Radiation source individual identification method in limited sample scene under digital predistortion

Abstract

The invention discloses a radiation source individual identification method in a limited sample scene under digital predistortion, relates to a radiation source individual identification method, and belongs to the field of radiation source individual identification. The objective of the invention is to solve the problem of low radiation source individual identification accuracy caused by the application of a DPD technology during actual deployment, insufficient data during online SEI deployment and the like. The method for identifying the individual radiation source in the limited sample scene under digital predistortion specifically comprises the following steps: preprocessing collected signals to obtain HHT, ITD-Hilbert, CWT, CWD and GT; the HHT graph, the ITD-Hilbert graph, the CWT graph, the CWD graph and the GT graph are preprocessed, and a data set is constructed; an FS-SEI network model is constructed; the FS-SEI network model comprises a CNN network model and a relation network model; the CNN network model sequentially comprises a feature extractor and a classifier; carrying out the training of the CNN FS-SEI network model, and obtaining a trained FS-SEI network model; and inputting the test set into the trained FS-SEI network model, and outputting the category of the test set by the trained FS-SEI network model.

Description

Technical Field

[0001] The invention relates to a method for identifying individual radiation sources, and belongs to the field of individual radiation source identification. Background Art

[0002] With the proliferation of wireless devices, securing strong security within the physical layer remains a major challenge. The main purpose of SEI is to identify transmitters by analyzing the unique characteristics of unintentional modulation of pulses (UMOPs) in signals. Compared with software-based security credentials, UMOPs remain stable in nature and are particularly resistant to changes, making SEI an essential element in various wireless communication environments. Before the advent of deep learning (DL), traditional SEI methods mainly relied on statistical methods to design features, including high-order spectra, cumulants, nonlinear dynamic features, and various time-frequency (TF) features derived from transforms such as short-time Fourier transforms. However, these traditional methods suffer from significant limitations, including poor performance, limited adaptability to different environments, and inability to cope with the escalating complexity and numerous transmitters. In recent years, deep learning has emerged as a promising data analysis tool and has gained widespread attention in wireless communication technology, especially in the field of SEI. Deep learning-based SEI methods utilize neural networks such as convolutional neural networks (CNNs), recurrent neural networks (RNNs), transformer models, and generative adversarial networks (GANs) to achieve unified feature extraction and classification. These deep learning-based SEI methods are divided into three main parts according to sample representation: time domain signal, spectrogram, and constellation diagram. Deep learning-based SEI techniques leverage a large repository of historical samples to extract more resilient and effective UMOP features, outperforming methods that rely on manually designed features. However, these methods face limitations in the availability of training signal samples for new categories and limited retraining opportunities during online deployment.

[0003] Amplifier nonlinear distortion is the main factor of SEI. However, in communication and radar systems, this distortion not only reduces the linear range but also reduces the overall efficiency. As the demand for wider bandwidth in these systems continues to grow, methods to linearize amplifiers and improve efficiency, such as negative feedback, envelope tracking, and digital predistortion (DPD), have emerged. DPD technology stands out among various linearization technologies due to its flexible digital algorithm, compensation capability, adaptability, and lower power consumption. Compared with other linearization methods, it can achieve a simpler circuit configuration to achieve a wider bandwidth, making it increasingly popular for PA linearization compensation. At present, a variety of DPD methods have been proposed, including piecewise linear method, discrete Newton method, least mean square (LMS) algorithm, rotation and scaling (RASCAL), and recursive least squares (RLS) algorithm. However, it is worth noting that while DPD technology mitigates amplifier nonlinearity in the emitter, it may inadvertently weaken the performance of SEI. Summary of the invention

[0004] The purpose of the present invention is to solve the problem of low accuracy of individual radiation source identification caused by the application of DPD technology in actual deployment and insufficient data in online SEI deployment, and proposes a method for individual radiation source identification in a finite sample scenario under digital predistortion.

[0005] The specific process of the radiation source individual identification method in a finite sample scenario under digital pre-distortion is as follows:

[0006] Step 1: pre-process the collected signals to obtain HHT graph, ITD-Hilbert graph, CWT graph, CWD graph and GT graph;

[0007] The HHT is the Hilbert-Huang transform;

[0008] The ITD-Hilbert is Hilbert transform;

[0009] The CWT is a continuous wavelet transform;

[0010] The CWD is Choi-Williams distribution;

[0011] The GT is Gabor transform;

[0012] Step 2: Preprocess the HHT graph, ITD-Hilbert graph, CWT graph, CWD graph and GT graph respectively to construct the data set;

[0013] Step 3: Construct FS-SEI network model;

[0014] The FS-SEI network model includes the CNN network model and the relational network model;

[0015] The CNN network model includes a feature extractor and a classifier in sequence;

[0016] Step 4: Train the FS-SEI network model to obtain a trained FS-SEI network model;

[0017] Step 5: Input the test set into the trained FS-SEI network model, and the trained FS-SEI network model outputs the category of the test set.

