Small sample radiation source individual identification method based on isopotential constellation diffusion enhancement

Abstract

The equal-potential constellation map diffusion enhancement-based small sample radiation source individual identification method belongs to the technical fields of radiation source signal processing and deep learning application, and solves the problems of low sample fidelity, weak feature distinction and serious misjudgment of existing methods under extremely small samples; the method comprises the following steps: mapping one-dimensional IQ signals to structured two-dimensional constellation profile images through continuous kernel density estimation of a two-dimensional Gaussian kernel function; pre-training a diffusion model by using a large-scale source domain data set, combining with elastic weight consolidation regularization, and migrating to the target domain extremely small sample to complete cross-domain distribution structure alignment; in the reverse denoising sampling, the inter-class margin bidirectional gradient force field guidance, Schmidt orthogonal projection correction and manifold anchoring triple constraints are fused to generate enhanced samples; an expanded data set is constructed by combining original samples, and an individual identification result is output by a dense feature reuse classification network. The present application effectively suppresses small sample overfitting and improves the identification accuracy and stability.

Description

Technical Field

[0001] This invention belongs to the field of radiation source signal processing and deep learning application technology, specifically involving a method for identifying individual radiation sources in small samples based on diffusion enhancement of equipotential constellation diagrams. Background Technology

[0002] With the rapid development of wireless communication, the Internet of Things, and electromagnetic countermeasures technologies, the electromagnetic spectrum environment is becoming increasingly complex and dense. Specific Emitter Identification (SEI), as a core technology for physical layer security authentication, illegal electromagnetic signal control, and non-cooperative electromagnetic reconnaissance, relies on the unique radio frequency fingerprint (RFF) resulting from the nonlinear defects in device hardware. It can accurately distinguish and trace different transmitting devices, possessing significant application value in both civilian wireless security protection and military electromagnetic spectrum countermeasures. In actual electromagnetic monitoring scenarios, target radiation sources are mostly non-cooperative, short-duration burst signals, and the number of available labeled samples is extremely limited, posing a significant challenge to high-precision specific emitter identification.

[0003] Existing radiation source identification technologies mostly rely on manual feature design or conventional deep learning models. While they can achieve stable identification under sufficient sample conditions, they exhibit significant shortcomings in scenarios with extremely small sample sizes. Traditional models are prone to severe overfitting due to scarce training data, and the network cannot fully learn the device-specific weak fingerprint features, resulting in a significant decrease in generalization ability. At the same time, conventional data augmentation methods have poor adaptability to weak radio frequency fingerprints, easily leading to low-quality sample generation and loss of true fingerprint features, making it difficult to effectively expand small sample datasets and improve model training performance.

[0004] In recent years, diffusion probabilistic models have been increasingly applied to the field of radio frequency (RF) signal data augmentation due to their excellent detail generation capabilities. However, existing diffusion models suffer from limited constraints, are susceptible to channel interference and invalid features during small-sample training, and generate constellation image samples with a large amount of invalid noise and spurious features, thus disrupting the inherent sparse distribution characteristics of RF signals and resulting in low sample fidelity and reliability. Furthermore, existing methods cannot effectively optimize the decision boundaries for overlapping features of similar radiation sources, are prone to misidentification of device fingerprints, exhibit poor model recognition stability, and suffer from large performance fluctuations, making it difficult to meet the requirements for high-precision, fine-grained radiation source identification.

[0005] Furthermore, Chinese patent CN113657138B discloses a method for individual radiation source identification based on equipotential constellation maps. This method maps IQ signals to constellation maps, calculates point density, colors the data, and then inputs it into a convolutional neural network for classification. This method belongs to a discriminative direct classification scheme and does not involve data augmentation or sample expansion in small-sample scenarios. Chinese patent CN116881769B discloses a method for small-sample radiation source data augmentation and individual identification based on equipotential constellation maps. It uses a generative adversarial network (GAN) to augment the equipotential constellation map and performs post-screening using structural similarity metrics. However, the quality control of this method is post-screening and does not participate in the generation process itself, making it impossible to remove non-physical artifacts in real-time during backsampling. Moreover, GANs are prone to pattern collapse in extremely small sample sizes, resulting in insufficient diversity of generated samples.

[0006] In summary, current small-sample radiation source identification technologies generally suffer from technical bottlenecks such as severe overfitting, poor enhanced sample quality, insufficient feature discrimination, and weak model stability. There is an urgent need for a high-fidelity, high-stability, and strong-generalization scheme for identifying individual radiation sources in small samples. Summary of the Invention

[0007] To address the problems in existing technologies, this invention provides a method for identifying individual radiation sources in small samples based on equipotential constellation diagram diffusion enhancement. The aim is to overcome the shortcomings of existing technologies, such as distortion of the sampling trajectory during inverse denoising, geometric and topological distortion of the generated samples, destruction of the physical sparsity of radio frequency fingerprints, and ambiguity of the decision boundaries of downstream classifiers, when enhancing data from extremely small radiation sources. By introducing multi-dimensional structural constraints and the synergistic guidance of discriminative gradients, the method improves the quality of data enhancement and the accuracy and robustness of identifying individual radiation sources.

