A radar signal intra-pulse modulation recognition method based on FSST2 and convolutional neural network

Abstract

The application relates to a radar signal intra-pulse modulation recognition method based on FSST2 and a convolutional neural network and belongs to the field of radar signal processing. The time-frequency images of seven radar intra-pulse modulation signals generated based on FSST2 are subjected to gray-scale and bilinear size transformation pretreatment, so that the obtained time-frequency images are better in noise resistance and higher in time-frequency concentration. Furthermore, deep convolution and point-by-point convolution are combined to construct a CNN network structure which is high in convergence speed and high in recognition rate, and training and testing are carried out. Simulation experiments verify the effectiveness of the application. Compared with methods adopting other time-frequency images and other neural network structures, the method of the application is higher in classification and recognition rate of the seven radar intra-pulse modulation signals in a low signal-to-noise ratio environment.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing, specifically to a radar signal intra-pulse modulation identification method based on second-order synchronous compressed short-time Fourier transform (FSST2) and convolutional neural network. This method has a higher classification and identification rate for radar signal intra-pulse modulation in low signal-to-noise ratio environments and can be used as a classification and identification method for radar signal intra-pulse modulation. Background Technology

[0002] Radar signal classification and identification plays 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 becoming increasingly harsh, and the signal-to-noise ratio (SNR) of radar signals is constantly decreasing. Therefore, improving the classification and identification rate of radar signals under low SNR conditions is becoming increasingly important.

[0003] Radar signal intra-pulse modulation classification and recognition technology mainly consists of two steps: feature extraction and classification. 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 Short-Time Fourier Transform (FSST) to improve the low time-frequency resolution. With the development of deep learning, classification and recognition methods such as Convolutional Neural Networks (CNNs), Deep Neural Networks (DNNs), and Recurrent Neural Networks (RNNs) are also continuously improving. Currently, CNNs, by learning classification methods based on the internal features of the data, have made radar signal recognition more accurate. Some researchers extract the smoothed pseudo-Wigger-Ville distribution (SPWVD) time-frequency map of radar signal intra-pulse modulation and feed it into an AlexNet network for training and classification; others extract the short-time Fourier transform (STFT) time-frequency map of radar signals and feed it into a ResNet network for classification. However, existing methods suffer from low classification and recognition rates at low signal-to-noise ratios, which significantly limits the performance of radar signal classification. Summary of the Invention

[0004] This invention provides a radar signal intra-pulse modulation recognition method based on FSST2 and convolutional neural network to solve the problem of low classification and recognition rate at low signal-to-noise ratio.

[0005] The technical solution adopted by this invention includes the following steps:

[0006] Step 1: Generate seven types of intra-pulse modulated radar signals, including conventional radar signal CW, linear frequency modulated signal LFM, cosine nonlinear frequency modulated signal CFM, even quadratic frequency modulated signal EQFM, two-frequency coded signal 2FSK, two-phase coded signal BPSK, and four-phase coded signal QPSK. Noise is added to the above seven types of intra-pulse modulated radar signals.

[0007] Step 2: Based on the expression of the second-order synchronous compressed short-time Fourier transform (FSST2), obtain the FSST2 time-frequency diagram from the above seven intra-pulse modulated radar signals.

[0008] Step 3: Preprocess the obtained time-frequency graph. First, convert the generated time-frequency graph to grayscale, then use bilinear transformation to change its size, and generate training and test sets for neural network training and testing respectively.

[0009] Step 4: Based on the characteristics of convolutional neural networks, design a new convolutional neural network module to replace the classic convolutional layer, combining depthwise convolution and pointwise convolution to obtain a replacement module for the convolutional layer.

[0010] Step 5: Design the overall architecture of the network, use the proposed convolutional module to replace the classic convolutional layer, obtain a new network structure, and feed the generated training set into the network for model training.

[0011] Step 6: Using the obtained training model, the test sets under different signal-to-noise ratios are fed into the neural network for classification and recognition to obtain the radar signal recognition rate under different signals and different signal-to-noise ratios.

