Radio signal modulation recognition method based on sparse complex-valued convolutional neural network

Abstract

The present application relates to the field of artificial intelligence and signal processing technology, in particular to a radio signal modulation recognition method based on sparse complex-valued convolutional neural network, comprising: modulating a radio signal to be transmitted to obtain an I / Q two-way signal data set, adding additive white Gaussian noise to the I / Q two-way signal data set to form a modulation signal data set, and preprocessing the modulation signal data set to obtain a preprocessed signal data set; constructing and initializing a complex-valued convolutional neural network model for radio signal modulation recognition, iteratively training the complex-valued convolutional neural network model based on the preprocessed modulation signal data set to obtain a trained sparse complex-valued convolutional neural network model; inputting a signal to be recognized into the trained sparse complex-valued convolutional neural network model to obtain a recognition result of the modulation mode of the signal to be recognized. The present application can significantly improve the recognition accuracy of the modulation method of the radio signal.

Description

Technical Field

[0001] The present invention relates to the technical field of radio signal processing, and in particular to a radio signal modulation recognition method based on a sparse complex-valued convolutional neural network. Background Art

[0002] Modulation recognition of radio signals involves analyzing and processing the received signal to determine its modulation method, even without sufficient prior knowledge. Currently, modulation signal recognition is primarily used in cognitive radio, communications reconnaissance, and radio frequency detection. The time-domain characteristics of received radio signals typically include instantaneous amplitude, frequency, and phase information. Designing an effective classifier can improve the accuracy of radio signal recognition.

[0003] Typical modulation recognition and classification methods include statistical pattern recognition, decision theory, and neural network-based methods. Among them, neural network-based methods can simulate human brain recognition and have high accuracy, making them a hot topic in current modulation recognition research.

[0004] Convolutional neural networks (CVCNNs) have attracted increasing attention due to their powerful learning and reasoning capabilities. In recent years, with the development of complex-valued optimization algorithms, complex-valued convolutional neural networks (CVCNNs) have been shown to outperform real-valued convolutional neural networks (CVCNNs) in a variety of fields, such as radio communications, synthetic aperture radar image processing, and medical image denoising. However, due to the introduction of complex-valued parameters, the number of parameters and floating-point computations required for CVCNNs are twice and four times that of real-valued CVCNNs, respectively, for the same network structure. This large number of parameters and complex computations increase the inference cost of CVCNNs.

[0005] In order to compress the model structure and reduce computational complexity, sparse optimization algorithms have been introduced into convolutional neural networks. However, current sparse methods are mostly applied to real-valued convolutional neural networks, and research on sparse optimization algorithms for complex-valued convolutional neural networks is relatively scarce.

[0006] After signal preprocessing, the radio signal is divided into two signals: I / Q (in-phase and quadrature). In a typical real-valued convolutional neural network, these two signals are usually input separately to perform signal recognition. However, this destroys the inherent connections between the radio signals, resulting in reduced network performance.

[0007] Although structured sparsity-based sparse neural networks using amplitude, dropout, and L0 regularization can directly input I / Q signals into the network as a single complex-valued signal, preserving the original feature data, this approach changes the size of the convolution kernel or the number of channels, resulting in reduced recognition accuracy. Compared to structured sparsity methods, unstructured sparsity offers the advantages of higher precision and sparsity, and methods based on gradients, momentum, and Hessian matrices can all achieve unstructured sparsity. However, the sparsity thresholds of these methods are often global and cannot be adjusted based on the characteristics of each network layer. Therefore, they cannot maximize model compression and improve network performance.