[0008] A method for identifying individual radiation sources from small samples based on equipotential constellation diagram diffusion enhancement includes the following steps: Step 1: Obtain the IQ signal of the radiation source in the target domain, and map the one-dimensional time-domain IQ signal sequence into a structured two-dimensional constellation map contour image with density-aware characteristics through continuous kernel density estimation of the two-dimensional Gaussian kernel function, which serves as a physical carrier characterizing the hardware RF fingerprint of the radiation source. Step 2: Use a large-scale source domain radiation source dataset to perform self-supervised pre-training on the unconditional diffusion probability model. Transfer the pre-trained network parameters to a very small sample radiation source dataset in the target domain for fine-tuning. In the fine-tuning stage, introduce elastic weights to consolidate the parameter regularization constraints. Based on the importance of the network parameters in preserving the general feature manifold of the source domain, selectively lock key network parameters to complete the cross-domain distribution structure alignment and obtain the fine-tuned diffusion probability model for the target domain. Step 3: In the reverse iterative denoising sampling process of the fine-tuned diffusion probability model, hierarchical structure constraint sampling is performed to obtain an enhanced structured two-dimensional constellation map contour image that satisfies the physical consistency constraint. Step 4: Fuse the enhanced structured 2D constellation map contour image with the original target domain minimal sample data to construct an expanded radiation source dataset; Step 5: Use the expanded radiation source dataset to train the parameters of the dense feature reuse classification network, and use the trained dense feature reuse classification network to classify and identify the target radiation source, and output the individual identity label of the target radiation source.

[0009] Furthermore, step 3 specifically involves: Step 3.1: Construct a bidirectional gradient force field function based on the auxiliary discriminant network, which includes the target attraction gradient and the competition repulsion gradient, to guide the sampling trajectory toward the center of the target class while approaching the boundary region of easily confused competition classes; Step 3.2: Construct the prior background mask matrix for the blank area of ​​the constellation diagram background, calculate the background energy violation function, and project the discrimination gradient obtained in sub-step 3.1 onto the null space of the negative gradient direction of the background energy violation function through the Schmitt orthogonalization principle to obtain the corrected orthogonal projection gradient, so as to eliminate the non-physical gradient components that cause geometric and topological distortion. Step 3.3: Construct the elastic recovery centripetal force term based on Euclidean distance, obtain the anchoring gradient by taking the derivative, and dynamically correct the inverse denoising sampling trajectory back to the implicit radio frequency prior support set; Step 3.4: Integrate the corrected orthogonal projection gradient and the anchoring gradient into the Langevin dynamics update equation to control the inverse denoising sampling trajectory update at each time step, and generate the enhanced structured two-dimensional constellation map contour image.

[0010] Furthermore, in step 3.1: The bidirectional gradient force field function is constructed based on the discriminant potential energy function, which is calculated as follows: in, This is the signal sample at the current iteration time. For target category The posterior probability, To exclude the target category The most confusing competitive category The log-conditional probability; The negative gradient of the discriminant potential function with respect to the current state is obtained to yield the bidirectional gradient force field function: in, Let the category label of the radiation source be a random variable. This represents the inverse denoising state at the current time t. Let be the gradient differential operator, representing the inverse denoised state. Find the differential gradient; Attract gradients for the target. To compete for gradient exclusion.

[0011] Furthermore, in step 3.2: The background energy violation function formula is: ⊙ in, For background energy violation value, This is the unbiased, denoised estimate for the current time step. The background mask matrix is ​​the prior background mask matrix for the background blank area, and ⊙ represents the Hadamard product operation; The negative gradient of the background energy violation function is obtained by taking the negative gradient of the physical sparsity. ; The matrix operation formula for the corrected orthogonal projection gradient is: in, To correct the gradient for orthogonal projection, For the discriminative gradient, This represents the vector dot product operation. Represents norm operations, To prevent extremely small adjustment constants where the denominator is zero.

[0012] Furthermore, in step 3.3: The formula for the elastic recovery centripetal force term is: in, This is the cumulative noise scheduling coefficient; The anchoring gradient is obtained by differentiating the elastic recovery centripetal force term. .

[0013] Furthermore, in step 3.4: The Langevin dynamics update equation is as follows: in, This is the inverse denoising state for the next time step. This is the base mean predicted by the diffusion probability model. To control the hyperparameter coefficients for determining guidance intensity, To control the hyperparameter coefficients of the manifold anchoring strength, The standard Gaussian white noise matrix is ​​used. For a moment The inherent variance step size.

[0014] Furthermore, in step 1, the mapping formula for the continuous kernel density estimation of the two-dimensional Gaussian kernel function is: in, For spatial coordinates on the complex plane, The total number of sampling points. To smooth bandwidth, For the first Discrete sampling points, It is a two-dimensional Gaussian kernel function. The structured two-dimensional constellation outline image.

