Physical guided deep learning signal modulation recognition method and system

Abstract

This invention provides a physical-guided deep learning-based signal modulation recognition method and system, belonging to the field of electromagnetic signal processing and machine learning. The method involves performing symplectic geometric mode decomposition on preprocessed in-phase and orthogonal sequences to obtain dynamic mode sequences of the in-phase and orthogonal sequences. Based on K-Means clustering, the dynamic mode sequences of the in-phase and orthogonal sequences are further clustered and reconstructed to obtain K mode clusters for the in-phase and orthogonal sequences. Original frequency domain information is extracted from each mode cluster of the in-phase and orthogonal sequences, and the weights of each mode cluster are obtained based on this information. These weights are then assigned to the corresponding mode clusters to obtain feature representations of the in-phase and orthogonal sequences. The feature representations of the in-phase and orthogonal sequences are concatenated to obtain a one-dimensional time series signal. This one-dimensional time series signal is then input into a one-dimensional time-series deep network, which outputs the modulation category, thus improving recognition performance.

Description

Technical Field

[0001] This invention relates to the fields of intelligent communication, cognitive wireless, electromagnetic signal processing and machine learning, and in particular to a signal modulation recognition method and system for physical-guided deep learning. Background Technology

[0002] Automatic modulation identification (EMI) is a key supporting technology for intelligent communication and cognitive wireless, aiming to reliably extract modulation categories from received signals in complex electromagnetic environments. While existing deep learning methods possess strong representation learning capabilities, under low signal-to-noise ratio (SNR) or non-stationary interference conditions, directly inputting the original in-phase / orthogonal (I / Q) sequences into the network easily leads to representation aliasing and the masking of discriminative cues by noise, resulting in a significant decline in recognition performance. This vulnerability stems from the fact that deep neural networks, in a purely data-driven mode, struggle to distinguish subtle modulation features from strong background noise because they lack inherent physical prior knowledge to guide the learning process. For example, Chinese invention patent application CN121149934A, entitled "Power Line Control Method, Device, Equipment, Medium and Product," utilizes Symptotic Geometry Mode Decomposition (SGMD) to decompose the target traveling wave of a power line, obtaining the target symptotic geometric components of the target traveling wave. These target symptotic geometric components are the symptotic geometric components of the target traveling wave that contain fault feature information. The target symptotic geometric components of the target traveling wave are then input into a fault type determination model to obtain the fault type of the power line. This fault type determination model employs a Convolutional Neural Network (CNN)-Long Short-Term Memory (LSTM) model. In this model, the CNN is only used as a conventional spatial feature extractor, and the LSTM is used to extract temporal evolution features. This feature extraction mechanism belongs to data-driven general pattern extraction. Due to the lack of inherent physical prior knowledge to guide the learning process, the feature extraction struggles to distinguish subtle modulation features from strong background noise.

[0003] To address noise issues, traditional signal processing has developed various decomposition techniques. These include wavelet transform (WT), empirical mode decomposition (EMD), and variational mode decomposition (VMD), typically applied to modulation recognition in a two-stage process of "denoising first, then classification." However, this process may discard crucial modulation details essential for classification, and the denoising objective (minimizing reconstruction error) inherently conflicts with the classification objective (maximizing class separability). Furthermore, different decomposition methods suffer from issues such as predefined basis functions, mode aliasing, and parameter sensitivity, making stable operation under varying channel conditions difficult. Therefore, a novel modulation recognition method is needed that can introduce physical priors at the representation level, enhance noise robustness, and be integrated end-to-end with deep learning. Summary of the Invention

[0004] The technical problem to be solved by this invention is: how to solve the problem that directly inputting the original in-phase / orthogonal sequence into the network in the prior art easily leads to aliasing of representations and masking of discrimination clues by noise, resulting in a decrease in recognition performance.

[0005] This invention solves the above-mentioned technical problems through the following technical solution: a signal modulation recognition method for physically guided deep learning, comprising:

[0006] Symplectic geometric mode decomposition was performed on the preprocessed in-phase and orthogonal sequences to obtain the dynamic mode sequences of the in-phase and orthogonal sequences, respectively. Based on K-Means clustering, the dynamic mode sequences of in-phase sequences and orthogonal sequences are respectively subjected to mode clustering and mode reconstruction to obtain K mode clusters of in-phase sequences and K mode clusters of orthogonal sequences. The original frequency domain information is extracted from each mode cluster of the in-phase sequence and the orthogonal sequence respectively. The weight of each mode cluster is obtained based on the original frequency domain information, and the weight of each mode cluster is assigned to the corresponding mode cluster to obtain the feature representation of the in-phase sequence and the feature representation of the orthogonal sequence. The feature representations of the in-phase sequence and the feature representations of the orthogonal sequence are concatenated to obtain a one-dimensional time series signal. One-dimensional time series signals are input into a one-dimensional temporal deep network for feature extraction and classification, and the modulation category is output.

[0007] This invention utilizes K-Means clustering to perform modal clustering on the dynamic modal sequences of in-phase and orthogonal sequences, and then reconstructs the modes to build a physically interpretable and robust representation space. This constructs a space that forcibly aligns dispersed dynamic modes into clusters with fixed physical meanings, effectively decoupling modulation information, carrier, and noise components, and mitigating the aliasing problem when the original in-phase / orthogonal sequences are directly input into the network. Fine-grained features of modulation signals are easily masked by noise in the time domain, but exhibit significant structural stability in the frequency domain. By extracting frequency domain features to calculate time-domain gating weights, this "frequency-domain sensing, time-domain application" mechanism better aligns with the mechanism of modulation signals: it automatically identifies which modal clusters contain the true modulation texture (assigning high weights) and which contain only noise (assigning low weights). Compared to the simple stacking of time-frequency features in existing technologies, this signal mechanism-based weight allocation mechanism offers higher physical interpretability and robustness against low signal-to-noise ratios.

[0008] Preferably, the process of performing symplectic geometric mode decomposition on the preprocessed in-phase sequences and orthogonal sequences includes: Based on Takens embedding, the phase space of the preprocessed in-phase and orthogonal sequences is reconstructed to construct the trajectory matrices of the in-phase and orthogonal sequences. Construct the covariance matrices of the in-phase sequence and the orthogonal sequence respectively based on the trajectory matrices of the in-phase sequence and the orthogonal sequence; The covariance matrix of the in-phase sequence and the orthogonal sequence is decomposed using the QR decomposition method to obtain the eigenvector matrix of the in-phase sequence and the orthogonal sequence. The reconstruction matrix of the in-phase sequence is constructed using the eigenvector matrix and trajectory matrix of the in-phase sequence, and the reconstruction matrix of the orthogonal sequence is constructed using the eigenvector matrix and trajectory matrix of the orthogonal sequence. The reconstruction matrix is ​​transformed to obtain the dynamic mode sequence of the in-phase sequence and the dynamic mode sequence of the orthogonal sequence.

