Communication signal automatic modulation recognition method and system based on symplectic geometry modal decomposition

Abstract

The application provides a communication signal automatic modulation recognition method based on symplectic geometry modal decomposition, belongs to the field of signal automatic modulation recognition, and carries out phase space reconstruction on a preprocessed modulation signal, obtains a trajectory matrix and constructs a covariance matrix, decomposes the covariance matrix, obtains an eigenvector matrix and an eigenvalue, constructs and converts a reconstruction matrix, and obtains a dynamic modal component; the dynamic modal component with an eigenvalue greater than a set value is taken as a main modal, the dynamic modal component with an eigenvalue less than the set value is superimposed to form a residual signal, a multi-channel time domain modal feature matrix is constructed, and a spectrum diagram is generated; the multi-channel time domain modal feature matrix and the spectrum diagram are input into a trained SGFN model, the multi-channel time domain modal feature matrix enters a time domain branch, the spectrum diagram enters a frequency domain branch, a time domain eigenvector and a frequency domain eigenvector are weightedly fused, classification is carried out, and a modulation type is obtained; and a system is also provided; and the modulation recognition accuracy under low signal-to-noise ratio and small sample conditions is improved.

Description

Technical Field

[0001] This invention relates to the field of automatic modulation and identification technology for communication signals, and in particular to a method and system for automatic modulation and identification of communication signals based on symplectic geometric mode decomposition. Background Technology

[0002] Automatic Modulation Classification (AMC) is a key technology in cognitive radio and intelligent communications, applicable to scenarios such as spectrum monitoring, interference detection, and non-cooperative communication identification. Under ideal conditions, deep learning-based AMC methods (such as Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) have achieved excellent performance on publicly available datasets. However, in real-world complex electromagnetic environments, factors such as channel fading, co-channel interference, and hardware mismatch can significantly reduce the signal-to-noise ratio (SNR) of the received signal. Furthermore, acquiring large-scale, high-quality labeled samples is costly, and the available training data for many IoT applications is very limited. Under conditions of low SNR and small sample size, the recognition performance of existing deep network models degrades significantly, exhibiting insufficient generalization ability and failing to meet practical needs.

[0003] To improve feature representation capabilities, some studies have introduced adaptive decomposition and denoising techniques before signal feature extraction. For example, Empirical Mode Decomposition (EMD) and Variational Mode Decomposition (VMD) can decompose the original I / Q baseband signal into several intrinsic mode components (IMFs), which are then combined with traditional classifiers or deep networks for modulation classification. However, EMD is susceptible to mode aliasing and endpoint effects, and the decomposition results are sensitive to noise. VMD requires pre-setting the number of mode components and penalty parameters; improper parameter selection can reduce the decomposition effect, and its robustness is limited in low signal-to-noise ratio and small sample situations. Wavelet transform (WT) is also commonly used to extract video features. For example, continuous wavelet transform (CWT) can be used to convert the signal into a time-frequency image, and then a convolutional neural network can be used to achieve end-to-end modulation recognition. However, the choice of wavelet basis function type and scale parameter has a significant impact on recognition performance, and a fixed time-frequency resolution is insufficient to fully characterize the nonlinear dynamic changes of the modulated signal. In the prior art, the Chinese invention patent application CN118348600A, entitled "Method and System for Processing Weak Magnetic Signals of Buried Targets Based on Symplectic Geometric Mode Decomposition", reconstructs weak magnetic anomaly signals based on an improved symplectic geometric mode decomposition method through cosine similarity and information entropy, so as to improve the accuracy of weak magnetic anomaly signal detection.

[0004] On the other hand, the structural complexity of deep learning models also affects their practicality in scenarios with small sample sizes and limited resources. Deeper and wider networks can achieve higher accuracy when there are sufficient training samples, but the large number of parameters not only relies on a large amount of labeled data to support training, but also consumes high computational and storage resources during inference, which is not conducive to real-time deployment on edge devices. If reasonable physical prior knowledge or structured features can be introduced and combined with a moderately simplified network, better robustness can be achieved under small sample conditions. Therefore, how to organically integrate physically guided adaptive decomposition methods with time-frequency feature modeling and lightweight deep networks while controlling model complexity, and achieve stable and reliable automatic modulation recognition under low signal-to-noise ratio and small sample conditions, has become an urgent problem to be solved. Summary of the Invention

[0005] The technical problem to be solved by this invention is: how to improve the modulation recognition accuracy and robustness of signals under low signal-to-noise ratio and small sample conditions while controlling the complexity of the model.

[0006] This invention solves the above-mentioned technical problems through the following technical solution: an automatic modulation and identification method for communication signals based on symplectic geometric mode decomposition, comprising:

[0007] The preprocessed modulated signal is reconstructed in phase space to obtain the trajectory matrix and construct the covariance matrix. The covariance matrix is ​​decomposed using the QR decomposition method to obtain the eigenvector matrix and eigenvalues. The eigenvector matrix and trajectory matrix are used to construct the reconstruction matrix. The reconstruction matrix is ​​then transformed to obtain the dynamic modal components.

[0008] The dynamic modal components are sorted based on eigenvalues. Dynamic modal components with eigenvalues ​​greater than a set value are taken as the main modes, and dynamic modal components with eigenvalues ​​less than the set value are superimposed to form a residual signal. The main modes are stacked alternately by channel and then stacked with the residual signal to construct a multi-channel time-domain modal feature matrix. The reconstruction matrix corresponding to the main modes is subjected to a fast Fourier transform to generate a spectrum.

[0009] The multi-channel time-domain modal feature matrix and spectrogram are input into the trained SGFN model. The trained SGFN model includes a lightweight time-domain branch and a frequency-domain branch. The multi-channel time-domain modal feature matrix is ​​input into the time-domain branch and outputs a time-domain feature vector. The spectrogram is input into the frequency-domain branch and outputs a frequency-domain feature vector. The time-domain feature vector and the frequency-domain feature vector are weighted and fused. The fused feature vector is then classified to obtain the modulation type.

[0010] This invention performs symplectic geometric mode decomposition on the preprocessed modulation signal to extract several physically meaningful dynamic mode components. These dynamic mode components are then selected based on their eigenvalues. The selected main modes are stacked alternately by channel and then stacked with the residual signal to construct a multi-channel time-domain modal feature matrix. The SGFN model is a dual-branch network, with both branches being lightweight residual convolutional neural networks. These branches share a consistent structure and network module design to control model complexity. The time-domain branch and frequency-domain branch receive the time-domain modal feature matrix and the spectrogram as input, respectively, and extract their multi-level feature representations through multi-layer convolution and residual units. This dual-branch network structure fully leverages the complementary information of the modulation signal in terms of temporal evolution and spectral distribution. Compared to identification methods that utilize only a single time-domain or frequency-domain feature, this significantly improves the modulation recognition accuracy and robustness under low signal-to-noise ratio and small sample conditions.