[0015] Furthermore, in step 2, the regularization constraint of the elastic weight consolidation parameter makes the total loss function in the fine-tuning stage as follows: in, To fine-tune the training loss function, Let be the denoising score matching loss function for a dataset of minimal radiation sources in the target domain. For weight balancing adjustment parameters, For the target domain, the current training of the first Network parameters, The optimal first-order result after source domain pre-training Network parameters, These are the diagonal elements of the Fisher information matrix.

[0016] Further: The dense feature reuse classification network includes a backbone feature extraction network with a dense connection architecture and a projection classification head containing a two-layer random deactivation mechanism; In the backbone feature extraction network, the first... The input to the layer is constructed by performing a channel-level concatenation operation on the output feature maps of all preceding layers, as shown in the formula: in, For the first The output feature map of the layer, This represents the channel-level concatenation and concatenation operator. This represents a composite nonlinear transformation function that includes batch normalization, linear rectified activation, and two-dimensional convolution. The projection classification head is sequentially connected to two random deactivation layers and an intermediate low-dimensional hidden layer at the output of the backbone feature extraction network.

[0017] Furthermore, the target domain minimum sample size is defined as no more than 30 labeled samples used for model training for each type of radiation source device.

[0018] The beneficial effects of this invention are as follows: By introducing an adaptive cross-domain distribution structure alignment module, robust migration of the diffusion probability model from the source domain to the target domain is achieved using elastic weights to consolidate parameter regularization. By quantifying the importance of network parameters to the general feature manifold of the source domain using the Fisher information matrix, key parameters are selectively locked during fine-tuning with minimal samples in the target domain. This solves the problems of catastrophic forgetting and mode collapse during fine-tuning of the diffusion model with small samples, ensuring effective alignment of cross-domain radio frequency feature distributions.

[0019] Through the synergistic effect of the triple constraints in the hierarchical structure constraint sampling module, multi-dimensional quality control of generated samples is achieved during the inverse iterative denoising process. The inter-class margin bidirectional gradient force field generates high-value, difficult-to-confuse samples through a synergistic mechanism of "target attraction + competitive repulsion," enhancing the ability to distinguish subtle RF fingerprints of similar devices. The Schmidt orthogonal projection correction accurately eliminates non-physical gradient components by projecting the discriminant gradient to the null space of the background energy violation direction, thus eliminating constellation map background artifacts. The manifold anchoring constraint dynamically corrects the sampling trajectory back to the implicit RF prior support set through elastic recovery of centripetal force. The triple constraints are also integrated into the Langevin dynamics update equation, achieving a balance between high physical fidelity of generated samples and strong decision boundary partitioning capabilities.

[0020] By using the full-channel cascaded structure of the dense feature reuse classification network, the weak radio frequency texture fingerprints extracted by the shallow network can be directly transmitted to the decision layer across layers, avoiding the excessive smoothing of fingerprint features by the deep network. By introducing multi-level random perturbations in the feature manifold space through the two-layer random deactivation projection classification head, the classification decision boundary is effectively smoothed, and the overfitting phenomenon under small sample conditions is suppressed to the maximum extent.

[0021] This invention forms an end-to-end enhancement and recognition link from one-dimensional signal acquisition to two-dimensional structured mapping, cross-domain distributed structure alignment, structural constraint sampling trajectory reconstruction, and dense feature classification output. It effectively improves the accuracy and robustness of individual radiation source identification under extremely small sample conditions and has excellent generalization ability and engineering application value. Attached Figure Description

[0022] Figure 1 This is a flowchart of the present invention; Figure 2 This is a schematic diagram illustrating the principle of the cross-domain distribution alignment module in this invention; Figure 3This is a schematic diagram of the hierarchical structure constraint sampling module. The arrow pointing to the center of the target category feature is the positive attraction arrow, which corresponds to the attraction gradient force field of the target category center. The arrows that move away from the target category and point to the neighboring easily confused competing category are the reverse repulsion arrows, which correspond to the repulsion gradient force field of the most competitive easily confused category. Figure 4 This is a confusion matrix diagram of approximately homogeneous radiation sources when 30 labeled samples are selected for a single class in the target domain radiation source identification scenario of this invention. Detailed Implementation

[0023] The present invention will now be described in detail with reference to the accompanying drawings. Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention. The directional terms such as left, center, right, top, and bottom in the embodiments of the present invention are only relative concepts or referenced to the normal use state of the product, and should not be considered restrictive.

[0024] Small sample radiation source individual identification method based on equipotential constellation diagram diffusion enhancement, such as Figure 1 As shown, the minimal sample radiation source data of the target domain to be detected is obtained, converted into a structured two-dimensional constellation map contour image, and input into a trained structured constraint discrimination guided diffusion enhancement network for enhancement, to obtain an enhanced structured two-dimensional constellation map contour image that satisfies physical consistency; the enhanced structured two-dimensional constellation map contour image and the original minimal sample data of the target domain are used to construct an expanded radiation source dataset, and input into a trained dense feature reuse classification network for individual identification, outputting the individual identification label of the target radiation source.