[0008] To address these issues, methods such as soft threshold reparameterization (STR) have been proposed to induce network sparsity by learning a sparsity threshold for each layer. However, STR sparsification methods are designed for real-valued convolutional networks and are difficult to directly process complex-valued signals. Furthermore, these sparsification methods fail to fully consider the characteristics of convolutional and fully connected layers in convolutional neural networks, leaving room for improvement in both sparsification speed and recognition accuracy. Summary of the Invention

[0009] To solve the above technical problems, the present invention provides a radio signal modulation recognition method based on a sparse complex-valued convolutional neural network, which includes the following steps:

[0010] S1: Modulating a radio signal to be transmitted to obtain an I / Q two-channel signal dataset, adding additive white Gaussian noise to the I / Q two-channel signal dataset to form a modulated signal dataset, and preprocessing the modulated signal dataset to obtain a preprocessed modulated signal dataset;

[0011] S2: constructing and initializing a complex-valued convolutional neural network model for radio signal modulation recognition, and iteratively training the complex-valued convolutional neural network model based on the preprocessed modulation signal data set to obtain a trained sparse complex-valued convolutional neural network model;

[0012] S3: Inputting the signal to be identified into the trained sparse complex-valued convolutional neural network model to obtain an identification result of the modulation mode of the signal to be identified;

[0013] The complex-valued convolutional neural network model includes a plurality of complex-valued convolutional layers and a plurality of complex-valued fully connected layers connected in sequence, each complex-valued convolutional layer includes a complex-valued convolution operation and a complex-valued activation function, and each complex-valued fully connected layer includes a complex-valued fully connected operation and a complex-valued activation function;

[0014] In S2, the iterative training of the complex-valued convolutional neural network model includes a forward propagation process and a backpropagation process to obtain a trained sparse complex-valued convolutional neural network model, and the method includes:

[0015] S21: During the forward propagation process, determine whether the current layer is a complex-valued convolutional layer or a complex-valued fully connected layer: if the current layer is a complex-valued convolutional layer, reset the weights of the complex-valued convolutional layer by a complex-valued soft threshold operator; if the current layer is a complex-valued fully connected .... log-sum The threshold operator resets the weights of the complex-valued fully connected layer;

[0016] S22: During the back-propagation process, optimizing the loss function using an adaptive complex-valued momentum estimation algorithm with weight decay, and updating the network weights and the sparsity threshold;

[0017] S23: Execute steps S21 to S22 repeatedly until the maximum number of iterations is reached or the algorithm converges.

[0018] In one embodiment of the present invention, the method of resetting the weights of the complex-valued convolutional layer by the complex-valued soft threshold operator is expressed as:

[0019] ,

[0020] in, Represents the updated value of the complex soft threshold operator l The weight matrix of the complex-valued convolutional layer; Before the update l The weight matrix of the complex-valued convolution layer is Rank Elements of the column, , is the weight before update The real part of is the weight before update The imaginary part of For the l The sparse threshold of the complex-valued convolutional layer, , , .

[0021] In one embodiment of the present invention, by resetting log-sum The method of resetting the weights of the complex-valued fully connected layer by the threshold operator is expressed as:

[0022] ,

[0023] in, To use complex values log-sum The threshold operator after adjustment l The weight matrix of the complex-valued fully connected layer, Before adjustment l The weights of the complex-valued fully connected layer, For the Sparse threshold for complex-valued fully connected layers; for function, , , .

[0024] In one embodiment of the present invention, the loss function Including network weights and sparse thresholds The regular term is expressed as follows:

[0025] , ,

[0026] in, is the cross entropy loss function, is a hyperparameter, and Represent the network weights and sparse threshold matrices respectively, The input sample is identified as a category The probability of is a category Tags, K is the total number of modulation types; express norm.

[0027] In one embodiment of the present invention, the method for updating the network weights and the sparse threshold is: the adaptive complex-valued momentum estimation algorithm with weight decay is used to calculate the first Tier The sparse threshold matrix after iteration update and weight matrix :

[0028] , ,

[0029] , ,

[0030] , ,

[0031] , ,

[0032] , ,

[0033] in, and is the complex gradient vector, is the cross entropy loss function, 、 、 and are transition variables. and is the first-order exponential sliding average of the complex gradient, and is the second-order exponential moving average of the complex gradient, is the step length, is the regularization parameter, and is a constant, is the shrinkage factor.