[0009] Preferably, the dynamic mode sequence of the in-phase sequence Dynamic mode sequences of orthogonal sequences They are respectively:

[0010] in, The first dynamic mode sequence representing an in-phase or orthogonal sequence. One modality, , , , To reconstruct the elements in the matrix, , , To determine the effective number of columns in the reconstructed trajectory matrix, For the embedding dimension, , The signal length of the original signal. For the delay time, if , ,otherwise .

[0011] This invention performs symplectic geometric mode decomposition on the preprocessed in-phase and orthogonal sequences to obtain the dynamic mode sequences of the in-phase and orthogonal sequences, which are signal components of multiple scales. Each component represents a different mode of the signal, covering multiple frequency components and time features.

[0012] Preferably, the process of performing mode clustering and reconstructing the modes based on K-Means clustering for the dynamic mode sequences of in-phase sequences and orthogonal sequences, respectively, includes: For the dynamic mode sequences of in-phase sequences respectively Dynamic mode sequences of orthogonal sequences K-Means clustering is performed to obtain K local mode cluster centers for in-phase sequences and K local mode cluster centers for orthogonal sequences. By minimizing the distance between the dynamic mode and the local mode cluster centers, several dynamic modes corresponding to each local mode cluster center are obtained. , They represent in-phase and orthogonal, respectively. K is the number of dynamic modes, and K is less than 1. ; The aggregated dynamic modes corresponding to the center of each local mode cluster are aggregated to obtain the aggregated signal of each mode cluster; By combining the aggregated signals of each mode cluster of the in-phase sequence and the orthogonal sequence respectively, we can obtain K mode clusters of the in-phase sequence and K mode clusters of the orthogonal sequence.

[0013] This invention further introduces K-Means-based modal clustering after SGMD, organizing dispersed dynamic modes into several modal clusters with stable physical meanings, thereby constructing a unified physical representation space. The physical representation space consists of K sequences of physical modal clusters, with each channel corresponding to a relatively stable type of physical property (e.g., carrier dominant mode, modulation sideband mode, noise dominant mode, etc.).

[0014] The preferred method for calculating the distance between the dynamic mode and the center of the local mode cluster is as follows:

[0015]

[0016] in, Represents the dynamic mode sequence of an in-phase sequence The Middle One modality, Dynamic mode sequence of in-phase sequence The set that is formed Dynamic mode sequence representing orthogonal sequences The Middle One modality, Dynamic mode sequence of orthogonal sequence The set that is formed , Represent the first and second phases of the in-phase sequence and the orthogonal sequence, respectively. The center of a local modal cluster , .

[0017] Preferably, the process of obtaining the weights of each mode cluster based on the original frequency domain information is as follows: The original frequency domain information is sequentially input into the first fully connected layer, the ReLU activation function layer, and the second fully connected layer to obtain the frequency domain features. The Sigmoid function is used to convert the frequency domain features into weights for each mode cluster.

[0018] Preferably, the feature representations of in-phase sequences and orthogonal sequences are as follows:

[0019]

[0020] in, , These are the characteristic representations of in-phase sequences and orthogonal sequences, respectively. Represents the first in-phase sequence The weights of each modal cluster, Represents the first orthogonal sequence The weights of each modal cluster, Represents the first in-phase sequence A modal cluster, Represents the first orthogonal sequence A modal cluster, K is the total number of in-phase or orthogonal sequence mode clusters.

[0021] This invention further constructs a frequency-domain gating mechanism within the attention module. It generates variable weights through a compression-excitation structure consisting of two fully connected layers and a nonlinear activation function, and then uses scalar weights to perform point-by-point weighting on the physical mode clusters, resulting in a representation that includes frequency-domain attention. Frequency-domain guided attention gating can utilize information such as frequency-domain structural features to guide weight allocation, better aligning with the physical mechanism of the modulation signal and outperforming simple time-frequency feature superposition.

[0022] Preferably, the one-dimensional temporal deep network adopts the trained InceptionTime network, which includes an input module, a multi-layer Inception structural unit, a global average pooling module, and a fully connected classification module connected in sequence. The m-th layer Inception structural unit and the (m+2)-th layer Inception structural unit are connected by a residual connection module, where m≥1.

[0023] Preferably, the training process of the InceptionTime network includes: The dynamic mode sequences of in-phase sequences and orthogonal sequences of multiple samples are obtained. Based on K-Means clustering, the dynamic mode sequences of in-phase sequences and orthogonal sequences of each sample are subjected to mode clustering and the modes are reconstructed to obtain K mode clusters of in-phase sequences and K mode clusters of orthogonal sequences. The original frequency domain information is extracted for each mode cluster of the in-phase sequence and the orthogonal sequence respectively. The original frequency domain information is then input into the first fully connected layer, the ReLU activation function layer and the second fully connected layer in sequence to obtain frequency domain features. The Sigmoid function is used to convert the frequency domain features into weights for each mode cluster. The weights of each mode cluster are assigned to the corresponding mode clusters to obtain the feature representations of the in-phase sequence and the orthogonal sequence. The feature representations of the in-phase sequence and the orthogonal sequence are concatenated to obtain the one-dimensional time series signal of each sample. The InceptionTime network is trained based on the one-dimensional time series signals of all samples, resulting in the trained InceptionTime network.

[0024] This invention constructs a modal cluster representation with a fixed number of channels K through single-sample K-Means modal clustering, which can alleviate the instability of batch training caused by the misalignment of modal indices between different samples and reduce redundancy and noise components.