[0018] The beneficial effects of the present invention are:

[0019] The present invention discloses a Few-Sample Source Individual Identification (FS-SEI) model, which integrates convolutional neural network (CNN) embedding and metric learning, and is aimed at scenarios with limited sample availability.

[0020] The present invention characterizes the signal by Hilbert-Huang transform (HHT), ITD-Hilbert transform (ITD-Hilbert), continuous wavelet transform (CWT) and Choi-Williams distribution (CWD), Gabor transform (GT). These methods help to represent various forms of transmitter signals as time-frequency images, thereby showing different characteristics of the signal.

[0021] In this paper, we propose a FS-SEI model under DPD. The model integrates a CNN for deep feature vector extraction and a relational network (RN) designed to autonomously learn a nonlinear distance metric. Our results show that while DPD techniques tend to mask the unique characteristics of the emitter, the FS-SEI model successfully addresses this challenge and shows significant performance improvements over traditional CNNs and other methods in SEI tasks. This enhancement is particularly significant in environments with low signal-to-noise ratios and limited sample availability. As DPD techniques continue to advance and become more integrated into modern communication systems, research on improving SEI methods for these conditions is of great significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is the framework diagram of FS-SEI model under DPD;

[0023] Figure 2 Extract network graph for features;

[0024] Figure 3 It is a relationship network architecture diagram;

[0025] Figure 4 Figure 2 shows the SEI results under different signal representation methods. a is based on the ResNet50 model, and b is based on the FS-SEI model.

[0026] Figure 5 The SEI results for different CNN feature vector dimensions are shown in Figure 1. a is the SEI result, and b is the complexity analysis.

[0027] Figure 6 The SEI result diagrams for different CNN feature vector dimensions are shown in Figure 1. a is K=1, b is K=5, c is K=10, d is K=20, e is K=50, and f is K=100.

[0028] Figure 7 The FS-SEI result diagrams under different signal-to-noise ratios when K=10, a is SNR=-5dB, accuracy=77.07%; b is SNR=10dB, accuracy=97.21%. DETAILED DESCRIPTION

[0029] Specific implementation method 1: The specific process of the method for identifying individual radiation sources in a limited sample scenario under digital predistortion in this implementation method is as follows:

[0030] Step 1: pre-process the collected signals to obtain HHT graph, ITD-Hilbert graph, CWT graph, CWD graph and GT graph (time-frequency graph);

[0031] The HHT is the Hilbert-Huang transform;

[0032] The ITD-Hilbert is Hilbert transform;

[0033] The CWT is a continuous wavelet transform;

[0034] The CWD is Choi-Williams distribution;

[0035] The GT is Gabor transform;

[0036] Step 2: Preprocess the HHT graph, ITD-Hilbert graph, CWT graph, CWD graph and GT graph respectively to construct the data set;

[0037] Step 3: Construct the FS-SEI (few-sample radiation source individual identification) network model;

[0038] The FS-SEI network model includes the CNN network model and the relational network model;

[0039] The CNN network model includes a feature extractor and a classifier in sequence;

[0040] A simple yet effective CNN architecture was designed for FS-SEI, including a two-component system of feature extractor and classifier, such as Figure 2 shown.

[0041] Taking CNN feature vector as input, CNN feature embedding is realized, and clustering is performed on the CNN feature vector extracted by metric learning, which enhances the SEI performance of traditional CNN.

[0042] Step 4: Train the CNNFS-SEI network model to obtain a trained FS-SEI network model;

[0043] Step 5: Input the test set into the trained FS-SEI network model, and the trained FS-SEI network model outputs the category of the test set.

[0044] Specific implementation method 2: This implementation method is different from the specific implementation method 1 in that in step 1, the collected signal is preprocessed to obtain HHT, ITD-Hilbert, CWT, CWD and GT (time-frequency diagram); the specific process is:

[0045] Step 11. Collect signal samples from different types of transmitters (different power amplifier chip models and different transmitter types composed of different aging times);

[0046] Perform wavelet denoising on the collected signal samples to obtain denoised signal samples;

[0047] Pulse extraction is performed on the denoised signal samples, with every 10 pulses as one signal sample, and 500 signal samples are obtained;

[0048] The 10 pulses in each signal sample are extracted separately to obtain a signal sample containing only a single pulse;