[0034] In one embodiment of the present invention, the complex-valued convolution operation is used to convert the first The input feature matrix of the layer Hedi The convolution kernel matrix of the layer Perform convolution operation to obtain the input feature matrix The complex-valued characteristic matrix of , the method includes:

[0035] Define the The input feature matrix of the layer for: , the said The convolution kernel matrix of the layer for: , and we get the complex-valued characteristic matrix:

[0036] ,

[0037] in, represents the convolution operation, for The real part of for The imaginary part of for The real part of for The imaginary part of .

[0038] In one embodiment of the present invention, the complex-valued full-connect operation is used to The input feature matrix of the layer After assigning weights, nonlinear transformation is performed, and the methods include:

[0039] Definition Layer and Weight matrix between layers , and the nonlinear transformation result is obtained:

[0040] wherein, is the real part of, is the imaginary part of, represents an activation function.

[0041] In an embodiment of the present application, the complex-valued activation function is a real-valued normalized exponential function or a split complex-valued linear rectifier function; wherein the expression of the real-valued normalized exponential function is:

[0042] wherein the input feature matrix , is the total number of modulation modes;

[0043] the expression of the split complex-valued linear rectifier function is:

[0044] wherein, .

[0045] In an embodiment of the present application, the method for obtaining the preprocessed modulation signal dataset is:

[0046] Based on the modulation signal dataset, set the division ratio of the training set, the validation set and the test set, and in each modulation type, randomly select the same number of data samples and distribute them to the training set, the validation set and the test set according to the division ratio;

[0047] Use one-hot encoding to encode the modulation type label of the data sample, and each modulation type corresponds to a one-hot encoding vector;

[0048] Splice the I / Q dual-channel signal into a complex-valued feature vector, each complex-valued feature vector is in complex form and contains a real part and an imaginary part;

[0049] Based on the data input format of the complex-valued convolutional neural network model, the encoded label and the spliced complex-valued feature vector are correspondingly combined together to form the preprocessed modulation signal dataset.

[0050] The above technical solutions of the present application have the following advantages compared with the prior art:

[0051] 1. The complex-valued convolutional neural network based on the sparse optimization algorithm proposed in the present application can directly process I / O two-way signals, i.e. complex-valued signals, avoiding the information loss that may be caused by converting complex-valued signals into real-valued signals in traditional methods, maintaining the integrity of the signals, thereby more accurately capturing signal features, improving recognition accuracy, and reducing model parameters while maintaining model performance.

[0052] 2、The application uses a complex soft threshold operator and a complex threshold weight reparameterization algorithm in the complex convolutional layer and the complex fully connected layer respectively during the forward propagation, which prunes the weights and effectively realizes the sparsification of the weights. log-sum During the backward propagation, the adaptive complex momentum estimation algorithm with weight decay is combined to dynamically adjust the sparse threshold of each layer in the network, which can improve the model performance while compressing the network structure to the maximum extent and reducing the network parameters.

[0053] 3、The complex threshold weight reparameterization algorithm proposed in the application is suitable for different complex convolutional neural networks and performs well in the recognition of complex radio signals. soft-log BRIEF DESCRIPTION OF DRAWINGS

[0054] In order to make the content of the application more easily understood, the application will be further described in detail below according to specific embodiments of the application and in conjunction with the drawings, in which

[0055] Figure 1 is an implementation flowchart of a radio signal modulation recognition method based on a sparse complex convolutional neural network provided in an embodiment of the application;

[0056] Figure 2 is a network architecture diagram of a radio signal modulation recognition model based on a complex convolutional neural network provided in an embodiment of the application;

[0057] Figure 3 is a training method flowchart of a complex convolutional neural network based on a sparse optimization algorithm provided in an embodiment of the application;

[0058] Figure 4 is the sparsity (Sparsity) and the recognition error rate (Error) of the complex soft threshold reparameterization algorithm (STR) and the complex threshold weight reparameterization algorithm (CV-SLTR) proposed in the application on the complex convolutional neural network; soft - log

[0059] Figure 5 is the accuracy of the modulation signal at different signal-to-noise ratios of the original model without using the sparse algorithm and the model after using the two sparse algorithms of the complex soft threshold reparameterization algorithm and the complex threshold weight reparameterization algorithm. soft - log DETAILED DESCRIPTION