[0011] Preferably, the dynamic modal components are:

[0012]

[0013] in, For the first One dynamic modal component, , , for The elements in , , For the embedding dimension, , The signal length of the original signal. For the delay time, if , ,otherwise .

[0014] Preferably, the process of sorting the dynamic modal components based on eigenvalues ​​includes:

[0015] The I and Q components of each dynamic modal component are extracted separately. The I and Q components of the dynamic modal component are sorted according to the magnitude of the corresponding eigenvalues. The I and Q components of each dynamic modal component are arranged according to the modal number and aligned according to the time sampling points.

[0016] Preferably, the primary mode is:

[0017]

[0018] in, , These are the I-component and Q-component of each dynamic modal component, respectively. For modal index, The time sampling point number, For setting value, This represents the total number of time sampling points.

[0019] Preferably, the residual signal includes residual signals of I-components and Q-components. The I-components of dynamic mode components with eigenvalues ​​less than a set value are superimposed to form the I-component residual signal, and the Q-components of dynamic mode components with eigenvalues ​​less than a set value are superimposed to form the Q-component residual signal. Through QR decomposition of the covariance matrix and eigenvalue sorting, the main dynamic modes are adaptively selected to construct the time-domain matrix and spectrum, eliminating the need for manually setting empirical parameters such as energy thresholds, highlighting the main structural components of the signal, and weakening the influence of noise.

[0020] Preferably, the temporal branch and the frequency branch each include an input module, a lightweight ResNet8 network, and a global average pooling module connected in sequence. The multi-channel temporal modality feature matrix enters the temporal branch, and the input module standardizes and aligns the size of the multi-channel temporal modality feature matrix to obtain the output features. Output features Feature extraction is performed using a lightweight ResNet8 network to obtain the output features. The global average pooling module affects the output features. Perform global mean calculation to obtain output features. Output features The feature vector is obtained by transforming it into a fixed-length one-dimensional vector through a feature flattening layer. The spectrogram enters the frequency domain branch; the input module normalizes and aligns the spectrogram to obtain the output features. Output features Feature extraction is performed using a lightweight ResNet8 network to obtain the output features. The global average pooling module affects the output features. Perform global mean calculation to obtain output features. Output features The frequency domain feature vector is obtained by converting the vector into a fixed-length one-dimensional vector through a feature flattening layer. Modal features are modeled complementaryly using two parallel branches in the time and frequency domains.

[0021] Preferably, the lightweight ResNet8 network includes a 1×3 convolutional layer, residual structure unit L0, residual structure unit M0, residual structure unit N0, an intra-branch global average pooling layer, and a feature flattening layer connected in sequence. The residual structure unit L0, residual structure unit M0, and residual structure unit N0 each include a first residual block and a second residual block connected in series. The main branches of the first residual block and the second residual block each include a first 1×3 convolutional layer and a second 1×3 convolutional layer connected in series. The first 1×3 convolutional layer is followed by a batch normalization layer and a GELU activation function connected in sequence. The second 1×3 convolutional layer is followed by a batch normalization layer. The shortcut branch of the first residual block includes a 1×1 convolutional layer followed by a batch normalization layer. The outputs of the main branch and the shortcut branch are added element-wise.

[0022] After the three-stage residual structures are stacked in sequence, the receptive field can be gradually expanded and multi-level time-frequency features can be extracted, while keeping the network parameter scale small, which is convenient for deployment in resource-constrained scenarios.

[0023] Preferably, the process of weighted fusion of time-domain feature vectors and frequency-domain feature vectors includes:

[0024] For time-domain feature vectors and frequency domain eigenvectors Feature concatenation is performed along the channel dimension to obtain a joint feature vector;

[0025] The joint feature vector is input into a two-layer fully connected network with a dimensionality reduction scaling factor and a non-linear activation function to generate a weight coefficient vector with the same number of channels.

[0026] Apply the weight coefficient vector to the time-domain feature vector. and frequency domain eigenvectors Adaptive recalibration is performed on information from different rows to obtain the fused feature vector.

[0027] After extracting the deep features of the two branches, this invention introduces a channel attention mechanism to adaptively weight and fuse the time-domain and frequency-domain features, thereby highlighting key modulation feature information and suppressing redundant noise interference.

[0028] Preferably, the training process of the SGFN model includes:

[0029] The preprocessed modulated signal is reconstructed in phase space to obtain the trajectory matrix and construct the covariance matrix. The covariance matrix is ​​decomposed to obtain the eigenvector matrix and eigenvalues. The eigenvector matrix and trajectory matrix are used to construct the reconstruction matrix. The reconstruction matrix is ​​then transformed to obtain the dynamic modal components.

[0030] The dynamic modal components are sorted based on eigenvalues. Dynamic modal components with eigenvalues ​​greater than a set value are taken as the main modes, and dynamic modal components with eigenvalues ​​less than the set value are superimposed to form a residual signal. The main modes are stacked alternately by channel and then stacked with the residual signal to construct a multi-channel time-domain modal feature matrix. The reconstruction matrix corresponding to the main modes is subjected to a fast Fourier transform to generate a spectrum.

[0031] A dataset was constructed based on multi-channel temporal modal feature matrices, spectrograms, and modulation labels, and the dataset was divided into a training set and a validation set.

[0032] The training set is input into the SGFN model, the prediction results are output, the loss value of the prediction results and the modulation tag is calculated, and the parameters of the SGFN model are updated through the backpropagation algorithm to obtain the pre-trained SGFN model.

[0033] The validation set is input into the pre-trained SGFN model for training until the preset convergence condition is met, thus obtaining the trained SGFN model.

[0034] This invention also provides an automatic modulation and identification system for communication signals based on symplectic geometric mode decomposition, comprising:

[0035] The symplectic geometric mode decomposition module is used to reconstruct the phase space of the preprocessed modulation signal, obtain the trajectory matrix and construct the covariance matrix. The covariance matrix is ​​decomposed using the QR decomposition method to obtain the eigenvector matrix and eigenvalues. The reconstruction matrix is ​​constructed using the eigenvector matrix and trajectory matrix. The reconstruction matrix is ​​then transformed to obtain the dynamic mode components.

[0036] The dynamic mode construction module is used to sort the dynamic mode components based on eigenvalues. Dynamic mode components with eigenvalues ​​greater than a set value are taken as the main modes, and dynamic mode components with eigenvalues ​​less than the set value are superimposed to form a residual signal. The main modes are stacked alternately by channel and then stacked with the residual signal to construct a multi-channel time-domain mode feature matrix. The reconstruction matrix corresponding to the main modes is subjected to a fast Fourier transform to generate a spectrum.

