Automatic Modulation Classification Method Based on Wavelet Transform and Multimodal Feature Fusion

Abstract

The present invention discloses an automatic modulation classification method based on wavelet transform and multi-modal feature fusion, which mainly solves the technical problem of low classification accuracy of existing models under low signal-to-noise ratio conditions. The solution includes: 1) obtaining the I / Q samples of signals in the existing dataset; 2) preprocessing the sample data through wavelet threshold denoising, extracting the A / P information of the denoised signal, and inputting it into the time series modal feature extraction network; at the same time, using the Gramian angular field to reconstruct the sample data, converting the one-dimensional sequence into a two-dimensional image as the input of the image modal feature extraction network; 3) using a feature fusion method based on the attention mechanism to fuse the multi-modal features extracted by the two networks; 4) obtaining the final modulation classification result through the fully connected layer. The present invention fully considers the differences and complementarities between different modal features, can effectively improve the modulation classification accuracy in a low signal-to-noise ratio environment, and at the same time solves the problem of modulation confusion.

Description

Technical Field

[0001] The present invention belongs to the field of artificial intelligence, and further relates to communication signal modulation technology. Specifically, it is an automatic modulation classification method based on wavelet transform and multi-modal feature fusion, which can be used in the fields of spectrum detection and spectrum sensing. Background Technique

[0002] Automatic Modulation Classification (AMC) is an important link between signal presence detection and demodulation, and can classify the modulation type of a signal when the channel state information is unknown. AMC is not only a prerequisite for the receiver to complete demodulation, but also an essential part of the entire communication system, playing an irreplaceable role in both civilian security and military electronic warfare. In the civilian field, AMC is mainly used for spectrum sensing and spectrum monitoring. The spectrum resources in wireless communication are not infinite and inexhaustible. A large number of communication services occupy most of the spectrum, causing resource shortages and greatly affecting people's normal communication. The AMC technology can classify the modulation methods of signals and analyze the properties of signals to achieve the purpose of spectrum resource management. In the military field, the AMC technology can detect the interference information and key intelligence information sent by the enemy, thus helping the military to formulate targeted reconnaissance and anti-reconnaissance strategies. It can be seen that the development of the AMC technology has important strategic significance.

[0003] In recent years, research on deep learning in the field of automatic modulation classification has also achieved certain development. For example, the CGDNet network structure proposed by Njoku et al. in [Njoku J N, Morocho-Cayamcela M E, Lim W. CGDNet: Efficient Hybrid Deep Learning Model for Robust Automatic Modulation Recognition[J]. IEEE Networking Letters, 2021, 3(2): 47-51] consists of a shallow convolution, gated recurrent unit, and DNN. It uses a shallow convolution network and GRU to extract the temporal features of the I / Q sequence, and then uses DNN to complete the classification task. When using the RadioML2016.10b modulation dataset, the classification accuracy can reach over 90% at 18 dB. The convolutional long short-term memory network model (Convolutional Long Short-term Deep Neural Network, CLDNN) proposed by West et al. in [West N E, O'shea T. Deep architectures for modulation recognition[C] / / 2017 IEEE International Symposium on Dynamic Spectrum Access Networks (DySPAN), 2017: 1-6], which consists of three layers of CNN and one layer of LSTM, gives full play to the advantages of the CNN and RNN models and further improves the modulation classification accuracy. Although the above-mentioned literature has achieved certain results, there are still the following deficiencies: on the one hand, the electromagnetic signal input is commonly represented in a single form, ignoring other potential important feature information and the complementarity between different modal features, resulting in confusion among modulation categories with similar single features; on the other hand, with the rapid development of wireless communication technology, the modulation schemes of signals will become more complex and diverse, and factors such as noise, frequency offset, and frequency attenuation will all affect the classification accuracy of modulation. Enhancing the classification robustness of the model in low signal-to-noise ratio communication scenarios has also become one of the urgent problems to be solved. Therefore, designing an automatic modulation algorithm with multi-modal feature fusion that can obtain better classification performance at low signal-to-noise ratio has important theoretical significance and research value. Summary of the Invention

[0004] The object of the present invention is to propose an automatic modulation classification method based on wavelet transform and multi-modal feature fusion in view of the deficiencies of the above-mentioned existing technologies, so as to solve the technical problem of low classification accuracy of the model under low signal-to-noise ratio conditions; while improving the classification accuracy in a low signal-to-noise ratio environment, the present invention effectively solves the confusion problem between 16-QAM (Quadrature Amplitude Modulation) and 64-QAM, and further enhances the noise robustness of the model.

