Radio frequency fingerprinting label-free performance estimation method based on multi-temperature energy regression

Abstract

The application discloses a radio frequency fingerprint identification label-free performance estimation method based on multi-temperature energy regression, and relates to the technical field of wireless communication and signal processing.The application comprises the following steps: acquiring a source domain data set with labels, a target domain data set without labels and a radio frequency fingerprint classifier trained on the source domain; constructing a controllable disturbance parameter space based on amplitude nonlinearity, carrier frequency offset, phase jitter and additive noise, generating a plurality of enhanced copy data sets retaining the source domain labels; calculating sample-level energy at different temperatures according to the logit vectors of each enhanced copy sample, obtaining multi-temperature energy indicators through averaging and stacking, and combining the corresponding real accuracy to construct energy-accuracy training sample pairs; fitting a linear regression function by using Huber loss; calculating the target domain multi-temperature energy indicators and inputting the linear regression function to obtain the target domain predicted accuracy.The application can be used for radio frequency fingerprint identification performance estimation under cross-channel and cross-receiver conditions without target domain labels.

Description

Technical Field

[0001] This invention relates to the field of wireless communication and signal processing technology, specifically to a tagless performance estimation method for radio frequency fingerprint recognition based on multi-temperature energy regression. Background Technology

[0002] Radio frequency fingerprinting (RFF) technology utilizes the unique characteristics of wireless devices formed by minor defects introduced during the manufacturing process of transmitter hardware (such as power amplifier nonlinearity, local oscillator frequency offset, and I / Q imbalance) to achieve device identification and authentication. Compared with traditional cryptographic methods, RFF has significant advantages such as being lightweight, based on hardware physical characteristics, and difficult to clone. In recent years, deep learning methods have been able to directly extract these features from the original I / Q samples, enabling deep learning-based RFF to achieve high recognition accuracy under various waveforms, devices, and communication protocols.

[0003] However, in actual deployments, an RFF model trained on signals acquired under specific channel and receiver conditions often needs to be run on previously unseen wireless environments and receivers. This mismatch introduces a distribution offset between training and test data, i.e., an out-of-distribution problem, which significantly reduces recognition performance.

[0004] To address these issues, existing research largely employs methods such as data augmentation, domain adaptation, domain generalization, contrastive representation learning, and semi-supervised and few-shot learning to improve the robustness of models to distribution shifts, achieving considerable accuracy improvements on labeled benchmark datasets. However, the problem of unlabeled performance estimation has received little attention. Without target domain labels, the true accuracy after deployment cannot be directly measured, making it impossible to quantify the performance degradation caused by distribution shifts and compromising the reliability of the deployed system.

[0005] To address this, the present invention proposes a tagless performance estimation method for radio frequency fingerprint recognition based on multi-temperature energy regression. Summary of the Invention

[0006] The purpose of this invention is to provide a tagless performance estimation method for radio frequency fingerprint recognition based on multi-temperature energy regression, which can accurately estimate the recognition accuracy of the RFF model under deployment conditions such as cross-channel and cross-receiver in the absence of tags.

[0007] According to a first aspect of the present invention, in order to achieve the above-mentioned objective, the present invention provides the following technical solution: a tagless performance estimation method for radio frequency fingerprint recognition based on multi-temperature energy regression, comprising the following steps: Obtain the labeled source domain dataset, the unlabeled target domain dataset, and the radio frequency fingerprint classifier trained on the source domain dataset; Based on the signal distortion types caused by the wireless channel and receiver front end acting on the I / Q signals, a controllable perturbation parameter space is constructed, including amplitude nonlinear perturbation, carrier frequency offset perturbation, phase jitter perturbation and additive noise perturbation. The source domain dataset is perturbed according to the perturbation parameters in the controllable perturbation parameter space to generate multiple enhanced copy datasets that retain the source domain labels. Each enhanced replica dataset is input into the radio frequency fingerprint classifier to obtain the logit vector corresponding to each sample in each enhanced replica dataset. Based on the logit vector and the predefined temperature set, the sample-level energy of each sample at different temperatures is calculated. The sample-level energy at the same temperature in the same enhanced replica dataset is averaged to obtain the average sample-level energy corresponding to each temperature. The average sample-level energies corresponding to each temperature are stacked to obtain the multi-temperature energy index corresponding to each enhanced replica dataset. Based on the source domain labels retained by each of the enhanced replica datasets, the true accuracy corresponding to each of the enhanced replica datasets is calculated, and the multi-temperature energy index corresponding to each of the enhanced replica datasets is associated with the true accuracy to construct energy-accuracy training sample pairs; Using the multi-temperature energy index as input and the corresponding true accuracy as output, the Huber loss is used to fit the energy-accuracy training sample pair to obtain a linear regression function from the multi-temperature energy index to the recognition accuracy. The target domain dataset is input into the radio frequency fingerprint classifier to obtain the target domain logit vector corresponding to each sample in the target domain dataset. Based on the target domain logit vector, the same predefined temperature set as when constructing the energy-precision training sample pairs is used to calculate the target domain sample-level energy of each target domain sample at different temperatures. The target domain sample-level energy at the same temperature is averaged to obtain the target domain average energy corresponding to each temperature. The target domain average energies corresponding to each temperature are stacked to obtain the target domain multi-temperature energy index. The target domain multi-temperature energy index is input into the linear regression function to obtain the prediction accuracy of the radio frequency fingerprint classifier on the target domain dataset.