[0025] This invention also provides a signal modulation recognition system for physically guided deep learning, comprising: The signal decomposition module is used to perform symplectic geometric mode decomposition on the preprocessed in-phase and orthogonal sequences to obtain the dynamic mode sequences of the in-phase and orthogonal sequences, respectively. The physical representation space construction module is used to perform mode clustering and mode reconstruction on the dynamic mode sequences of in-phase sequences and orthogonal sequences based on K-Means clustering, respectively, to obtain K mode clusters of in-phase sequences and K mode clusters of orthogonal sequences; The frequency domain guided attention module is used to extract the original frequency domain information for each mode cluster of the in-phase sequence and the orthogonal sequence, respectively. Based on the original frequency domain information, the weight of each mode cluster is obtained, and the weight of each mode cluster is assigned to the corresponding mode cluster to obtain the feature representation of the in-phase sequence and the feature representation of the orthogonal sequence. The feature representations of the in-phase sequence and the feature representations of the orthogonal sequence are concatenated to obtain a one-dimensional time series signal. The feature extraction and classification module is used to input one-dimensional time series signals into a one-dimensional time series deep network for feature extraction and classification, and output modulation category. Attached Figure Description

[0026] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0027] Figure 1 A flowchart of the signal modulation recognition method for physically guided deep learning provided in Embodiment 1 of the present invention; Figure 2 This is a schematic diagram of the signal modulation recognition method for physical-guided deep learning provided in Embodiment 1 of the present invention. Figure 3 This is a schematic diagram of the frequency domain feature extraction module in the physical-guided deep learning signal modulation recognition method provided in Embodiment 1 of the present invention; Figure 4 This is a schematic diagram of the Inception structure unit in the InceptionTime network of the signal modulation recognition method for physical-guided deep learning provided in Embodiment 1 of the present invention; Figure 5 This is a schematic diagram of the multi-layer Inception structure unit in the InceptionTime network of the signal modulation recognition method for physical-guided deep learning provided in Embodiment 1 of the present invention; Figure 6 The recognition accuracy of the physical-guided deep learning signal modulation recognition method provided in Embodiment 1 of the present invention compared with existing signal decomposition methods under different signal-to-noise ratios; Figure 7 The signal modulation recognition method of physical-guided deep learning provided in Embodiment 1 of the present invention and the recognition accuracy of existing end-to-end recognition networks under different signal-to-noise ratios; Figure 8 This refers to the confusion matrix between different modulation signals in the physical-guided deep learning signal modulation recognition method provided in Embodiment 1 of the present invention. Figure 9 The F1 gain of the signal modulation recognition method for physical-guided deep learning provided in Embodiment 1 of the present invention under different modulation types; Figure 10(a) shows the modal cluster components and their attention weights of the signal sample of the signal modulation recognition method of physical guided deep learning provided in Embodiment 1 of the present invention at a signal-to-noise ratio of -10dB. Figure 10(b) shows the modal cluster components and their attention weights of the signal sample of the physical-guided deep learning signal modulation recognition method provided in Embodiment 1 of the present invention at a signal-to-noise ratio of 0dB. Figure 10(c) shows the modal cluster components and their attention weights of a signal sample at a signal-to-noise ratio of 18dB in the signal modulation recognition method of physical-guided deep learning provided in Embodiment 1 of the present invention.

[0028] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0029] 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.

[0030] Example 1 like Figure 1 and Figure 2 As shown, this embodiment provides a signal modulation recognition method for physically guided deep learning, including the following steps: S1. Perform symplectic geometric mode decomposition on the preprocessed in-phase and orthogonal sequences to obtain the dynamic mode sequence of the in-phase sequence. Dynamic mode sequences of orthogonal sequences The preprocessing includes amplitude normalization, DC component removal, and fixed-length segment truncation. In this embodiment, the in-phase / quadrature sequence (I / Q sequence) or equivalent two real-valued sequences of the complex baseband modulation signal to be identified are first obtained. Then, amplitude normalization, DC component removal, and fixed-length segment truncation are performed sequentially on the in-phase and quadrature sequences to obtain the preprocessed in-phase and quadrature sequences, respectively. The process of performing symplectic geometric mode decomposition on the preprocessed in-phase and quadrature sequences includes: S1.1. Based on the Takens embedding process, the phase space of the preprocessed in-phase and orthogonal sequences is reconstructed to construct the trajectory matrix of the in-phase sequence. Trajectory matrix of orthogonal sequences :

[0031]

[0032] The preprocessed in-phase and quadrature sequences, used as the original signals, are each a time series signal. , Indicates the first in-phase sequence after preprocessing. One sampled signal, processed orthogonal sequence , Indicates the first orthogonal sequence after preprocessing. One sampled signal, , For signal length, To delay time, take , . To reconstruct the effective number of columns of the trajectory matrix, i.e. the total number of phase points in phase space, The embedding dimension is determined by: defining the original signal. or The frequency at which the power spectral density is at its maximum If frequency Less than ,but ,otherwise, , The sampling frequency of the signal.

[0033] S1.2 Construct the covariance matrices of the in-phase sequence and the orthogonal sequence respectively based on their trajectory matrices; construct the covariance matrices of the in-phase sequence and the orthogonal sequence respectively based on their trajectory matrices. Construct the covariance matrix of in-phase sequences Based on the trajectory matrix of orthogonal sequences Construct the covariance matrix of orthogonal sequences The covariance matrix of in-phase sequences Covariance matrix of orthogonal sequences They are respectively:

[0034]

[0035] in, Trajectory matrix representing in-phase sequence The transpose of , Trajectory matrix representing orthogonal sequences The transpose of .

[0036] S1.3. The covariance matrices of the in-phase and orthogonal sequences are decomposed using the QR decomposition method to obtain the eigenvector matrices of the in-phase and orthogonal sequences. The reconstruction matrix of the in-phase sequence is constructed using the eigenvector matrix and trajectory matrix of the orthogonal sequence. The reconstruction matrix is ​​then transformed to obtain the dynamic modal sequence of the in-phase sequence. Dynamic mode sequences of orthogonal sequences .

[0037] Among them, the matrix is ​​decomposed using the QR decomposition method. The eigenvector matrix of the in-phase sequence is obtained. eigenvector matrix of in-phase sequence The essential characteristics of the preprocessed in-phase sequence were preserved, and the matrix was decomposed using the QR decomposition method. The eigenvector matrix of the in-phase sequence is obtained. eigenvector matrix of orthogonal sequences The essential characteristics of the preprocessed orthogonal sequences are preserved. Based on the principle of symplectic geometric similarity transformation, the structural properties of the original signal can be retained.

[0038] Using the eigenvector matrix of in-phase sequences trajectory matrix Constructing the reconstruction matrix of in-phase sequences Using the eigenvector matrix of orthogonal sequences trajectory matrix Constructing the reconstruction matrix of orthogonal sequences Reconstructing the matrix Reconstructing the matrix They are respectively:

[0039]

[0040] in, The eigenvector matrix of the in-phase sequence The first in 1 eigenvector for The transpose of , The eigenvector matrix of an orthogonal sequence The first in 1 eigenvector for The transpose of , , The embedding dimension.

[0041] The reconstruction matrix of the initial single components is obtained by diagonal averaging. Reconstructing the matrix Perform transformation and reconstruct the matrix. Reconstructing the matrix For a one-dimensional single-component signal, the in-phase sequence can be obtained. A length of One-dimensional time series and orthogonal sequences A length of One-dimensional time series . The original signal is composed of multiple dynamic modal components.