[0005] The idea of implementing the present invention is as follows: First, obtain the original I / Q data of the signals in the dataset RML2016.10A, then preprocess the original I / Q data through wavelet threshold denoising, extract the A / P information of the denoised signal, and input it into the time series modal feature extraction network; at the same time, use GAF (Gray-level Co-occurrence Matrix Feature) image coding to reconstruct the original I / Q data, and convert the one-dimensional sequence into a two-dimensional image as the input of the image modal feature extraction network; then, use a feature fusion method based on the attention mechanism to fuse the multi-modal features extracted by the two networks, and finally obtain the final modulation classification result through the fully connected layer.

[0006] The specific steps for the present invention to achieve the above object are as follows:

[0007] (1) Obtain the original I / Q data in the dataset RML2016.10A and divide it into a training set and a test set;

[0008] (2) Construct a multi-modal feature fusion model:

[0009] (2.1) Build a time series modal feature extraction network including three convolutional layers, two Convolutional Block Attention Modules (CBAM) and two Bidirectional Long Short-Term Memory networks (Bi-LSTM). After each convolutional layer, a batch normalization layer and a Rectified Linear Unit (ReLU) activation layer are connected. A CBAM module is connected after the first convolutional layer and the second convolutional layer respectively, and two Bi-LSTM are used after the third convolutional layer;

[0010] (2.2) In the original Deep Residual Shrinkage Network, replace the pooling layer and the strided convolutional layer with the Discrete Wavelet Transform (DWT) to obtain the image modal feature extraction network;

[0011] (2.3) Combine the time series modal feature extraction network and the image modal feature extraction network to form a feature extraction unit; design an input end for receiving external data, a preprocessing module for preprocessing the data received at the input end, and sending the preprocessed data into the feature extraction unit; after the feature extraction unit, an Attention Feature Fusion Module (AFF) and a classifier are connected in sequence to obtain the multi-modal feature fusion model;

[0012] (3) Use the training set data to train the multi-modal feature fusion model constructed in step (2) to obtain a trained model;

[0013] (4) Input the data in the test set into the trained model to achieve automatic modulation classification of the signal to be measured.

[0014] Compared with the prior art, the present invention has the following advantages:

[0015] First, the multi-modal feature fusion network architecture designed in the present invention fully considers the complementarity between different modal features and the importance of the feature fusion mechanism in the field of automatic modulation classification, and has significant superiority compared with the single-modal network model.

[0016] Second, in the time series and image modal feature extraction networks of the present invention, the idea of wavelet transform is respectively introduced to improve them: for time series modal feature extraction, the wavelet threshold denoising technology is used to preprocess the original modulation signal to obtain a more pure and significant feature expression; for image modal feature extraction, the two-dimensional discrete wavelet transform is used to replace the average pooling layer and the strided convolutional layer in the deep residual shrinkage network to suppress the influence of noise in the image on the classification performance of the model.

[0017] Third, since the present invention combines the idea of multi-modal feature fusion with wavelet transform, the classification performance under low signal-to-noise ratio is effectively improved, the model obtains stronger noise robustness, and at the same time, the confusion problem of QAM16 and QAM64 modulations is also solved. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a flowchart for the implementation of the present invention;

[0019] Figure 2 is a schematic diagram of the overall structure of the multi-modal feature fusion model constructed in the present invention;

[0020] Figure 3 is a schematic diagram of the structure of the time series modal feature extraction network of the present invention;

[0021] Figure 4 is a schematic diagram of the improved residual shrinkage unit structure in the image modal feature extraction network of the present invention;

[0022] Figure 5 is a schematic diagram of the confusion matrix of the present invention;

[0023] Figure 6 is a comparison chart of the correct classification rates of using the present invention and different deep learning network models. DETAILED DESCRIPTION OF THE INVENTION

[0024] The present invention will be further described below with reference to the accompanying drawings.

[0025] Example 1: Referring to Appendix Figure 1 and Figure 2 , an automatic modulation classification method based on wavelet transform and multi-modal feature fusion proposed by the present invention specifically includes the following steps:

[0026] Step 1. Obtain the original I / Q data in the dataset RML2016.10A and divide it into a training set and a test set; in this embodiment, the data from -6dB to 18dB in the dataset RML2016.10A is selected and divided according to the allocation ratio of 80% training set and 20% test set, and the training set data is randomly shuffled. Of course, the quantity and division ratio of the sample data can also be adjusted according to actual needs here.