[0008] Further, obtaining the labeled source domain dataset, the unlabeled target domain dataset, and the radio frequency fingerprint classifier trained on the source domain dataset includes: The received I / Q signal samples are represented as: in, This indicates the number of sampling points contained in the I / Q signal sample, where 2 represents the I-channel signal and the Q-channel signal; The labeled source domain dataset is represented as: The unlabeled target domain dataset is represented as follows: in, Indicates the first One source domain I / Q signal sample, Indicates the first The device identification tag corresponding to each source domain I / Q signal sample. Indicates the first One target domain I / Q signal sample, and These represent the number of samples contained in the source domain dataset and the target domain dataset, respectively. The device identity tag belongs to the device identity tag set: In the formula, Indicates the number of equipment categories; The source domain dataset was used to classify the radio frequency fingerprint. The trained radio frequency fingerprint classifier will be used for training. Deployed on the target domain dataset.

[0009] Furthermore, based on the signal distortion types caused by the wireless channel and receiver front-end acting on the I / Q signals, a controllable disturbance parameter space is constructed, including amplitude nonlinear disturbance, carrier frequency offset disturbance, phase jitter disturbance, and additive noise disturbance, as follows: The received signal in the radio frequency fingerprint recognition system is modeled as follows: in, Indicates a specific hardware defect in the portable device. The transmitted signal, Indicates the discrete-time sampling point number, and the specific hardware defect of the device. Constructing a radio frequency fingerprint, Indicates wireless channel response, This indicates the receiver front-end response. This represents additive white noise. This represents the convolution operation; The received signal is approximately decomposed into: in, This represents the composite amplitude response formed by the wireless channel and the receiver front end. Indicates carrier frequency offset, This indicates phase noise and slow phase drift. Represents the imaginary unit; Based on the composite amplitude response, carrier frequency offset, phase noise and slow phase drift, and additive noise, amplitude operators, frequency operators, phase operators, and noise operators are constructed respectively, and the amplitude nonlinear disturbance, carrier frequency offset disturbance, phase jitter disturbance, and additive noise disturbance are formed by the amplitude operator, frequency operator, phase operator, and noise operator respectively.

[0010] Furthermore, the amplitude operator uses the Rapp model to model the AM-AM nonlinearity of the amplifier; Record No. The number of I / Q sampling points is: Its complex baseband sample is: in, and They represent the first The I-path in-phase component and the Q-path quadrature component of each sampling point; Indicates the time index of the sampling point. The superscript T indicates transpose. Defined by compression level Amplitude operator with parameters The complex baseband sample is subjected to amplitude nonlinear compression processing according to the following formula: in: In the formula, This represents the complex baseband sample after amplitude nonlinear perturbation processing. Indicates compression level A defined saturation factor Represents the Rapp smoothing parameter. This represents the maximum value of the complex baseband amplitude across all sampling points of the signal sample; This represents the normalized input amplitude; Indicates complex baseband sample The phase angle; express The model; symbol It is defined as; Defined by carrier frequency offset Frequency operator of parameters It applies a deterministic carrier frequency offset according to the following formula, expressed as: in The carrier frequency offset normalized to the sampling rate; Defined by the standard deviation of phase jitter Phase operator with parameters Its Gaussian phase jitter is superimposed according to the following formula, and is expressed as: in The standard deviation of phase jitter, Indicates the first Phase jitter superimposed on each sampling point; This indicates that the mean is 0 and the variance is 0. Gaussian distribution; This indicates that each sampling point independently and identically distributed follows this distribution; Define the target signal-to-noise ratio noise operator with parameters Additive white noise is introduced into the I / Q signal samples according to the following formula, expressed as: in Indicates the first A two-dimensional additive Gaussian white noise vector added to each sampling point; Represents a 2×2 identity matrix; The average signal power, The target signal-to-noise ratio.

[0011] Furthermore, the source domain dataset is perturbed according to the perturbation parameters in the controllable perturbation parameter space to generate multiple enhanced replica datasets that retain the source domain labels, as follows: The controllable disturbance parameter space is parameterized using a parameter set, which is represented as follows: in, , , and These represent the disturbance parameters corresponding to amplitude nonlinear disturbance, carrier frequency offset disturbance, phase jitter disturbance, and additive noise disturbance, respectively. The perturbation parameters in the parameter set are enumerated on a predefined parameter grid, and the source domain dataset is processed using the amplitude operator, frequency operator, phase operator, and noise operator with different perturbation levels to obtain... One enhanced replica dataset: Among them, the Enhanced replica dataset The samples in the database inherit the device identity tags of the corresponding source domain samples; The identification category of each enhanced replica sample is determined based on the logit vector output by the radio frequency fingerprint classifier. The identification category is compared with the corresponding device identity label, and the proportion of the number of samples with the same identification category and device identity label to the total number of samples in the corresponding enhanced replica dataset is determined as the true accuracy of the enhanced replica dataset.

[0012] Further, each enhanced replica dataset is input into the radio frequency fingerprint classifier to obtain the logit vector corresponding to each sample in each enhanced replica dataset. Based on the logit vector and a predefined temperature set, the sample-level energy of each sample at different temperatures is calculated. The sample-level energies at the same temperature in the same enhanced replica dataset are averaged to obtain the average sample-level energy corresponding to each temperature. The average sample-level energies corresponding to each temperature are stacked to obtain the multi-temperature energy index corresponding to each enhanced replica dataset, as follows: The radio frequency fingerprint classifier Input sample Mapping to include A logit vector with 1 component: For any temperature in the predefined set of temperatures The sample-level energy is calculated based on the logit vector according to the following formula: In the formula, Indicates sample At temperature The sample-level energy below, This represents the temperature parameter, and ; This represents the c-th logit component output by the radio frequency fingerprint classifier; c represents the number of device categories. Represents the natural logarithm; This represents an exponential function with the natural constant e as its base. The predefined temperature set is represented as: For the Enhanced replica dataset and the first in the predefined temperature set Temperature The average sample-level energy is calculated using the following formula: in, Indicates the first The first enhanced replica dataset One sample; This indicates the number of samples contained in each augmented replica dataset; The first The average sample-level energy of each enhanced replica dataset at various temperatures is stacked in temperature order to obtain the first... Multi-temperature energy metrics corresponding to each enhanced replica dataset: in, This indicates the number of temperatures included in the predefined temperature set.