[0037] The identification module is used to input the multi-channel time-domain modal feature matrix and spectrogram into the trained SGFN model. The trained SGFN model includes a lightweight time-domain branch and a frequency-domain branch. The multi-channel time-domain modal feature matrix is ​​input into the time-domain branch and outputs a time-domain feature vector. The spectrogram is input into the frequency-domain branch and outputs a frequency-domain feature vector. The time-domain feature vector and the frequency-domain feature vector are weighted and fused. The fused feature vector is then classified to obtain the modulation type.

[0038] The advantages provided by this invention are:

[0039] 1. This invention decomposes the modulated signal into multiple modal components with independent dynamic characteristics using SGMD, avoiding spectral aliasing and mode mixing problems. It combines the magnitude of eigenvalues ​​after QR decomposition to select the dominant mode and construct time-domain features, while simultaneously constructing a frequency-domain spectrum using Fast Fourier Transform, preserving the main physical information of the signal without relying on parameter adjustments. Compared to traditional methods, this invention more effectively highlights useful structural components, enhances the expressive power of modulation features, and provides more discriminative input features for subsequent neural network recognition.

[0040] 2. This invention combines physically interpretable dynamic modes obtained from symplectic geometric mode decomposition with a lightweight dual-branch residual network. On the one hand, by QR decomposition of the covariance matrix and eigenvalue sorting, it adaptively selects the main dynamic modes to construct the time-domain matrix and spectrum, eliminating the need for manually setting empirical parameters such as energy thresholds, highlighting the main structural components of the signal and weakening the influence of noise. On the other hand, it performs complementary modeling of modal features through two parallel branches in the time and frequency domains, and introduces an SE channel attention mechanism at the feature level to achieve adaptive weighted fusion, which can significantly improve the robustness and accuracy of modulation recognition under different signal-to-noise ratios and small sample conditions. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the automatic modulation and identification method for communication signals based on symplectic geometric mode decomposition provided in Embodiment 1 of the present invention.

[0042] Figure 2 This is a flowchart illustrating the process of obtaining dynamic mode components in the automatic modulation and identification method for communication signals based on symplectic geometric mode decomposition provided in Embodiment 1 of the present invention.

[0043] Figure 3 This is an architecture diagram of the residual structure unit in the automatic modulation and identification system for communication signals based on symplectic geometric mode decomposition provided in Embodiment 2 of the present invention;

[0044] Figure 4 A comparison of the recognition accuracy of the automatic modulation and recognition method for communication signals based on symplectic geometric mode decomposition provided in Embodiment 1 of the present invention with existing decomposition methods under various signal-to-noise ratio conditions;

[0045] Figure 5 The graph shows a comparison of the recognition accuracy of the automatic modulation and recognition method for communication signals based on symplectic geometric mode decomposition provided in Embodiment 1 of the present invention with that of single-branch networks (SGFN-T, SGFN-F, SGFN) under different signal-to-noise ratio conditions.

[0046] Figure 6 The graph shows the recognition accuracy of the automatic modulation and recognition method for communication signals based on symplectic geometric mode decomposition provided in Embodiment 1 of the present invention under different training sample ratios.

[0047] Figure 7 The set values ​​for the automatic modulation and identification method for communication signals based on symplectic geometric mode decomposition provided in Embodiment 1 of the present invention in different dynamic modes. K The graph below shows the change in recognition accuracy.

[0048] Figures 8(a) to 8(f) are confusion matrix diagrams of the modulation signal classification results of the automatic modulation identification method for communication signals based on symplectic geometric mode decomposition provided in Embodiment 1 of the present invention under different typical signal-to-noise ratios and training sample ratios. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments and with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0050] Example 1

[0051] like Figure 1 As shown, this embodiment provides an automatic modulation identification method for communication signals based on Symptotic geometry mode decomposition (SGMD), including the following steps:

[0052] Step 1: Acquire the modulation signal to be identified and convert it into I / Q two-channel timing data of complex baseband. For example, downconvert the received RF signal to obtain the in-phase component I(t) and the quadrature component Q(t), and discretely sample them to form digital sequences, namely the in-phase component sequence and the quadrature component sequence. Preprocess the in-phase component sequence and the quadrature component sequence separately for each channel. The preprocessing method is DC bias removal and amplitude normalization to eliminate the difference in amplitude dimensions, and obtain the preprocessed modulation signal. The two preprocessed modulation signals can be represented as a dual-channel sequence matrix of length N, which is used to prepare for subsequent decomposition and feature extraction.

[0053] Performing symplectic geometric mode decomposition on the preprocessed modulation signal yields several dynamic mode components. , , ... , Indicates the first One dynamic modal component, , This represents the total number of dynamic modal components. See also: Figure 2The specific process of performing symplectic geometric mode decomposition on the preprocessed modulation signal includes:

[0054] Step 1.1, Phase Space Reconstruction: According to Takens' embedding theorem, the preprocessed modulation signal is reconstructed in phase space to obtain the trajectory matrix. X Trajectory matrix X The expression is:

[0055]

[0056] The original signal is a time series signal. , n For signal length, τ To delay time, take τ =1, m = n -( d -1) τ Embedded dimension d The selection method is as follows: determine the original signal x The frequency at which the power spectral density is at its maximum ,like Less than 0.001 ,but d = n / 3, otherwise, d =1.2 ( / ).

[0057] Step 1.2: Based on the trajectory matrix X Constructing the covariance matrix A : .

[0058] Step 1.3: Decompose the matrix using the QR decomposition method. We obtain the eigenvector matrix Q and eigenvalues. Based on the principle of symplectic geometric similarity transformation—preserving structural properties—the eigenvector matrix... Q It preserves the essential characteristics of the original signal.

[0059] Step 1.4: Construct a reconstruction matrix using the eigenvector matrix Q and the trajectory matrix X. The reconstructed matrix is ​​the initial single-component reconstructed matrix. for:

[0060]

[0061] in, .

[0062] Step 1.5: Reconstruct the matrix by diagonal averaging. Perform transformation and reconstruct the matrix. Corresponding to a one-dimensional single-component signal ,available d A length of n One-dimensional time series, i.e., dynamic modal components , ... . d The original signal is composed of symplectic geometric mode components. The initial single-component reconstruction matrix is ​​then obtained by diagonal averaging. The conversion method is as follows:

[0063]

[0064] in, For the first One dynamic modal component, , , for The elements in , , For the embedding dimension, , The signal length of the original signal. For the delay time, if , ,otherwise .