[0049] A total of 5000 signal samples containing only single pulses were obtained;

[0050] Step 12: Perform Hilbert-Huang transform on the signal containing only a single pulse obtained in step 11 to obtain a HHT time-frequency diagram;

[0051] Step 13: firstly perform intrinsic time scale decomposition on the signal containing only a single pulse obtained in step 11 to obtain a rotation component, and then calculate the Hilbert spectrum of the rotation component to obtain an ITD-Hilbert time-frequency diagram;

[0052] Step 14: Use Morlet wavelet as mother wavelet ψ(·), scale and translate the mother wavelet ψ(·) in sequence to generate A (a series of) wavelet functions;

[0053] The convolution of the signal x(t) containing only a single pulse obtained in step 1 with each wavelet function ψ(t) produces a signal representation across different time and frequency scales, and obtains the CWT time-frequency diagram; the expression is:

[0054]

[0055] Among them, a represents the scale parameter of the wavelet function, b represents the translation parameter, ψ * (·) represents the complex conjugate of the mother wavelet, and t represents time;

[0056] This equation facilitates multi-scale and multi-location signal analysis by adjusting the scale a and translation b values;

[0057] Step 15: Calculate the Choi-Williams distribution of the pulse signal and obtain the CWD time-frequency diagram; the expression is:

[0058] CWD can effectively improve the identifiability of emitter characteristics through its unique time-frequency analysis features. It provides a clearer time-frequency representation by reducing the interference of cross terms, which is particularly important for distinguishing signals from different emitters.

[0059]

[0060] Where x(t) represents the signal containing only a single pulse obtained in step 1, and x * (t) represents the complex conjugate of x(t), σ represents the parameter that controls the mildness of the distribution; f represents frequency; t represents time; τ represents the time delay variable, which is used to represent the offset of the wavelet function on the time axis. By changing τ, the wavelet function can be compared and analyzed with the signal at different time positions; j represents the imaginary unit, j 2 = -1;

[0061] e -j2πfτ is a complex exponential function used to realize the conversion of the signal in the frequency domain. This term is responsible for converting the delay τ information in the time domain to f in the frequency domain.

[0062] is a Gaussian window function used to weight the signal in the τ domain, where σ controls the width of the window. The influence of cross terms is mitigated, thereby enhancing the clarity of time-frequency depictions.

[0063] Step 16: Perform Gabor transform on the signal containing only a single pulse obtained in step 11 to obtain a GT time-frequency diagram;

[0064] Step 17: Store the HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram, and GT time-frequency diagram in a size of 700×525.

[0065] The other steps and parameters are the same as those in the first embodiment.

[0066] Specific implementation method three: This implementation method is different from specific implementation method one or two in that in step two, the HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram and GT time-frequency diagram are preprocessed to construct a data set; the specific process is:

[0067] Step 21: The signal sample data set containing only a single pulse obtained in step 11 is randomly divided into a training set and a test set in a ratio of 7:3; the training set is further divided into two parts, K samples are used for training, and the remaining samples are used for verification.

[0068] Step 22: Normalize the HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram and GT time-frequency diagram obtained in step 1 to obtain the normalized HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram and GT time-frequency diagram, and crop the normalized HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram and GT time-frequency diagram into HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram and GT time-frequency diagram of size 100×100 respectively;

[0069] Step 23: Put the cropped HHT frequency spectrum, ITD-Hilbert frequency spectrum, CWT frequency spectrum, CWD frequency spectrum and GT frequency spectrum corresponding to the same type of transmitter into the same folder. Each folder contains five subfolders, and each subfolder corresponds to a type of frequency spectrum.

[0070] A folder represents the secondary representation of the signal in different forms of time-frequency diagrams corresponding to the same type of transmitter.

[0071] The other steps and parameters are the same as those in the first or second embodiment.

[0072] Specific implementation method 4: This implementation method is different from any one of the specific implementation methods 1 to 3 in that the FS-SEI network model is constructed in step 3;

[0073] The FS-SEI network model includes the CNN network model and the relational network model;

[0074] The CNN network model includes a feature extractor and a classifier in sequence;

[0075] The specific process is:

[0076] Step 3: Build a CNN network model. The CNN network model includes a feature extractor and a classifier in sequence.

[0077] The feature extractor includes a first convolution block, a maximum pooling layer, a second convolution block, a maximum pooling layer, a third convolution block, a maximum pooling layer, a flattening layer Faltten, a fully connected layer FC, a batch normalization BN, and a linear rectification function ReLU in sequence;

[0078] The classifier includes a fully connected layer FC, a batch normalization BN, a linear rectification function ReLU, a fully connected layer FC, a batch normalization BN, a linear rectification function ReLU, and a Softmax layer in sequence;

[0079] Each of the first convolution block, the second convolution block, and the third convolution block includes a convolution layer (Conv), a batch normalization BN, and a linear rectification function ReLU in sequence;

[0080] The task of the feature extractor is to further refine the graph into a 1024-dimensional feature vector, which is subsequently introduced into the CNN classifier and the relation network.