[0013] Furthermore, energy-precision training sample pairs are constructed as follows: The first Multi-temperature energy metrics corresponding to each enhanced replica dataset With true accuracy Combine and construct an energy-precision training sample set: .

[0014] Furthermore, using the aforementioned multi-temperature energy index as input and the corresponding true accuracy as output, the Huber loss is applied to fit the energy-accuracy training sample pairs to obtain a linear regression function from the multi-temperature energy index to the recognition accuracy, as follows: Take the linear regression function A linear regressor trained with Huber loss is represented as: Among them, parameters Solve it using the following method: Where the threshold is Huber's losses are: In the formula, Indicates the threshold is Huber loss; e represents the regression residual, which is the difference between the true accuracy and the linear regression prediction. ; This represents the threshold for Huber's loss, and This is used to distinguish between small and large residuals; This represents the absolute value of the residual e.

[0015] Furthermore, the output yields the prediction accuracy of the radio frequency fingerprint classifier on the target domain dataset, as follows: For the first in the predefined temperature set Temperature According to the target domain dataset The target domain logit vector corresponding to each target domain sample is used to calculate the average energy of the target domain according to the following formula: in, Represents the first in the target domain dataset One target domain sample; The average energy of the target domain corresponding to each temperature is stacked in the same temperature order as when constructing the multi-temperature energy index to obtain the target domain multi-temperature energy index: The target domain multi-temperature energy index Substituting into the linear regression function, the prediction accuracy is obtained according to the following formula: In the formula, This indicates the prediction accuracy of the radio frequency fingerprint classifier on the target domain dataset; This indicates multiple temperature energy indices within the target domain; and These represent the fitted linear regression weight vector and bias term, respectively; This represents a truncation operation that restricts the value to the interval [0,1].

[0016] According to a second aspect of the present invention, the present invention provides a tagless performance estimation system for radio frequency fingerprint recognition based on multi-temperature energy regression, used to implement the tagless performance estimation method for radio frequency fingerprint recognition based on multi-temperature energy regression described in the first aspect, comprising: The data acquisition module is used to acquire the labeled source domain dataset, the unlabeled target domain dataset, and the radio frequency fingerprint classifier trained on the source domain dataset. The enhanced copy generation module is used to construct a controllable perturbation parameter space, including amplitude nonlinear perturbation, carrier frequency offset perturbation, phase jitter perturbation and additive noise perturbation, based on the signal distortion type formed by the wireless channel and receiver front end acting on the I / Q signal. The module then performs perturbation processing on the source domain dataset according to the perturbation parameters in the controllable perturbation parameter space to generate multiple enhanced copy datasets that retain the source domain labels. The source domain multi-temperature energy index generation module is used to input each of the enhanced replica datasets into the radio frequency fingerprint classifier to obtain the logit vector corresponding to each sample in each of the enhanced replica datasets. Based on the logit vector and the predefined temperature set, the sample-level energy of each sample at different temperatures is calculated. The sample-level energy at the same temperature in the same enhanced replica dataset is averaged to obtain the average sample-level energy corresponding to each temperature. The average sample-level energies corresponding to each temperature are stacked to obtain the multi-temperature energy index corresponding to each of the enhanced replica datasets. The training sample pair construction module is used to calculate the true precision corresponding to each of the enhanced replica datasets based on the source domain labels retained by each of the enhanced replica datasets, and to associate the multi-temperature energy index corresponding to each of the enhanced replica datasets with the true precision to construct energy-precision training sample pairs. The regression function fitting module is used to fit the energy-precision training sample pairs with the multi-temperature energy index as input and the corresponding true accuracy as output, using Huber loss to obtain a linear regression function from the multi-temperature energy index to the recognition accuracy. The target domain multi-temperature energy index generation module is used to input the target domain dataset into the radio frequency fingerprint classifier to obtain the target domain logit vector corresponding to each sample in the target domain dataset. Based on the target domain logit vector, using the same predefined temperature set as when constructing the energy-precision training sample pair, the target domain sample-level energy of each target domain sample at different temperatures is calculated. The target domain sample-level energy at the same temperature is averaged to obtain the target domain average energy corresponding to each temperature. The target domain average energies corresponding to each temperature are stacked to obtain the target domain multi-temperature energy index. The prediction accuracy generation module is used to input the target domain multi-temperature energy index into the linear regression function to obtain the prediction accuracy of the radio frequency fingerprint classifier on the target domain dataset.

[0017] The present invention has at least the following beneficial effects: 1. This invention constructs energy-precision training sample pairs using labeled source domain data and predicts the recognition accuracy of the RF fingerprint classifier based on the multi-temperature energy index corresponding to the unlabeled target domain data. This makes the performance estimation process independent of the target domain device identity label, which is beneficial for quantitatively evaluating the operating performance of the RF fingerprint classifier under actual deployment conditions where the target domain label is difficult to obtain. It also reduces the problem of unclear model performance status caused by the inability to directly obtain the true accuracy of the target domain.