[0060] The application will be further described below in conjunction with the drawings and specific embodiments, so that those skilled in the art can better understand the application and implement it, but the embodiments are not limiting to the application.​​​

[0061] Reference Figure 1 As shown, the present invention provides a radio signal modulation recognition method based on a sparse complex-valued convolutional neural network, the method comprising the following steps:

[0062] S1: Modulating a radio signal to be transmitted to obtain an I / Q two-channel signal dataset, adding additive white Gaussian noise to the I / Q two-channel signal dataset to form a modulated signal dataset, and preprocessing the modulated signal dataset to obtain a preprocessed modulated signal dataset;

[0063] S2: constructing and initializing a complex-valued convolutional neural network model for radio signal modulation recognition, and iteratively training the complex-valued convolutional neural network model based on the preprocessed modulation signal data set to obtain a trained sparse complex-valued convolutional neural network model;

[0064] S3: Inputting the signal to be identified into the trained sparse complex-valued convolutional neural network model to obtain an identification result of the modulation mode of the signal to be identified.

[0065] Specifically, the method for obtaining the preprocessed modulated signal data set is:

[0066] The RadioML 2016.10A dataset, generated by GNURadio, includes 11 modulation signals, including eight digital and three analog modulation signals. Radio signal recognition is performed using the RadioML 2016.10A dataset. To ensure realistic communication simulations, additive white Gaussian noise (AWGN) is added to the dataset, potentially causing channel impairments. This creates a modulation signal dataset.

[0067] In order to balance the number of samples in the training set, the validation set, and the test set, the modulated signal dataset is preprocessed to obtain a preprocessed modulated signal dataset, and the method includes the following steps:

[0068] Based on the modulated signal data set, setting the division ratio of the training set, the validation set and the test set, and randomly selecting the same number of data samples in each modulation type and distributing them into the training set, the validation set and the test set according to the division ratio;

[0069] Use one-hot encoding to encode the modulation type label of the data sample, and each modulation type corresponds to a one-hot encoding vector;

[0070] Splice the I / Q dual-channel signals into complex-valued eigenvectors, each of which is in complex form and contains real and imaginary parts;

[0071] Based on the data input format of the complex-valued convolutional neural network model, the encoded labels and the spliced ​​complex-valued feature vectors are correspondingly combined together to form the preprocessed modulated signal data set.

[0072] Among them, Figure 2 As shown, the complex-valued convolutional neural network model includes four complex-valued convolutional layers and two complex-valued fully-connected layers connected in sequence. Each complex-valued convolutional layer includes a complex-valued convolution operation and a complex-valued activation function, and each complex-valued fully-connected layer includes a complex-valued fully-connected operation and a complex-valued activation function. During the training phase, the complex-valued feature matrix is ​​first input into the network. After passing through four complex-valued convolutional layers and two complex-valued fully-connected layers, the final output is the probability distribution of the label.

[0073] In this embodiment, the complex-valued convolution operation is used to convert the The input feature matrix of the layer Hedi The convolution kernel matrix of the layer Perform convolution operation to obtain the input feature matrix The complex-valued characteristic matrix of , the method includes:

[0074] Define the The input feature matrix of the layer for: , the said The convolution kernel matrix of the layer for: , and we get the complex-valued characteristic matrix:

[0075] ,

[0076] in, represents the convolution operation, for The real part of for The imaginary part of for The real part of for The imaginary part of .

[0077] The complex-valued full connection operation is used to The input feature matrix of the layer After assigning weights, nonlinear transformation is performed, and the methods include:

[0078] Definition Layer and Weight matrix between layers , and the nonlinear transformation result is obtained:

[0079] ,in, for The real part of for The imaginary part of Represents the activation function.

[0080] In this embodiment, the complex-valued activation function is a real-valued normalized exponential function or a split complex-valued linear rectifier function. Figure 2 The last complex-valued fully connected layer in

[15] uses the real-valued normalized exponential function as the activation function, and the remaining layers use the divisive complex-valued linear rectifier function as the activation function.