[0081] Step 32: Build a relationship network model;

[0082] The relational network model includes concatenation layer, flattening layer Faltten, fully connected layer FC, batch normalization BN, linear rectification function ReLU, fully connected layer FC, batch normalization BN, linear rectification function ReLU, fully connected layer FC, batch normalization BN, linear rectification function ReLU, fully connected layer FC, and Sigmoid activation function.

[0083] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0084] Specific implementation method 5: This implementation method is different from any one of specific implementation methods 1 to 4 in that in step 4, the FS-SEI network model is trained to obtain a trained FS-SEI network model; the specific process is:

[0085] Step 41: Input the secondary representation of the signal into the CNN network model, and the CNN network model outputs the emitter type result; the specific process is:

[0086] The cropped HHT frequency spectrum, ITD-Hilbert frequency spectrum, CWT frequency spectrum, CWD frequency spectrum and GT frequency spectrum corresponding to the secondary representation of the signal are input into the feature extractor, and the feature extractor outputs a 1024-dimensional feature vector;

[0087] The 1024-dimensional feature vector is input into the classifier, and the classifier outputs the emitter type result;

[0088] Step 42: Input the 1024-dimensional feature vector into the relational network model, and the relational network model outputs the relational score;

[0089] Step 43: Train the CNN network model until convergence to obtain a trained CNN network model; the specific process is:

[0090] The loss function is J(θ). In order to minimize the loss function J(θ), the stochastic gradient descent (SGD) algorithm is used to optimize the CNN network model.

[0091]

[0092] Among them, J(θ) is the loss function;

[0093] Represents the secondary representation of the signal, output represents the probability that the signal belongs to each emitter category; C, H, W, and N represent the number of channels, height, width, and category, respectively. represents the set of real numbers;

[0094] M represents the total number of training samples; i and n represent the indexes of training samples and emitter categories, respectively; y i represents the category label; θ represents the parameters of the CNN network model;

[0095] When the true label of the i-th training sample is consistent with n, the p value is 1; otherwise, the p value is 0;

[0096] P θ Represents the output of the softmax layer in the classifier;

[0097] The feature extractor output in the CNN network model was experimentally selected to be 1024 dimensions.

[0098] Step 44: Train the relationship network model until convergence to obtain a trained CNN network model; the specific process is:

[0099] Step 441: Define the support set and queryset

[0100] Among them, f θ (x i ) represents the feature extractor f θ The CNN feature vector extracted from the examples in the support set S, f θ (x j ) represents the CNN feature vector extracted by the feature extractor from the examples in the query set Q;

[0101] Where M represents the number of support set samples, S includes all training set samples, when the support set S contains N emitter categories and each category has K samples, then M = N × K;

[0102] The query set Q consists of randomly selected samples from the training set or continuous samples from the test set, and L represents the number of samples in the query set;

[0103] x i represents the support set sample, x j Represents a query set sample;

[0104] y i represents the support set sample label, y j Represents the query set sample label;

[0105] Step 442: Support set Take the average of all feature vectors in and calculate the class prototype o for each category n ;

[0106]

[0107] Step 443: Create a prototype for each category n and f θ (x j ) Input the relational network model, and the relational network model outputs the relational score; the expression is:

[0108] rj,n=g ψ (Concat(on,f θ (xj))) (6)

[0109] Concat(·) represents the concatenation layer; it represents the concatenation of the class prototype o of each category. n and f θ (x j ) Input the concatenation layer in the relational network model, and the output of the concatenation layer;

[0110] g ψ (·) represents the relational network model; ψ represents the parameters of the relational network model;

[0111] r j,n Represents the class prototype o n and query sample x j The relationship score between

[0112] Use the concatenation layer Concat(o n ,f θ (x j )) Smartly connect the eigenvectors f θ (x i ) and f θ (x j ), thereby combining the data from the two collections.

[0113] The relational network model includes concatenation layer, flattening layer Faltten, fully connected layer FC, batch normalization BN, linear rectification function ReLU, fully connected layer FC, batch normalization BN, linear rectification function ReLU, fully connected layer FC, batch normalization BN, linear rectification function ReLU, fully connected layer FC, and Sigmoid activation function.