[0018] 2. Based on the signal distortion caused by the wireless channel and receiver front-end acting on the I / Q signal, this invention decomposes the composite distributed offset into amplitude nonlinear disturbance, carrier frequency offset disturbance, phase jitter disturbance, and additive noise disturbance. It then uses the corresponding controllable disturbance parameters to generate multiple enhanced replica datasets, enabling the enhanced replicas to characterize the data distribution changes under different distortion types and disturbance levels. This is beneficial for improving the correlation between energy-precision training sample pairs and actual cross-channel and cross-receiver deployment conditions, and enhancing the physical interpretability of the performance estimation process.

[0019] 3. This invention calculates sample-level energy at multiple temperatures based on the logit vector output by the radio frequency fingerprint classifier, and stacks the average sample-level energy corresponding to different temperatures to form a multi-temperature energy index. This allows the peak state and overall distribution state of the classifier output to be reflected at different temperature scales, effectively improving the problem of insufficient sensitivity of a single temperature energy index to distribution shift changes when the classifier output is overly concentrated, and enhancing the ability of the multi-temperature energy index to characterize changes in classifier performance.

[0020] 4. This invention correlates the multi-temperature energy index corresponding to the enhanced replica dataset with the true accuracy, and uses Huber loss to fit a linear regression function from the multi-temperature energy index to the recognition accuracy. This allows the multi-temperature energy index of the target domain to be converted into the prediction accuracy of the RF fingerprint classifier on the target domain dataset. At the same time, it reduces the impact of the large fitting residual corresponding to some perturbed replicas on the regression parameter solution process, which is beneficial to improving the stability of the labelless performance estimation results under cross-channel and cross-receiver conditions and its engineering application value.

[0021] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 This is a schematic diagram of the overall process of the method described in this invention; Figure 2 This is a schematic diagram illustrating the framework principle of the method described in this invention; Figure 3 This is a schematic diagram illustrating the working principle of the amplitude operator, frequency operator, phase operator, and noise operator in this invention. Detailed Implementation

[0024] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0025] Example 1: This embodiment provides a labelless performance estimation method for radio frequency fingerprint recognition based on multi-temperature energy regression. It is applicable to applications where the radio frequency fingerprint classifier is deployed to the target domain environment after the source domain training is completed, and the channel conditions or receiver front-end conditions change, and the target domain data does not have device identification tags. This embodiment uses labeled source domain data to generate enhanced replica datasets with different physical distortion types and different perturbation levels. A linear regression function is established based on the classifier output energy and true accuracy corresponding to each enhanced replica dataset. Then, the prediction accuracy of the radio frequency fingerprint classifier on the target domain dataset is obtained by using the multi-temperature energy index corresponding to the target domain data. Radio frequency fingerprinting utilizes device-specific features formed by differences in the hardware manufacturing of transmitting equipment to identify devices. Nonlinearity of the power amplifier, local oscillator frequency offset, and I / Q imbalance in the transmitting equipment can form an RF fingerprint related to device identity in the wireless signal. When there are differences in the wireless channel or receiver front end between the source domain training environment and the target domain deployment environment, a distribution offset occurs between the source domain data and the target domain data, which may reduce the classifier's true recognition accuracy in the target domain. Since the target domain data does not have device identity labels, it is impossible to directly compare the classification results with the true device identity during the actual deployment stage. This embodiment constructs labeled and controllable distribution offset samples to obtain the mapping relationship between multiple temperature energy indicators and the true accuracy, so that the target domain recognition accuracy can be estimated from the energy indicators corresponding to the unlabeled data.

[0026] Please see Figure 1 This invention provides a technical solution: a tagless performance estimation method for radio frequency fingerprint recognition based on multi-temperature energy regression, comprising the following steps: S1. Obtain the labeled source domain dataset, the unlabeled target domain dataset, and the radio frequency fingerprint classifier trained on the source domain dataset, as follows: S11. The received I / Q signal samples are represented as: in, This indicates the number of sampling points contained in the I / Q signal sample, where 2 represents the I-channel signal and the Q-channel signal; S12. Represent the labeled source domain dataset as follows: S13. Represent the unlabeled target domain dataset as follows: in, Indicates the first One source domain I / Q signal sample, Indicates the first The device identification tag corresponding to each source domain I / Q signal sample. Indicates the first One target domain I / Q signal sample, and These represent the number of samples contained in the source domain dataset and the target domain dataset, respectively. Device identification tags belong to the device identification tag set: In the formula, Indicates the number of equipment categories; It should be further explained that the radio frequency fingerprint classifier is a deep neural network classifier aimed at device identification. It only uses the output logit vector in subsequent energy calculations. The method does not depend on the specific network structure of the classifier and can adopt any of the following six representative structures. The classifier input is a normalized I / Q dual-channel signal with a shape of (batch size, 2, L), where L is the number of sampling points. In this embodiment, L is 256.

[0027] The six architectures are: (1) CNN, consisting of two one-dimensional convolutional blocks and a fully connected layer, outputting logit; (2) ResNet, a one-dimensional ResNet-18, containing four residual stages (64, 128, 256, 512 channels), which outputs logit after adaptive average pooling and a linear layer; (3) CVCNN, a complex convolutional network, consisting of multiple complex convolutional blocks cascaded and then connected to a fully connected layer to output logit; (4) CVSRN, a complex multi-branch residual network, containing three parallel complex residual branches with kernels of 3, 5, and 7 respectively, which output logit after being concatenated and connected to a fully connected layer; (5) MSCAN, a multi-scale attention convolutional network, containing multiple convolutional blocks with three parallel convolutional paths (kernels 3, 6, and 12) and SE. The module consisting of channel attention outputs logit at the end through a fully connected layer; (6) KAN, which uses a one-dimensional ResNet-18 as the backbone and replaces the fully connected layer of the classification head with a KAN layer based on B splines, outputs logit.