[0042] Dynamic mode sequence of in-phase sequence Dynamic mode sequences of orthogonal sequences for:

[0043] in, The first dynamic mode sequence representing an in-phase or orthogonal sequence. One modality, , , , To reconstruct the elements in the matrix, , , To determine the effective number of columns in the reconstructed trajectory matrix, For the embedding dimension, , The signal length of the original signal. For the delay time, if , ,otherwise .

[0044] By performing symplectic geometric mode decomposition on the preprocessed in-phase and orthogonal sequences, the dynamic mode sequence of the in-phase sequence is obtained. Dynamic mode sequences of orthogonal sequences These are signal components at multiple scales, each representing a different mode of the signal, encompassing various frequency components and temporal characteristics.

[0045] S2. Based on K-Means clustering, the dynamic modal sequences of in-phase sequences are respectively... Dynamic mode sequences of orthogonal sequences Modal clustering and mode reconstruction are performed to obtain K mode clusters for in-phase sequences and K mode clusters for orthogonal sequences. The process of modal clustering and mode reconstruction based on K-Means clustering for the dynamic mode sequences of in-phase sequences and orthogonal sequences includes: S2.1, For the dynamic mode sequences of in-phase sequences respectively Dynamic mode sequences of orthogonal sequences K-Means clustering is performed to obtain K local mode cluster centers for in-phase sequences and K local mode cluster centers for orthogonal sequences. By minimizing the distance between the dynamic mode and the local mode cluster centers, several dynamic modes corresponding to each local mode cluster center are obtained. , They represent in-phase and orthogonal, respectively. K is the number of dynamic modes, and K is less than 1. The method for minimizing the distance between the dynamic mode and the center of the local mode cluster is as follows:

[0046]

[0047] in, Represents the dynamic mode sequence of an in-phase sequence The Middle One modality, Dynamic mode sequence of in-phase sequence The set that is formed Dynamic mode sequence representing orthogonal sequences The Middle One modality, Dynamic mode sequence of orthogonal sequence The set that is formed , Represent the first and second phases of the in-phase sequence and the orthogonal sequence, respectively. The center of a local modal cluster , .

[0048] S2.2, aggregate the several dynamic modes corresponding to the center of each local mode cluster to obtain the aggregated signal of each mode cluster; the first in-phase sequence Aggregated signal of a modal cluster for:

[0049] The first orthogonal sequence Aggregated signal of a modal cluster for:

[0050] in, .

[0051] S2.3 Combine the aggregated signals of each mode cluster of the in-phase sequence and the orthogonal sequence respectively to obtain K mode clusters of the in-phase sequence and K mode clusters of the orthogonal sequence.

[0052] The K modal clusters of an in-phase sequence constitute the physical representation space of the in-phase sequence. The K modal clusters of an orthogonal sequence constitute the physical representation space of the orthogonal sequence. Physical representation space Physical representation space They are respectively:

[0053]

[0054] in, This represents the total number of modal clusters of in-phase or orthogonal sequences. This is the signal length.

[0055] Physical representation space of in-phase sequences Physical representation space of orthogonal sequences The multi-channel signal consists of K physical mode cluster sequences, each channel carrying a mode cluster with certain physical properties, and obtains a more compact and clearer mode cluster representation while maintaining physical information.

[0056] After SGMD decomposition, each observed signal is represented as a set of dynamic mode sequences. Directly feeding all modes into a deep network introduces significant redundancy and noise, and the lack of a one-to-one correspondence between mode indices of different samples makes it difficult to establish stable "alignment of similar modes" during batch training. Therefore, this invention further introduces K-Means-based mode clustering after SGMD, organizing the dispersed dynamic modes into several mode clusters with stable physical meaning, thereby constructing a unified physical representation space. The physical representation space consists of K physical mode cluster sequences, with each channel corresponding to a relatively stable physical attribute (e.g., carrier dominant mode, modulation sideband mode, noise-dominant mode, etc.).

[0057] By constructing a dynamic mode set and forming a physical representation space through SGMD, modulation information, carrier and noise components can be more effectively decoupled, alleviating the representation aliasing problem of the original I / Q direct input network.

[0058] S3. Extract the original frequency domain information for each mode cluster of the in-phase sequence and the orthogonal sequence respectively. Obtain the weight of each mode cluster based on the original frequency domain information, and assign the weight of each mode cluster to the corresponding mode cluster to obtain the feature representation of the in-phase sequence and the feature representation of the orthogonal sequence. Concatenate the feature representation of the in-phase sequence and the feature representation of the orthogonal sequence to obtain a one-dimensional time series signal.

[0059] This embodiment extracts the original frequency domain information of the in-phase sequence by performing Fourier transform (FFT) on each mode cluster of the in-phase and orthogonal sequences to obtain amplitude spectrum and energy spectrum statistics. Original frequency domain information of orthogonal sequences :

[0060]

[0061] in, Physical representation space for in-phase sequences The Middle A modal cluster, Physical representation space of orthogonal sequences The Middle A modal cluster, This represents the Fourier transform.

[0062] The process of obtaining the weights of each mode cluster based on the original frequency domain information is as follows: S3.1. Input the original frequency domain information sequentially into the first fully connected layer, the ReLU activation function layer, and the second fully connected layer to obtain the frequency domain features; see [link to relevant documentation]. Figure 3 The original frequency domain information of the in-phase sequence By sequentially inputting the first fully connected layer, the ReLU activation function layer, and the second fully connected layer, the frequency domain features are obtained. The original frequency domain information of the orthogonal sequence By sequentially inputting the first fully connected layer, the ReLU activation function layer, and the second fully connected layer, the frequency domain features are obtained. The expression is:

[0063]

[0064] in, This indicates feature extraction.

[0065] S3.2. The Sigmoid function is used to convert the frequency domain features into weights for each mode cluster. The first... Weights of each modality for:

[0066] The first orthogonal sequence Weights of each modality for:

[0067] The characteristic representations of in-phase sequences and orthogonal sequences are as follows:

[0068]

[0069] in, , These are the characteristic representations of in-phase sequences and orthogonal sequences, respectively. Represents the first in-phase sequence The weights of each modal cluster, Represents the first orthogonal sequence The weights of each modal cluster, Represents the first in-phase sequence A modal cluster, Represents the first orthogonal sequence A modal cluster, K is the total number of in-phase or orthogonal sequence mode clusters.