[0025] The structure constraint discrimination guided diffusion enhancement network includes a cross-domain distribution alignment module, a hierarchical structure constraint sampling module, and a fingerprint feature extraction and classification module; the cross-domain distribution alignment module includes a self-supervised pre-training unit and an elastic weight consolidation unit; the hierarchical structure constraint sampling module includes an inter-class margin guidance submodule, a Schmitt orthogonal projection correction submodule, and a manifold anchoring submodule.

[0026] The cross-domain distribution alignment module establishes a structured alignment of radio frequency visual manifolds between heterogeneous source domains and sparse target domains through self-supervised pre-training and parameter regularization transfer mechanisms.

[0027] In the process of reverse iterative denoising trajectory reconstruction, the hierarchical structure constraint sampling module introduces a multi-objective closed-loop control mechanism. By coordinating the inter-class discrimination gradient and physical manifold constraints, it ensures that the generated enhanced samples have high physical fidelity and strong decision boundary partitioning ability.

[0028] The dense feature reuse classification network achieves comprehensive reuse of weak texture fingerprints at both shallow and deep layers through a densely connected backbone, and provides highly generalizable radiation source individual identity labels at the output end through a nonlinear projection classification head.

[0029] The method for identifying individual radiation sources in a small sample includes the following steps: Step 1: Obtain the IQ signal of the target domain radiation source and map the one-dimensional time-domain IQ signal sequence into a structured two-dimensional constellation diagram outline image; The data input is the raw one-dimensional complex time-domain in-phase quadrature (IQ) signal intercepted by the receiving system. In this embodiment, the input data is a one-dimensional baseband complex sequence. In order to transform the weak hardware defects in the one-dimensional discrete waveform into a physical topology in a high-dimensional space that is easy for the diffusion model to learn, the mapping module performs continuous kernel density estimation based on a two-dimensional Gaussian kernel function, projecting the discrete sampling points onto the complex plane.

[0030] In this embodiment, the mapping formula for continuous kernel density estimation using a two-dimensional Gaussian kernel function is as follows: in, For spatial coordinates on the complex plane, The total number of sampling points. To smooth bandwidth, For the first Discrete sampling points, It is a two-dimensional Gaussian kernel function. The generated structured two-dimensional constellation outline image with density-aware characteristics serves as a physical carrier characterizing the hardware radio frequency fingerprint of the radiation source.

[0031] Through this transformation, the instantaneous displacement of discrete sampling points is converted into a continuous two-dimensional spatial probability density distribution function, outputting a structured two-dimensional image representation. Specifically, this structured two-dimensional image representation is a two-dimensional structured constellation diagram contour image with a size of 256×256 pixels. This two-dimensional structured constellation diagram contour image not only carries the geometric boundaries of a conventional constellation diagram but also explicitly represents the statistical clustering fingerprint caused by power amplifier nonlinear distortion, local oscillator phase noise, and in-phase orthogonal imbalance through probability density gradients.

[0032] This embodiment utilizes a publicly available real-world radio frequency fingerprint dataset for method validation. The specific configuration includes two independent electromagnetic signal domains. The source domain dataset uses the ADS-B dataset, containing heterogeneous pulse position modulation (PPM) signals, comprising 33,582 unlabeled samples covering 100 source domain radiation source devices, used for self-supervised fingerprint manifold pre-training of the diffusion model. The target domain dataset uses the NJUPT-RFF dataset, containing orthogonal amplitude modulation (OAM) signals, specifically 16QAM modulation format, a carrier frequency of 433 MHz, and a sampling rate of 5 MHz, containing 7 target radiation source devices.

[0033] To simulate extreme, non-cooperative, sudden, small-sample scenarios, this embodiment randomly selects only a fixed number of samples from each target radiation source device. The samples are used as the training set with known labels, where The optional configuration sets are 5, 10, 15, 20, 25, and 30, with the remaining target domain data used as the test set. The signal sample shape dimensions of the training and test sets are distributed as a dual-channel 6000-point time-domain discrete sequence in the source domain and a dual-channel 200000-point time-domain discrete sequence in the target domain. The two domains are completely separated in terms of modulation scheme, carrier frequency band, and physical pulse shape.

[0034] Determining the correctness of the individual radiation source identity is a fine-grained multi-classification task. The system uses the recognition accuracy to measure the percentage of correctly predicted radiation source samples out of the total test samples. At the same time, the ratio of the standard deviation to the arithmetic mean (coefficient of variation) after 10 rounds of Monte Carlo trials is used to quantitatively reflect the training stability of the enhancement algorithm in complex and variable electromagnetic environments.

[0035] Step 2: Cross-domain distributed structure alignment module like Figure 2 As shown, the unconditional diffusion probability model is pre-trained in a self-supervised manner using a large-scale source domain radiation source dataset. The pre-trained network parameters are then transferred to a very small sample radiation source dataset in the target domain for fine-tuning. Elastic weights are introduced during the fine-tuning stage to reinforce parameter regularization constraints. Based on the importance of the network parameters in preserving the general feature manifold of the source domain, key network parameters are selectively locked to complete the cross-domain distribution structure alignment, resulting in a fine-tuned diffusion probability model oriented towards the target domain.