[0081] Wherein, the expression of the real-valued normalized exponential function is: , where the input feature matrix , is the total number of modulation types;

[0082] The expression of the split complex-valued linear rectifier function is: ,in, .when x is a matrix hour, Representation matrix Each element in Compare with 0, if ,but ,otherwise .

[0083] Furthermore, if Figure 3 As shown, the iterative training of the complex-valued convolutional neural network model includes a forward propagation process and a backpropagation process to obtain a trained sparse complex-valued convolutional neural network model, and the method includes:

[0084] S21: During the forward propagation process, determine whether the current layer is a complex-valued convolutional layer or a complex-valued fully connected layer: if the current layer is a complex-valued convolutional layer, reset the weights of the complex-valued convolutional layer by a complex-valued soft threshold operator; if the current layer is a complex-valued fully connected .... log-sum The threshold operator resets the weights of the complex-valued fully connected layer;

[0085] S22: During the back-propagation process, optimizing the loss function using an adaptive complex-valued momentum estimation algorithm with weight decay, and updating the network weights and the sparsity threshold;

[0086] S23: Execute steps S21 to S22 repeatedly until the maximum number of iterations is reached or the algorithm converges.

[0087] If the current layer is a complex-valued convolutional layer, the method of resetting the weights of the complex-valued convolutional layer through the complex-valued soft threshold operator is expressed as:

[0088] ,

[0089] in, Represents the updated value of the complex soft threshold operator l The weight matrix of the complex-valued convolutional layer; Before the update l The weight matrix of the complex-valued convolution layer is Rank Elements of the column, , is the weight before update The real part of is the weight before update The imaginary part of For the l The sparse threshold of the complex-valued convolutional layer, , , .

[0090] If the current layer is a complex-valued fully connected layer, through the complex value log-sum The method of resetting the weights of the complex-valued fully connected layer by the threshold operator is expressed as:

[0091] ,

[0092] in, To use complex values log-sum The threshold operator after adjustment l The weight matrix of the complex-valued fully connected layer, Before adjustment l The weights of the complex-valued fully connected layer, For the Sparse threshold for complex-valued fully connected layers; for function, , , .

[0093] In this embodiment, in order to speed up the sparseness, in the loss function Added network weights and sparse threshold of The regular term is expressed as follows:

[0094] , ,

[0095] in, is the cross entropy loss function, is a hyperparameter, and Represent the network weights and sparse threshold matrices respectively, The input sample is identified as a category The probability of is a category Tags, K is the total number of modulation types; express norm.

[0096] The adaptive complex-valued momentum estimation algorithm with weight decay is used to update the network weights and sparse thresholds to obtain the Tier The sparse threshold matrix after iteration update and weight matrix The method is:

[0097] , ,

[0098] , ,

[0099] , ,

[0100] , ,

[0101] , ,

[0102] in, and is the complex gradient vector, is the cross entropy loss function, 、 、 and are transition variables. and is the first-order exponential sliding average of the complex gradient, and is the second-order exponential moving average of the complex gradient, is the step length, is the regularization parameter, and is a constant, is the shrinkage factor.

[0103] The effectiveness of the method proposed in the present invention is verified by a specific example below. The specific steps are as follows:

[0104] S1: RadioML 2016.10A dataset is used to implement the recognition of radio signals. RadioML 2016.10A dataset includes 11 kinds of modulation signals, of which 3 kinds of analog modulation signal modes include AM-DSB, AM-SSB and WB-FM, and 8 kinds of digital modulation signal modes include BPSK, 8PSK, CPFSK, GFSK, PAM4, QAM16, QAM64 and QPSK. The signal-to-noise ratio of each modulation signal is from -20 dB to 18 dB. The dataset contains 220,000 signal samples, each signal sample consists of 2x128 I / Q dual-channel signals. For each signal-to-noise ratio, there are 1000 samples for each modulation type. In addition, in order to simulate the authenticity of communication effect, additive white Gaussian noise that may cause channel damage is added to the dataset.