[0070] This invention further constructs a frequency-domain gating mechanism within the attention module. It generates variable weights through a compression-excitation structure consisting of two fully connected layers and a nonlinear activation function, and then uses scalar weights to perform point-by-point weighting on the physical mode clusters, resulting in a representation that includes frequency-domain attention. Frequency-domain guided attention gating can utilize information such as frequency-domain structural features to guide weight allocation, better aligning with the physical mechanism of the modulation signal and outperforming simple time-frequency feature superposition.

[0071] Frequency-domain guided attention is superior because it achieves end-to-end coupling between "physical knowledge guidance (frequency-domain structure)" and "deep feature extraction (temporal network)." Fine-grained features of modulated signals are easily masked by noise in the time domain, but exhibit significant structural stability in the frequency domain. By guiding the model "where to look" through frequency-domain priors, it effectively addresses the shortcomings of traditional models in characterizing complex phase structures, rather than simply relying on increasing the number of network parameters.

[0072] Step S3 extracts frequency domain structural features for each modal cluster channel, assigns adaptive weights to different modal cluster channels based on the globally aggregated statistics, and feeds these weights back to the time domain modal cluster sequence to implement gated reweighting, thereby realizing a natural fusion mechanism of "frequency domain perception and time domain application", which emphasizes key modulation components and suppresses noise-dominant components.

[0073] S4. Input the one-dimensional time series signal into a one-dimensional temporal deep network for feature extraction and classification, and output the modulation category.

[0074] The one-dimensional temporal deep network employs a trained InceptionTime network, capturing discriminative patterns at different temporal scales through multi-scale convolutional paths and outputting modulation category predictions. The trained InceptionTime network comprises a sequentially connected input module, multi-layer Inception structural units, a global average pooling module, and a fully connected classification module. (See [link to documentation]). Figure 5 A residual connection module is connected between the m-th layer Inception structural unit and the (m+2)-th layer Inception structural unit, where m≥1.

[0075] See Figure 4Each Inception structural unit includes a first bottleneck convolutional layer (Bottleneck1), three parallel one-dimensional convolutional layers, a second bottleneck convolutional layer (Bottleneck2), a channel concatenation layer, a batch normalization layer, and a ReLU activation function layer connected in sequence. The first bottleneck convolutional layer has a kernel size of 1 and is used to transform the number of input channels to F. The kernel sizes of the three parallel one-dimensional convolutional layers are 10, 20, and 40, respectively. The kernel size of the max pooling layer is 3. The kernel size of the second bottleneck convolutional layer is 1 and is used to process the output after pooling. The channel concatenation layer is used to concatenate the outputs of the above three convolutional layers and the output of the bottleneck convolutional layer in the channel dimension. The number of channels in the batch normalization layer is 4×F.

[0076] The global average pooling module is used to average all channels over time, with an output size of 4×F. The fully connected classification module includes a linear layer, which maps the 4×F-dimensional feature vector to N-class outputs, where N is the number of target classification categories.

[0077] The training process of the InceptionTime network includes: S4.1 Obtain the dynamic mode sequences of in-phase sequences and orthogonal sequences of multiple samples. Based on K-Means clustering, perform mode clustering on the dynamic mode sequences of in-phase sequences and orthogonal sequences of each sample and reconstruct the modes to obtain K mode clusters of in-phase sequences and K mode clusters of orthogonal sequences. S4.2 Extract the original frequency domain information for each mode cluster of the in-phase sequence and the orthogonal sequence respectively. Input the original frequency domain information into the first fully connected layer, the ReLU activation function layer and the second fully connected layer in sequence to obtain the frequency domain features. Use the Sigmoid function to convert the frequency domain features into the weights of each mode cluster. S4.3 Assign the weights of each mode cluster to the corresponding mode cluster to obtain the feature representations of the in-phase sequence and the orthogonal sequence. Concatenate the feature representations of the in-phase sequence and the orthogonal sequence to obtain the one-dimensional time series signal of each sample. S4.4. Train the InceptionTime network based on the one-dimensional time series signals of all samples to obtain the trained InceptionTime network.

[0078] By constructing a modal cluster representation with a fixed number of channels K through single-sample K-Means modal clustering, redundancy and noise are reduced and training stability is improved.

[0079] The first fully connected layer, ReLU activation function layer, and second fully connected layer connected sequentially in this invention constitute a frequency domain feature extraction module. In the network architecture of this invention, two frequency domain feature extraction modules are used to extract features from the original frequency domain information of in-phase sequences and the original frequency domain information of orthogonal sequences, respectively. The two frequency domain feature extraction modules, Fourier transform layer, Sigmoid function, and InceptionTime network together constitute the Freq-AttNet neural network. The training process of the InceptionTime network in this invention is the same as the training process of the Freq-AttNet neural network. SGMD and single-sample K-Means clustering can maintain consistent configurations during training and testing to ensure consistency in physical representation. During the training phase, cross-entropy loss is used for supervised training of the classification network, and the Adam optimizer and a validation set-driven learning rate scheduling strategy are used. This invention utilizes K-Means clustering to perform modal clustering on the dynamic modal sequences of in-phase and orthogonal sequences, and then reconstructs the modes to build a physically interpretable and robust representation space. This constructs a space that forcibly aligns dispersed dynamic modes into clusters with fixed physical meanings, effectively decoupling modulation information, carrier, and noise components, and mitigating the aliasing problem when the original in-phase / orthogonal sequences are directly input into the network. By extracting frequency domain features to calculate time-domain gating weights, this "frequency-domain sensing, time-domain application" mechanism better aligns with the mechanism of modulation signals: it automatically identifies which modal clusters contain the true modulation texture (assigning high weights) and which contain only noise (assigning low weights). Compared to the simple stacking of time-frequency features in existing technologies, this signal mechanism-based weight allocation mechanism offers higher physical interpretability and robustness against low signal-to-noise ratios.

[0080] Example 2 A physical-guided deep learning signal modulation recognition system includes: The signal decomposition module is used to perform symplectic geometric mode decomposition on the preprocessed in-phase and orthogonal sequences to obtain the dynamic mode sequences of the in-phase and orthogonal sequences, respectively.

[0081] The process of performing symplectic geometric mode decomposition on the preprocessed in-phase and orthogonal sequences includes: Based on Takens embedding, the phase space of the preprocessed in-phase and orthogonal sequences is reconstructed to construct the trajectory matrices of the in-phase and orthogonal sequences. Construct the covariance matrices of the in-phase sequence and the orthogonal sequence respectively based on the trajectory matrices of the in-phase sequence and the orthogonal sequence; The covariance matrix of the in-phase sequence and the orthogonal sequence is decomposed using the QR decomposition method to obtain the eigenvector matrix of the in-phase sequence and the orthogonal sequence. The reconstruction matrix of the in-phase sequence is constructed using the eigenvector matrix and trajectory matrix of the in-phase sequence, and the reconstruction matrix of the orthogonal sequence is constructed using the eigenvector matrix and trajectory matrix of the orthogonal sequence. The reconstruction matrix is ​​transformed to obtain the dynamic mode sequence of the in-phase sequence and the dynamic mode sequence of the orthogonal sequence.