[0065] This invention decomposes the modulated signal into multiple modal components with independent dynamic characteristics using SGMD, avoiding spectral aliasing and mode mixing problems. It combines the magnitude of eigenvalues ​​after QR decomposition to select the dominant mode and construct time-domain features, while simultaneously constructing a frequency-domain spectrum using Fast Fourier Transform, preserving the main physical information of the signal without relying on parameter adjustments. Compared to traditional methods, this approach more effectively highlights useful structural components, enhances the expressive power of modulation features, and provides more discriminative input features for subsequent neural network recognition.

[0066] Step 2: After applying SGMD to the modulated signal, construct the time-domain dynamic modes from the decomposed components: Sort the dynamic mode components based on eigenvalues. The sorting method is as follows: Extract the I-component of each dynamic mode component. and Q component The I component of the dynamic modal component is determined by the magnitude of the eigenvalues ​​corresponding to the dynamic modal components. and Q component Sort the I-components of each dynamic modal component. and Q component Arranged according to modal number combination and aligned according to time sampling points.

[0067] The dynamic modal components with eigenvalues ​​greater than a set value are taken as the principal modes. The principal modes are:

[0068]

[0069] in, , These are the I-component and Q-component of each dynamic modal component, respectively. For modal index, The time sampling point number, For setting value, This represents the total number of time sampling points.

[0070] The residual signal is formed by the superposition of dynamic modal components with eigenvalues ​​less than a set value. The residual signal includes the residual signal of the I component. residual signal of Q component The residual signal of the I component is formed by superimposing the I components of the dynamic modal components whose eigenvalues ​​are less than a set value. The residual signal of the Q component is formed by superimposing the Q components of the dynamic modal components whose eigenvalues ​​are less than a set value. The primary mode and residual signals together form the original mode matrix M, which can be expressed as:

[0071]

[0072] The primary modes are stacked alternately by channel and then stacked with the residual signal. Using the mode number as an index, the I and Q components of the same mode are considered as a group and arranged sequentially along the channel dimension in the order of "I first, then Q". This process is then repeated in ascending order of mode number, thus forming a multi-channel time-domain modal feature matrix composed of multiple alternating groups of I / Q mode components. A Fast Fourier Transform is performed on the reconstructed matrices corresponding to the primary modes to generate a spectrogram.

[0073] In step 1 of this invention, after the modulated signal undergoes SGMD, multiple signal components at various scales are obtained. Each component represents a different dynamic mode of the signal, encompassing multiple frequency components and temporal features, and each mode represents a dynamic subsystem of the original signal. In step 2, the obtained dynamic mode components are screened. Based on the magnitude of the eigenvalues ​​obtained from the QR decomposition of the SGMD covariance matrix, the dynamic mode components are sorted, and several mode components with larger eigenvalues ​​are selected as the principal modes for subsequent feature construction, without the need for preset energy or correlation thresholds. The remaining mode components are then superimposed to form the residual signal. and Then, the selected modal components of the I and Q paths are alternately stacked by channel and then stacked with the residual signal to form a multi-channel temporal modal feature matrix, which serves as the input to the branches of the temporal convolutional network. This temporal feature matrix integrates the main modal information and residual components of the original signal, and can retain sufficient signal features while reducing noise interference.

[0074] Step 3: Input the multi-channel time-domain modal feature matrix and spectrogram into the trained Symptotic Geometry Fusion Network (SGFN) model. The trained SGFN model includes a lightweight time-domain branch and a frequency-domain branch. The multi-channel time-domain modal feature matrix is ​​input into the time-domain branch and outputs a time-domain feature vector. The spectrogram is input into the frequency-domain branch and outputs a frequency-domain feature vector. The time-domain feature vector and the frequency-domain feature vector are weighted and fused. The fused feature vector is then classified to obtain the modulation type.

[0075] The time-domain branch and frequency-domain branch each consist of a sequentially connected input module, a lightweight ResNet8 network, and a global average pooling module. The multi-channel time-domain modal feature matrix enters the time-domain branch, which receives two types of features obtained from SGMD decomposition and modality construction: one type has a number of channels... A multi-channel temporal modal feature matrix of length L, one type having the number of channels L. The input module standardizes and aligns the multi-channel temporal modal feature matrix to obtain the output feature. Output features Feature extraction is performed using a lightweight ResNet8 network to obtain the output features. The global average pooling module affects the output features. The output features are obtained by globally averaging across all channels. Output features The feature vector is obtained by transforming it into a fixed-length one-dimensional vector through a feature flattening layer. The spectrogram enters the frequency domain branch; the input module normalizes and aligns the spectrogram to obtain the output features. Output features Feature extraction is performed using a lightweight ResNet8 network to obtain the output features. The global average pooling module affects the output features. The output features are obtained by globally averaging across all channels. Output features The frequency domain feature vector is obtained by converting the vector into a fixed-length one-dimensional vector through a feature flattening layer. .

[0076] See also Figure 1The lightweight ResNet8 network structures for both branches are identical. The lightweight ResNet8 network includes sequentially connected 1×3 convolutional layers, residual structure units L0, M0, and N0, intra-branch global average pooling layers, and feature flattening layers. The 1×3 convolutional layers are used to extract local patterns along the time or frequency axis, and the stride is set as needed in the first residual block of each stage. Downsampling is completed. When the stride is 2, the shortcut path of this branch linearly projects the input through a 1×1 convolutional layer and a batch normalization layer, so that the shortcut output is consistent with the main branch output in terms of length and number of channels.

[0077] See Figure 3 The residual structure units L0, M0, and N0 each comprise a first residual block and a second residual block, respectively, stacked in series. The main branches of the first and second residual blocks each comprise a first 1×3 convolutional layer and a second 1×3 convolutional layer, respectively. The first 1×3 convolutional layer is followed by a batch normalization layer and a GELU activation function to enhance nonlinear expressiveness. The second 1×3 convolutional layer is followed only by a batch normalization layer to stabilize gradients and suppress internal covariate shifts. The shortcut branch of the first residual block comprises a 1×1 convolutional layer followed by a batch normalization layer. The outputs of the main branch and the shortcut branch are added element-wise in the addition module, and then activated by GELU to obtain the output of the residual block. The three-stage residual structure composed of residual structure units L0, M0, and N0, stacked sequentially, can gradually expand the receptive field and extract multi-level time-frequency features while maintaining a small network parameter size, facilitating deployment in resource-constrained scenarios.