[0027] Step 2. Construct a multi-modal feature fusion model:

[0028] (2.1) Build a temporal modal feature extraction network including three convolutional layers, two convolutional block attention modules CBAM and two bidirectional long short-term memory networks Bi-LSTM, where each convolutional layer is followed by a batch normalization layer and a rectified linear unit ReLU activation layer, and a CBAM module is connected after the first convolutional layer and the second convolutional layer respectively, and two Bi-LSTM are used after the third convolutional layer;

[0029] (2.2) In the original deep residual shrinkage network, use discrete wavelet transform DWT to replace the pooling layer and the strided convolutional layer therein to obtain an image modal feature extraction network;

[0030] (2.3) Combine the temporal modal feature extraction network and the image modal feature extraction network to form a feature extraction unit; design an input end for receiving external data, a preprocessing module for preprocessing the data received by the input end, and sending the preprocessed data into the feature extraction unit; an attention feature fusion module AFF and a classifier are connected in sequence after the feature extraction unit to obtain a multi-modal feature fusion model;

[0031] Step 3. Use the training set data to train the multi-modal feature fusion model constructed in step (2) to obtain a trained model; this training process is completed by adopting a dynamic learning rate adjustment strategy after setting the number of iterations, the number of samples per batch, the initial learning rate, the optimizer, and the loss function. In this embodiment, the number of iteration rounds is set to 80, the number of samples per batch is set to 128, the optimizer is set to Adam, the loss function is set to the cross-entropy function, the initial learning rate is set to 0.001, and the learning rate is set to be reduced to 1 / 10 of the original every 30 rounds to accelerate the model convergence to obtain better results.

[0032] Step 4. Input the data in the test set into the trained model to realize the automatic modulation classification of the signal to be measured.

[0033] Embodiment 2: The overall implementation steps of the automatic modulation classification method proposed in this embodiment are the same as those in Embodiment 1. Now, refer to the attached Figure 2 For the constructed multi-modal feature fusion model, a further detailed description is made as follows:

[0034] The multi-modal feature fusion model constructed by the present invention is composed of an input end, a preprocessing module, a feature extraction unit, an attention feature fusion module AFF, and a classifier that are cascaded in sequence; among them:

[0035] The input end is used to receive the original data provided to the model externally and send these original I / Q data to the preprocessing module; the preprocessing module is used to preprocess the original I / Q data and send the preprocessed data to the feature extraction unit; specifically, the wavelet threshold denoising technology is used to perform wavelet denoising on the original input signal, and then the denoised data is converted into the I / Q and A / P forms and input into the time series modal feature extraction network of the feature extraction unit; the original I / Q data is converted into a two-dimensional image using GAF coding and then input into the image modal feature extraction network of the feature extraction unit. In this embodiment, the wavelet basis function is set to db8, the number of wavelet decomposition layers is 3, the threshold function is a compromise function between hard and soft thresholds, and the threshold is 0.05 to perform wavelet threshold denoising processing on the original data to obtain the denoised signal.

[0036] The feature extraction unit includes two parts: a time series modal feature extraction network and an image modal feature extraction network. Among them, the structure of the time series modal feature extraction network refers to Figure 3 , specifically including three convolutional layers, with a batch normalization layer and a rectified linear unit ReLU activation layer connected after each convolutional layer, and a convolutional block attention module CBAM is connected after the first convolutional layer and the second convolutional layer respectively, and two bidirectional long short-term memory networks Bi-LSTM are used after the third convolutional layer. In this embodiment, the number of convolutional kernels of the three convolutional layers is set to 128, 256, and 512 respectively, the size is 1×3, the zero padding and the stride are both 1; the input feature dimension and the hidden layer state dimension of the Bi-LSTM layer are both 128. The image modal feature extraction network is obtained by replacing the pooling layer and the strided convolutional layer in the original deep residual shrinkage network with the discrete wavelet transform DWT, as shown in Figure 4 . For the improvement of this module, the idea of wavelet transform is introduced into the original deep residual shrinkage network, and the discrete wavelet transform DWT is used to replace the pooling layer and the strided convolutional layer in the original network to enhance the noise filtering ability of the network and suppress the influence of noise on the classification performance.