[0082] Dynamic mode sequence of in-phase sequence Dynamic mode sequences of orthogonal sequences They are respectively:

[0083] in, The first dynamic mode sequence representing an in-phase or orthogonal sequence. One modality, , , , To reconstruct the elements in the matrix, , , To determine the effective number of columns in the reconstructed trajectory matrix, For the embedding dimension, , The signal length of the original signal. For the delay time, if , ,otherwise .

[0084] The physical representation space construction module is used to perform mode clustering and mode reconstruction on the dynamic mode sequences of in-phase sequences and orthogonal sequences based on K-Means clustering, respectively, to obtain K mode clusters of in-phase sequences and K mode clusters of orthogonal sequences.

[0085] The process of performing mode clustering and mode reconstruction based on K-Means clustering on the dynamic mode sequences of in-phase sequences and orthogonal sequences includes: For the dynamic mode sequences of in-phase sequences respectively Dynamic mode sequences of orthogonal sequences K-Means clustering is performed to obtain K local mode cluster centers for in-phase sequences and K local mode cluster centers for orthogonal sequences. By minimizing the distance between the dynamic mode and the local mode cluster centers, several dynamic modes corresponding to each local mode cluster center are obtained. , They represent in-phase and orthogonal, respectively. K is the number of dynamic modes, and K is less than 1. The method for minimizing the distance between the dynamic mode and the center of the local mode cluster is as follows:

[0086]

[0087] in, Represents the dynamic mode sequence of an in-phase sequence The Middle One modality, Dynamic mode sequence of in-phase sequence The set that is formed Dynamic mode sequence representing orthogonal sequences The Middle One modality, Dynamic mode sequence of orthogonal sequence The set that is formed , Represent the first and second phases of the in-phase sequence and the orthogonal sequence, respectively. The center of a local modal cluster , .

[0088] The aggregated dynamic modes corresponding to the center of each local mode cluster are aggregated to obtain the aggregated signal of each mode cluster; By combining the aggregated signals of each mode cluster of the in-phase sequence and the orthogonal sequence respectively, we can obtain K mode clusters of the in-phase sequence and K mode clusters of the orthogonal sequence.

[0089] The frequency domain guided attention module is used to extract the original frequency domain information for each mode cluster of the in-phase sequence and the orthogonal sequence, respectively. Based on the original frequency domain information, the weight of each mode cluster is obtained, and the weight of each mode cluster is assigned to the corresponding mode cluster to obtain the feature representation of the in-phase sequence and the feature representation of the orthogonal sequence. The feature representations of the in-phase sequence and the feature representations of the orthogonal sequence are concatenated to obtain a one-dimensional time series signal.

[0090] The process of obtaining the weights of each mode cluster based on the original frequency domain information is as follows: The original frequency domain information is sequentially input into the first fully connected layer, the ReLU activation function layer, and the second fully connected layer to obtain the frequency domain features. The Sigmoid function is used to convert the frequency domain features into weights for each mode cluster.

[0091] The characteristic representations of in-phase sequences and orthogonal sequences are as follows:

[0092]

[0093] in, , These are the characteristic representations of in-phase sequences and orthogonal sequences, respectively. Represents the first in-phase sequence The weights of each modal cluster, Represents the first orthogonal sequence The weights of each modal cluster, Represents the first in-phase sequence A modal cluster, Represents the first orthogonal sequence A modal cluster, K is the total number of in-phase or orthogonal sequence mode clusters.

[0094] The feature extraction and classification module is used to input one-dimensional time series signals into a one-dimensional time series deep network for feature extraction and classification, and output modulation category.

[0095] The one-dimensional temporal deep network uses the trained InceptionTime network, which includes an input module, a multi-layer Inception structural unit, a global average pooling module, and a fully connected classification module connected in sequence. The m-th layer Inception structural unit and the (m+2)-th layer Inception structural unit are connected by a residual connection module, where m≥1.

[0096] The training process of the InceptionTime network includes: The dynamic mode sequences of in-phase sequences and orthogonal sequences of multiple samples are obtained. Based on K-Means clustering, the dynamic mode sequences of in-phase sequences and orthogonal sequences of each sample are subjected to mode clustering and the modes are reconstructed to obtain K mode clusters of in-phase sequences and K mode clusters of orthogonal sequences. The original frequency domain information is extracted for each mode cluster of the in-phase sequence and the orthogonal sequence respectively. The original frequency domain information is then input into the first fully connected layer, the ReLU activation function layer and the second fully connected layer in sequence to obtain frequency domain features. The Sigmoid function is used to convert the frequency domain features into weights for each mode cluster. The weights of each mode cluster are assigned to the corresponding mode clusters to obtain the feature representations of the in-phase sequence and the orthogonal sequence. The feature representations of the in-phase sequence and the orthogonal sequence are concatenated to obtain the one-dimensional time series signal of each sample. The InceptionTime network is trained based on the one-dimensional time series signals of all samples, resulting in the trained InceptionTime network.

[0097] Experimental Analysis This invention utilizes the DeepRadar2022 radar signal database created by the Radar and Microwave Group at the Polytechnic University of Madrid. DeepRadar2022 is commonly used for radar signal modulation classification. This database contains 23 different modulation types, including LFM, 2 / 4 / 8-FSK, 2 / 4 / 8-PSK, Costas, Barker, Huffman, Frank, P1–P4, Px, Zadoff-Chu, T1–T4, non-modulation, and noise modulation. Each signal sample is 1024 in length, covering a signal-to-noise ratio range from -12 dB to 20 dB with a step size of 2 dB. Given that the research focuses on the impact of signal denoising on recognition performance, pure noise samples were removed during the experiment to eliminate the influence of interference terms. The signals in the dataset are processed using SGMD to construct a new physical representation space, which is then input into the Freq-AttNet network for training and testing.

[0098] In this experiment, radar signals were classified and identified using the Physics-Guided Representational Learning (PGRL) framework to obtain the recognition accuracy under different signal-to-noise ratios. Figure 6 The signal modulation recognition method of the present invention, guided by physical learning, is compared with the recognition accuracy of existing signal decomposition methods at different signal-to-noise ratios. Figure 6 In this context, Raw-InceptionTime means the raw signal without signal decomposition is directly input into the InceptionTime network; WT-InceptionTime means the signal is input into the InceptionTime network after being processed by the WT denoising algorithm; EMD-InceptionTime means the signal is input into the InceptionTime network after being processed by the EMD denoising algorithm; VMD-InceptionTime means the signal is input into the InceptionTime network after being processed by the VMD denoising algorithm; and PGRL refers to the signal modulation recognition method for physically guided deep learning proposed in this invention.