[0114] The distance between the feature vector of the query sample and the class prototype is measured in the feature space. ψTo evaluate the distance between the query sample and the prototype. In order to develop a nonlinear and more adaptable distance metric between the query set Q and the support set S, a relational network RN that is more general and robust than fixed metrics is used. The architecture of the relational network RN for metric learning is shown in Figure 3 shown.

[0115] Step 444: Train the relationship network model until convergence to obtain a trained CNN network model; the specific process is:

[0116] The input of the relational network model is the support set and query set of step 441, and the output of the relational network model is the relation score (which can quantify x i and x j The similarity between the two is a scalar between 0 and 1 r j,n ), determine the category of the query sample based on the score;

[0117] The mean square error (MSE) loss function is used to optimize the relationship network model. The loss function is as follows:

[0118]

[0119] The variable q represents the number of samples in the query set Q;

[0120] When the query set Q and the class prototype o n When matching, the binary variable The value is 1, and 0 if it is inconsistent;

[0121] The objective function of the relational network model is expressed as follows:

[0122]

[0123] Taking CNN feature vector as input, CNN feature embedding is realized, and clustering is performed on the CNN feature vector extracted by metric learning, which enhances the SEI performance of traditional CNN.

[0124] Metric learning network model such as Figure 3 As shown, it specifically includes 1 splicing layer, 1 Faltten layer, 4 fully connected layers and a Sigmoid layer.

[0125] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0126] The following examples are used to verify the beneficial effects of the present invention:

[0127] Example 1: A variety of signal processing methods, including HHT, CWD, ITD-Hilbert, GT and CWT, are used to obtain the TF feature image of the signal, and the influence of the RFF representation of the signal on the SEI model is studied based on the ResNet50 model and the FS-SEI model. The results show that the FS-SEI model is always better than the ResNet50 model under each RFF representation, highlighting the effectiveness of the FS-SEI model.

[0128] Considering the impact of the intelligent representation of RFF on the SEI model, we used a variety of signal processing methods, including HHT, CWD, ITD-Hilbert, GT and CWT, to obtain the TF feature image of the signal. The residual network (ResNet) is mainly used for its deep learning features, which effectively overcomes the vanishing gradient problem. This makes ResNet particularly suitable for our complex image recognition tasks, and it is able to learn rich feature representations from data, thereby significantly improving model performance and generalization ability. Therefore, these TF feature images are separately input into the ResNet and FS-SEI models for SEI, K = 500. As Figure 4 As shown, the FS-SEI model consistently outperforms the ResNet50 model under each RFF representation, highlighting the performance advantage of the FS-SEI model. Regarding the ResNet50 model, the performance difference between the intelligent RFF representations is very obvious, with the CWD representation having a clear advantage. This is particularly evident in environments with low signal-to-noise ratio (SNR), where the CWD feature continues to show excellent recognition accuracy. On the other hand, while the CWD, CWT, and Gabor performance are similar when the SNR is above 0dB in the FS-SEI model, CWD maintains the best performance. It is worth noting that the GT-based FS-SEI model shows a significant performance drop at lower SNRs, indicating lower robustness than other features.

[0129] Based on the experimental results presented in Table 2, a detailed comparison of TF feature extraction techniques has been conducted in terms of computational complexity and accuracy. Multiple feature vectors for machine learning via SVM and for DL ​​models such as ResNet 50 were evaluated by generating intelligent representations of the RFF of the signal. With a computational complexity of 3731894 floating point operations / second (FLOPs) and an inference time of 0.80432 seconds, CWD features achieved an impressive 95.6% accuracy at 0dB with K=500. This shows that CWD maintains high accuracy while keeping its computational requirements and inference time within acceptable limits. The ITD-GSCM feature, while showing high recognition performance with an accuracy of 88.1%, requires significantly more computational resources than other features for SVM. Other features analyzed in the study, such as Bispec, HVG, and various EMD-based representations, showed varying degrees of performance, ranging from 59.5% to 79.9% accuracy at SNR=0dB. These features currently have a lower computational cost, but do not reach the high accuracy level seen in CWD or ITD-GSCM. Therefore, the FS-SEI model proposed in this study uses CWD time-frequency graphs as input, denoted as CWD-Metric.