[0037] The attention feature fusion module AFF is a module commonly used for feature fusion in the prior art and is used to fuse temporal features and image features in the model constructed in the present invention; the classifier is used to flatten the fused features to further obtain the classification result.

[0038] Embodiment 3: The overall implementation steps of the automatic modulation classification method proposed in this embodiment are the same as those in Embodiment 1. Now, the implementation process of extracting image features by the image modality feature extraction network in the multi-modal feature fusion model is described in detail as follows:

[0039] The image modality feature extraction network specifically decomposes the noisy data X into a low-frequency component and three high-frequency components by DWT, and finally only retains the low-frequency component containing useful information and removes other high-frequency components to achieve this.

[0040] Forward propagation process of 2D DWT in the image modality feature extraction network:

[0041] X ll = LXL T ,

[0042] X lh = HXL T ,

[0043] X hl = LXH T ,

[0044] X hh = HXH T ,

[0045] Among them, L and H are the matrix vectors of the low-pass and high-pass filters of the orthogonal wavelet respectively; X represents the noisy data, and X ll represents the low-frequency component containing the main information of X, and X lh , X hl , X hh are all high-frequency components, which respectively contain the horizontal, vertical, and diagonal noise detail information of X;

[0046] Backward propagation process of 2D DWT in the image modality feature extraction network:

[0047]

[0048]

[0049]

[0050]

[0051] Among them, G represents the backward propagation output of the layer after 2D DWT.

[0052] Example 4: The overall implementation steps of the automatic modulation classification method proposed in this example are the same as those in Example 1. Now, refer to the attached Figure 1 For the automatic modulation classification process of the signal to be measured in step 4, a further detailed description is given as follows:

[0053] Step 4.1: Send the original I / Q data to be measured to the preprocessing module of the model through the input end;

[0054] Step 4.2: After receiving the data, the preprocessing module performs the following operations:

[0055] (4.2.1) Use the wavelet threshold denoising technique to process the original input signal, that is, wavelet denoising; and convert the denoised data into I / Q and A / P forms, and then input it into the time series modal feature extraction network of the feature extraction unit. The conversion of the denoised data into I / Q and A / P forms is achieved as follows:

[0056] Convert the denoised signal into in-phase and quadrature components I / Q according to the following formula to obtain the I / Q components x of the m-th group of data m I / Q :

[0057]

[0058] where x m I is the in-phase component of the m-th group of data in the signal, x m Q is the quadrature component of the m-th group of data in the signal, (·) T represents the transpose operation; (x m I ) T , (x m Q ) T ∈R N , x m I / Q ∈R 2×N , N is the total number of samples;

[0059] Convert the denoised signal into amplitude component and phase component A / P according to the following formula to obtain the A / P components x of the m-th group of data m A / P :

[0060]

[0061] where x m A is the amplitude component of the m-th group of data in the signal, x m Pis the phase component of the m-th group of data in the signal; (x m A ) T 、(x m P ) T ∈R N ,x m A / P ∈R 2×N ;

[0062] The conversion expressions for the amplitude component and the phase component are as follows:

[0063]

[0064]

[0065] where r m I [n] and r m Q [n] are the in-phase component and the quadrature component of the n-th sample of r m respectively, and r m represents the m-th group of data vectors in the signal.

[0066] (4.2.2) Use GAF coding to convert the original I / Q data into a two-dimensional image. Specifically, for the two-way data of the original data set, namely the I-channel data and the Q-channel data, they are respectively converted into a 64×64 two-dimensional image through Gram angular field combination, and then input into the image modality feature extraction network of the feature extraction unit.

[0067] Step 4.3: The temporal modality feature extraction network and the image modality feature extraction network of the feature extraction unit respectively extract features from the data they receive, obtaining temporal features and image features;

[0068] Step 4.4: The attention feature fusion module AFF performs a fusion operation on the temporal features and the image features to obtain the fused features;

[0069] Step 4.5: The classifier flattens the fused features, and then through the fully connected layer and the Softmax function, obtains the final classification result, that is, the probabilities of the 11 modulated signals to be classified belonging to each category.

[0070] The effects of the present invention will be further described below in conjunction with simulation experiments.