[0099] Figure 7 The signal modulation recognition method of the present invention, which is based on physical guidance deep learning, is compared with the recognition accuracy of existing end-to-end recognition networks under different signal-to-noise ratios. Figure 7Among them, TodyNet (Temporal Dynamic Graph Neural Network) is a temporal dynamic graph neural network for multivariate time series classification; ConvtimeNet is a deep hierarchical fully convolutional model for multivariate time series analysis; DeepConvContext (Deep Convolutional Context Network) is a deep convolutional context network; DUET (Dual Clustering Enhanced Time-series Forecasting) is a dual clustering enhanced time series prediction model; Mantis is a lightweight calibrated time series classification base model; MEGAT (Graph Attention Network with Multidimensional Edge Feature Learning) is a graph attention time series model; and SHAP (SHapley Additive exPlanations) is a classification network based on game theory-based attribution analysis.

[0100] In practical deployments, balancing recognition accuracy and resource consumption is crucial. To assess this, this invention analyzes the model's complexity from two aspects: learnable parameters and the number of floating-point operations (FLOPs).

[0101] Table 1 provides a comprehensive comparison. While lightweight models like TodyNet and CnovTimeNet have lower complexity, they typically lack the ability to capture fine-grained features in low signal-to-noise ratio environments. Conversely, high-performance baseline models often suffer from parameter explosion. Notably, compared to the strongest competing baseline models such as Mantis and DeepCnovContext, the PGRL framework proposed in this invention requires only 1.99 million parameters, resulting in a significantly smaller footprint. This demonstrates that the superior accuracy of PGRL is not solely achieved through layer stacking, but rather through efficient structure-preserving representations and physically guided filtering.

[0102] Table 1 Comparison of computational complexity of different models

[0103] A key design goal of PGRL is to enhance the discriminative power of features without significantly increasing computational overhead. To verify this, we explicitly compare the standalone backbone network MSTB with the full PGRL framework. As shown in the last two rows of Table 1, the increase in complexity introduced by the frequency-guided modal gating module is negligible: the number of parameters increases by only about 0.033M (1.7%), and at the shown accuracy, FLOPs remain almost unchanged.

[0104] Regarding computational overhead, PGRL has higher FLOPs than simple end-to-end convolutional neural networks. This is an intentional design trade-off aimed at achieving better robustness in complex electromagnetic environments, thus requiring a larger receptive field and deeper channels for thorough signal analysis. However, due to the relatively low computational cost of the SGMD modules used in the front end and the gating units themselves, in resource-constrained scenarios, the MSTB network can be replaced with a lighter structure (such as MobileNet), thereby achieving an adjustable trade-off between robustness and latency.

[0105] Figure 6 and Figure 7 The advantages of the PGRL method compared to other signal decomposition methods and end-to-end recognition networks are demonstrated under different signal-to-noise ratios, especially at low signal-to-noise ratios, where the advantages are more significant. The physically guided deep learning framework algorithm of this invention has been tested and achieves an accuracy of 82.83%, with a precision of 82.2%, a recall of 82.83%, and an F1 score of 82.78%.

[0106] The confusion matrix between different modulated signals is as follows Figure 8 As shown, Figure 8 The modulation types include: LFM, 2FSK, 4FSK, 8FSK, Costas, 2PSK, 4PSK, 8PSK, Barker, Huffman, Frank, P1, P2, P3, P4, Px, Zadoff_Chu, T1, T2, T3, T4, NM.

[0107] This invention calculates the F1-score for each class on the DeepRadar2022 test set and uses TodyNet, which has the best overall performance among end-to-end comparison methods, as a reference. The results are as follows: Figure 9 As shown, Figure 9In the graph, the horizontal axis represents the modulation type, and the vertical axis represents the F1 score gain. Modulation types include: 8PSK, 4PSK, 2PSK, 8FSK, T4, 4FSK, Zadoff_Chu, Barker, P1, P2, Px, Costas, NM, T2, Huffman, P3, P4, LFM, T3, T1, Frank, and 2FSK. This indicates that the physical modality cluster representation constructed by PGRL does not simply "overall improve" classification performance, but rather tends to address the shortcomings of end-to-end models in depicting complex phase structures, code sequence textures, and sideband details, resulting in clearer class boundaries and less confusion. This class-level gain spectrum indirectly verifies the mechanism of "physical prior-driven modality deconstruction + attention selection": its gains mainly come from the enhanced representation of fine-grained modulation textures and sideband structures, rather than relying on simple stacking of network capacity.

[0108] This invention selects three samples of the same modulation type, LFM, from the DeepRadar2022 test set, corresponding to low, medium, and high signal-to-noise ratios respectively. The attention module (10dB, 0dB, and 18dB) and its DM modal clusters and component-level attention weights are shown in Figures 10(a), 10(b), and 10(c). The attention module implements an adaptive filtering mechanism at the component level that prioritizes structurally clear components over clear ones. Its decision logic is highly consistent with the experience of prioritizing structurally clear components in traditional manual analysis, thus providing intuitive and strong evidence for the physical interpretability claimed by the PGRL framework.

[0109] 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. A signal modulation recognition method guided by physics and deep learning, characterized in that: include: Symplectic geometric mode decomposition was performed on the preprocessed in-phase and orthogonal sequences to obtain the dynamic mode sequences of the in-phase and orthogonal sequences, respectively. Based on K-Means clustering, the dynamic mode sequences of in-phase sequences and orthogonal sequences are respectively subjected to mode clustering and mode reconstruction to obtain K mode clusters of in-phase sequences and K mode clusters of orthogonal sequences. The original frequency domain information is extracted from each mode cluster of the in-phase sequence and the orthogonal sequence respectively. The weight of each mode cluster is obtained based on the original frequency domain information, and the weight of each mode cluster is assigned to the corresponding mode cluster to obtain the feature representation of the in-phase sequence and the feature representation of the orthogonal sequence. The feature representations of the in-phase sequence and the feature representations of the orthogonal sequence are concatenated to obtain a one-dimensional time series signal. One-dimensional time series signals are input into a one-dimensional temporal deep network for feature extraction and classification, and the modulation category is output.

