. Traditionally extracted features include cyclic moments, the signal's spectral correlation function, instantaneous features, and higher-order statistical features. The time-frequency characteristics of radar signals are constantly evolving. To address the shortcomings of low resolution and significant influence from window length in short-time Fourier transforms (SFTs), some researchers have proposed synchronous compressed SFTs, combining them with synchronous compressed transforms to improve time-frequency resolution. With the rapid development of deep learning, various deep learning techniques have been introduced into intra-pulse modulation recognition of low probability of intercept (PRC) radar signals in recent years. Because time-frequency analysis can effectively reflect the joint characteristics of different modulation signals in the time-frequency domain, the advantages of convolutional neural networks in image recognition can be utilized to extract deep features from time-frequency images, thereby improving recognition performance.

[0004] Therefore, a major problem with existing technologies is that they are limited by the time-frequency resolution in time-frequency images and the difficulty in collecting radar signal samples, as well as the insufficient performance of existing deep learning models. They are not very targeted to radar signal time-frequency images, and deep learning models cannot fully explore the highly discriminative features between different types of signals. Summary of the Invention

[0005] The purpose of this invention is to provide an automatic identification method for intra-pulse modulation of LPI radar signals based on LMSST time-frequency distribution and deep convolutional neural network. This method has a higher classification and identification rate for intra-pulse modulation of radar signals under low signal-to-noise ratio and small sample conditions, and can be used as a classification and identification method for intra-pulse modulation of radar signals.

[0006] The technical solution to achieve the purpose of this invention is: a radar signal intra-pulse modulation identification method based on LMSST and DCNN, the method comprising the following steps:

[0007] Step 1: Perform Local Maximum Synchronization Transform (LMSST) on the low probability of intercept (LPI) radar signal to obtain the LMSST time-frequency image;

[0008] Step 2: Preprocess the LMSST time-frequency image obtained in Step 1;

[0009] Step 3: Add modulation scheme labels to the LMSST time-frequency images to construct a radar signal time-frequency image dataset, and divide the radar signal time-frequency image dataset into training set, validation set and test set according to a preset ratio;

[0010] Step 4: Construct a deep concatenated convolutional neural network and train it using the training set to obtain a modulation recognition model;

[0011] Step 5: Use the modulation recognition model to perform modulation recognition on the LPI radar signal under test.

[0012] Further, the low probability of intercept (LPI) radar signal mentioned in step 1 includes LFM, Costas, Frank, P1 to P4, and T1 to T4. The parameters of LFM include carrier frequency fc and bandwidth B. The parameters of Costas include frequency hopping sequence L and reference frequency fmin. The parameters of Frank and P1 to P4 include carrier frequency fc, phase control number M, and phase sub-wavelength number cpp. The parameters of T1 and T2 include carrier frequency fc and waveform segment number k. The parameters of T3 and T4 include carrier frequency fc, waveform segment number k, and modulation bandwidth B.

[0013] Furthermore, step 1 specifically includes the following processes:

[0014] Step 1-1: Using a Gaussian window as the window function for the short-time Fourier transform, set the length parameter of the window function to extend the one-dimensional time series to a two-dimensional time-frequency plane, and extract the time-frequency distribution map of the short-time Fourier transform.

[0015] Steps 1-2: Set the time width parameter of LMSST transform, perform post-processing on the result of short-time Fourier transform, perform LMSST transform on the obtained short-time Fourier transform time-frequency distribution, and redistribute the fuzzy time-frequency energy to the intermediate frequency estimation in the frequency direction.

[0016] Further, step 2, which involves preprocessing the LMSST time-frequency image obtained in step 1, specifically includes:

[0017] Step 2-1: Perform grayscale processing on the LMSST time-frequency image;

[0018] Step 2-2: Adaptive threshold binarization is performed using the Otsu method;

[0019] Steps 2-3 involve median filtering for smoothing.

[0020] Steps 2-4: Adjust the size of the time-frequency image and perform scaling and dimensionality reduction processing.

[0021] Furthermore, in step 3, the radar signal time-frequency image dataset is divided into training set, validation set, and test set according to a ratio of 70%, 15%, and 15%.

