A Modulation Recognition Method Based on Markov Switching Field and Deep Learning

Abstract

The present invention provides a modulation recognition method based on Markov switching fields and deep learning, which relates to the field of cognitive radio technology and includes the following steps: S1, receiving a radio signal and generating Markov switching field features by using the in-phase / quadrature data of the radio signal; S2, reducing the dimension and reshaping the Markov switching field features, and then splicing them with the in-phase / quadrature data into hybrid data; S3, establishing and training a convolutional assisted Transformer model to obtain a trained Transformer model; S4, using the trained Transformer model to identify the modulation mode of an unknown signal, using the test set of the hybrid data as the input and the modulation mode label as the output. The present invention uses two complementary data, namely the I / Q sequence and the Markov transition graph, as the input of the model, greatly improving the recognition accuracy. The convolutional assisted Transformer model proposed by the present invention can simultaneously extract the local and global features of the data, enhancing the recognition accuracy.

Description

Technical Field

[0001] The present invention relates to the field of cognitive radio technology, and in particular, to a modulation recognition method based on Markov switching field and deep learning. Background Art

[0002] With the wide use of Internet of Things devices and the wide application of the fifth-generation (5G) communication technology, the demand for spectrum resources in modern society has increased rapidly, and the electromagnetic environment has become increasingly complex. To solve the current radio spectrum management problem, intelligent systems have been developed using cognitive radio (CR) technology, which can effectively alleviate the above problems. Automatic modulation recognition (AMR) is an effective basic part of CR, which can automatically identify the modulation scheme of the received signal under unknown channel and noise conditions. Therefore, AMR plays a key role in civilian communication applications such as interference recognition and spectrum monitoring.

[0003] Traditional AMR methods can be divided into likelihood-based (LB) methods and feature-based (FB) methods. However, due to the explosive growth of wireless communication data and the high complexity of the electromagnetic environment, it is difficult for traditional algorithms to achieve fast and accurate modulation recognition. Data-driven deep learning (DL) methods have become a popular choice for solving the AMR problem.

[0004] Common DL-based AMR methods mainly include convolutional neural network (CNN), recurrent neural network (RNN) and transformer methods. CNN can quickly extract features by performing convolution operations on data using weight-sharing filters. However, CNN cannot effectively utilize the time information in the signal. RNN can extract long-range dependencies in time series. Therefore, some researchers combine CNN and RNN to fuse spatio-temporal features, effectively improving the recognition accuracy. However, it will increase the additional computational amount, and the training of RNN is very difficult. Recently, the Transformer model with global modeling ability has been used in AMR, proving the effectiveness of Transformer in AMR tasks. However, these methods have a high computational complexity and may seriously reduce the recognition performance for short signals. Therefore, it is necessary to develop lightweight and effective AMR algorithms. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to propose a modulation recognition method based on Markov switching field and deep learning. First, hybrid features are designed to improve the recognition accuracy by utilizing the complementarity between in-phase / quadrature (I / Q) signals and Markov transition field features. Then, a modulation recognition algorithm based on convolutional assisted Transformer is proposed, which can be used to identify the modulation mode of radio signals. By this method, the reliability of the radio signal modulation mode recognition method in practical applications is improved.

[0006] The technical means adopted by the present invention are as follows:

[0007] A modulation recognition method based on Markov switching field and deep learning, comprising the following steps:

[0008] S1. Receive radio signals, and generate Markov switching field features by using the in-phase / quadrature data of the radio signals;

[0009] S2. Reduce the dimension and reshape the Markov switching field features, and then splice them with the in-phase / quadrature data into hybrid data;

[0010] S3. Establish and train a convolutional assisted Transformer model to obtain a trained Transformer model;

[0011] S31. Establish a two-dimensional convolutional downsampling module, which includes three two-dimensional convolutions for preliminary feature extraction and dimension reduction of the input signal data;

[0012] S32. Embed class tokens and positional relationships into the preliminarily extracted features;

[0013] S33. Establish a convolutional assisted encoder, with the preliminary features of S31 as the input, and the globally and locally features fused with trainable parameters as the output of the convolutional assisted encoder;

[0014] S34. Use a fully connected layer classifier to output the probabilities of each possible class for the class tokens in the output features of the last convolutional assisted encoder through a linear layer, take the maximum value of the probabilities, and output the class result;

[0015] S35. Divide the public dataset into a training set, a validation set, and a test set according to a ratio. Among them, the training set is used for training, with the labeled hybrid data form as the input of the proposed convolutional assisted Transformer, use the cross-entropy loss function to calculate the loss value between the output probability and the true label, and optimize the model parameters according to the loss value through the gradient descent algorithm;

[0016] S4. Use the trained Transformer model to identify the modulation mode of unknown signals, with the test set of the hybrid data as the input and the modulation mode label as the output.