[0012] The seven intra-pulse modulated radar signals in step 1 of this invention, within the duration of a single pulse, have envelope shapes, carrier frequencies, or phase changes that constitute amplitude modulation, phase modulation, or frequency modulation, respectively, collectively referred to as intra-pulse modulation. The expression for signal s(t) is as follows:

[0013]

[0014] Where A is the amplitude of the intra-pulse modulated radar signal, which is taken as 1 here, f i (t) is the frequency function of the i-th intra-pulse modulated radar signal at time t. Let f be the phase of the i-th intra-pulse modulated radar signal, and n(t) be the noise, where f is the phase of the CW signal. i (t) is f0t, where f0 is the starting frequency, and f is the LFM frequency. i (t) is k is the frequency modulation slope (CFM) of f i (t) is f0t+cost, and f in EQFM is... i (t) is 2FSK's fi (t) is f i t, N is 2, f of BPSK and QPSK i (t) is f0t, where BPSK has two phases, which are encoded using 13-bit Barker code [1 1 1 1 1 -1 -1 1 1 -1 1 -1 1]*π; QPSK has four phases, which are encoded using 16-bit Frank code [0,0,0,0,0,π / 2,π,3*π / 2,0,π,0,π,0,3*π / 2,π,π / 2].

[0015] In step 2 of this invention, the FSST2 time-frequency diagram of the intra-pulse modulated radar signal is generated. For the second-order synchronous compressed short-time Fourier transform (FSST2) expression, the local modulation operator is first generated, then the instantaneous frequency expression is obtained, and finally the FSST2 time-frequency diagram of the radar signal is obtained. First, the short-time Fourier transform (STFT) in FSST2 is analyzed. The STFT obtains a set of local spectral sequences by multiplying the signal by a time-finite window function and then performing a Fourier transform. The window function is moved to continue performing Fourier transforms until the local spectrum of the entire signal is obtained. The STFT expression of the signal is as follows:

[0016]

[0017] Where η(t) represents the window function, * represents the conjugate, s(t) represents the time-domain signal, f represents the frequency, and t represents the time.

[0018] Furthermore, the Synchronous Compressed Short-Time Fourier Transform (FSST) is analyzed. It is a time-frequency transform and an effective method for lumped representation of signals. This transform belongs to the time-frequency redistribution method family. By redistributing coefficients on a scale or frequency basis, and operating in the time-frequency domain of the STFT, the resulting time-frequency representation is more explicit, making it easier to distinguish different signal waveforms. The Ti of FSST... f (t,ω) is the STFT(t,f) based on STFT, from the time-frequency distribution (t,f) to... The corrected result, FSST is defined as follows:

[0019]

[0020] Where ω represents the corrected frequency, and δ is the impulse response. For the local instantaneous frequency, the expression is:

[0021]

[0022] in, Re represents the partial derivative with respect to t, where Re denotes the real part;

[0023] Although FSST has proven to be an effective method for enhancing time-frequency representation, its effectiveness is generally more pronounced in applications involving signals with slowly changing frequencies. To achieve more accurate time-frequency representation, FSST is extended to form the second-order synchronous compressed short-time Fourier transform FSST2. First, a second-order local modulation operator is defined. for:

[0024]

[0025] in, For local reference frequency, For local reference delay:

[0026]

[0027]

[0028] and Let STFT(t,f) denote the partial derivatives of STFT(t,f) with respect to t and f, respectively. Thus, a second-order local instantaneous frequency estimate is defined. as follows:

[0029]

[0030] The FSST2 expression is obtained as follows:

[0031]

[0032] The intra-pulse modulated radar signal is processed by STFT and FSST2 to obtain a two-dimensional time-frequency diagram.

[0033] In step 3 of this invention, the time-frequency image is preprocessed by first converting the generated image to grayscale. Grayscale images occupy less memory and are processed faster. The process of converting a color image to a grayscale image is called grayscale conversion. Here, a weighted average method is used to convert the RGB image to a grayscale image. After obtaining the grayscale image, a bilinear transformation is applied to change the size of the grayscale image of the time-frequency image to d×d. The bilinear transformation refers to: assuming the original image size is P k×g The changed image size is Q. m×n Bilinear interpolation is used, and its calculation method is as follows:

[0034] Q(x,y)=P(i+a,j+b)

[0035] P(i+a,j+b)=(1+a)(1-b)P(i,j)+(1-a)bP(i,j+1)+a(1-b)P(i+1,j)+abP(i+1,j+1)

[0036] Where k×g is the original image size, m×n is the size of the image after modification, (x,y) represents the position of a point in the image, and i and a are respectively... The integer part and the fractional part, j and b are respectively The integer and fractional parts are then separated to generate the resized image. Next, training and test set data are generated for the experiments.