[0036] Under the constraint of extremely small sample sizes, directly training a diffusion model with a large number of parameters on the target domain can lead to severe gradient dispersion and mode collapse. To address this, the cross-domain distribution alignment module performs two-stage transfer learning.

[0037] In the first stage of self-supervised pre-training, the unconditional diffusion probability model is trained on the large-scale two-dimensional structured constellation map contour image of the source domain using a standard score-matching loss function, so that its denoising network can fully capture the common continuous manifold prior of the constellation distribution of radio signals.

[0038] In the second fine-tuning stage, the pre-trained weight parameters are transferred to a very small sample of data in the target domain. To prevent the model from erasing learned common radio features when fitting to a very small number of target radiation sources, an elastic weight consolidation parameter regularization constraint term is introduced into the total loss function of the model fine-tuning. The total loss function formula is: in, To fine-tune the training loss function, To determine the denoising score matching loss function for a dataset of radiation sources with minimal sample size in the target domain. To reinforce the regularization constraint term of the introduced elastic weights, For weight balancing adjustment parameters, For the target domain, the current training of the first Network parameters, The optimal first-order result after source domain pre-training Network parameters, These are the diagonal elements of the Fisher information matrix, used to quantify and lock in important network parameters that play a key supporting role in preserving the general characteristic manifold of the source domain.

[0039] Diagonal elements of the Fisher information matrix The first one was rigorously quantified. The importance of each network parameter to preserving the general feature manifold of the source domain. Through the aforementioned secondary penalty term, the weight parameters that play a key supporting role in the source domain fingerprint skeleton will be forcibly locked, while parameters with lower importance are allowed to align to the unique fingerprint of the new radiation source in the target domain, thereby achieving robust cross-domain structural distribution alignment under extremely scarce labeled samples.

[0040] Step 3: Hierarchical Structure Constraint Sampling Module During the inverse iterative denoising sampling process of the fine-tuned diffusion probability model, hierarchical structure constraint sampling is performed to obtain an enhanced structured two-dimensional constellation map contour image that satisfies physical consistency constraints.

[0041] like Figure 3As shown, in the inverse iterative denoising trajectory reconstruction process of the diffusion probability model, if a traditional classifier without constraints is directly used as the guide, the noise gradient released by the auxiliary classifier under small sample sizes will forcibly pull the inverse state, introducing a large number of non-physical illusionary spots in the background blank area of ​​the two-dimensional structured constellation map contour image and destroying the geometric edges of the constellation map. To solve this problem, this module introduces a hierarchical structure constraint sampling mechanism with multi-objective closed-loop control. Specifically: Step 3.1: Class Margin Guidance Based on the auxiliary discriminant network, a bidirectional gradient force field function containing target attraction gradient and competitive repulsion gradient is constructed. The sampling trajectory is guided towards the center of the target category (i.e., the target radiation source category) while approaching the boundary region of easily confused competing categories (i.e., competing radiation source categories). This induces the model to synthesize a structured two-dimensional constellation contour image located in the boundary region, thereby enhancing the model's ability to distinguish subtle radio frequency fingerprints of similar radiation sources.

[0042] Inter-class margin guidance of radiation sources is performed through an inter-class margin guidance submodule to enhance boundary separability. A discriminant potential function is constructed based on an auxiliary discriminant network, and the formula for the discriminant potential function is: in, This is the signal sample at the current iteration time. For target category The posterior probability, To exclude the target category The most confusing competitive category The log-conditional probability.

[0043] By obtaining the negative gradient of the discriminant potential function with respect to the current state, the bidirectional gradient force field function can be output: in, Let the category label of the radiation source be a random variable. This represents the inverse denoising state at the current time t. Let be the gradient differential operator, representing the inverse denoised state. Find the differential gradient; Attract gradients for the target to guide the sampling trajectory toward the center of the target class in order to preserve the core hardware fingerprint; The competitive repulsive gradient counterbalances the target attractive gradient, guiding the sampling trajectory to converge to the easily confused category decision boundary region. This gradient synergy creates boundary feature tension, inducing the model to synthesize a structured two-dimensional constellation contour image located in the boundary region.

[0044] In this embodiment, the auxiliary discriminant network shares the same architecture parameters with the subsequent classification network, and the parameters are frozen during the hierarchical structure constraint sampling process. Only its gradient information is used to guide the sampling trajectory, and it does not participate in backpropagation updates.

[0045] For ease of subsequent description, the gradient of the discriminant potential function is calculated to obtain the bidirectional gradient force field, thus yielding the discriminant gradient. .

[0046] Step 3.2: Schmidt orthographic projection correction Construct a prior background mask matrix for the blank areas of the constellation diagram background, calculate the background energy violation function, and then use the discriminant gradient. By projecting the gradient onto the null space of the negative gradient direction of the background energy violation function using the Schmitt orthogonalization principle, a corrected orthogonal projection gradient is obtained, thereby eliminating non-physical gradient components that cause geometric and topological distortions.