[0017] Further, the training set, validation set, and test set are included in the dataset. The division ratio of the training set, validation set, and test set is 7:1:2. The dataset is the open-source dataset RadioML2016.10a, which contains 11 modulation methods: 8PSK, AM-DSB, AM-SSB, BPSK, QPSK, 8PSK, 16QAM, 64QAM, BFSK, CPFSK, WBFM. The signal-to-noise ratio ranges from -20 dB to 20 dB, with an interval of 2 dB, and the length of the signal is 128.

[0018] Further, S1 includes the following steps:

[0019] First, group the and in-phase / quadrature one-dimensional sequences. The number of each group is calculated by the following formula:

[0020] (1)

[0021] where represents 's interquartile range. The number of groups can be obtained through and is

[0022] (2)

[0023] When is not an integer, take the closest , , Each point in the channel signal sequence is assigned to the corresponding , where . A weighted adjacency matrix is obtained by calculating the transition probability between . The formula is:

[0024] (3)

[0025] where is the transition probability between the sample in and the sample in . The Markov transition field matrix is obtained by normalizing and representing the transition probability in chronological order;

[0026] (4)

[0027] where represents the transition probability from a point to , The elements on the main diagonal represent the probability of self-transition, Convert to , and and are added together:

[0028] (5)

[0029] The generated MTF matrix has a size of . It is adjusted to an appropriate size using the Gaussian blur method, the dimension of the MTF matrix is reduced and reshaped into the shape of an in-phase / quadrature sequence, and the mixed features are obtained by concatenating the in-phase / quadrature sequence of the MTF sequence with the MTF features:

[0030] (6)

[0031] Among them, represents the feature concatenation operation, is a function for transforming dimensions, .

[0032] Furthermore, the convolutional auxiliary encoder described in S33 includes hourglass attention and convolutional residual connections; the hourglass attention consists of two linear layers and multi-head self-attention. The two linear layers reduce the computational complexity by reducing and expanding the channels of the features; when the features enter the hourglass attention, the channels are halved after passing through the first linear layer, and the multi-head self-attention performs dot product calculations to generate a global weight matrix. Multiplying this weight matrix with the features can enhance the effective features and suppress the ineffective features, generating global features; the global features are restored to the original number of channels through a linear layer.

[0033] Furthermore, the hourglass attention is achieved by controlling the reduction and increase of the feature dimensions through linear projection;

[0034] (7)

[0035] Among them, is the input of the encoder, B is the number of samples, is the sequence length, C is the number of channels. For the multi-head attention mechanism with heads, the input features will be divided into , and then linear projection is performed to generate . The self-attention operation of one head can be expressed as:

[0036] (8)

[0037] Then, the groups of outputs are concatenated to obtain the complete output:

[0038] (9)

[0039] The output of the hourglass attention is obtained through the dimension elevation operation of linear projection:

[0040] (10)

[0041] In the convolutional residual branch, the input data is divided along the channels into , , processed by one-dimensional convolution, without processing, the output of the convolutional residual connection can be expressed as:

[0042] (11)

[0043] Two trainable parameters α and β are designed to fuse local-global features, and the initial values of the parameters are 1. The output of the convolutional auxiliary encoder is expressed as:

[0044] (12)

[0045] Batch normalization and the ReLU activation function are performed after each convolution calculation, and the formula is as follows:

[0046] (13)

[0047] (14)

[0048] Among them, is the mean of the batch data, is the variance of the batch data, is the learnable parameter.

[0049] Furthermore, in S35, the multi-class cross-entropy loss function is used to calculate the loss value of the output recognition result of the deep learning model, and the formula is as follows:

[0050] (15)

[0051] Among them, is the true label of the signal sample modulation method, is the model output, is the number of samples, is the number of classes.