[0028] All six classifiers mentioned above use cross-entropy as the training loss function, employ the Adam optimizer, set the learning rate to 10, the batch size to 128, the training epochs to 200, and the random seed to 2023. During training, the source domain data is divided into a training subset and a validation subset in a 1:1 ratio. After each epoch, the accuracy is evaluated on the validation subset and the optimal weights are retained. Early stopping is not set, and training stops when the number of epochs reaches 200. S14. Using the source domain dataset to classify the radio frequency fingerprint. Train the RF fingerprint classifier and then use the trained one. Deployed on the target domain dataset; S2. Based on the signal distortion types caused by the wireless channel and receiver front-end acting on the I / Q signals, a controllable perturbation parameter space is constructed, including amplitude nonlinear perturbation, carrier frequency offset perturbation, phase jitter perturbation, and additive noise perturbation. The source domain dataset is then perturbed according to the perturbation parameters in the controllable perturbation parameter space to generate multiple enhanced replica datasets that retain the source domain labels, as follows: S21. The received signal in the radio frequency fingerprint recognition system is modeled as follows: in, Indicates a specific hardware defect in the portable device. The transmitted signal, Indicates the discrete-time sampling point number, and the specific hardware defect of the device. Constructing a radio frequency fingerprint, Indicates wireless channel response, This indicates the receiver front-end response. This represents additive white noise. This represents the convolution operation; S22. The received signal is approximately decomposed into: in, This represents the composite amplitude response formed by the wireless channel and the receiver front end. Indicates carrier frequency offset, This indicates phase noise and slow phase drift. Represents the imaginary unit; S23. Based on the composite amplitude response, carrier frequency offset, phase noise and slow phase drift, and additive noise, amplitude operators, frequency operators, phase operators, and noise operators are constructed respectively. Amplitude nonlinear disturbances, carrier frequency offset disturbances, phase jitter disturbances, and additive noise disturbances are generated through the amplitude operator, frequency operator, phase operator, and noise operator, as detailed below: The S23.1 amplitude operator uses the Rapp model to model the AM-AM nonlinearity of the amplifier; Record No. The number of I / Q sampling points is: Its complex baseband sample is: in, and They represent the first The I-path (in-phase) component and Q-path (quadrature) component of each sampling point; Indicates the time index of the sampling point. The superscript T indicates transpose. S23.2 defines compression levels Amplitude operator with parameters The complex baseband sample is subjected to amplitude nonlinear compression processing according to the following formula: in: In the formula, This represents the complex baseband sample after amplitude nonlinear perturbation processing. Indicates compression level A defined saturation factor Represents the Rapp smoothing parameter. This represents the maximum value of the complex baseband amplitude across all sampling points of the signal sample; This represents the normalized input amplitude; Indicates complex baseband sample The phase angle; express The model; symbol The definition is as follows: In this embodiment, p is 2, and the compression level is... The value ranges from 10.0 dB to 30.0 dB; S23.3 with carrier frequency offset Frequency operator of parameters It applies a deterministic carrier frequency offset according to the following formula, expressed as: in The carrier frequency offset is normalized to the sampling rate; in this embodiment, the normalized carrier frequency offset ranges from 0.025 to 0.100. Phase is defined by the standard deviation of phase jitter. Phase operator with parameters It is expressed as follows: Gaussian phase jitter is superimposed according to the following formula: in The standard deviation of phase jitter, Indicates the first Phase jitter superimposed on each sampling point; This indicates that the mean is 0 and the variance is 0. Gaussian distribution; This indicates that each sampling point independently and identically follows this distribution; in this embodiment, the standard deviation of phase jitter ranges from 0.175 rad to 1.571 rad, which corresponds to approximately 10 degrees to 90 degrees; S23.4 defines the target signal-to-noise ratio noise operator with parameters Additive white noise is introduced into the I / Q signal samples according to the following formula, expressed as: in Indicates the first A two-dimensional additive Gaussian white noise vector added to each sampling point; Represents a 2×2 identity matrix; The average signal power, The target signal-to-noise ratio; in this embodiment, the target signal-to-noise ratio ranges from 0.0 dB to 10.0 dB; S24. Perturb the source domain dataset according to the perturbation parameters in the controllable perturbation parameter space to generate multiple enhanced replica datasets that retain the source domain labels, as follows: S24.1 The parameter space of the controllable disturbance is parameterized using a parameter set, which is represented as follows: in, , , and These represent the disturbance parameters corresponding to amplitude nonlinear disturbance, carrier frequency offset disturbance, phase jitter disturbance, and additive noise disturbance, respectively. S24.2 enumerates the perturbation parameters in the parameter set on the predefined parameter grid, and processes the source domain dataset using amplitude operators, frequency operators, phase operators, and noise operators with different perturbation levels, respectively, to obtain... One enhanced replica dataset: Among them, the Enhanced replica dataset The samples in the database inherit the device identity tags of the corresponding source domain samples; S24.3 Determine the identification category of each enhanced copy sample based on the logit vector output by the radio frequency fingerprint classifier, compare the identification category with the corresponding device identity label, and determine the true accuracy of the enhanced copy dataset by the proportion of the number of samples with the same identification category as the device identity label to the total number of samples in the corresponding enhanced copy dataset. It should be further clarified that, in determining the identification category of each enhanced replica sample using the logit vector output by the RF fingerprint classifier trained on the source domain dataset, the device category corresponding to the component with the largest value in the logit vector is taken as the identification category of that sample. In the formula, This represents the classification category of the i-th sample in the k-th augmented copy dataset; This represents the c-th component of the logit vector; C represents the number of device categories; S3. Input each enhanced replica dataset into the RF fingerprint classifier to obtain the logit vector corresponding to each sample in each enhanced replica dataset. Calculate the sample-level energy of each sample at different temperatures based on the logit vector and a predefined temperature set. Then, average the sample-level energies at the same temperature in the same enhanced replica dataset to obtain the average sample-level energy corresponding to each temperature. Stack the average sample-level energies corresponding to each temperature to obtain the multi-temperature energy index corresponding to each enhanced replica dataset, as follows: S31. By radio frequency fingerprint classifier Input sample Mapping to include A logit vector with 1 component: S32. For any temperature in a predefined set of temperatures The sample-level energy is calculated based on the logit vector using the following formula: In the formula, Indicates sample At temperature The sample-level energy below, This represents the temperature parameter, and ; This represents the c-th logit component output by the radio frequency fingerprint classifier; c represents the number of device categories. Represents the natural logarithm; This represents an exponential function with the natural constant e as its base. S33. Represent the predefined temperature set as follows: S34. For the first Enhanced replica dataset and the first in the predefined temperature set Temperature The average sample-level energy is calculated using the following formula: in, Indicates the first The first enhanced replica dataset One sample; This indicates the number of samples contained in each augmented copy dataset (the same as the number of samples in the source dataset). S35. The first The average sample-level energies of the enhanced replica datasets at various temperatures are stacked in temperature order to obtain the... Multi-temperature energy metrics corresponding to each enhanced replica dataset: in, This indicates the number of temperatures contained in a predefined temperature set; S4. Based on the source domain labels retained in each augmented replica dataset, calculate the true accuracy corresponding to each augmented replica dataset, and associate the multi-temperature energy index corresponding to each augmented replica dataset with the true accuracy to construct energy-accuracy training sample pairs, as follows: The first Multi-temperature energy metrics corresponding to each enhanced replica dataset With true accuracy Combine and construct an energy-precision training sample set: S5. Using the multi-temperature energy index as input and the corresponding true accuracy as output, the Huber loss is used to fit the energy-accuracy training sample pairs to obtain a linear regression function from the multi-temperature energy index to the recognition accuracy, as follows: Take the linear regression function A linear regressor trained with Huber loss is represented as: Among them, parameters Solve it using the following method: Where the threshold is Huber's losses are: In the formula, Indicates the threshold is Huber loss; e represents the regression residual, which is the difference between the true accuracy and the linear regression prediction. ; This represents the threshold for Huber's loss, and This is used to distinguish between small and large residuals; This represents the absolute value of the residual e; S6. Input the target domain dataset into the RF fingerprint classifier to obtain the target domain logit vector corresponding to each sample in the target domain dataset. Based on the target domain logit vector, using the same predefined temperature set as when constructing the energy-accuracy training sample pairs, calculate the target domain sample-level energy of each target domain sample at different temperatures. Then, average the target domain sample-level energies at the same temperature to obtain the target domain average energy at each temperature. Stack the target domain average energies at each temperature to obtain the target domain multi-temperature energy index. Input the target domain multi-temperature energy index into a linear regression function to obtain the prediction accuracy of the RF fingerprint classifier on the target domain dataset, as detailed below: For the first in the predefined temperature set Temperature Based on the target domain dataset The target domain logit vector corresponding to each target domain sample is used to calculate the average energy of the target domain according to the following formula: in, Represents the first in the target domain dataset One target domain sample; The average energy of the target domain corresponding to each temperature is stacked in the same temperature order as when constructing the multi-temperature energy index to obtain the target domain multi-temperature energy index: Multi-temperature energy index of the target domain Substitute the values ​​into the linear regression function and obtain the prediction accuracy using the following formula: In the formula, This indicates the prediction accuracy of the radio frequency fingerprint classifier on the target domain dataset; This indicates multiple temperature energy indices within the target domain; and These represent the fitted linear regression weight vector and bias term, respectively; This represents a truncation operation that restricts the value to the interval [0,1].