[0078] The weighted fusion of time-domain and frequency-domain feature vectors is completed in the channel fusion module. The channel fusion module adopts an SE (squeeze-and-excitation) channel attention structure, including a cascaded feature concatenation unit, a channel compression unit, and a channel recalibration unit. The specific process of weighted fusion includes:

[0079] Step 3.1.1: Process the time-domain feature vectors and frequency domain eigenvectors Feature concatenation is performed along the channel dimension to obtain a joint feature vector;

[0080] Step 3.1.2: Input the joint feature vector into a two-layer fully connected network with a dimensionality reduction scaling factor and a non-linear activation function to generate a weight coefficient vector with the same number of channels;

[0081] Step 3.1.3: Apply the weight coefficient vector to the time-domain feature vector. and frequency domain eigenvectors Adaptive recalibration is performed on different rows of information to obtain fused feature vectors, highlighting channels that are more critical for modulation classification and suppressing redundant and noisy channels.

[0082] The training process of the SGFN model includes:

[0083] Step 3.2.1: Perform phase space reconstruction on the preprocessed modulation signal to obtain the trajectory matrix and construct the covariance matrix. Decompose the covariance matrix to obtain the eigenvector matrix and eigenvalues. Use the eigenvector matrix and trajectory matrix to construct the reconstruction matrix. Transform the reconstruction matrix to obtain the dynamic modal components.

[0084] Step 3.2.2: Sort the dynamic modal components based on eigenvalues. Take the dynamic modal components with eigenvalues ​​greater than the set value as the main modes and the dynamic modal components with eigenvalues ​​less than the set value as the residual signal. Stack the main modes alternately by channel and then stack them with the residual signal to construct a multi-channel time-domain modal feature matrix. Perform a fast Fourier transform on the reconstruction matrix corresponding to the main modes to generate a spectrum.

[0085] Step 3.2.3: Construct a dataset based on the multi-channel time-domain modal feature matrix, spectrogram, and modulation label, and divide the dataset into a training set and a validation set;

[0086] Step 3.2.4: Input the training set into the SGFN model, output the prediction results, calculate the loss value between the prediction results and the actual modulation tags, update the parameters of the SGFN model through the backpropagation algorithm, and obtain the pre-trained SGFN model.

[0087] Step 3.2.5: Input the validation set into the pre-trained SGFN model for training until the preset convergence condition is met, and obtain the trained SGFN model.

[0088] This invention employs a fully connected classification module to make classification decisions on the fused feature vectors. The fully connected classification module includes a linear layer that maps the feature vectors recalibrated by the channel fusion module to N classes of output, where N is the number of classes of the target modulation type. Subsequently, the predicted probability of each modulation type is obtained through the Softmax function, and the class corresponding to the highest probability is output as the final recognition result.

[0089] This invention proposes an automatic modulation identification method based on a symplectic geometric mode decomposition (SGMD) fusion structure of physical guided mode decomposition and time-frequency dual-branch residual network. First, the modulated signal is reconstructed in phase space and mode extracted using symplectic SGMD, obtaining modal components with clear dynamic meaning under physical constraints. Then, the main dynamic modes are adaptively selected based on the eigenvalues ​​obtained from the QR decomposition of the covariance matrix, constructing a time-domain modal feature matrix and the corresponding spectrum, and feeding them into the structurally consistent lightweight time-domain / frequency-domain residual network branches. The weighted fusion and classification of time-frequency features are achieved through the SE channel attention module.

[0090] This invention feeds the time-domain mode matrix and spectrogram obtained from SGMD decomposition into structurally consistent time-domain and frequency-domain branches, respectively. Multi-level features are extracted using a lightweight ResNet8 network, and adaptive weighting and joint modeling of time-frequency features are achieved through an SE channel fusion module. Finally, a fully connected classification module outputs the modulation type. Compared to network structures that rely solely on single time-domain or frequency-domain features, this embodiment can fully exploit the complementary information of the modulation signal in terms of temporal evolution and spectral distribution, significantly improving the accuracy and robustness of automatic modulation identification under low signal-to-noise ratio and small sample conditions.

[0091] This invention performs phase space reconstruction and mode extraction on modulated signals based on SGMD. It selects the main dynamic mode components by utilizing the magnitude of eigenvalues ​​after QR decomposition, avoiding the subjectivity of manually setting thresholds in traditional methods. Furthermore, it significantly improves overall recognition performance while maintaining a lightweight structure by jointly inputting the selected physically interpretable mode features into time-domain and frequency-domain dual-branch residual networks for modeling. By constructing a physically interpretable mode feature matrix and reconstructing the signal spectrum, and inputting them into time-domain and frequency-domain neural network branches for parallel modeling, and introducing an SE channel attention mechanism to achieve adaptive feature fusion, the robustness and accuracy of modulation recognition are significantly improved, especially under low signal-to-noise ratio and small sample conditions, exhibiting stronger generalization ability.

[0092] Example 2

[0093] This embodiment provides an automatic modulation and identification system for communication signals based on symplectic geometric mode decomposition, including:

[0094] The symplectic geometric mode decomposition module is used to reconstruct the phase space of the preprocessed modulated signal, obtain the trajectory matrix, and construct the covariance matrix. The covariance matrix is ​​then decomposed using the QR decomposition method to obtain the eigenvector matrix and eigenvalues. The reconstructed matrix is ​​constructed using the eigenvector matrix and the trajectory matrix, and the reconstructed matrix is ​​transformed to obtain the dynamic mode components. The dynamic mode components are:

[0095]

[0096] in, For the first One dynamic modal component, , , for The elements in , , For the embedding dimension, , The signal length of the original signal. For the delay time, if , ,otherwise .

[0097] The dynamic mode construction module is used to sort the dynamic mode components based on eigenvalues. Dynamic mode components with eigenvalues ​​greater than a set value are taken as the main modes, and dynamic mode components with eigenvalues ​​less than the set value are superimposed to form residual signals. The main modes are stacked alternately by channel and then stacked with the residual signals to construct a multi-channel time-domain mode feature matrix. The reconstruction matrix corresponding to the main modes is subjected to fast Fourier transform to generate a spectrum.

[0098] The process of sorting the dynamic modal components based on eigenvalues ​​includes:

[0099] The I and Q components of each dynamic modal component are extracted separately. The I and Q components of the dynamic modal component are sorted according to the magnitude of the corresponding eigenvalues. The I and Q components of each dynamic modal component are arranged according to the modal number and aligned according to the time sampling points.

[0100] The main modes are:

[0101]

[0102] in, , These are the I-component and Q-component of each dynamic modal component, respectively. For modal index, The time sampling point number, For setting value, This represents the total number of time sampling points.

[0103] The residual signal includes the residual signal of the I component and the residual signal of the Q component. The residual signal of the I component is formed by superimposing the I components of the dynamic modal components whose eigenvalues ​​are less than the set value, and the residual signal of the Q component is formed by superimposing the Q components of the dynamic modal components whose eigenvalues ​​are less than the set value.