[0052] Furthermore, S35 specifically includes: adopting the Adam algorithm to minimize the loss function through the first-order momentum and the second-order momentum, that is, the mean and variance of the gradient, and the formula is as follows:

[0053] (16)

[0054] Among them, is the parameter to be optimized, is the round, is the objective function, i.e., the loss function, is the current parameter gradient, is the first-order momentum, is the second-order momentum, is the hyperparameter, is the learning rate, i.e., the step size.

[0055] Furthermore, it also includes judging the effect of the deep learning model according to the evaluation index, including measuring the performance of the network model, modulation recognition effect, setting the Acc evaluation index, and the formula is as follows:

[0056] (17)

[0057] Among them, represents the number of correctly recognized modulation modes, represents the number of incorrectly recognized modulation modes.

[0058] A storage medium, the storage medium includes a stored program, wherein when the program runs, it executes any one of the above modulation recognition methods based on the Markov transition field and deep learning.

[0059] An electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, and the processor runs through the computer program to execute any one of the above modulation recognition methods based on the Markov transition field and deep learning.

[0060] Compared with the prior art, the present invention has the following advantages:

[0061] The model of the present invention automatically extracts information in the data for accurate modulation scheme recognition, without the need for the parameters of the received signal and the prior information of the channel.

[0062] The present invention uses two complementary data, i.e., the I / Q sequence and the Markov transition graph, as the input of the model, greatly improving the recognition accuracy.

[0063] The proposed convolutional assisted Transformer model of the present invention can simultaneously extract local and global features of the data, enhancing the recognition accuracy.

[0064] The hourglass design of the attention mechanism and the adoption of partial convolution in the residual connection of the present invention effectively reduce the computational complexity of the model. Description of the Drawings

[0065] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required for the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can also be obtained based on these drawings.

[0066] Figure 1 This is the flowchart of the method of the present invention.

[0067] Figure 2 This is the Markov transition field diagram for different modulation signals of the present invention.

[0068] Figure 3 This is the structural diagram of the convolutional assisted Transformer model of the present invention.

[0069] Figure 4 This is the schematic diagram of the accuracy of the test set in the embodiment. Detailed implementation manners

[0070] In order to enable those skilled in the art of the present technology to better understand the solution of the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0071] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above accompanying drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that such used data can be interchanged under appropriate circumstances so that the embodiments of the present invention described here can be implemented in an order different from those illustrated or described here. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device comprising a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0072] As Figure 1 shown, a modulation recognition method based on Markov transition field and deep learning specifically includes the following steps:

[0073] 1) Generation of Markov transition field (MTF) features. First, for and The one-dimensional sequence is grouped. The number of each group can be calculated as follows

[0074] (1)

[0075] Among them, represents the interquartile range of. The number of groups can be obtained by to get, which is

[0076] (2)

[0077] Usually, when is not an integer, take the closest , . Each point in the channel signal sequence is assigned to the corresponding , among which . By calculating the transition probability between to obtain a weighted adjacency matrix , given as

[0078] (3)

[0079] Among them, is the transition probability between the samples in and the samples in. The Markov transition field matrix is obtained by normalizing and representing the transition probability in chronological order.

[0080] (4)

[0081] Among them represents the transition probability from a point to .. The elements on the main diagonal represent the probability of self-transition. Similarly, is converted to , and and are added together.

[0082] (5)

[0083] The generated MTF matrix has a size of , and can be adjusted to an appropriate size using the Gaussian blur method. We reduce the dimension of the MTF matrix and reshape it into the shape of the I / Q sequence. The hybrid feature is obtained by concatenating the I / Q sequence of the MTF sequence with the MTF feature.

[0084] (6)

[0085] Among them, represents the feature splicing operation, is a function for transforming dimensions, . The Markov transition fields of different modulation signals are as Figure 2 shown;

[0086] 2) Reduce the dimension and reshape the Markov transition field features, and then splice them with the I / Q sequence into hybrid data. Divide the hybrid data into a training set, a validation set, and a test set;

[0087] 3) The main component of the Transformer model is the convolutional auxiliary encoder. As Figure 3 shown, this encoder consists of two parts: hourglass attention and convolutional residual connection. Among them, the hourglass attention is achieved by controlling the reduction and increase of the feature dimension through linear projection. Specifically, it includes:

[0088] Establish a two-dimensional convolutional downsampling module. This module contains three two-dimensional convolutions to achieve preliminary feature extraction and dimension reduction of the input signal data.