[0130] Example 2: When K=20, the SEI results of the CWD-Metric model using CNN feature vectors of different dimensions are analyzed to verify the rationality of setting the feature vector dimension to 1024;

[0131] The experimental results are as follows Figure 5 As shown, Figure 5 Figure a shows the SEI results at various SNRs, where the symbol "F_x" represents the result with a feature vector dimension of x, and "None" represents the result using a traditional feature vector extraction network. It is observed that the CWD-Metric model performs best with a feature vector dimension of 1024 (denoted as F1024), consistently showing superior performance at all SNRs. In addition, the CWD-Metric model of different dimensions consistently outperforms the traditional CNN structure, highlighting the high robustness of the proposed model while maintaining high accuracy. Figure 5The computational and time complexity metrics of different methods are intuitively compared in Figure b. Notably, despite the different dimensions of the feature vectors, all models maintained a similar training speed of approximately 5.95 iterations per second (it / s), indicating that the training efficiency remains constant across changes in feature size. A deeper look into the computational requirements shows that while FLOPs remain relatively stable across models, there is a clear correlation between parameter count and the size of the feature vector. Specifically, the F_2048 model requires significantly more parameters (6,668,182) than the F_128 model, which requires only 2,380,694 parameters. This suggests that larger feature vector dimensions significantly increase model complexity, which may affect memory usage and model scalability. However, the model equipped with F_1024 achieves the highest accuracy of 91.7% and provides a commendable balance between computational efficiency and model performance. Furthermore, the accuracy improvement from the smallest to the most significant feature vector size (from 89.3% to 91.7% and then to 90.6%) suggests that there are diminishing returns from increasing the feature vector size beyond a certain point.

[0132] Example 3: Performance of the FS-SEI model under few sample conditions;

[0133] When the number of training samples K = 1, 5, 10, 20, 50 and 100, the recognition rate of the proposed FS-SEI model under different signal-to-noise ratios is investigated under the condition of randomly selecting different numbers of training samples. The results are shown in Figure 6 Among them, CWD-CNN represents the common CNN model with CWD time-frequency graph as input, reflecting the structure of CNN feature extractor. Figure 6As shown in Figure 1, CWD-Metric shows superior accuracy compared to CWD-CNN at all K values, especially at low SNR and with fewer samples. For example, at K = 1 and SNR of -5dB, the CWD-Metric model is about 20% more accurate than CWD-CNN. As the number of launches increases to 0, the gap narrows, but it is still significant, and at the same SNR level, the CWD-Metric model performs about 15% better than CWD-CNN. This trend continues with increasing K values; however, the performance gap decreases with the number of samples. At K = 100 and SNR = 25dB, both models converge to similarly high levels of accuracy, but the CWD-Metric model still shows a slight advantage. The robustness of the CWD-Metric model is particularly evident under low SNR conditions and with fewer training samples, and its accuracy remains relatively stable compared to the sharp drop observed in the CWD-CNN model. For example, at -5dB SNR and K = 1, CWD-Metric maintains close to 65% accuracy, while CWD-CNN drops by about 45%. These results demonstrate the ability of the FS-SEI model to maintain high recognition accuracy even under challenging conditions. This is preferred in real-world applications where limited labeled data or low-quality signals are common.

[0134] The DPD technique corrects the nonlinear effects of the amplifier, thereby reducing individual variance and degrading the SEI's identification performance. Figure 6 In sub-figure (c), the CWD-Metric model (K=10, DPD) is compared with the best ITD-GSCM model (K=500, DPD). The results show that CWD-Metric achieves comparable and best performance to the ITD-GSCM model at SNRs of 10 and 15 dB, despite significantly fewer training samples. This suggests that the CWD-Metric model has robust adaptability with significantly fewer training samples. Extending this analysis, Figure 6 The sub-figure in c compares the performance of CWD-Metric (K=50, DPD) with the best performing ITD-GSCM (K=500, without DPD) algorithm, showing that CWD-Metric with DPD achieves the same accuracy as the ITD-GSCM model without DPD. The experimental results show that the proposed CWD-Metric can maintain a relatively stable recognition rate even with the application of DPD technology and insufficient training samples.

[0135] The confusion matrices at -5dB and 10dB SNR clearly illustrate the variation in the performance of the FS-SEI model in distinguishing different transmitters, especially at different SNRs. Figure 7, the confusion matrix at -5dB SNR indicates an overall accuracy of 77.07%. This lower accuracy stems primarily from the apparent confusion between transmitters E5 and E6, likely due to similar aging cycles and amplifier characteristics, which complicate different classifications at lower signal quality levels. In contrast, the model achieves a very high accuracy of 99.5% for transmitter E3, despite having the same aging cycle as E1 and E2. This exceptional accuracy likely highlights the different effects that different chip families have on detection capabilities, suggesting that chip variations play a critical role in the model’s ability to accurately distinguish between transmitters. As Figure 7 As shown in (b), when the SNR is increased to 10dB, the overall accuracy increases significantly to 97.21%. The improved accuracy at higher SNRs confirms that, with more precise signals, the model adeptly handles the identification challenges posed by transmitters from the same series and batches that were previously prone to misclassification at lower SNR levels. Based on these findings, it is clear that transmitters from the same series and batches are prone to misclassification under low SNR conditions; however, our model maintains high identification rates as the SNR increases. In addition, our model demonstrates strong discrimination capabilities for transmitters from different series even under small sample sizes and challenging SNR situations. Notably, the CWD-Metric shows low confusion for transmitters with different aging states (such as E4, E5, and E7), indicating a sophisticated ability to identify subtle differences between transmitters.