[0022] Furthermore, in step 4, the deep cascaded convolutional neural network includes a sequentially connected input layer, a first convolutional layer, three core convolutional modules, a skip connection layer, a global average pooling layer, and a fully connected layer; each core convolutional module includes a sequentially connected max pooling layer, a deep connection layer, a second convolutional layer, a first batch normalization layer, a first activation layer Elu function, and two branches connected in parallel between the max pooling layer and the deep connection layer, each branch including a sequentially connected third convolutional layer, a second batch normalization layer, and a second activation layer Elu function.

[0023] Furthermore, the first convolutional layer has a 7*7 kernel and a stride of 1; the second convolutional layer has a 1*1 kernel and a stride of 1; and the third convolutional layer has a 3*1 kernel and a stride of 1.

[0024] Furthermore, step 4 is followed by the execution of:

[0025] The test set is fed into the deep convolutional neural network for classification and recognition, and the modulation recognition rate under different signals and different signal-to-noise ratios is obtained.

[0026] Compared with the prior art, the significant advantages of this invention are:

[0027] 1) Compared to traditional manual feature extraction, deep learning models can quickly and accurately extract subtle features from LPI radar time-frequency images with various modulation patterns. The deep cascaded convolutional neural network model in this invention, compared to conventional convolutional neural networks, uses a cascaded structure of three core convolutional modules for feature fusion. While slightly increasing model complexity, it extracts highly discriminative features, introduces deep connections and skip connections to retain important information in the gradient, and adds a global average pooling layer to reduce the number of parameters that need to be learned in subsequent fully connected layers. Experimental results show a significant improvement in the accuracy of automatic identification of intra-pulse modulation in LPI radar signals.

[0028] 2) This invention is based on LMSST time-frequency transformation for LPI radar signal feature extraction. Compared with traditional STFT time-frequency transformation, the time-frequency image has better time-frequency aggregation, higher time-frequency resolution, and more obvious two-dimensional features, which improves the accuracy of automatic recognition of intra-pulse modulation of LPI radar signals.

[0029] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0030] Figure 1 This is a flowchart of the radar signal intra-pulse modulation recognition method based on LMSST and DCNN of the present invention.

[0031] Figure 2 Here is an LMSST time-frequency diagram of 11 types of LPI radar signals in one embodiment, where Figure 2 (a) to (k) are the LMSST time-frequency diagrams corresponding to LFM, Costas, Frank, P1, P2, P3, P4, T1, T2, T3, and T4, respectively.

[0032] Figure 3 This is a schematic diagram illustrating the time-frequency image preprocessing process and its effects in one embodiment.

[0033] Figure 4 Here is a structural diagram of a deep cascaded convolutional neural network and a structural diagram of each convolutional module in one embodiment, wherein Figure 4 (a) in the diagram is the structure of a deep cascaded convolutional neural network. Figure 4 (b) in the diagram is the structure diagram of the convolution module.

[0034] Figure 5 This is a schematic diagram of the intra-pulse modulation recognition rate of 11 LPI radar signals with a signal-to-noise ratio of -10dB to 10dB in one embodiment. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0036] It should be noted that if the embodiments of the present invention involve directional indicators (such as up, down, left, right, front, back, etc.), the directional indicators are only used to explain the relative positional relationship and movement of the components in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indicators will also change accordingly.

[0037] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. If the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0038] In one embodiment, combined Figure 1 This paper provides a radar signal intra-pulse modulation identification method based on LMSST and DCNN, the method comprising the following steps:

[0039] Step 1: Perform Local Maximum Synchronization Transform (LMSST) on the low probability of intercept (LPI) radar signal to obtain the LMSST time-frequency image;

[0040] Step 2: Preprocess the LMSST time-frequency image obtained in Step 1;

[0041] Step 3: Add modulation scheme labels to the LMSST time-frequency images to construct a radar signal time-frequency image dataset, and divide the radar signal time-frequency image dataset into training set, validation set and test set according to a preset ratio;

[0042] Step 4: Construct a deep concatenated convolutional neural network and train it using the training set to obtain a modulation recognition model;

[0043] Step 5: Use the modulation recognition model to perform modulation recognition on the LPI radar signal under test.

[0044] Furthermore, in one embodiment, the low probability of intercept (LPI) radar signal in step 1 is obtained through simulation and includes LFM, Costas, Frank, P1-P4, and T1-T4. The parameters of LFM include carrier frequency fc and bandwidth B. The parameters of Costas include frequency hopping sequence L and reference frequency fmin. The parameters of Frank and P1-P4 include carrier frequency fc, phase control number M, and phase sub-wavelength number cpp. The parameters of T1 and T2 include carrier frequency fc and waveform segment number k. The parameters of T3 and T4 include carrier frequency fc, waveform segment number k, and modulation bandwidth B. Specific parameters are shown in Table 1 below.