[0037] In step 4 of this invention, a novel neural network module structure is designed to replace the classic convolutional layer. This structure combines depthwise convolution and pointwise convolution. The depthwise convolution uses a single kernel with only one one-dimensional channel. The pointwise convolution kernel has a size of 1×1×M, where M is the input data dimension. The output has the same size as the input data, only changing the data dimension. The resulting structure first uses pointwise convolution to increase the input data dimension, then uses pointwise convolution to decrease the data dimension, and finally uses depthwise convolution to fully extract data features. The entire structure replaces the classic convolutional layer as a module. The ReLU6 activation function is used here, and its expression is as follows:

[0038] RELU6 = min(6, max(0, x))

[0039] This results in a replacement module for the convolutional layer.

[0040] In step 5 of this invention, the overall architecture of the network is designed, and the proposed convolutional modules are used to replace the classic convolutional layers to obtain a new CNN network structure, including a classic convolutional layer Conv, three proposed convolutional modules Module1, Module2, and Module3, three max pooling layers Map1, Map2, and Map3, as well as a Flatten layer, a fully connected layer, and a Softmax layer. First, the training set data is fed into the classic convolutional layer for feature extraction, and then sequentially fed into the three alternating structures of the convolutional modules and max pooling layers to extract features and reduce the feature dimension. Finally, it is fed into the Flatten layer, the fully connected layer, and the Softmax layer to obtain the trained model.

[0041] In step 6 of this invention, the test set generated per dB for each signal is fed into the model to test and obtain the recognition rate results of each signal under different signal-to-noise ratios, thus completing the radar signal classification and recognition test results.

[0042] The advantage of this invention is that it selects seven intra-pulse modulated radar signals against a Gaussian noise background and generates time-frequency diagrams for each signal. It is the first to introduce the second-order synchronous compressed short-time Fourier transform (FSST2) into radar signal classification and recognition. The results are compared with the time-frequency diagrams of short-time Fourier transform (STFT) and first-order synchronous compressed short-time Fourier transform (FSST), verifying that the time-frequency diagram is superior.

[0043] This invention designs a novel convolutional neural network structure to train and classify the obtained radar signal time-frequency maps, and compares it with existing MobileNet, Inception, and ResNet network structures. The effectiveness of the proposed network structure is verified by testing it under Gaussian noise and signal-to-noise ratios of -14dB and above for each type of signal. Attached Figure Description

[0044] Figure 1 This is a flowchart of the present invention;

[0045] Figure 2 This is a schematic diagram of the time and frequency domain waveforms of the seven intra-pulse modulated radar signals of the present invention, wherein a represents CW signal, b represents LFM signal, c represents EQFM signal, d represents NLFM signal, e represents 2FSK signal, f represents BPSK signal, and g represents QPSK signal;

[0046] Figure 3 This is the FSST2 time-frequency diagram of seven intra-pulse modulated radar signals with a signal-to-noise ratio of 10dB, where a represents CW signal, b represents LFM signal, c represents EQFM signal, d represents NLFM signal, e represents 2FSK signal, f represents BPSK signal, and g represents QPSK signal.

[0047] Figure 4 This is a diagram of the novel convolutional neural network structure module of this invention;

[0048] Figure 5 This is a diagram showing the overall structure of the convolutional neural network of this invention;

[0049] Figure 6 This is a diagram showing the recognition rate of seven intra-pulse modulated radar signals under signal-to-noise ratio conditions of -14dB to 8dB according to the present invention.

[0050] Figure 7 This is a comparison chart of the recognition rates of the present invention under the same network structure, using three time-frequency diagrams (STFT, FSST, and FSST2 in the present invention) at different signal-to-noise ratios;

[0051] Figure 8 This is a comparison chart of the recognition rates of the present invention under different signal-to-noise ratios, using MobileNet, Inception, ResNet, and the network structure of the present invention. Detailed Implementation

[0052] like Figure 1 As shown, it includes the following steps:

[0053] Step 1: Generate intra-pulse modulated radar signals. Within the duration of a single pulse, the envelope shape, carrier frequency, or phase change within the pulse constitutes amplitude modulation, phase modulation, or frequency modulation, collectively referred to as intra-pulse modulation. These include conventional radar signals (CW), linear frequency modulated signals (LFM), cosine-type nonlinear frequency modulated signals (CFM), even quadratic frequency modulated signals (EQFM), two-frequency coded signals (2FSK), two-phase coded signals (BPSK), and four-phase coded signals (QPSK). These seven types of intra-pulse modulated radar signals are uniformly represented as:

[0054]

[0055] Where A is the amplitude of the intra-pulse modulated radar signal, which is taken as 1 here, f i (t) is the frequency function of the i-th intra-pulse modulated radar signal at time t. Let f be the phase of the i-th intra-pulse modulated radar signal, and n(t) be the noise, where f is the phase of the CW signal. i (t) is f0t, where f0 is the starting frequency, and f is the LFM frequency. i (t) is k is the frequency modulation slope (CFM) of f i (t) is f0t+cost, and f in EQFM is... i (t) is 2FSK's f i (t) is f i t, N is 2, f of BPSK and QPSK i (t) is f0t, where BPSK has two phases, which are encoded using 13-bit Barker code [1 1 1 1 1 -1 -1 1 1 -1 1 -1 1]*π; QPSK has four phases, which are encoded using 16-bit Frank code [0,0,0,0,0,π / 2,π,3*π / 2,0,π,0,π,0,3*π / 2,π,π / 2].

[0056] Step 2: Generate the FSST2 time-frequency diagram of the intra-pulse modulated radar signal. For the second-order synchronous compressed short-time Fourier transform (FSST2) expression, first generate the local modulation operator, then obtain the instantaneous frequency expression, and finally obtain the FSST2 time-frequency diagram of the radar signal. First, analyze the short-time Fourier transform (STFT) in FSST2. STFT obtains a set of local spectral sequences by multiplying the signal by a time-finite window function and then performing a Fourier transform. The window function is then moved to continue performing Fourier transforms until the local spectrum of the entire signal is obtained. The STFT expression is as follows:

[0057]

[0058] Where η(t) represents the window function, * represents the conjugate, s(t) represents the time-domain signal, f represents the frequency, and t represents the time.

[0059] Furthermore, the Synchronous Compressed Short-Time Fourier Transform (FSST) is analyzed. It is a time-frequency transform and an effective method for condensed signal representation. This transform belongs to the time-frequency redistribution method family. By redistributing coefficients on a scale or frequency basis, and operating in the time-frequency domain of the STFT, the resulting time-frequency representation is more explicit, making it easier to distinguish different signal waveforms. The Ti of FSST... f (t,ω) is the STFT(t,f) based on STFT, from the time-frequency distribution (t,f) to... The corrected result. FSST is defined as follows:

[0060]

[0061] Where ω represents the corrected frequency, and δ is the impulse response. For the local instantaneous frequency, the expression is:

[0062]

[0063] in, Re represents the partial derivative with respect to t, where Re denotes the real part;

[0064] Although FSST has proven to be an effective method for enhancing time-frequency representation, its effectiveness is generally more pronounced in applications involving signals with slowly changing frequencies. To achieve more accurate time-frequency representation, FSST is extended to form the second-order synchronous compressed short-time Fourier transform (FSST2). First, a second-order local modulation operator is defined. for:

[0065]

[0066] in, For local reference frequency, For local reference delay:

[0067]

[0068]

[0069] and Let STFT(t,f) denote the partial derivatives of STFT(t,f) with respect to t and f, respectively. Thus, a second-order local instantaneous frequency estimate is defined. as follows:

[0070]

[0071] The FSST2 expression is obtained as follows:

[0072]

[0073] The intra-pulse modulated radar signal is processed by STFT and FSST2 to obtain a two-dimensional time-frequency diagram.

[0074] Step 3: Preprocess the obtained time-frequency image. First, convert the generated image to grayscale. Grayscale images occupy less memory and are processed faster. The process of converting a color image to a grayscale image is called grayscale conversion. Here, we use the weighted average method to convert an RGB image to a grayscale image. After obtaining the grayscale image, apply a bilinear transformation to change the size of the time-frequency image grayscale image to d×d. The bilinear transformation means: assuming the original image size is P... k×g The changed image size is Q. m×n Bilinear interpolation is used, and its calculation method is as follows:

[0075] Q(x,y)=P(i+a,j+b)

[0076] P(i+a,j+b)=(1+a)(1-b)P(i,j)+(1-a)bP(i,j+1)+a(1-b)P(i+1,j)+abP(i+1,j+1)

[0077] Where k×g is the original image size, m×n is the size of the image after modification, (x,y) represents the position of a point in the image, and i and a are respectively... The integer part and the fractional part, j and b are respectively The integer and fractional parts are then used to generate the resized image. Time-frequency plots are then generated for different signal-to-noise ratios for neural network training and testing. The training set is -16 to 8 dB, with 500 samples generated every 2 dB for each signal; the test set is -14 to 8 dB, with 100 samples generated every 2 dB for each signal.