[0105] S2: 600 samples are randomly selected for the training set, 200 samples are randomly selected for the validation set, and the remaining 200 samples are randomly selected for the test set under each signal-to-noise ratio of each modulation type. The labels of the modulation signals are encoded using one-hot encoding format, and the I / Q dual channels of each sample are spliced into a complex value vector of one channel, and then a complex value convolutional neural network model for radio signal modulation recognition is constructed as shown in Figure 2 , and the parameters of the model are initialized.

[0106] S3: The complex value soft - log threshold weight reparameterization algorithm is used to train the above complex value neural network until the iteration stopping condition is reached, and the sparse complex value convolutional neural network with the optimal structure is output.

[0107] The parameters of the sparse complex value convolutional neural network are set as follows:

[0108] The iteration stopping condition is that the iteration number reaches 200 times, the step size , the batch size is 128, and the initial threshold value of sparsity is , The parameters of the regularization are .

[0109] S4: The signal to be recognized is input into the optimal sparse complex value neural network, so as to realize the recognition of radio signals.

[0110] Figure 4 , where the legend "STR" represents the complex value soft threshold reparameterization algorithm, and the legend "CV-SLTR" represents the complex value soft - log threshold weight reparameterization algorithm proposed by the present application. The two sparse algorithms reach the same sparsity after 200 iterations. From Figure 4It can be seen that the sparse speed of the CV-SLTR algorithm is faster than that of the STR algorithm, and the recognition error rate is lower than that of the STR algorithm.

[0111] Figure 5 The figure shows the accuracy of the original model without the sparse algorithm and the models after using the two sparse algorithms at different signal-to-noise ratios. As can be seen from the figure, the model using the CV-SLTR algorithm performs the best.

[0112] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0113] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0114] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0115] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0116] Obviously, the above embodiments are merely examples for clarity of explanation and are not intended to limit the implementation methods. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all implementation methods here. Obvious variations or modifications arising therefrom remain within the scope of protection of the present invention.

Claims

1. A radio signal modulation recognition method based on sparse complex-valued convolutional neural network, characterized in that: The following steps are involved: S1: Modulating a radio signal to be transmitted to obtain an I / Q two-channel signal dataset, adding additive white Gaussian noise to the I / Q two-channel signal dataset to form a modulated signal dataset, and preprocessing the modulated signal dataset to obtain a preprocessed modulated signal dataset; S2: constructing and initializing a complex-valued convolutional neural network model for radio signal modulation recognition, and iteratively training the complex-valued convolutional neural network model based on the preprocessed modulation signal data set to obtain a trained sparse complex-valued convolutional neural network model; S3: inputting the signal to be identified into the trained sparse complex-valued convolutional neural network model to obtain an identification result of the modulation mode of the signal to be identified; The complex-valued convolutional neural network model includes a plurality of complex-valued convolutional layers and a plurality of complex-valued fully connected layers connected in sequence, each complex-valued convolutional layer includes a complex-valued convolution operation and a complex-valued activation function, and each complex-valued fully connected layer includes a complex-valued fully connected operation and a complex-valued activation function; In S2, the iterative training of the complex-valued convolutional neural network model includes a forward propagation process and a backpropagation process to obtain a trained sparse complex-valued convolutional neural network model, and the method includes: S21: During the forward propagation process, determine whether the current layer is a complex-valued convolutional layer or a complex-valued fully connected layer: if the current layer is a complex-valued convolutional layer, reset the weights of the complex-valued convolutional layer by a complex-valued soft threshold operator; if the current layer is a complex-valued fully connected .... log-sum The threshold operator resets the weights of the complex-valued fully connected layer; S22: During the back-propagation process, optimizing the loss function using an adaptive complex-valued momentum estimation algorithm with weight decay, and updating the network weights and the sparsity threshold; S23: Execute steps S21 to S22 in a loop until the maximum number of iterations is reached or the algorithm converges.