[0029] Combination Figure 2 , Figure 1This paper presents the overall framework for label-free performance estimation based on multi-temperature energy regression. Labeled source domain data first enters the distribution offset space construction process, and then forms an enhanced replica dataset through amplitude operator, frequency operator, phase operator and noise operator. Each enhanced replica dataset is passed through an RF fingerprint classifier to obtain a logit vector and further form a multi-temperature energy index. At the same time, the true accuracy is obtained based on the retained source domain labels. The multi-temperature energy index and the true accuracy constitute an energy-accuracy training sample pair and are used to fit a linear regression function. The label-free target domain data is passed through the same RF fingerprint classifier and the same predefined temperature set to form the target domain multi-temperature energy index, and then the prediction accuracy is output by the linear regression function. Combination Figure 3 , Figure 2 The effects of four types of physically interpretable perturbation operators on the original signal are shown. The amplitude operator changes the nonlinear compression state of the signal amplitude, the frequency operator forms a phase shift that accumulates with the sampling point number, the phase operator superimposes random phase jitter at each sampling point, and the noise operator adds additive white noise to both the I and Q channels at a specified target signal-to-noise ratio. By changing the corresponding perturbation parameters of the four types of operators, multiple enhanced signals with different perturbation levels can be generated under the same distortion type.