[0104] The identification module is used to input the multi-channel time-domain modal feature matrix and spectrogram into the trained SGFN model. The trained SGFN model includes a lightweight time-domain branch and a frequency-domain branch. The multi-channel time-domain modal feature matrix is ​​input into the time-domain branch and outputs a time-domain feature vector. The spectrogram is input into the frequency-domain branch and outputs a frequency-domain feature vector. The time-domain feature vector and the frequency-domain feature vector are weighted and fused. The fused feature vector is then classified to obtain the modulation type.

[0105] The temporal and frequency domain branches each consist of a sequentially connected input module, a lightweight ResNet8 network, and a global average pooling module. The multi-channel temporal modality feature matrix enters the temporal branch, where the input module standardizes and aligns the multi-channel temporal modality feature matrix to obtain the output features. Output features Feature extraction is performed using a lightweight ResNet8 network to obtain the output features. The global average pooling module affects the output features. Perform global mean calculation to obtain output features. Output features The feature vector is obtained by transforming it into a fixed-length one-dimensional vector through a feature flattening layer. The spectrogram enters the frequency domain branch; the input module normalizes and aligns the spectrogram to obtain the output features. Output features Feature extraction is performed using a lightweight ResNet8 network to obtain the output features. The global average pooling module affects the output features. Perform global mean calculation to obtain output features. Output features The frequency domain feature vector is obtained by converting the vector into a fixed-length one-dimensional vector through a feature flattening layer. .

[0106] The lightweight ResNet8 network consists of sequentially connected 1×3 convolutional layers, residual structural units L0, M0, and N0, in-branch global average pooling layers, and feature flattening layers. Residual structural units L0, M0, and N0 each include a first residual block and a second residual block connected in series. The main branches of the first and second residual blocks each include a first 1×3 convolutional layer and a second 1×3 convolutional layer connected in series. After the first 1×3 convolutional layer, a batch normalization layer and a GELU activation function are connected in series. After the second 1×3 convolutional layer, a batch normalization layer is connected. The shortcut branch of the first residual block includes a 1×1 convolutional layer followed by a batch normalization layer. The outputs of the main branch and the shortcut branch are added element-wise.

[0107] The process of weighted fusion of time-domain and frequency-domain feature vectors includes:

[0108] For time-domain feature vectors and frequency domain eigenvectors Feature concatenation is performed along the channel dimension to obtain a joint feature vector;

[0109] The joint feature vector is input into a two-layer fully connected network with a dimensionality reduction scaling factor and a non-linear activation function to generate a weight coefficient vector with the same number of channels.

[0110] Apply the weight coefficient vector to the time-domain feature vector. and frequency domain eigenvectors Adaptive recalibration is performed on information from different rows to obtain the fused feature vector.

[0111] The training process of the SGFN model includes:

[0112] The preprocessed modulated signal is reconstructed in phase space to obtain the trajectory matrix and construct the covariance matrix. The covariance matrix is ​​decomposed to obtain the eigenvector matrix and eigenvalues. The eigenvector matrix and trajectory matrix are used to construct the reconstruction matrix. The reconstruction matrix is ​​then transformed to obtain the dynamic modal components.

[0113] The dynamic modal components are sorted based on eigenvalues. Dynamic modal components with eigenvalues ​​greater than a set value are taken as the main modes, and dynamic modal components with eigenvalues ​​less than the set value are superimposed to form a residual signal. The main modes are stacked alternately by channel and then stacked with the residual signal to construct a multi-channel time-domain modal feature matrix. The reconstruction matrix corresponding to the main modes is subjected to a fast Fourier transform to generate a spectrum.

[0114] A dataset was constructed based on multi-channel temporal modal feature matrices, spectrograms, and modulation labels, and the dataset was divided into a training set and a validation set.

[0115] The training set is input into the SGFN model, the prediction results are output, the loss value of the prediction results and the modulation tag is calculated, and the parameters of the SGFN model are updated through the backpropagation algorithm to obtain the pre-trained SGFN model.

[0116] The validation set is input into the pre-trained SGFN model for training until the preset convergence condition is met, thus obtaining the trained SGFN model.

[0117] This invention organically combines the dynamic modal features extracted by SGMD with a lightweight time-frequency dual-branch network structure. End-to-end parameter learning is achieved through a training module, and rapid online identification of unknown modulation signals is realized through an identification module. Compared to systems relying solely on empirical features or single-domain deep networks, this invention exhibits higher identification accuracy and better robustness under complex electromagnetic environments and small sample conditions, making it suitable for deployment in practical communication monitoring, spectrum regulation, and smart radio terminal scenarios.

[0118] Experimental Analysis

[0119] This invention selects the publicly available radio modulation signal dataset RadioML2016.10a as the main experimental dataset. This dataset contains various common digital and analog modulation schemes, with a signal-to-noise ratio range of -20dB to 18dB and a step size of 2dB. It is commonly used for performance evaluation of automatic modulation recognition algorithms. For the complex baseband I / Q sequences of various modulation signals in the dataset, preprocessing and SGMD decomposition are first performed according to the steps in Example 1 to obtain a set of physically meaningful dynamic mode components. Based on this, a time-domain mode matrix is ​​constructed, and the corresponding spectrogram is further generated as the input to the time-domain and frequency-domain branches of the SGFN network, completing the network training and testing.

[0120] In comparing the decomposition methods, using the same network structure and training configuration, SGMD, EMD, and VMD were used as front-end decomposition modules and respectively connected to the same recognition network for comparative experiments. The recognition accuracy curves of different decomposition methods at various signal-to-noise ratios are shown below. Figure 4 As shown, across the entire signal-to-noise ratio range from -20dB to 18dB, the overall accuracy curve of the SGMD-based method consistently outperforms that of the EMD and VMD methods. Particularly in the mid-to-high signal-to-noise ratio region, the SGMD front-end achieves a performance gain of approximately 1% to 2%. This indicates that, while maintaining symplectic structure and geometric invariants, SGMD can more stably extract the main dynamic modes of the modulated signal, thereby improving the discriminative ability of the back-end classifier.

[0121] In terms of network architecture comparison, SGFN-T (retaining only the time-domain branch), SGFN-F (retaining only the frequency-domain branch), and a dual-branch SGFN (utilizing both time-domain and frequency-domain information) were constructed and tested under the same SGMD front-end and training configuration. The recognition accuracy curves of the three structures at different signal-to-noise ratios are shown below. Figure 5As shown, in the low signal-to-noise ratio (SNR) range (around -10 dB), the performance gap between the three structures gradually widens, with the dual-branch SGFN significantly outperforming the single time-domain or single frequency-domain branch. In the medium-to-high SNR region (SNR ≥ 0 dB), the dual-branch structure still maintains a slightly higher accuracy. These results demonstrate that the proposed time-frequency dual-branch structure can effectively mine the complementary information of the modulated signal in terms of temporal evolution and spectral distribution, and the adaptive weighting of key features by the SE channel fusion module also plays a crucial role in improving overall performance.