[0047] The two-dimensional constellation outline of radio frequency signals possesses inherent physical sparsity, meaning that energy must be highly concentrated within fixed level clusters, while the background region should maintain extremely high sparsity. To address this, the system constructs a priori background mask matrix for the blank areas of the constellation diagram background. And define the background energy violation function for the current inverse state: ⊙ in, For background energy violation value, This is the unbiased, denoised estimate for the current time step. This is the mask matrix for the background blank area of ​​the constellation diagram, and ⊙ represents the Hadamard product operation.

[0048] The negative gradient of physical sparsity is obtained by taking the negative gradient of the background energy violation function. It indicates the direction in which the background noise energy accumulates most intensely.

[0049] At this point, the discriminative gradient is obtained by utilizing the Schmitt orthogonalization principle. Projected onto the physical sparsity negative gradient In the null space, the corrected orthogonal projection gradient is calculated: in, To correct the gradient for orthogonal projection, Schmitt orthogonalization is used to remove harmful gradient components in the discrimination gradient that cause distortion of the constellation diagram background and violate the physical sparsity characteristics of radio frequency signals, retaining only the legitimate and valid category discrimination guidance gradient. This represents the vector dot product operation. Represents norm operations, To prevent extremely small adjustment constants with a denominator of zero, the projection operation eliminates all gradient components that would cause background distortion and speckle contamination at the geometric upper bound, retaining only the discrimination direction conjugate to the legitimate subspace of the RF fingerprint.

[0050] Step 3.3: Manifold Anchoring Constraints Construct an elastic recovery centripetal force term based on Euclidean distance, obtain the anchoring gradient by taking its derivative, and dynamically correct the inverse denoising sampling trajectory back to the implicit RF prior support set.

[0051] To prevent excessively large orthogonal gradient projections from causing the state to deviate from the implicit prior support set of the diffusion probability model, the system constructs an elastic recovery centripetal force term based on Euclidean distance: in, For the current moment The inverse denoising state. This is the cumulative noise scheduling coefficient.

[0052] The anchoring gradient is obtained by differentiating the elastic recovery centripetal force term. Step 3.4: Triple Constraint Collaborative Integration The corrected orthogonal projection gradient and the anchoring gradient are simultaneously integrated into the Langevin dynamics update equation to control the inverse denoising sampling trajectory update at each time step, generating an enhanced structured two-dimensional constellation contour image that satisfies the physical consistency constraint.

[0053] The hierarchical structure constraint sampling module uses the corrected orthogonal projection gradient and the anchoring gradient as guiding components, along with the base mean predicted by the diffusion probability model, and substitutes them into the Langevin dynamics update equation to reconstruct the unbiased inverse iterative denoising trajectory update formula for each time step: in, This is the inverse denoising state for the next time step. This is the base mean predicted by the diffusion probability model. To control the hyperparameter coefficients for determining guidance intensity, To control the hyperparameter coefficients of the manifold anchoring strength, The standard Gaussian white noise matrix is ​​used. For a moment The inherent variance step size.

[0054] Through the closed-loop trajectory control described above, the sampling module outputs a high-quality enhanced two-dimensional structured constellation outline image.

[0055] Step 4: Construct an expanded radiation source dataset The enhanced structured 2D constellation image (enhanced dataset) generated in step 3 is mixed with the original structured 2D constellation image (target dataset) obtained by mapping the original minimal samples of the target domain in step 1 to construct an expanded radiation source dataset with sufficient quantity, rich features, and high fidelity. This provides sufficient sample support for the training of downstream classification networks and solves the problem of scarce small sample data.

[0056] Step 5: Train a dense feature reuse classification network and perform classification and recognition. The parameters of the dense feature reuse classification network are trained using the expanded radiation source dataset, and the trained dense feature reuse classification network is used to classify and identify the target radiation source, outputting the individual identity label of the target radiation source.

[0057] The dense feature reuse classification network includes a backbone feature extraction network with a dense connection architecture and a projection classification head containing a two-layer random deactivation mechanism.

[0058] The backbone feature extraction network employs a cascaded stack of multi-level convolutional blocks. To prevent fingerprint textures caused by weak nonlinear defects in the transmitter hardware from being heavily smoothed and lost in the deep network structure due to continuous downsampling operations and nonlinear activation functions, the input of each layer is constructed by performing a concatenated operation on the output feature maps of all previous layers at the channel level. The formula is as follows: in, For the first The output feature map of the layer, This represents the channel-level concatenation and concatenation operator. This represents a composite nonlinear mapping function consisting of batch normalization, linear rectified activation, and two-dimensional convolution. This dense feature reuse mechanism allows the fine and weak radio frequency texture fingerprints extracted by shallow networks to be directly passed across layers to the final decision layer.

[0059] At the output of the backbone feature extraction network, the system inputs the feature vector into a nonlinear projection classification head containing a dual random deactivation mechanism. The projection classification head continuously embeds two deactivation layers with a random deactivation rate set to 0.5, with a low-dimensional linear hidden layer inserted in between. By introducing multi-level random perturbations into the feature manifold space, the classification decision boundary between different individual radiation sources is effectively smoothed, maximally suppressing overfitting under small sample sizes.

[0060] In the actual inference deployment phase, the system first performs kernel density estimation mapping in step 1 on the multimodal electromagnetic signal data of the unknown individual identity to be detected, generating the corresponding structured two-dimensional constellation diagram contour image.