[0045] Table 1 Simulation parameters of LPI radar signal

[0046]

[0047] Furthermore, in one embodiment, step 1 specifically includes the following process:

[0048] Step 1-1: Using a Gaussian window as the window function for the short-time Fourier transform, set the length parameter hlength of the window function (preferably, it should be a fraction of the number of signal sampling points). This method extends the one-dimensional time series to a two-dimensional time-frequency plane, extracting the time-frequency distribution map of the short-time Fourier transform.

[0049] Steps 1-2: Set the time-width parameter le of the LMSST transform (preferably, it is a fraction of the Gaussian window length). The results of the short-time Fourier transform are post-processed, and the obtained short-time Fourier transform time-frequency distribution is subjected to LMSST transform. The ambiguous time-frequency energy is redistributed to the intermediate frequency estimate in the frequency direction, thereby obtaining a time-frequency distribution with better time-frequency clustering and higher time-frequency resolution.

[0050] The LMSST transform expression for signal s(t) is:

[0051]

[0052] Where t is the number of sampling time points, w is the instantaneous frequency of the signal, η is the instantaneous frequency of the Local Maximum Synchronous Transform (LMSST), and STFT is the short-time Fourier transform of the signal. h(t) is the short-time Fourier window function, which is a Gaussian window function used in this invention; τ is the STFT moving step size, which is 1; δ(·) is the Dirac impulse function; s(t) is the LPI signal; w m (t,w) represents the reassignment rule for the frequency direction of LMSST.

[0053] The frequency-direction redistribution operator used in this method is:

[0054]

[0055] Where Δ is the discrete frequency interval.

[0056] In this embodiment, time-frequency analysis was performed on 11 types of LPI radar signals. Figure 2 The paper presents time-frequency images of 11 radar signals at a signal-to-noise ratio of 5 dB. The 11 LPI radar signals are: LFM, Costas, Frank, T1~T4, and P1~P4.

[0057] Furthermore, in one embodiment, step 2, which involves preprocessing the LMSST time-frequency image obtained in step 1, specifically includes:

[0058] Step 2-1: Perform grayscale processing on the LMSST time-frequency image;

[0059] Here, grayscale conversion takes up less memory and has a faster processing speed; it also increases visual contrast and highlights the target area.

[0060] Step 2-2: Adaptive threshold binarization is performed using the Otsu method;

[0061] The specific process includes: First, converting the image to grayscale and counting the number of pixels at each grayscale level. Then, calculating the probability distribution for each grayscale level, which is the number of pixels at each grayscale level divided by the total number of pixels. Next, calculating the intra-class variance and between-class variance. Intra-class variance is the weighted sum of the variances of pixel grayscale values ​​across different classes (background and foreground), while between-class variance is the variance of pixel grayscale values ​​between two classes. After calculating the intra-class and between-class variances, the grayscale threshold that minimizes the between-class variance is selected as the image segmentation threshold. This threshold divides the image into two parts: foreground and background.

[0062] Steps 2-3 involve median filtering for smoothing.

[0063] Here, the specific process includes: using a 3*3 moving window and aligning the center of the template with a certain pixel position in the image; reading the corresponding pixel grayscale values ​​under the template from smallest to largest; selecting the grayscale value of the middle pixel in the grayscale sequence; and assigning the middle value to the pixel at the center position of the template.

[0064] Here, median filtering has a good filtering effect on isolated noise pixels, namely salt-and-pepper noise and impulse noise, and can preserve the edge characteristics of the image without causing significant blurring.

[0065] Steps 2-4: In order to reduce the training time of the model, dimensionality reduction is performed by adjusting the size of the time-frequency image to 100*100, which will then be used as the input for the subsequent model.

[0066] In this embodiment, Figure 3 The images shown are the preprocessed LFM modulated time-frequency images at SNR=5dB. Each image represents the original video image, grayscale binarization, median filtering smoothing, and image resizing. Overall, the preprocessed time-frequency images occupy less space while better preserving the subtle time-frequency features of the LPI intra-pulse modulation signal.

[0067] Furthermore, in one embodiment, in step 3, the radar signal time-frequency image dataset is divided into a training set, a validation set, and a test set according to a ratio of 70%, 15%, and 15%.