[0078] Step 4: Based on the characteristics of convolutional neural networks, a new neural network module structure is designed to replace the classic convolutional layer. This combines depthwise convolution and pointwise convolution. Depthwise convolution uses a single kernel with only one one-dimensional channel. Pointwise convolution uses a 1×1×M kernel, where M is the input data dimension. The output has the same size as the input data, only changing the data dimension. The resulting structure first uses pointwise convolution to increase the input data dimension, then uses pointwise convolution to decrease the data dimension, and finally uses depthwise convolution to fully extract data features. The entire structure replaces the classic convolutional layer as a module. The ReLU6 activation function is used here, and its expression is as follows:

[0079] RELU6 = min(6, max(0, x))

[0080] This results in a replacement module for the convolutional layer;

[0081] Step 5: Design the overall architecture of the network and apply the proposed convolutional modules to replace the classic convolutional layers to obtain a new CNN network structure, including a classic convolutional layer Conv, three proposed convolutional modules Module1, Module2, and Module3, three max pooling layers Map1, Map2, and Map3, as well as a Flatten layer, a fully connected layer, and a Softmax layer. First, the training set data is fed into the classic convolutional layer for feature extraction. Then, it is sequentially fed into the three alternating structures of the convolutional modules and the max pooling layer to extract features and reduce the feature dimensionality. Finally, it is fed into the Flatten layer, the fully connected layer, and the Softmax layer to obtain the trained model.

[0082] Step 6: Using the trained model, the test sets under different signal-to-noise ratios are fed into the neural network for classification processing to obtain the recognition rate of intra-pulse modulated radar signals under different signals and different signal-to-noise ratios.

[0083] The beneficial effects of the present invention will be further explained below with reference to simulation experiments and results.

[0084] The simulation tools used in the simulation experiment are Matlab and Python 3.8.

[0085] Experiment 1: The recognition rate of seven intra-pulse modulated radar signals was compared using the method of this invention under signal-to-noise ratio conditions of -14dB to 8dB.

[0086] Simulation parameter settings: sampling frequency Fs is 200MHz, carrier frequency f c The training set has a signal-to-noise ratio of -16dB to 8dB and a signal-to-noise ratio of -14dB to 8dB. The training set has a signal-to-noise ratio of -14dB to 8dB and a learning rate of 0.0003. The number of iterations is 30.

[0087] Depend on Figure 6 It can be seen that the method used in this invention has a high recognition rate. At -12dB, the recognition rate of the seven radar signals is above 80%, at -10dB and above, the recognition rate of the seven radar signals reaches 90%, and at -8dB, almost all seven radar signals can be correctly identified, which verifies the high efficiency of the method of this invention.

[0088] Experiment 2: The method using FSST2 time-frequency plot in this invention is compared with the method using STFT and FSST time-frequency plot, and the performance is analyzed based on the simulation results.

[0089] Simulation parameter settings: sampling frequency Fs is 200MHz, carrier frequency f c The training set has a signal-to-noise ratio of -16dB to 8dB and a signal-to-noise ratio of -14dB to 8dB. The training set has a signal-to-noise ratio of -14dB to 8dB and a learning rate of 0.0003. The number of iterations is 30.

[0090] Depend on Figure 7 It can be seen that the accuracy of signal identification using the FSST2 time-frequency plot is significantly higher, verifying the high efficiency of using the FSST2 time-frequency plot.

[0091] Experiment 3: The method using the network structure of this invention will be compared with the methods using MobileNet, Inception, and ResNet structures, and the performance will be analyzed based on the simulation results.

[0092] Simulation parameter settings: sampling frequency Fs is 200MHz, carrier frequency f c The training set has a signal-to-noise ratio of -16dB to 8dB and a signal-to-noise ratio of -14dB to 8dB. The training set has a signal-to-noise ratio of -14dB to 8dB and a learning rate of 0.0003. The number of iterations is 30.