[0030] The technical solution of this embodiment will be further elaborated below with the aid of simulation experiments: The experiment used a subset of the publicly available WiSig dataset, the ManyRx subset (10 Wi-Fi devices and 32 receivers), as a benchmark. Six representative RFF models—CNN, ResNet, CVCNN, CVSRN, MSCAN, and KAN—were employed. Two deployment scenarios were set up: In the cross-channel scenario, the same set of transmitters and receivers was fixed, and subsets D1-D4 with different channel conditions were obtained only over four collection days. Data from three days was used as the source domain each time, and the remaining day as the target domain, rotating sequentially to obtain four sets of evaluations. In the cross-receiver scenario, data from 10 receivers was used as the source domain, and data from six unseen receivers was used as independent target domains. All models were trained only in the source domain; the target domain labels were not visible throughout the training process and were only used for verification during the final evaluation. The estimation errors of each model in the two scenarios are listed in Tables 1-3, where Tables 1 and 2 show the cross-channel results (before and after channel equalization), and Table 3 shows the cross-receiver results.

[0031] Table 1. Estimation errors (%) of each model on D1–D4 under cross-channel conditions (without channel equalization) Table 2. Estimation errors (%) of each model on D1–D4 under cross-channel conditions (after channel equalization) Table 3. Estimation errors (%) of each model on six unseen receivers under cross-receiver conditions. In summary, the average estimation errors of this invention are as low as 1.70% and 7.36% under cross-channel and cross-receiver conditions, respectively. Experimental results show that under both cross-channel and cross-receiver conditions, multi-temperature energy indices can serve as observable representations of changes in the target domain performance of the classifier. The energy-precision mapping established by enhancing the replicas with controllable perturbations can output prediction accuracy even when the target domain label is not visible. Multi-temperature processing reflects the peak state and overall distribution state of the logit vector through multiple temperature scales, reducing the problem of insensitivity to distribution shift changes when the single temperature energy is overly concentrated in the classifier output.

[0032] Example 2: This embodiment provides a tagless performance estimation system for radio frequency fingerprint recognition based on multi-temperature energy regression, used to implement the tagless performance estimation method for radio frequency fingerprint recognition based on multi-temperature energy regression described in Embodiment 1, including: The data acquisition module is used to acquire the labeled source domain dataset, the unlabeled target domain dataset, and the radio frequency fingerprint classifier trained on the source domain dataset. The enhanced copy generation module is used to construct a controllable perturbation parameter space, including amplitude nonlinear perturbation, carrier frequency offset perturbation, phase jitter perturbation and additive noise perturbation, based on the signal distortion types formed by the wireless channel and receiver front end acting on the I / Q signal. The module then performs perturbation processing on the source domain dataset according to the perturbation parameters in the controllable perturbation parameter space to generate multiple enhanced copy datasets that retain the source domain labels. The source domain multi-temperature energy index generation module is used to input each enhanced replica dataset into the radio frequency fingerprint classifier to obtain the logit vector corresponding to each sample in each enhanced replica dataset. Based on the logit vector and the predefined temperature set, the sample-level energy of each sample at different temperatures is calculated. The sample-level energy at the same temperature in the same enhanced replica dataset is averaged to obtain the average sample-level energy corresponding to each temperature. The average sample-level energies corresponding to each temperature are stacked to obtain the multi-temperature energy index corresponding to each enhanced replica dataset. The training sample pair construction module is used to calculate the true accuracy corresponding to each enhanced replica dataset based on the source domain labels retained by each enhanced replica dataset, and to associate the multi-temperature energy index corresponding to each enhanced replica dataset with the true accuracy to construct energy-accuracy training sample pairs. The regression function fitting module is used to fit the energy-precision training sample pairs with multiple temperature energy indicators as input and the corresponding true accuracy as output, using Huber loss to obtain a linear regression function from multiple temperature energy indicators to recognition accuracy. The target domain multi-temperature energy index generation module is used to input the target domain dataset into the radio frequency fingerprint classifier to obtain the target domain logit vector corresponding to each sample in the target domain dataset. Based on the target domain logit vector, using the same predefined temperature set as when constructing the energy-precision training sample pairs, the target domain sample-level energy of each target domain sample at different temperatures is calculated. The target domain sample-level energy at the same temperature is averaged to obtain the target domain average energy corresponding to each temperature. The target domain average energies corresponding to each temperature are stacked to obtain the target domain multi-temperature energy index. The prediction accuracy generation module is used to input the target domain multi-temperature energy index into the linear regression function to obtain the prediction accuracy of the radio frequency fingerprint classifier on the target domain dataset.

[0033] Example 3: The present invention provides a terminal device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor. The memory stores the computer program capable of running on the processor. When the processor loads and executes the computer program, it adopts the tagless performance estimation method for radio frequency fingerprint recognition based on multi-temperature energy regression described in Embodiment 1.

[0034] It should be noted that the terminal device can be a computer device such as a desktop computer, a laptop computer, or a cloud server, and the terminal device includes, but is not limited to, a processor and a memory. For example, the terminal device may also include input / output devices, network access devices, and buses.

[0035] Furthermore, the processor can be a central processing unit (CPU). Of course, depending on the actual use, other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), off-the-shelf programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. can also be used. The general-purpose processor can be a microprocessor or any conventional processor, etc., and this application does not limit it in this regard.

[0036] Example 4: The present invention provides a storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to perform the tagless performance estimation method for radio frequency fingerprint recognition based on multi-temperature energy regression described in Embodiment 1.

[0037] The computer program can be stored in a computer-readable medium. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or certain middleware. The computer-readable medium includes any entity or device capable of carrying computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the computer-readable medium includes, but is not limited to, the above-mentioned components.