[0068] For each LPI radar signal, 500 single-pulse signals are generated at each signal-to-noise ratio. Real labels are added to the preprocessed LMSST time-frequency images. The same modulation method is saved to a folder named after its modulation method. A radar signal time-frequency image dataset is constructed, and the pre-time-frequency image set is divided into training set, validation set and test set according to the proportions of 70%, 15% and 15%.

[0069] In this embodiment, the 110,000 preprocessed single-pulse signal samples are divided into a training set, a validation set, and a test set, with the training set comprising 70%, the validation set 15%, and the test set 15%. The signal-to-noise ratio of the test set ranges from -10dB to 10dB.

[0070] Furthermore, in one embodiment, combined with Figure 4 In step 4, the deep cascaded convolutional neural network includes a sequentially connected input layer, a first convolutional layer, three core convolutional modules, a skip connection layer, a global average pooling layer, and a fully connected layer. Each core convolutional module includes a sequentially connected max pooling layer, a deep connection layer, a second convolutional layer, a first batch normalization layer, a first activation layer Elu function, and two parallel branches located between the max pooling layer and the deep connection layer. Each branch includes a sequentially connected third convolutional layer, a second batch normalization layer, and a second activation layer Elu function.

[0071] Preferably, the first convolutional layer has a 7*7 kernel and a stride of 1; the second convolutional layer has a 1*1 kernel and a stride of 1; and the third convolutional layer has a 3*1 kernel and a stride of 1.

[0072] Here, to address the vanishing gradient problem in multi-layer networks, deep connections and skip connections are introduced. Deep connections concatenate features from previous layers with features from the current layer, thereby obtaining richer pattern information. Skip connections use element-wise addition to sum features from previous layers with features from the current layer, thus preserving important information from the gradient. After the final processing module, a global average pooling layer is used to downsample by calculating the average of the spatial dimensions across each channel. This reduces the number of parameters that need to be learned in subsequent fully connected layers, thus reducing the network size. Specifically:

[0073] Skip connection layer: The outputs of the previous processing modules are skipped by adding them element by element to prevent the gradient vanishing problem.

[0074] Global average pooling layer: Performs global average pooling on the output of the last processing module to reduce spatial dimensionality and calculates the mean for each channel.

[0075] Fully connected layers: This consists of two fully connected layers, a dropout layer, and a softmax layer. These layers are used for the final waveform classification.

[0076] Here, three core convolutional modules are arranged in a cascaded manner to extract highly discriminative features at multiple scales. The structure of the core convolutional modules enables the extraction of highly discriminative features at multiple scales. Specifically: max pooling layers are used to reduce the spatial dimension of the input feature map; parallel convolutional layers use asymmetric kernels (1×3 and 3×1) to reduce the number of trainable parameters; deep connection layers connect the output feature maps of two convolutional layers to obtain a new feature map; and unity convolutional layers control the depth of the feature map and perform channel pooling.

[0077] In step 4, during model training, the model parameters are first initialized. This invention uses Matlab 2023a for training, with hardware including an Intel(R) Core i7-12650H CPU 2.30GHz, an NVIDIA GeForce GTX 4060, and 32GB of RAM. The optimizer used during training is the Stochastic Gradient Descent optimizer, with a batch size of 64 and an initial learning rate of 0.01. The learning rate scheduling strategy uses 'piecewise' scheduling, meaning the learning rate will abruptly decrease at specified time points. The learning rate decrease factor is 0.1, and the learning rate is multiplied by 0.1 after each decrease cycle to reduce the learning rate and help the model converge. The training execution environment is set to 'multi-gpu', indicating the use of multiple GPUs for accelerated training.

[0078] Furthermore, in one embodiment, step 4 is followed by the execution of:

[0079] The test set is fed into the deep convolutional neural network for classification and recognition, and the modulation recognition rate under different signals and different signal-to-noise ratios is obtained.

[0080] In one embodiment, a radar signal intra-pulse modulation identification system based on LMSST and DCNN is provided, the system comprising:

[0081] The first module is used to perform Local Maximum Synchronization Transform (LMSST) on the Low Probability of Interception (LPI) radar signal to obtain the LMSST time-frequency image.

[0082] The second module is used for preprocessing the LMSST time-frequency image;

[0083] The third module is used to add modulation scheme labels to LMSST time-frequency images, construct radar signal time-frequency image datasets, and divide the radar signal time-frequency image datasets into training set, validation set and test set according to a preset ratio;

[0084] The fourth module is used to construct a deep cascaded convolutional neural network and train it using the training set to obtain a modulation recognition model.