[0089] Embed the class token and the positional relationship into the preliminarily extracted features. The class token is essentially a trainable vector, and its function is to aggregate global features to output the predicted class. The positional relationship is essentially a trainable matrix, and its function is to add positional information, which for signal data is to record the sequential relationship of each data point.

[0090] Establish a convolutional auxiliary encoder with the above features as the input. This encoder mainly consists of two parts: hourglass attention and convolutional residual connection. Among them, the hourglass attention consists of two linear layers and multi-head self-attention. These two linear layers can reduce the computational complexity by reducing and expanding the channels of the features. When the features enter the hourglass attention, the number of channels is halved after passing through the first linear layer. Then, the multi-head self-attention performs dot product calculations to generate a global weight matrix, and multiplying this weight matrix with the features can enhance the effective features and suppress the ineffective features to generate global features. Finally, the global features are restored to the original number of channels through a linear layer. The convolutional residual connection is a lightweight convolutional branch that can add local information to the encoder and accelerate the convergence of the model. It consists of a one-dimensional convolutional layer and a linear layer, and can extract local features at a relatively low computational cost by only convolving some of the features. The global features and local features fused through trainable parameters are the output of the convolutional auxiliary encoder. In the model we proposed, N convolutional auxiliary encoders are cascaded to jointly extract features.

[0091] The fully connected layer classifier outputs the probabilities of each category for the class token in the output features of the last convolutional auxiliary encoder through a linear layer, takes the maximum value of the probabilities, and outputs the class result.

[0092] (7)

[0093] Among them, is the input of the encoder, B is the number of samples, is the sequence length, and C is the number of channels. For the multi-head attention mechanism with heads, the input features will be divided into . Then, through linear projection, is generated. The self-attention operation of one head can be expressed as

[0094] (8)

[0095] Then, the groups of outputs are concatenated to obtain the complete output.

[0096] (9)

[0097] The output of the hourglass attention is obtained through the upsampling operation of linear projection

[0098] (10)

[0099] In the convolutional residual branch, the input data is divided along the channels into , . After one-dimensional convolutional processing, is not processed, and the output of the convolutional residual connection can be expressed as

[0100] (11)

[0101] In particular, to better fuse local-global features, we designed two trainable parameters α and β. The initial values of the parameters are 1. The output of the convolutional auxiliary encoder can be expressed as

[0102] (12)

[0103] In addition, batch normalization and ReLU activation functions are performed after each convolutional calculation, as shown in Formulas 13 and 14:

[0104] (13)

[0105] (14)

[0106] Among them, is the mean of the batch data, is the variance of the batch data, is a learnable parameter.

[0107] 4) Train the established convolutional assisted Transformer model, using the training set of the mixed data as the input and the modulation method as the output, and optimize the model parameters by calculating the loss value between the input and the output. Divide the public dataset into a training set, a validation set, and a test set according to a certain proportion. Among them, the training set is used for training, and the labeled mixed data form is used as the input of the proposed convolutional assisted Transformer. Use the cross-entropy loss function to calculate the loss value between the output probability and the true label, and optimize the model parameters according to the loss value through the gradient descent algorithm; during the training process, use the validation set for testing to verify the model performance and facilitate understanding the model situation and making timely adjustments.

[0108] Calculate the loss value of the output recognition result of the deep learning model using the multi-class cross-entropy loss function, as shown in Equation 15:

[0109] (15)

[0110] Among them is the true label of the damage, is the model output, is the number of samples, is the number of classes.

[0111] Adopt the Adam algorithm to minimize the loss

[0112] function through the first-order momentum and the second-order momentum, that is, the mean and variance of the gradient. The parameter relationship involved is as shown in Equation 16:

[0113] (16)

[0114] Among them is the parameter to be optimized, is the number of epochs, is the objective function, that is, the loss function, is the current parameter gradient, is the first-order momentum, is the second-order momentum, is the hyperparameter, is the learning rate, that is, the step size.

[0115] Set the Acc evaluation index to judge the effect of the deep learning model, as shown in Equation 17:

[0116] (17)

[0117] Among them, , that is, true positives represent the number of damaged pixels correctly identified, , that is, true negatives, representing the number of non-damaged areas correctly identified, , that is, false positives, representing the number of damaged areas misidentified, while , that is, false negatives, representing the number of non-damaged areas misidentified.