[0093] Depend on Figure 8 It can be seen that the network structure designed in this invention improves the radar signal recognition rate under low signal-to-noise ratio conditions, verifying the high efficiency of the designed new network.

[0094] This invention applies the second-order synchronous compressed short-time Fourier transform (FSST2) time-frequency diagram to the classification and recognition design of intra-pulse modulation of radar signals, and designs a novel convolutional neural network structure to improve the signal recognition rate under low signal-to-noise ratio (SNR) conditions. Simulation experiments verify the effectiveness of the method. Compared with methods using other time-frequency diagrams and other neural network structures, the method of this invention achieves better classification and recognition results for seven types of intra-pulse modulation of radar signals under low SNR conditions.

Claims

1. A radar signal intra-pulse modulation recognition method based on FSST2 and convolutional neural network, characterized in that, It comprises the following steps: Step 1, seven intra-pulse modulation radar signals are generated, including a conventional radar signal CW, a linear frequency modulation signal LFM, a cosine type nonlinear frequency modulation signal CFM, an even quadratic frequency modulation signal EQFM, a two-frequency coded signal 2FSK, a binary phase coded signal BPSK and a quadrature phase coded signal QPSK, and the above seven intra-pulse modulation radar signals are subjected to noise processing; Step 2, according to the second-order synchronous compression short-time Fourier transform FSST2 expression, the FSST2 time-frequency diagram is obtained from the above seven intra-pulse modulation radar signals; Step 3, the obtained time-frequency diagram is preprocessed, the generated time-frequency diagram is first subjected to gray scale processing, then the size is changed by using bilinear transformation, and a training set and a test set for neural network training and testing are respectively generated; Step 4, according to the characteristics of the convolutional neural network, a new convolutional neural network module is designed to replace the classical convolutional layer, the deep convolution and the point-by-point convolution are combined to obtain a replacement module of a convolutional layer; Step 5, the overall architecture of the network is designed, the proposed convolutional module is used to replace the classical convolutional layer, a new network structure is obtained, and the generated training set is sent into the network for model training; Step 6, using the obtained training model, the test set under different signal-to-noise ratios is sent into the neural network for classification and identification, and the radar signal recognition rate under different signals and different signal-to-noise ratios is obtained.

2. The FSST2 and convolutional neural network based radar signal intra-pulse modulation recognition method according to claim 1, characterized in that, The seven intra-pulse modulation radar signals in step 1, in a single pulse duration, the envelope shape, the carrier frequency or the phase change in the pulse are respectively constituted as amplitude modulation, phase modulation or frequency modulation, collectively referred to as intra-pulse modulation, and the expression of the signal s(t) is as follows: where A is the amplitude of the intra-pulse modulated radar signal, which is taken as 1 here, f i (t) is the frequency function of the ith intra-pulse modulated radar signal at time t, is the phase of the ith intra-pulse modulated radar signal, and n(t) is noise, where f i (t) is f0t, f0 is the initial frequency, f i (t) is f0t+cost, f k is the frequency modulation slope f i (t) is f0t+cost, f i (t) is f0t+cost, f 2FSK f i (t) is f i t, N is 2, f i (t) is f0t, where BPSK has two phases, and the phase is encoded with a 13-bit Barker code [1 1 1 1 1 -1 -1 1 1 -1 1 -1 1]*π; QPSK has four phases, and the phase is encoded with a 16-bit Frank code [0, 0, 0, 0, 0, π / 2, π, 3*π / 2, 0, π, 0, π, 0, 3*π / 2, π, π / 2].