[0085] The fifth module is used to perform modulation identification on the LPI radar signal under test using the modulation identification model.

[0086] Specific limitations regarding the LMSST and DCNN-based radar signal intra-pulse modulation recognition system can be found in the above description of the limitations of the LMSST and DCNN-based radar signal intra-pulse modulation recognition method, and will not be repeated here. Each module in the aforementioned LMSST and DCNN-based radar signal intra-pulse modulation recognition system can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the computer device's memory as software, so that the processor can call and execute the corresponding operations of each module.

[0087] In one embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to perform the following steps:

[0088] Step 1: Perform Local Maximum Synchronization Transform (LMSST) on the low probability of intercept (LPI) radar signal to obtain the LMSST time-frequency image;

[0089] Step 2: Preprocess the LMSST time-frequency image obtained in Step 1;

[0090] Step 3: Add modulation scheme labels to the LMSST time-frequency images to construct a radar signal time-frequency image dataset, and divide the radar signal time-frequency image dataset into training set, validation set and test set according to a preset ratio;

[0091] Step 4: Construct a deep concatenated convolutional neural network and train it using the training set to obtain a modulation recognition model;

[0092] Step 5: Use the modulation recognition model to perform modulation recognition on the LPI radar signal under test.

[0093] For specific limitations on each step, please refer to the limitations on the radar signal intra-pulse modulation recognition method based on LMSST and DCNN mentioned above, which will not be repeated here.

[0094] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program performing the following steps when executed by a processor:

[0095] Step 1: Perform Local Maximum Synchronization Transform (LMSST) on the low probability of intercept (LPI) radar signal to obtain the LMSST time-frequency image;

[0096] Step 2: Preprocess the LMSST time-frequency image obtained in Step 1;

[0097] Step 3: Add modulation scheme labels to the LMSST time-frequency images to construct a radar signal time-frequency image dataset, and divide the radar signal time-frequency image dataset into training set, validation set and test set according to a preset ratio;

[0098] Step 4: Construct a deep concatenated convolutional neural network and train it using the training set to obtain a modulation recognition model;

[0099] Step 5: Use the modulation recognition model to perform modulation recognition on the LPI radar signal under test.

[0100] For specific limitations on each step, please refer to the limitations on the radar signal intra-pulse modulation recognition method based on LMSST and DCNN mentioned above, which will not be repeated here.

[0101] This invention is convenient, fast, practical, and highly accurate. It fully leverages the advantages of deep learning to achieve automatic identification of LPI radar signal intra-pulse modulation, which is of great significance for studying LPI radar signal modulation identification in electronic reconnaissance and reducing the workload of reconnaissance personnel.

[0102] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention without departing from its spirit and scope should be included within the protection scope of the present invention.

Claims

1. A radar signal intra-pulse modulation identification method based on LMSST and DCNN, characterized in that, The method includes the following steps: Step 1: Perform Local Maximum Synchronization Transform (LMSST) on the low probability of intercept (LPI) radar signal to obtain the LMSST time-frequency image; Step 2: Preprocess the LMSST time-frequency image obtained in Step 1; Step 3: Add modulation scheme labels to the LMSST time-frequency images to construct a radar signal time-frequency image dataset, and divide the radar signal time-frequency image dataset into training set, validation set and test set according to a preset ratio; Step 4: Construct a deep concatenated convolutional neural network and train it using the training set to obtain a modulation recognition model; Step 5: Use the modulation recognition model to perform modulation recognition on the LPI radar signal under test; In step 4, the deep cascaded convolutional neural network includes a sequentially connected input layer, a first convolutional layer, three core convolutional modules, a skip connection layer, a global average pooling layer, and a fully connected layer. Each core convolutional module includes a sequentially connected max pooling layer, a deep connection layer, a second convolutional layer, a first batch normalization layer, a first activation layer Elu function, and two parallel branches located between the max pooling layer and the deep connection layer. Each branch includes a sequentially connected third convolutional layer, a second batch normalization layer, and a second activation layer Elu function. Three core convolutional modules are arranged in a cascaded manner to extract highly discriminative features at multiple scales. The structure of the core convolutional modules enables the extraction of highly discriminative features at multiple scales. Specifically: max pooling layers are used to reduce the spatial dimension of the input feature map; parallel convolutional layers use asymmetric kernels to reduce the number of trainable parameters; deep connection layers connect the output feature maps of two convolutional layers to obtain a new feature map; and unit convolutional layers are used to control the depth of the feature map and perform channel pooling.