[0118] 5) Use the trained model to identify the modulation method of the sample, with the test set of the mixed data as the input and the modulation method label as the output.

[0119] Embodiment

[0120] In this embodiment, the identified signals come from the test set of the public dataset. The specific steps are as follows:

[0121] First, this embodiment uses the open-source dataset RadioML2016.10a, which includes 11 modulation methods: 8PSK, AM-DSB, AM-SSB, BPSK, QPSK, 8PSK, 16QAM, 64QAM, BFSK, CPFSK, WBFM. The signal-to-noise ratio ranges from -20 dB to 20 dB, with an interval of 2 dB. The length of the signal is 128;

[0122] Next, convert the original signal into Markov transition field features and splice them into mixed features. The mixed features are used as the input of the deep learning model. The mixed features are divided into a training set, a validation set, and a test set in the ratio of 7:1:2. No signal-to-noise ratio categories are set in the training set and the test set. That is to say, we use all the signal-to-noise ratio samples for training, and the output type of the model is only the modulation method. In the test set, we separate the samples with different signal-to-noise ratios and conduct separate tests;

[0123] The algorithm of the present invention is implemented. The experimental environment of the network model: Python3.7, PyTorch1.10, Torchvision0.3.0, Intel Xeon Silver 4210R CPU, NVIDIA GeForce RTX 3060 GPU, 63.7 GB of memory and 476 GB of storage. During training, we use the Adam optimizer with 100 epochs, and the initial learning rate is set to 0.0005.

[0124] The test set accuracy is as Figure 4As shown. The results show that our method can effectively identify signals with high signal-to-noise ratio, reaching the highest accuracy rate of 93.58% at 18 dB. The average accuracy rate from 0 dB to 18 dB reaches 92.01%. In the case of low signal-to-noise ratio, the recognition accuracy is poor due to the interference of noise, which is normal. The number of parameters of the proposed convolutional assisted Transformer model is 157,291. It can be seen from the results that the radio signal modulation mode recognition method based on feature fusion and convolutional assisted Transformer has excellent performance and broad application prospects.

[0125] The present invention also provides a storage medium, which includes a stored program. When the program runs, it executes a modulation recognition method based on a Markov transition field and deep learning.

[0126] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored on the memory and operable on the processor. The processor runs through the computer program to execute a modulation recognition method based on a Markov transition field and deep learning.

[0127] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A modulation recognition method based on Markov switching fields and deep learning, characterized in that It includes the following steps: S1. Receive a radio signal and generate a Markov transition field feature using the in-phase / quadrature data of the radio signal; S2. Reduce the dimension and reshape the Markov transition field feature, and then splice it with the in-phase / quadrature data into hybrid data; S3. Establish and train a convolutional-assisted Transformer model to obtain a trained Transformer model; S31. Establish a two-dimensional convolutional downsampling module, which includes three two-dimensional convolutions for preliminary feature extraction and dimensionality reduction of the input signal data; S32. Embed the class token and positional relationship into the preliminarily extracted features; S33. Establish a convolutional-assisted encoder, with the preliminary features of S31 as the input and the globally and locally fused features with trainable parameters as the output of the convolutional-assisted encoder; S34. Use a fully connected layer classifier to output the probabilities of each class for the class token in the output features of the last convolutional-assisted encoder through a linear layer, take the maximum value of the probabilities, and output the class result; S35. Divide the public dataset into a training set, a validation set, and a test set according to a ratio. Among them, the training set is used for training, with the labeled hybrid data as the input of the proposed convolutional-assisted Transformer, use the cross-entropy loss function to calculate the loss value between the output probability and the true label, and optimize the model parameters according to the loss value through the gradient descent algorithm; S4. Use the trained Transformer model to identify the modulation mode of the unknown signal, with the test set of the hybrid data as the input and the modulation mode label as the output.

2. The modulation recognition method based on Markov switching field and deep learning according to claim 1, wherein The training set, validation set, and test set are included in the dataset. The division ratio of the training set, validation set, and test set is 7:1:

2. The dataset is the open-source dataset RadioML2016.10a, which includes 11 modulation modes: 8PSK, AM-DSB, AM-SSB, BPSK, QPSK, 8PSK, 16QAM, 64QAM, BFSK, CPFSK, WBFM, signal-to-noise ratio range from -20dB to 20dB, interval 2dB, and the signal length is 128.