3. The FSST2 and convolutional neural network based radar signal intra-pulse modulation recognition method according to claim 1, characterized in that: In step 2, the FSST2 time-frequency diagram of the intra-pulse modulation radar signal is obtained, for the second-order synchronous compression short-time Fourier transform FSST2 expression, first, a local modulation operator is generated, then an instantaneous frequency expression is obtained, and finally, the FSST2 time-frequency diagram of the radar signal is obtained, first, the short-time Fourier transform STFT in FSST2 is analyzed, STFT is obtained by multiplying a signal with a time-limited window function, and then Fourier transform is performed, to obtain a set of local frequency spectrum sequence, the window function is moved to continue Fourier transform, until the local frequency spectrum of the entire signal is obtained, and the expression of the signal STFT is as follows: Wherein, η(t) represents a window function, * represents a conjugate, s(t) represents a time domain signal, f represents a frequency, and t represents a time; Further, the Synchronized Compressive Short-Time Fourier Transform (FSST) is analyzed, which is a time-frequency transform and an effective method for the concentrated representation of signals. The transform belongs to the time-frequency redistribution method family, which operates on the time-frequency domain of the STFT by redistributing the coefficients in scale or frequency, resulting in a more explicit time-frequency representation that makes it easier to distinguish different signal waveforms. The T f (t,ω) is the modified result of the STFT(t,f) based on the STFT, and the FSST is defined as follows: (t,ω) is the modified result of the STFT(t,f) based on the STFT, and the FSST is defined as follows: where ω denotes the modified frequency, and δ is the impulse response, is the local instantaneous frequency, expressed as wherein denotes the partial derivative with respect to t, Re denotes the real part; For more accurate time-frequency representation, the FSST is extended to form the 2nd-order synchronous compression short-time Fourier transform (FSST2). First, the 2nd-order local modulation operator is defined as = wherein, is a local reference frequency, is a local reference time delay: and denote the partial derivatives of STFT(t,f) with respect to t and f, respectively, whereby a second-order local instantaneous frequency estimate is defined as follows: The FSST2 expression is as follows: After the intra-pulse modulation radar signal is subjected to STFT and FSST2 processing, a two-dimensional time-frequency diagram is obtained.

4. The FSST2 and convolutional neural network based radar signal intra-pulse modulation recognition method according to claim 1, characterized in that: In step 3, for preprocessing the time-frequency graph, the generated image is first subjected to grayscale processing, the grayscale image occupies less memory and is faster to process, the process of converting a color image into a grayscale image is grayscale, here the weighted average method is adopted to convert the RGB image into a grayscale image, and the grayscale image is obtained; then the size of the time-frequency graph grayscale image is changed to d x d by using a bilinear transformation, the bilinear transformation refers to: assuming that the size of an original image is P k×g , the size of the changed image is Q m×n , a bilinear interpolation is adopted, and the calculation method is as follows: Q(x,y)=P(i+a,j+b) P(i+a,j+b)=(1+a)(1-b)P(i,j)+(1-a)bP(i,j+1)+a(1-b)P(i+1,j)+abP(i+1,j+1) where k x g is the original image size, m x n is the size after changing the image, (x, y) represents the position of a certain point of the image, i and a are the integer part and the decimal part of respectively, and j and b are the integer part and the decimal part of respectively, so that the image after adjusting the size can be generated, and then the training set data and the test set data for the experiment are generated.

5. The FSST2 and convolutional neural network based radar signal intra-pulse modulation recognition method according to claim 1, characterized in that: The step 4 designs a new neural network module structure to replace the classic convolution layer, which combines deep convolution and pointwise convolution. The deep convolution is a convolution kernel with only one channel being one-dimensional. The size of the pointwise convolution kernel is 1x1xM, M is the dimension of the input data, and the output is the same size as the input data, only changing the data dimension. The obtained structure block is to first increase the input data dimension by pointwise convolution, then reduce the data dimension by pointwise convolution, and finally extract the data features by deep convolution. The whole is a module to replace the classic convolution layer. Here, the RELU6 activation function is used, and the expression of the RELU6 activation function is as follows: RELU6 = min(6, max(0, x)) Thus, a convolution layer replacement module is obtained.

6. The FSST2 and convolutional neural network based radar signal intra-pulse modulation recognition method according to claim 1, characterized in that: The step 5 designs the overall architecture of the network, applies the proposed convolution module to replace the classic convolution layer, and obtains a new CNN network structure, which includes a classic convolution layer Conv, three proposed convolution modules Module1, Module2, Module3, and three maximum pooling layers Map1, Map2, Map3, as well as a Flatten layer, a fully connected layer, and a Softmax layer. First, the training set data is input into the classic convolution layer for feature extraction, then is input into the convolution module and the maximum pooling layer in turn for feature extraction and dimension reduction, and finally is input into the Flatten layer, the fully connected layer, and the Softmax layer to obtain the trained model.

7. The FSST2 and convolutional neural network based radar signal intra-pulse modulation recognition method according to claim 1, characterized in that: In the step 6, the test set of each signal per dB is input into the model to test the recognition rate of each signal under different signal-to-noise ratios, and the radar signal classification and recognition test results are obtained.

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