[0136] Table 1 Signal parameter configuration

[0137]

[0138] Table 2 Performance comparison of different RFF representations

[0139]

[0140] The present invention may also have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A method for identifying individual radiation sources in a finite sample scenario under digital predistortion, characterized in that: The specific process of the method is: Step 1: pre-process the collected signals to obtain HHT graph, ITD-Hilbert graph, CWT graph, CWD graph and GT graph; The HHT is the Hilbert-Huang transform; The ITD-Hilbert is Hilbert transform; The CWT is a continuous wavelet transform; The CWD is Choi-Williams distribution; The GT is Gabor transform; Step 2: Preprocess the HHT graph, ITD-Hilbert graph, CWT graph, CWD graph and GT graph respectively to construct the data set; Step 3: Construct FS-SEI network model; The FS-SEI network model includes the CNN network model and the relational network model; The CNN network model includes a feature extractor and a classifier in sequence; Step 4: Train the FS-SEI network model to obtain a trained FS-SEI network model; Step 5: Input the test set into the trained FS-SEI network model, and the trained FS-SEI network model outputs the category of the test set.

2. The method for identifying individual radiation sources in a finite sample scene under digital predistortion according to claim 1, characterized in that: In the step 1, the collected signal is preprocessed to obtain the HHT graph, ITD-Hilbert graph, CWT graph, CWD graph and GT graph; the specific process is: Step 1. Collect signal samples from different types of transmitters; Perform wavelet denoising on the collected signal samples to obtain denoised signal samples; Pulse extraction is performed on the denoised signal samples, with every 10 pulses as one signal sample, and 500 signal samples are obtained; The 10 pulses in each signal sample are extracted separately to obtain a signal sample containing only a single pulse; A total of 5000 signal samples containing only single pulses were obtained; Step 12: Perform Hilbert-Huang transform on the signal containing only a single pulse obtained in step 11 to obtain a HHT time-frequency diagram; Step 13: firstly perform intrinsic time scale decomposition on the signal containing only a single pulse obtained in step 11 to obtain a rotation component, and then calculate the Hilbert spectrum of the rotation component to obtain an ITD-Hilbert time-frequency diagram; Step 14: Use Morlet wavelet as mother wavelet ψ(·), scale and translate the mother wavelet ψ(·) in sequence to generate A wavelet functions; The convolution of the signal x(t) containing only a single pulse obtained in step 1 with each wavelet function ψ(t) gives the CWT time-frequency diagram; the expression is: Among them, a represents the scale parameter of the wavelet function, b represents the translation parameter, ψ * (·) represents the complex conjugate of the mother wavelet, and t represents time; Step 15: Calculate the Choi-Williams distribution of the pulse signal and obtain the CWD time-frequency diagram; the expression is: Where x(t) represents the signal containing only a single pulse obtained in step 1, and x * (t) represents the complex conjugate of x(t), σ represents a parameter, f represents frequency, t represents time, τ represents a time delay variable, j represents an imaginary unit, 2 = -1; Step 16: Perform Gabor transform on the signal containing only a single pulse obtained in step 11 to obtain a GT time-frequency diagram; Step 17: Store the HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram, and GT time-frequency diagram in a size of 700×525.

3. The method for identifying individual radiation sources in a finite sample scene under digital predistortion according to claim 2, characterized in that: In the step 2, the HHT time-frequency diagram, the ITD-Hilbert time-frequency diagram, the CWT time-frequency diagram, the CWD time-frequency diagram and the GT time-frequency diagram are preprocessed to construct a data set; the specific process is: Step 21: The signal sample data set containing only a single pulse obtained in step 11 is randomly divided into a training set and a test set in a ratio of 7:3; Step 22: Normalize the HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram and GT time-frequency diagram obtained in step 1 to obtain the normalized HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram and GT time-frequency diagram, and crop the normalized HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram and GT time-frequency diagram into HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram and GT time-frequency diagram of size 100×100 respectively; Step 23: Put the cropped HHT frequency spectrum, ITD-Hilbert frequency spectrum, CWT frequency spectrum, CWD frequency spectrum and GT frequency spectrum corresponding to the same type of transmitter into the same folder. Each folder contains five subfolders, and each subfolder corresponds to a type of frequency spectrum. A folder represents the secondary representation of the signal in different forms of time-frequency diagrams corresponding to the same type of transmitter.