[0071] 1. Simulation conditions:

[0072] For the simulation experiments conducted in the present invention, the detailed parameters of the experimental environment and the data set used are shown in the following table respectively:

[0073] Table 1: Software and Hardware Environment of the Simulation Experiment of the Present Invention

[0074]

[0075] Table 2: Detailed Parameters of the Dataset Used in the Present Invention

[0076]

[0077] 2. Simulation Content:

[0078] Using the dataset given in the simulation conditions, set the number of iteration rounds to 80, the number of batch samples to 128, and the initial learning rate to 0.001 for training; and adopt a dynamic learning rate adjustment strategy to reduce the learning rate to 1 / 10 of the original every 30 rounds to accelerate model convergence.

[0079] 3. Simulation Results:

[0080] The confusion matrix of the present invention at a signal-to-noise ratio of 16 dB is as Figure 5 shown. Observing Figure 5 it can be seen that the classification accuracies of QAM16 and QAM64 are 86% and 87% respectively, and the confusion problem between the two has been solved.

[0081] Name the method of the present invention Wave_MFF, and conduct a comparative experiment with the ResNet, CLDNN, DenseNet, and Inception networks in the prior art. The modulation classification accuracies of different network models are as Figure 6 shown. From Figure 6It can be seen that the classification level of the present invention at each signal-to-noise ratio is significantly higher than that of the other four models, and its peak correct rate is 5.88% more than that of the second-highest ResNet. In particular, at low signal-to-noise ratios from -6dB to 0dB, since the present invention fully considers the complementarity between different modalities and effectively adopts two denoising methods to obtain a more significant and pure feature expression of the modulation signal, its classification level far leads that of other models. At -6dB, it is improved by 7.71% compared to the second-highest CLDNN; at -4dB, it is 8.87% higher than the second-highest CLDNN; at -2dB, it leads the second-highest ResNet model by 8.07%; at 0dB, it is increased by 6.28% compared to the ResNet network. In addition, at -6dB and -4dB, the classification performance of the CLDNN network is the best among the four comparison models. This network combining CNN and LSTM overcomes the limitations of feature extraction of a single model architecture at low signal-to-noise ratios and provides superior performance for the classification of time series data. In a high signal-to-noise ratio environment above 0dB, the classification performance of the present invention is still the best. Its classification correct rate remains at 88% and above, and can reach up to 92.52%. Among the other four comparison models, the best classification performance is shown by ResNet. It adopts a residual architecture to effectively increase the network depth while avoiding the problem of decreasing correct rate. Its classification correct rate remains above 82% and the classification peak can reach 86.64%.

[0082] The above simulation analysis proves the correctness and effectiveness of the method proposed by the present invention.

[0083] The parts not described in detail in the present invention belong to the common general knowledge of those skilled in the art.

[0084] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Obviously, for professionals in the field, after understanding the content and principle of the present invention, various modifications and changes in form and details may be made without departing from the principle and structure of the present invention. However, these modifications and changes based on the idea of the present invention are still within the protection scope of the claims of the present invention.

Claims

1. An automatic modulation classification method based on wavelet transform and multi-modal feature fusion, characterized in that It includes the following steps: (1) Obtain the original I / Q data in the dataset RML2016.10A and divide it into a training set and a test set; (2) Construct a multi-modal feature fusion model: (2.1) Build a temporal modal feature extraction network including three convolutional layers, two Convolutional Block Attention Modules (CBAM) and two Bidirectional Long Short-Term Memory (Bi-LSTM) networks. After each convolutional layer, a batch normalization layer and a Rectified Linear Unit (ReLU) activation layer are connected. A CBAM module is connected after the first and the second convolutional layers respectively, and two Bi-LSTMs are used after the third convolutional layer; (2.2) In the original deep residual shrinkage network, replace the pooling layer and the strided convolutional layer with the Discrete Wavelet Transform (DWT) to obtain an image modal feature extraction network; (2.3) Combine the temporal modal feature extraction network and the image modal feature extraction network to form a feature extraction unit; Design an input end for receiving external data, and a preprocessing module for preprocessing the data received by the input end and sending the preprocessed data into the feature extraction unit; After the feature extraction unit, an Attention Feature Fusion Module (AFF) and a classifier are connected in sequence to obtain a multi-modal feature fusion model; (3) Use the training set data to train the multi-modal feature fusion model constructed in step (2) to obtain a trained model; (4) Input the data in the test set into the trained model to realize the automatic modulation classification of the signal to be measured.

2. The method according to claim 1, wherein: For the training set and the test set in step (1), the division method is as follows: Select the data from -6dB to 18dB in the dataset RML2016.10A, divide it according to the allocation ratio of 80% training set and 20% test set, and randomly shuffle the training set data.