[0061] Next, the corresponding structured two-dimensional constellation outline image is input into the dense feature reuse classification network that has been trained in steps 2 and 4. The fingerprint features are deeply reused through multi-level dense connection channel-level stitching. Then, the nonlinear projection classification head outputs the posterior probability distribution vector of the current signal sample on the 7 target radiation source device categories. in, This is the final fully cascaded feature output of the backbone network. This is a multilayer perceptron. Ultimately, based on the maximum probability selection criterion, the system determines the radiation source device category corresponding to the index with the largest value in the posterior probability distribution vector as the true individual identity label of the currently detected unknown electromagnetic signal.

[0062] To quantitatively verify the technical advantages of the present invention, this paper conducts a small-sample radiation source identification comparison experiment based on the NJUPT-RFF dataset. The method of the present invention is comprehensively tested with six mainstream small-sample identification and radio frequency data augmentation algorithms. The classification accuracy results of each method are shown in Table 1.

[0063] Table 1 Experimental data from the NJUPT-RFF dataset Note: The values ​​outside the parentheses in Table 1 are the recognition accuracy (%), and the values ​​inside the parentheses are the standard deviations (%) of 10 Monte Carlo trials.

[0064] As shown in Table 1, under the extremely stringent small sample training condition of 5-shot, traditional methods based on one-dimensional waveform transformation, such as DMEL and CRCN-AT, are prone to severe overfitting, with recognition accuracy only around 58%. The CSI-DA method introduces the idea of ​​two-dimensional spatial mapping, but this method relies on a fixed confidence classifier to complete data augmentation, which is easily affected by non-physical gradient interference, and the accuracy rate in the 5-shot scenario is 84.77%.

[0065] In comparison, this invention introduces Schmidt orthogonal gradient projection and manifold anchoring mechanisms in the diffusion model denoising stage, effectively correcting geometric distortions in the radio frequency constellation diagram, and simultaneously synthesizing hard samples at the classification boundaries. Under 5-shot conditions, the recognition accuracy of this method is improved to 87.09%; as the number of labeled samples increases to 30-shot, the accuracy further reaches 96.54%, which is very close to the theoretical performance limit of this radio frequency dataset.

[0066] As can be seen from the coefficient of variation curve, the present invention maintains a low and continuously converging coefficient of variation across all small sample intervals, with the value gradually decreasing from 0.0267 in 5-shot to 0.0085 in 30-shot. Compared with traditional adversarial generative models such as SA2SEI and PSPD, this scheme effectively suppresses the problem of drastic performance fluctuations caused by model pattern collapse in extremely small sample scenarios.

[0067] like Figure 4 As shown, the confusion matrix results of the test set indicate that the fingerprint feature manifolds of radiation source 3 and radiation source 6 are highly overlapping, which are typical samples that are prone to misjudgment by traditional algorithms. This invention achieves feature boundary stretching through a bidirectional margin force field, which stably improves the single-class recognition accuracy of the two easily confused radiation sources to over 80.68% and 84.00%, respectively.

[0068] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for identifying individual radiation sources from small samples based on diffusion enhancement using equipotential constellation diagrams, characterized in that: Includes the following steps: Step 1: Obtain the IQ signal of the radiation source in the target domain, and map the one-dimensional time-domain IQ signal sequence into a structured two-dimensional constellation map contour image with density-aware characteristics through continuous kernel density estimation of the two-dimensional Gaussian kernel function, which serves as a physical carrier characterizing the hardware RF fingerprint of the radiation source. Step 2: Use a large-scale source domain radiation source dataset to perform self-supervised pre-training on the unconditional diffusion probability model. Transfer the pre-trained network parameters to a very small sample radiation source dataset in the target domain for fine-tuning. In the fine-tuning stage, introduce elastic weights to consolidate the parameter regularization constraints. Based on the importance of the network parameters in preserving the general feature manifold of the source domain, selectively lock key network parameters to complete the cross-domain distribution structure alignment and obtain the fine-tuned diffusion probability model for the target domain. Step 3: In the reverse iterative denoising sampling process of the fine-tuned diffusion probability model, hierarchical structure constraint sampling is performed to obtain an enhanced structured two-dimensional constellation map contour image that satisfies the physical consistency constraint. Step 4: Fuse the enhanced structured 2D constellation map contour image with the original target domain minimal sample data to construct an expanded radiation source dataset; Step 5: Use the expanded radiation source dataset to train the parameters of the dense feature reuse classification network, and use the trained dense feature reuse classification network to classify and identify the target radiation source, and output the individual identity label of the target radiation source.