3. The modulation recognition method based on Markov switching field and deep learning according to claim 1, wherein S1 includes the following steps: First, and the in-phase / quadrature one-dimensional sequences are grouped, and the number of each group is calculated by the following formula: （1） Among them, represents the interquartile range of obtained by （2） When is not an integer, take the closest , , Each point in the channel signal sequence is assigned to the corresponding , where , a weighted adjacency matrix is obtained by calculating the transition probability between , and the formula is: （3） Among them, is the transition probability between the samples in and the samples in, and the Markov transition field matrix is obtained by normalizing and representing the transition probabilities in chronological order; （4） Among them, represents a point to the transition probability , where the elements on the main diagonal represent the probability of self-transition, is converted to , and and are added together: （5） Generated MTF matrix has a size of , is adjusted to an appropriate size using the Gaussian blur method, reduces the dimension of the MTF matrix and reshapes it into the shape of an in-phase / quadrature sequence, and the mixed features are obtained by connecting the in-phase / quadrature sequence of the MTF sequence with the MTF features: （6） Among them, represents a feature splicing operation, is a function for changing the dimension, .

4. The modulation recognition method based on Markov switching field and deep learning according to claim 1, characterized in that, The convolutional-assisted encoder in S33 includes hourglass attention and convolutional residual connection; the hourglass attention consists of two linear layers and multi-head self-attention. The two linear layers reduce the computational complexity by reducing and expanding the channels of the features; When the features enter the hourglass attention, the number of channels is halved after passing through the first linear layer. The multi-head self-attention performs dot product calculation to generate a global weight matrix, and multiplying this weight matrix with the features can enhance the effective features and suppress the ineffective features to generate global features; The global features are restored to the original number of channels through a linear layer.

5. The modulation recognition method based on Markov switching field and deep learning according to claim 4, characterized in that, The hourglass attention is realized by controlling the reduction and increase of the feature dimension through linear projection; （7） Among them, is the input of the encoder, B is the number of samples, is the sequence length, C is the number of channels. For the multi-head attention mechanism with heads, the input features will be divided into , and then linearly projected to produce . The self-attention operation of one head is expressed as: （8） Then, connect the group outputs to obtain the complete output: （9） The output of the hourglass attention is obtained through the upsampling operation of linear projection: （10） In the convolutional residual branch, the input data is divided along the channels into , , processed by one-dimensional convolution, left unprocessed, and the output of the convolutional residual connection is expressed as: （11） Design two trainable parameters α and β to fuse the local-global features. The initial values of the parameters are 1, and the output of the convolutional-assisted encoder is expressed as: （12） After each convolution calculation, batch normalization and the ReLU activation function are performed, and the formula is as follows: （13） （14） wherein, is the mean of the batch data, is the variance of the batch data, is a learnable parameter.

6. The modulation recognition method based on Markov switching field and deep learning according to claim 1, characterized in that In S35, the multi-class cross-entropy loss function is used to calculate the loss value of the output recognition result of the Transformer model, and the formula is as follows: （15） Among them, is the true label of the signal sample modulation method, is the model output, is the number of samples, is the number of categories.

7. The modulation recognition method based on Markov switching field and deep learning according to claim 1, characterized in that S35 specifically includes: using the Adam algorithm to minimize the loss function through the first-order momentum and the second-order momentum, that is, the mean and variance of the gradient, and the formula is as follows: （16） Among them, is the parameter to be optimized, is the round, is the objective function, i.e., the loss function, is the current parameter gradient, is the first-order momentum, is the second-order momentum, is the hyperparameter, is the learning rate, i.e., the step size.

8. The modulation recognition method based on Markov switching field and deep learning according to claim 1, characterized in that, It also includes judging the effect of the Transformer model according to the evaluation index, including measuring the performance of the network model, modulating the recognition effect, and setting the Acc evaluation index, and the formula is as follows: （17） Among them, represents the number of correctly identified modulation methods, represents the number of incorrectly identified modulation methods.

9. A storage medium, characterized in that, The storage medium includes a stored program, wherein when the program runs, it executes the modulation recognition method based on the Markov transition field and deep learning described in any one of claims 1 to 8.

10. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor runs through the computer program to execute the modulation recognition method based on the Markov transition field and deep learning described in any one of claims 1 to 8.

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