3. The method according to claim 1, wherein: For the temporal modal feature extraction network described in step (2.1), the number of convolutional kernels used in the three convolutional layers are 128, 256 and 512 respectively, with a size of 1×3, zero padding and a stride of 1; the input feature dimension and the hidden layer state dimension of the Bi-LSTM layer are both set to 128.

4. The method according to claim 1, characterized in that: For the image modal feature extraction network described in step (2.2), specifically, the noisy data X is decomposed by DWT into a low-frequency component and three high-frequency components, and finally only the low-frequency component containing useful information is retained, and other high-frequency components are removed; The implementation process is as follows: The forward propagation process of the 2D DWT in the image modal feature extraction network: X ll = LXL T , X lh = HXL T , X hl = LXH T , X hh = HXH T , where L and H are the matrix vectors of the low-pass and high-pass filters of the orthogonal wavelet, respectively; X represents the noisy data, and X ll represents the low-frequency component containing the main information of X, and X lh , X hl , X hh are all high-frequency components, which respectively contain the noise detail information of the horizontal, vertical, and diagonal directions of X; The backward propagation process of the 2D DWT in the image modal feature extraction network: Among them, G represents the backward propagation output of the layer after the 2D DWT.

5. The method according to claim 1, characterized in that: The preprocessing described in step (2.3) is specifically to perform wavelet threshold denoising on the original data by setting the wavelet basis function as db8, the wavelet decomposition level as 3, the threshold function as a compromise function between hard and soft thresholds, and the threshold as 0.05 to obtain the denoised signal.

6. The method according to claim 1, wherein: The training in step (3) is completed by adopting a dynamic learning rate adjustment strategy after setting the number of iterations, the number of samples in each batch, the initial learning rate, the optimizer and the loss function. Specifically, the learning rate is reduced to 1 / 10 of the original every preset number of rounds.

7. The method according to claim 1, wherein: The automatic modulation classification of the signal to be measured in step (4) is implemented as follows: (4.1) Send the original I / Q data to be measured to the preprocessing module of the model through the input end; (4.2) After receiving the data, the preprocessing module performs the following operations: (4.2.1) Use wavelet threshold denoising technology to process the original input signal, that is, wavelet denoising; and convert the denoised data into I / Q and A / P forms, and then input it into the time series modal feature extraction network of the feature extraction unit; (4.2.2) Use GAF coding to convert the original I / Q data into a two-dimensional image, and input it into the image modal feature extraction network of the feature extraction unit; (4.3) The time series modal feature extraction network and the image modal feature extraction network of the feature extraction unit respectively extract features from the received data to obtain time series features and image features; (4.4) The attention feature fusion module AFF performs a fusion operation on the time series features and the image features to obtain the fused features; (4.5) The classifier flattens the fused features, and then passes through the fully connected layer and the Softmax function to obtain the final classification result.

8. The method according to claim 7, wherein: In step (4.2.1), the conversion of the denoised data into I / Q and A / P forms is implemented as follows: Convert the denoised signal into in-phase and quadrature components I / Q according to the following formula to obtain the I / Q components x of the m-th group of data m I / Q : where, x m I is the in-phase component of the m-th group of data in the signal, and x m Q is the quadrature component of the m-th group of data in the signal, (·) T represents the transpose operation; (x m I ) T and (x m Q ) T ∈R N , x m I / Q ∈R 2×N , and N is the total number of samples; Convert the denoised signal into amplitude and phase components A / P according to the following formula to obtain the A / P components x of the m-th group of data m A / P : where x m A is the amplitude component of the m-th group of data in the signal, and x m P is the phase component of the m-th group of data in the signal; (x m A ) T and (x m P ) T ∈R N , x m A / P ∈R 2×N ; The conversion expressions of the amplitude component and the phase component are as follows: where r m I [n] and r m Q [n] are the in-phase component and the quadrature component of the nth sample of r m respectively, and r m represents the mth group of data vectors in the signal.

9. The method according to claim 7, wherein: In step (4.2.2), using GAF coding to convert the original I / Q data into a two-dimensional image specifically means that the I-channel data and the Q-channel data of the original data set are respectively converted into two-dimensional images with a size of 64×64 through Gram angle field combination.

10. The method according to claim 7, wherein: The final classification result in step (4.5) is specifically the probability that 11 modulation signals to be classified belong to each category.

Images