2. The method for identifying individual radiation sources from small samples based on equipotential constellation diagram diffusion enhancement according to claim 1, characterized in that: Step 3 specifically involves: Step 3.1: Construct a bidirectional gradient force field function based on the auxiliary discriminant network, which includes the target attraction gradient and the competition repulsion gradient, to guide the sampling trajectory toward the center of the target class while approaching the boundary region of easily confused competition classes; Step 3.2: Construct the prior background mask matrix for the blank area of ​​the constellation diagram background, calculate the background energy violation function, and project the discrimination gradient obtained in sub-step 3.1 onto the null space of the negative gradient direction of the background energy violation function through the Schmitt orthogonalization principle to obtain the corrected orthogonal projection gradient, so as to eliminate the non-physical gradient components that cause geometric and topological distortion. Step 3.3: Construct the elastic recovery centripetal force term based on Euclidean distance, obtain the anchoring gradient by taking the derivative, and dynamically correct the inverse denoising sampling trajectory back to the implicit radio frequency prior support set; Step 3.4: Integrate the corrected orthogonal projection gradient and the anchoring gradient into the Langevin dynamics update equation to control the inverse denoising sampling trajectory update at each time step, and generate the enhanced structured two-dimensional constellation map contour image.

3. The method for identifying individual radiation sources in a small sample based on equipotential constellation diagram diffusion enhancement according to claim 2, characterized in that: In step 3.1: The bidirectional gradient force field function is constructed based on the discriminant potential energy function, which is calculated as follows: in, The signal sample at the current iteration time. For target category The posterior probability, To exclude the target category The most confusing competitive category The log-conditional probability; The negative gradient of the discriminant potential function with respect to the current state is obtained to yield the bidirectional gradient force field function: in, Let the category label of the radiation source be a random variable. This represents the inverse denoising state at the current time t. Let be the gradient differential operator, representing the inverse denoised state. Find the differential gradient; Attract gradients for the target. To compete for gradient exclusion.

4. The method for identifying individual radiation sources in a small sample based on diffusion enhancement of equipotential constellation diagrams according to claim 3, characterized in that: In step 3.2: The background energy violation function formula is: ⊙ in, For background energy violation value, This is the unbiased, denoised estimate for the current time step. The background mask matrix is ​​the prior background mask matrix for the background blank area, and ⊙ represents the Hadamard product operation; The negative gradient of the background energy violation function is obtained by taking the negative gradient of the physical sparsity. ; The matrix operation formula for the corrected orthogonal projection gradient is: in, To correct the gradient for orthogonal projection, For the discriminative gradient, This represents the vector dot product operation. Represents norm operations, To prevent extremely small adjustment constants where the denominator is zero.

5. The method for identifying individual radiation sources in a small sample based on equipotential constellation diagram diffusion enhancement according to claim 4, characterized in that: In step 3.3: The formula for the elastic recovery centripetal force term is: in, This is the cumulative noise scheduling coefficient; The anchoring gradient is obtained by differentiating the elastic recovery centripetal force term. .

6. The method for identifying individual radiation sources in a small sample based on equipotential constellation diagram diffusion enhancement according to claim 5, characterized in that: In step 3.4: The Langevin dynamics update equation is as follows: in, This is the inverse denoising state for the next time step. This is the base mean predicted by the diffusion probability model. To control the hyperparameter coefficients for determining guidance intensity, To control the hyperparameter coefficients of the manifold anchoring strength, The standard Gaussian white noise matrix is ​​used. For a moment The inherent variance step size.

7. The method for identifying individual radiation sources in a small sample based on equipotential constellation diagram diffusion enhancement according to claim 1, characterized in that: In step 1, the mapping formula for the continuous kernel density estimation of the two-dimensional Gaussian kernel function is: in, For spatial coordinates on the complex plane, The total number of sampling points. To smooth bandwidth, For the first Discrete sampling points, It is a two-dimensional Gaussian kernel function. The structured two-dimensional constellation outline image.

8. The method for identifying individual radiation sources in a small sample based on equipotential constellation diagram diffusion enhancement according to claim 1, characterized in that: In step 2, the regularization constraint of the elastic weight consolidation parameter makes the total loss function in the fine-tuning stage as follows: in, To fine-tune the training loss function, Let be the denoising score matching loss function for a dataset of minimal radiation sources in the target domain. For weight balancing adjustment parameters, For the target domain, the current training of the first Network parameters, The optimal first-order result after source domain pre-training Network parameters, These are the diagonal elements of the Fisher information matrix.

9. The method for identifying individual radiation sources in a small sample based on equipotential constellation diagram diffusion enhancement according to claim 1, characterized in that: The dense feature reuse classification network includes a backbone feature extraction network with a dense connection architecture and a projection classification head containing a two-layer random deactivation mechanism; In the backbone feature extraction network, the first... The input to the layer is constructed by performing a channel-level concatenation operation on the output feature maps of all preceding layers, as shown in the formula: in, For the first The output feature map of the layer, This represents the channel-level concatenation and concatenation operator. This represents a composite nonlinear transformation function that includes batch normalization, linear rectified activation, and two-dimensional convolution. The projection classification head is sequentially connected to two random deactivation layers and an intermediate low-dimensional hidden layer at the output of the backbone feature extraction network.

10. The method for identifying individual radiation sources in a small sample based on equipotential constellation diagram diffusion enhancement according to claim 1, characterized in that: The target domain minimum sample size is defined as no more than 30 labeled samples used for model training for each type of radiation source device.

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