2. The radar signal intra-pulse modulation identification method based on LMSST and DCNN according to claim 1, characterized in that, The low probability of intercept (LPI) radar signals mentioned in step 1 include LFM, Costas, Frank, P1~P4, and T1~T4. The parameters of LFM include carrier frequency fc and bandwidth B. The parameters of Costas include frequency hopping sequence L and reference frequency fmin. The parameters of Frank and P1~P4 include carrier frequency fc, phase control number M, and phase sub-wavelength number cpp. The parameters of T1 and T2 include carrier frequency fc and waveform segment number k. The parameters of T3 and T4 include carrier frequency fc, waveform segment number k, and modulation bandwidth B.

3. The radar signal intra-pulse modulation identification method based on LMSST and DCNN according to claim 1, characterized in that, Step 1 includes the following specific steps: Step 1-1: Using a Gaussian window as the window function for the short-time Fourier transform, set the length parameter of the window function to extend the one-dimensional time series to a two-dimensional time-frequency plane, and extract the time-frequency distribution map of the short-time Fourier transform. Steps 1-2: Set the time width parameter of LMSST transform, perform post-processing on the result of short-time Fourier transform, perform LMSST transform on the obtained short-time Fourier transform time-frequency distribution, and redistribute the fuzzy time-frequency energy to the intermediate frequency estimation in the frequency direction.

4. The radar signal intra-pulse modulation identification method based on LMSST and DCNN according to claim 1, characterized in that, Step 2 involves preprocessing the LMSST time-frequency image obtained in step 1, specifically including: Step 2-1: Perform grayscale processing on the LMSST time-frequency image; Step 2-2: Adaptive threshold binarization is performed using the Otsu method; Steps 2-3 involve median filtering for smoothing. Steps 2-4: Adjust the size of the time-frequency image and perform scaling and dimensionality reduction processing.

5. The radar signal intra-pulse modulation identification method based on LMSST and DCNN according to claim 1, characterized in that, In step 3, the radar signal time-frequency image dataset is divided into training set, validation set and test set according to the proportions of 70%, 15% and 15%.

6. The radar signal intra-pulse modulation identification method based on LMSST and DCNN according to claim 1, characterized in that, In step 4, the deep cascaded convolutional neural network includes a sequentially connected input layer, a first convolutional layer, three core convolutional modules, a skip connection layer, a global average pooling layer, and a fully connected layer. Each core convolutional module includes a sequentially connected max pooling layer, a deep connection layer, a second convolutional layer, a first batch normalization layer, a first activation layer (Elu function), and two parallel branches located between the max pooling layer and the deep connection layer. Each branch includes a sequentially connected third convolutional layer, a second batch normalization layer, and a second activation layer (Elu function).

7. The radar signal intra-pulse modulation identification method based on LMSST and DCNN according to claim 2, characterized in that, The first convolutional layer has a 7*7 kernel and a stride of 1; the second convolutional layer has a 1*1 kernel and a stride of 1; and the third convolutional layer has a 3*1 kernel and a stride of 1.

8. The radar signal intra-pulse modulation identification method based on LMSST and DCNN according to claim 1, characterized in that, Step 4 is followed by execution: The test set is fed into the deep convolutional neural network for classification and recognition, and the modulation recognition rate under different signals and different signal-to-noise ratios is obtained.

9. A radar signal intra-pulse modulation identification system based on LMSST and DCNN, based on the method of any one of claims 1 to 8, characterized in that, The system includes: The first module is used to perform Local Maximum Synchronization Transform (LMSST) on the Low Probability of Interception (LPI) radar signal to obtain the LMSST time-frequency image. The second module is used for preprocessing the LMSST time-frequency image; The third module is used to add modulation scheme labels to LMSST time-frequency images, construct radar signal time-frequency image datasets, and divide the radar signal time-frequency image datasets into training set, validation set and test set according to a preset ratio; The fourth module is used to construct a deep cascaded convolutional neural network and train it using the training set to obtain a modulation recognition model. The fifth module is used to perform modulation identification on the LPI radar signal under test using the modulation identification model.

10. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method according to any one of claims 1 to 8.

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