2. The signal modulation recognition method for physically guided deep learning according to claim 1, characterized in that: The process of performing symplectic geometric mode decomposition on the preprocessed in-phase and orthogonal sequences includes: Based on Takens embedding, the phase space of the preprocessed in-phase and orthogonal sequences is reconstructed to construct the trajectory matrices of the in-phase and orthogonal sequences. Construct the covariance matrices of the in-phase sequence and the orthogonal sequence respectively based on the trajectory matrices of the in-phase sequence and the orthogonal sequence; The covariance matrix of the in-phase sequence and the orthogonal sequence is decomposed using the QR decomposition method to obtain the eigenvector matrix of the in-phase sequence and the orthogonal sequence. The reconstruction matrix of the in-phase sequence is constructed using the eigenvector matrix and trajectory matrix of the in-phase sequence, and the reconstruction matrix of the orthogonal sequence is constructed using the eigenvector matrix and trajectory matrix of the orthogonal sequence. The reconstruction matrix is ​​transformed to obtain the dynamic mode sequence of the in-phase sequence and the dynamic mode sequence of the orthogonal sequence.

3. The signal modulation recognition method for physically guided deep learning according to claim 2, characterized in that: Dynamic mode sequence of in-phase sequence Dynamic mode sequences of orthogonal sequences They are respectively: in, The first dynamic mode sequence representing an in-phase or orthogonal sequence. One modality, , , , To reconstruct the elements in the matrix, , , To determine the effective number of columns in the reconstructed trajectory matrix, For the embedding dimension, , The signal length of the original signal. For the delay time, if , ,otherwise .

4. The signal modulation recognition method for physically guided deep learning according to claim 1, characterized in that: The process of performing mode clustering and mode reconstruction based on K-Means clustering on the dynamic mode sequences of in-phase sequences and orthogonal sequences includes: For the dynamic mode sequences of in-phase sequences respectively Dynamic mode sequences of orthogonal sequences K-Means clustering is performed to obtain K local mode cluster centers for in-phase sequences and K local mode cluster centers for orthogonal sequences. By minimizing the distance between the dynamic mode and the local mode cluster centers, several dynamic modes corresponding to each local mode cluster center are obtained. , They represent in-phase and orthogonal, respectively. K is the number of dynamic modes, and K is less than 1. ; The aggregated dynamic modes corresponding to the center of each local mode cluster are aggregated to obtain the aggregated signal of each mode cluster; By combining the aggregated signals of each mode cluster of the in-phase sequence and the orthogonal sequence respectively, we can obtain K mode clusters of the in-phase sequence and K mode clusters of the orthogonal sequence.

5. The signal modulation recognition method for physically guided deep learning according to claim 4, characterized in that: The method for minimizing the distance between the dynamic mode and the center of the local mode cluster is as follows: in, Represents the dynamic mode sequence of an in-phase sequence The Middle One modality, Dynamic mode sequence of in-phase sequence The set that is formed Dynamic mode sequence representing orthogonal sequences The Middle One modality, Dynamic mode sequence of orthogonal sequence The set that is formed , Represent the first and second phases of in-phase sequences and orthogonal sequences, respectively. The center of a local modal cluster , .

6. The signal modulation recognition method for physically guided deep learning according to claim 1, characterized in that: The process of obtaining the weights of each mode cluster based on the original frequency domain information is as follows: The original frequency domain information is sequentially input into the first fully connected layer, the ReLU activation function layer, and the second fully connected layer to obtain the frequency domain features. The Sigmoid function is used to convert the frequency domain features into weights for each mode cluster.

7. The signal modulation recognition method for physically guided deep learning according to claim 1, characterized in that: The characteristic representations of in-phase sequences and orthogonal sequences are as follows: in, , These are the characteristic representations of in-phase sequences and orthogonal sequences, respectively. Represents the first in-phase sequence The weights of each modal cluster, Represents the first orthogonal sequence The weights of each modal cluster, Represents the first in-phase sequence A modal cluster, Represents the first orthogonal sequence A modal cluster, K is the total number of in-phase or orthogonal sequence mode clusters.

8. The signal modulation recognition method for physically guided deep learning according to claim 1, characterized in that: The one-dimensional temporal deep network uses the trained InceptionTime network, which includes an input module, a multi-layer Inception structural unit, a global average pooling module, and a fully connected classification module connected in sequence. The m-th layer Inception structural unit and the (m+2)-th layer Inception structural unit are connected by a residual connection module, where m≥1.

9. The signal modulation recognition method for physically guided deep learning according to claim 1, characterized in that: The training process of the InceptionTime network includes: The dynamic mode sequences of in-phase sequences and orthogonal sequences of multiple samples are obtained. Based on K-Means clustering, the dynamic mode sequences of in-phase sequences and orthogonal sequences of each sample are subjected to mode clustering and the modes are reconstructed to obtain K mode clusters of in-phase sequences and K mode clusters of orthogonal sequences. The original frequency domain information is extracted for each mode cluster of the in-phase sequence and the orthogonal sequence respectively. The original frequency domain information is then input into the first fully connected layer, the ReLU activation function layer and the second fully connected layer in sequence to obtain frequency domain features. The Sigmoid function is used to convert the frequency domain features into weights for each mode cluster. The weights of each mode cluster are assigned to the corresponding mode clusters to obtain the feature representations of the in-phase sequence and the orthogonal sequence. The feature representations of the in-phase sequence and the orthogonal sequence are concatenated to obtain the one-dimensional time series signal of each sample. The InceptionTime network is trained based on the one-dimensional time series signals of all samples, resulting in the trained InceptionTime network.

10. A signal modulation recognition system guided by physical deep learning, characterized in that: include: The signal decomposition module is used to perform symplectic geometric mode decomposition on the preprocessed in-phase and orthogonal sequences to obtain the dynamic mode sequences of the in-phase and orthogonal sequences, respectively. The physical representation space construction module is used to perform mode clustering and mode reconstruction on the dynamic mode sequences of in-phase sequences and orthogonal sequences based on K-Means clustering, respectively, to obtain K mode clusters of in-phase sequences and K mode clusters of orthogonal sequences; The frequency domain guided attention module is used to extract the original frequency domain information for each mode cluster of the in-phase sequence and the orthogonal sequence, respectively. Based on the original frequency domain information, the weight of each mode cluster is obtained, and the weight of each mode cluster is assigned to the corresponding mode cluster to obtain the feature representation of the in-phase sequence and the feature representation of the orthogonal sequence. The feature representations of the in-phase sequence and the feature representations of the orthogonal sequence are concatenated to obtain a one-dimensional time series signal. The feature extraction and classification module is used to input one-dimensional time series signals into a one-dimensional time series deep network for feature extraction and classification, and output modulation category.

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