4. The method for identifying individual radiation sources in a finite sample scene under digital predistortion according to claim 3, characterized in that: In the step 3, a FS-SEI network model is constructed; The FS-SEI network model includes the CNN network model and the relational network model; The CNN network model includes a feature extractor and a classifier in sequence; The specific process is: Step 3: Build a CNN network model. The CNN network model includes a feature extractor and a classifier in sequence. The feature extractor includes a first convolution block, a maximum pooling layer, a second convolution block, a maximum pooling layer, a third convolution block, a maximum pooling layer, a flattening layer Faltten, a fully connected layer FC, a batch normalization BN, and a linear rectification function ReLU in sequence; The classifier includes a fully connected layer FC, a batch normalization BN, a linear rectification function ReLU, a fully connected layer FC, a batch normalization BN, a linear rectification function ReLU, and a Softmax layer in sequence; Each of the first convolution block, the second convolution block, and the third convolution block includes a convolution layer, a batch normalization BN, and a linear rectification function ReLU in sequence; Step 32: Build a relationship network model; The relational network model includes concatenation layer, flattening layer Faltten, fully connected layer FC, batch normalization BN, linear rectification function ReLU, fully connected layer FC, batch normalization BN, linear rectification function ReLU, fully connected layer FC, batch normalization BN, linear rectification function ReLU, fully connected layer FC, and Sigmoid activation function.

5. The method for identifying individual radiation sources in a finite sample scene under digital predistortion according to claim 4, characterized in that: In step 4, the FS-SEI network model is trained to obtain a trained FS-SEI network model; the specific process is: Step 41: Input the secondary representation of the signal into the CNN network model, and the CNN network model outputs the emitter type result; the specific process is: The cropped HHT frequency spectrum, ITD-Hilbert frequency spectrum, CWT frequency spectrum, CWD frequency spectrum and GT frequency spectrum corresponding to the secondary representation of the signal are input into the feature extractor, and the feature extractor outputs a 1024-dimensional feature vector; The 1024-dimensional feature vector is input into the classifier, and the classifier outputs the emitter type result; Step 42: Input the 1024-dimensional feature vector into the relational network model, and the relational network model outputs the relational score; Step 43: Train the CNN network model until convergence to obtain a trained CNN network model; the specific process is: Among them, J(θ) is the loss function; Represents the secondary representation of the signal, output represents the probability that the signal belongs to each emitter category; C, H, W, and N represent the number of channels, height, width, and category, respectively. represents the set of real numbers; M represents the total number of training samples; i and n represent the indexes of training samples and emitter categories, respectively; θ represents the parameters of the CNN network model; When the true label of the i-th training sample is consistent with n, the p value is 1; otherwise, the p value is 0; P θ Represents the output of the softmax layer in the classifier; Step 44: Train the relationship network model until convergence to obtain a trained CNN network model; the specific process is: Step 441: Define the support set and queryset Among them, f θ (x i ) represents the feature extractor f θ The CNN feature vector extracted from the examples in the support set S, f θ (x j ) represents the CNN feature vector extracted by the feature extractor from the examples in the query set Q; Where M represents the number of support set samples, S includes all training set samples, when the support set S contains N emitter categories and each category has K samples, then M = N × K; The query set Q consists of randomly selected samples from the training set or continuous samples from the test set, and L represents the number of samples in the query set; x i represents the support set sample, x j Represents a query set sample; y i represents the support set sample label, y j Represents the query set sample label; Step 442: Support set Take the average of all feature vectors in and calculate the class prototype o for each category n ; Step 443: Create a prototype for each category n and f θ (x j ) Input the relational network model, and the relational network model outputs the relational score; the expression is: rj,n=g ψ (Concat(on,f θ (xj))) (6) Among them, Concat(·) represents the concatenation layer; g ψ (·) represents the relational network model; ψ represents the parameters of the relational network model; r j,n Represents the class prototype o n and query sample x j The relationship score between Step 444: Train the relationship network model until convergence to obtain a trained CNN network model; the specific process is: The input of the relational network model is the support set and query set of step 441, and the output of the relational network model is the relation score, based on which the category of the query sample is determined; The mean square error loss function is used to optimize the relationship network model. The loss function is as follows: The variable q represents the number of samples in the query set Q; When the query set Q and the class prototype o n When matching, the binary variable The value is 1, and 0 if it is inconsistent; The objective function of the relational network model is expressed as follows:

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