2. The radio signal modulation recognition method based on sparse complex-valued convolutional neural network according to claim 1, characterized in that: The method of resetting the weights of the complex-valued convolutional layer through the complex-valued soft threshold operator is expressed as: ， in, Represents the updated value of the complex soft threshold operator l The weight matrix of the complex-valued convolutional layer; Before the update l The weight matrix of the complex-valued convolution layer is Rank Elements of the column, , is the weight before update The real part of is the weight before update The imaginary part of For the l The sparse threshold of the complex-valued convolutional layer, , , .

3. The radio signal modulation recognition method based on sparse complex-valued convolutional neural network according to claim 1, characterized in that: Through complex value log-sum The method of resetting the weights of the complex-valued fully connected layer by the threshold operator is expressed as: ， in, To use complex values log-sum The threshold operator after adjustment l The weight matrix of the complex-valued fully connected layer, Before adjustment l The weights of the complex-valued fully connected layer, For the Sparse threshold for complex-valued fully connected layers; for function, , , .

4. The radio signal modulation recognition method based on sparse complex-valued convolutional neural network according to claim 1, characterized in that: The loss function Including network weights and sparse thresholds The regular term is expressed as follows: ， ， in, is the cross entropy loss function, is a hyperparameter, and Represent the network weights and sparse threshold matrices respectively, The input sample is identified as a category The probability of is a category Tags, K is the total number of modulation types; express norm.

5. The radio signal modulation recognition method based on sparse complex-valued convolutional neural network according to claim 1, characterized in that: The method for updating the network weights and sparse thresholds is: the adaptive complex-valued momentum estimation algorithm with weight decay is used to calculate the first Tier The sparse threshold matrix after iteration update and weight matrix : ， ， ， ， ， ， ， ， ， ， in, and is the complex gradient vector, is the cross entropy loss function, 、 、 and are transition variables. and is the first-order exponential sliding average of the complex gradient, and is the second-order exponential moving average of the complex gradient, is the step length, is the regularization parameter, and is a constant, is the shrinkage factor.

6. The radio signal modulation recognition method based on sparse complex-valued convolutional neural network according to claim 1, characterized in that: The complex-valued convolution operation is used to convert the The input feature matrix of the layer Hedi The convolution kernel matrix of the layer Perform convolution operation to obtain the input feature matrix The complex-valued characteristic matrix of , the method includes: Define the The input feature matrix of the layer for: , the said The convolution kernel matrix of the layer for: , and we get the complex-valued characteristic matrix: ， in, represents the convolution operation, for The real part of for The imaginary part of for The real part of for The imaginary part of .

7. The radio signal modulation recognition method based on sparse complex-valued convolutional neural network according to claim 6, characterized in that: The complex-valued full connection operation is used to The input feature matrix of the layer After assigning weights, nonlinear transformation is performed, and the methods include: Definition Layer and Weight matrix between layers , and the nonlinear transformation result is obtained: ,in, for The real part of for The imaginary part of Represents the activation function.

8. The radio signal modulation recognition method based on sparse complex-valued convolutional neural network according to claim 7, characterized in that: The complex-valued activation function is a real-valued normalized exponential function or a split-type complex-valued linear rectifier function; wherein the expression of the real-valued normalized exponential function is: , where the input feature matrix , is the total number of modulation types; The expression of the split complex-valued linear rectifier function is: ,in, .

9. The radio signal modulation recognition method based on sparse complex-valued convolutional neural network according to claim 1, characterized in that: The method for obtaining the preprocessed modulation signal data set is: Based on the modulated signal data set, setting the division ratio of the training set, the validation set and the test set, and randomly selecting the same number of data samples in each modulation type and distributing them into the training set, the validation set and the test set according to the division ratio; Use one-hot encoding to encode the modulation type label of the data sample, and each modulation type corresponds to a one-hot encoding vector; Splice the I / Q dual-channel signals into complex-valued eigenvectors, each of which is in complex form and contains real and imaginary parts; Based on the data input format of the complex-valued convolutional neural network model, the encoded labels and the spliced ​​complex-valued feature vectors are correspondingly combined together to form the preprocessed modulated signal data set.

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