[0122] In experiments with small sample sizes, the impact of training sample size on the performance of this invention was investigated by varying the proportion of samples used in training. The average recognition accuracy under different training sample proportions is shown below. Figure 6 As shown, when training with only 10% of the total data, the average recognition accuracy of this invention still reaches approximately 57.89%. As the proportion of training samples gradually increases, the accuracy generally shows a monotonically increasing trend, reaching an average accuracy of approximately 62.99% when using all training samples. This result demonstrates that, relying on the physical guidance dynamic modal features provided by SGMD and the lightweight network structure, this invention still exhibits good generalization ability and robustness even with limited labeled data.

[0123] Regarding the selection of the number of dynamic modes K, sensitivity analysis of system performance was conducted by varying the number of modes retained by SGMD under the same network structure. The impact of different modes K on the average recognition accuracy is as follows: Figure 7 As shown, the recognition accuracy initially increases and then decreases with increasing K, peaking around K=16. When K is too small, important dynamic modes are not fully preserved, resulting in insufficient feature information; when K is too large, it introduces more noise and redundant components, degrading classification performance. These experimental results provide a basis for the reasonable setting of the number of SGMD modes in engineering applications.

[0124] To further analyze the recognition effect of the present invention on various modulation types, the classification confusion matrix under typical signal-to-noise ratio and different training sample ratios is given. Figures 8(a) to 8(f) show the typical modulation signal types involved in the present invention, including 11 common digital and analog modulation methods: BPSK, AM-DSB, AM-SSB, 8PSK, QPSK, GFSK, PAM4, QAM16, QAM64, QPSK and WBPM. Among them, BPSK (Binary Phase Shift Keying) and QPSK (Quadrature Phase Shift Keying) are phase modulation methods that represent different symbols by changing the carrier phase; GFSK (Gaussian Frequency Shift Keying) is a frequency modulation method that modulates the signal by the frequency shift after Gaussian filtering; PAM4 (Pulse Amplitude Modulation, 4-level) uses different amplitude levels to represent symbol information; QAM16 and QAM64 (Quadrature Amplitude Modulation) combine amplitude and phase modulation, enabling the transmission of more bits of information within a limited bandwidth; AM-DSB (Double Sideband Amplitude Modulation) and AM-SSB (Single Sideband Amplitude Modulation) are analog modulation methods used to demonstrate how the carrier envelope changes with the amplitude of the modulating signal; WBPM (Wideband Phase Modulation) is a wideband phase modulation signal commonly used in high-bandwidth communication systems, and has strong spectral spread characteristics. These modulation types exhibit different time-domain and frequency-domain characteristics in their waveforms: phase-modulated signals show abrupt phase changes while maintaining stable amplitude; amplitude-modulated signals show significant envelope fluctuations; and frequency-modulated signals exhibit instantaneous frequency changes over time. By comparing these typical signals, the differences in waveform characteristics between different modulation methods can be intuitively reflected.

[0125] In high signal-to-noise ratio (SNR) scenarios (e.g., SNR ≥ 0dB), the recognition rates of various modulation types on the diagonal of the confusion matrix are generally close to or exceed 0.9, with an overall average accuracy of approximately 92.13%, and a peak accuracy of 93.66% at certain SNR points. Even when the training samples account for only 10% of the total sample, most modulation types still maintain a high recognition rate, with only slight confusion between a few higher-order modulation schemes. Overall, the results demonstrate that the method of this invention can achieve stable and high-precision automatic modulation recognition under complex electromagnetic environments and small sample conditions.

[0126] The experimental results above demonstrate that this invention, by organically combining symplectic geometric mode decomposition (SGMD) with a time-frequency dual-branch lightweight network structure, effectively improves the accuracy and robustness of modulated signal classification while maintaining moderate model complexity. Compared with existing methods that do not employ SGMD decomposition or only use single-domain features, this invention exhibits superior recognition performance across the entire signal-to-noise ratio range, making it particularly suitable for applications such as wireless communication monitoring, spectrum sensing, and intelligent electromagnetic countermeasures. The above experimental analysis is only intended to illustrate the effectiveness of the technical solution of this invention and does not constitute a limitation on the scope of protection of this invention.

[0127] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An automatic modulation and identification method for communication signals based on symplectic geometric mode decomposition, characterized in that: include: The preprocessed modulated signal is reconstructed in phase space to obtain the trajectory matrix and construct the covariance matrix. The covariance matrix is ​​then decomposed using the QR decomposition method. The eigenvector matrix and eigenvalues ​​are obtained. The eigenvector matrix and trajectory matrix are used to construct a reconstruction matrix. The reconstruction matrix is ​​then transformed to obtain the dynamic modal components. The dynamic modal components are sorted based on eigenvalues. The I and Q components of each dynamic modal component are extracted separately. The I and Q components of the dynamic modal components are sorted according to the magnitude of the corresponding eigenvalues. The I and Q components of each dynamic modal component are arranged according to the mode number and aligned according to the time sampling points. The dynamic modal components with eigenvalues ​​greater than a set value are taken as the main modes, and the dynamic modal components with eigenvalues ​​less than the set value are superimposed to form the residual signal. The main modes are stacked alternately by channel and then stacked with the residual signal. Using the mode number as an index, the I and Q components under the same mode are regarded as a group and arranged in the channel dimension in the order of I first and then Q. The arrangement process is repeated in the order of increasing mode number to construct a multi-channel time-domain modal feature matrix. Fast Fourier transform is performed on the reconstruction matrix corresponding to the main modes to generate a spectrum. The multi-channel time-domain modal feature matrix and spectrogram are input into the trained SGFN model. The trained SGFN model includes a lightweight time-domain branch and a frequency-domain branch. The multi-channel time-domain modal feature matrix is ​​input into the time-domain branch and outputs a time-domain feature vector. The spectrogram is input into the frequency-domain branch and outputs a frequency-domain feature vector. The time-domain feature vector and the frequency-domain feature vector are weighted and fused. The fused feature vector is then classified to obtain the modulation type.

2. The automatic modulation and identification method for communication signals based on symplectic geometric mode decomposition according to claim 1, characterized in that: The dynamic modal components are: in, For the first One dynamic modal component, , , for The elements in , , For the embedding dimension, , The signal length of the original signal. For the delay time, if , ,otherwise .

3. The automatic modulation and identification method for communication signals based on symplectic geometric mode decomposition according to claim 1, characterized in that: The main modes are: in, , These are the I-component and Q-component of each dynamic modal component, respectively. For modal index, The time sampling point number, For setting value, This represents the total number of time sampling points.

4. The automatic modulation and identification method for communication signals based on symplectic geometric mode decomposition according to claim 1, characterized in that: The residual signal includes the residual signal of the I component and the residual signal of the Q component. The residual signal of the I component is formed by superimposing the I components of the dynamic modal components whose eigenvalues ​​are less than the set value, and the residual signal of the Q component is formed by superimposing the Q components of the dynamic modal components whose eigenvalues ​​are less than the set value.

5. The automatic modulation and identification method for communication signals based on symplectic geometric mode decomposition according to claim 1, characterized in that: The temporal and frequency domain branches each consist of a sequentially connected input module, a lightweight ResNet8 network, and a global average pooling module. The multi-channel temporal modality feature matrix enters the temporal branch, where the input module standardizes and aligns the multi-channel temporal modality feature matrix to obtain the output features. Output features Feature extraction is performed using a lightweight ResNet8 network to obtain the output features. The global average pooling module affects the output features. Perform global mean calculation to obtain output features. Output features The feature vector is obtained by transforming it into a fixed-length one-dimensional vector through a feature flattening layer. The spectrogram enters the frequency domain branch; the input module normalizes and aligns the spectrogram to obtain the output features. Output features Feature extraction is performed using a lightweight ResNet8 network to obtain the output features. The global average pooling module affects the output features. Perform global mean calculation to obtain output features. Output features The frequency domain feature vector is obtained by converting the vector into a fixed-length one-dimensional vector through a feature flattening layer. .

6. The automatic modulation and identification method for communication signals based on symplectic geometric mode decomposition according to claim 5, characterized in that: The lightweight ResNet8 network consists of sequentially connected 1×3 convolutional layers, residual structural units L0, M0, and N0, in-branch global average pooling layers, and feature flattening layers. Residual structural units L0, M0, and N0 each include a first residual block and a second residual block connected in series. The main branches of the first and second residual blocks each include a first 1×3 convolutional layer and a second 1×3 convolutional layer connected in series. After the first 1×3 convolutional layer, a batch normalization layer and a GELU activation function are connected in series. After the second 1×3 convolutional layer, a batch normalization layer is connected. The shortcut branch of the first residual block includes a 1×1 convolutional layer followed by a batch normalization layer. The outputs of the main branch and the shortcut branch are added element-wise.

7. The automatic modulation and identification method for communication signals based on symplectic geometric mode decomposition according to claim 5, characterized in that: The process of weighted fusion of time-domain and frequency-domain feature vectors includes: For time-domain feature vectors and frequency domain eigenvectors Feature concatenation is performed along the channel dimension to obtain a joint feature vector; The joint feature vector is input into a two-layer fully connected network with a dimensionality reduction scaling factor and a non-linear activation function to generate a weight coefficient vector with the same number of channels. Apply the weight coefficient vector to the time-domain feature vector. and frequency domain eigenvectors Adaptive recalibration is performed on information from different rows to obtain the fused feature vector.

8. The automatic modulation and identification method for communication signals based on symplectic geometric mode decomposition according to claim 1, characterized in that: The training process of the SGFN model includes: The preprocessed modulated signal is reconstructed in phase space to obtain the trajectory matrix and construct the covariance matrix. The covariance matrix is ​​decomposed to obtain the eigenvector matrix and eigenvalues. The eigenvector matrix and trajectory matrix are used to construct the reconstruction matrix. The reconstruction matrix is ​​then transformed to obtain the dynamic modal components. The dynamic modal components are sorted based on eigenvalues. Dynamic modal components with eigenvalues ​​greater than a set value are taken as the main modes, and dynamic modal components with eigenvalues ​​less than the set value are superimposed to form a residual signal. The main modes are stacked alternately by channel and then stacked with the residual signal to construct a multi-channel time-domain modal feature matrix. The reconstruction matrix corresponding to the main modes is subjected to a fast Fourier transform to generate a spectrum. A dataset was constructed based on multi-channel temporal modal feature matrices, spectrograms, and modulation labels, and the dataset was divided into a training set and a validation set. The training set is input into the SGFN model, the prediction results are output, the loss value of the prediction results and the modulation tag is calculated, and the parameters of the SGFN model are updated through the backpropagation algorithm to obtain the pre-trained SGFN model. The validation set is input into the pre-trained SGFN model for training until the preset convergence condition is met, thus obtaining the trained SGFN model.

9. An automatic modulation and identification system for communication signals based on symplectic geometric mode decomposition, characterized in that: include: The symplectic geometric mode decomposition module is used to reconstruct the phase space of the preprocessed modulation signal, obtain the trajectory matrix and construct the covariance matrix. The covariance matrix is ​​decomposed using the QR decomposition method to obtain the eigenvector matrix and eigenvalues. The reconstruction matrix is ​​constructed using the eigenvector matrix and trajectory matrix. The reconstruction matrix is ​​then transformed to obtain the dynamic mode components. The dynamic mode construction module is used to sort dynamic mode components based on eigenvalues, extract the I and Q components of each dynamic mode component, sort the I and Q components of the dynamic mode component according to the magnitude of the corresponding eigenvalue, arrange the I and Q components of each dynamic mode component according to the mode number and align them according to the time sampling points; dynamic mode components with eigenvalues ​​greater than a set value are regarded as the main modes, and dynamic mode components with eigenvalues ​​less than the set value are superimposed to form a residual signal. The main modes are stacked alternately by channel and then stacked with the residual signal. Using the mode number as an index, the I and Q components under the same mode are regarded as a group and arranged in the channel dimension in the order of I first and then Q. The arrangement process is repeated in the order of increasing mode number to construct a multi-channel time-domain modal feature matrix. Fast Fourier transform is performed on the reconstruction matrix corresponding to the main modes to generate a spectrum. The identification module is used to input the multi-channel time-domain modal feature matrix and spectrogram into the trained SGFN model. The trained SGFN model includes a lightweight time-domain branch and a frequency-domain branch. The multi-channel time-domain modal feature matrix is ​​input into the time-domain branch and outputs a time-domain feature vector. The spectrogram is input into the frequency-domain branch and outputs a frequency-domain feature vector. The time-domain feature vector and the frequency-domain feature vector are weighted and fused. The fused feature vector is then classified to obtain the modulation type.

10. The automatic modulation and identification system for communication signals based on symplectic geometric mode decomposition according to claim 9, characterized in that: The residual signal includes the residual signal of the I component and the residual signal of the Q component. The residual signal of the I component is formed by superimposing the I components of the dynamic modal components whose eigenvalues ​​are less than the set value, and the residual signal of the Q component is formed by superimposing the Q components of the dynamic modal components whose eigenvalues ​​are less than the set value.

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