[0038] In the description of this specification, the references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0039] The foregoing has shown and described the basic principles, main features, and advantages of this application. Those skilled in the art should understand that this application is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of this application. Various changes and modifications can be made to this application without departing from the spirit and scope thereof, and all such changes and modifications fall within the scope of the claims of this application.

Claims

1. A tagless performance estimation method for radio frequency fingerprint recognition based on multi-temperature energy regression, characterized in that, Includes the following steps: Obtain the labeled source domain dataset, the unlabeled target domain dataset, and the radio frequency fingerprint classifier trained on the source domain dataset; Based on the signal distortion types caused by the wireless channel and receiver front end acting on the I / Q signals, a controllable perturbation parameter space is constructed, including amplitude nonlinear perturbation, carrier frequency offset perturbation, phase jitter perturbation and additive noise perturbation. The source domain dataset is perturbed according to the perturbation parameters in the controllable perturbation parameter space to generate multiple enhanced copy datasets that retain the source domain labels. Each enhanced replica dataset is input into the radio frequency fingerprint classifier to obtain the logit vector corresponding to each sample in each enhanced replica dataset. Based on the logit vector and the predefined temperature set, the sample-level energy of each sample at different temperatures is calculated. The sample-level energy at the same temperature in the same enhanced replica dataset is averaged to obtain the average sample-level energy corresponding to each temperature. The average sample-level energies corresponding to each temperature are stacked to obtain the multi-temperature energy index corresponding to each enhanced replica dataset. Based on the source domain labels retained by each of the enhanced replica datasets, the true accuracy corresponding to each of the enhanced replica datasets is calculated, and the multi-temperature energy index corresponding to each of the enhanced replica datasets is associated with the true accuracy to construct energy-accuracy training sample pairs; Using the multi-temperature energy index as input and the corresponding true accuracy as output, the Huber loss is used to fit the energy-accuracy training sample pair to obtain a linear regression function from the multi-temperature energy index to the recognition accuracy. The target domain dataset is input into the radio frequency fingerprint classifier to obtain the target domain logit vector corresponding to each sample in the target domain dataset. Based on the target domain logit vector, the same predefined temperature set as when constructing the energy-precision training sample pairs is used to calculate the target domain sample-level energy of each target domain sample at different temperatures. The target domain sample-level energy at the same temperature is averaged to obtain the target domain average energy corresponding to each temperature. The target domain average energies corresponding to each temperature are stacked to obtain the target domain multi-temperature energy index. The target domain multi-temperature energy index is input into the linear regression function to obtain the prediction accuracy of the radio frequency fingerprint classifier on the target domain dataset.

2. The tagless performance estimation method for radio frequency fingerprint recognition based on multi-temperature energy regression according to claim 1, characterized in that: Obtaining the labeled source domain dataset, the unlabeled target domain dataset, and the radio frequency fingerprint classifier trained on the source domain dataset includes: The received I / Q signal samples are represented as: in, This indicates the number of sampling points contained in the I / Q signal sample, where 2 represents the I-channel signal and the Q-channel signal; The labeled source domain dataset is represented as: The unlabeled target domain dataset is represented as follows: in, Indicates the first One source domain I / Q signal sample, Indicates the first The device identification tag corresponding to each source domain I / Q signal sample. Indicates the first One target domain I / Q signal sample, and These represent the number of samples contained in the source domain dataset and the target domain dataset, respectively. The device identity tag belongs to the device identity tag set: In the formula, Indicates the number of equipment categories; The source domain dataset was used to classify the radio frequency fingerprint. The trained radio frequency fingerprint classifier will be used for training. Deployed on the target domain dataset.

3. The tagless performance estimation method for radio frequency fingerprint recognition based on multi-temperature energy regression according to claim 1, characterized in that: Based on the signal distortion types caused by the wireless channel and receiver front-end acting on the I / Q signals, a controllable disturbance parameter space is constructed, including amplitude nonlinear disturbance, carrier frequency offset disturbance, phase jitter disturbance, and additive noise disturbance, as follows: The received signal in the radio frequency fingerprint recognition system is modeled as follows: in, Indicates a specific hardware defect in the portable device. The transmitted signal, Indicates the discrete-time sampling point number, and the specific hardware defect of the device. Constructing a radio frequency fingerprint, Indicates wireless channel response, This indicates the receiver front-end response. This represents additive white noise. This represents the convolution operation; The received signal is approximately decomposed into: in, This represents the composite amplitude response formed by the wireless channel and the receiver front end. Indicates carrier frequency offset, This indicates phase noise and slow phase drift. Represents the imaginary unit; Based on the composite amplitude response, carrier frequency offset, phase noise and slow phase drift, and additive noise, amplitude operators, frequency operators, phase operators, and noise operators are constructed respectively, and the amplitude nonlinear disturbance, carrier frequency offset disturbance, phase jitter disturbance, and additive noise disturbance are formed by the amplitude operator, frequency operator, phase operator, and noise operator respectively.

4. The tagless performance estimation method for radio frequency fingerprint recognition based on multi-temperature energy regression according to claim 3, characterized in that: The amplitude operator uses the Rapp model to model the AM-AM nonlinearity of the amplifier; Record No. The number of I / Q sampling points is: Its complex baseband sample is: in, and They represent the first The I-path in-phase component and the Q-path quadrature component of each sampling point; Indicates the time index of the sampling point. The superscript T indicates transpose. Defined by compression level Amplitude operator with parameters The complex baseband sample is subjected to amplitude nonlinear compression processing according to the following formula: in: In the formula, This represents the complex baseband sample after amplitude nonlinear perturbation processing. Indicates compression level A defined saturation factor Represents the Rapp smoothing parameter. This represents the maximum value of the complex baseband amplitude across all sampling points of the signal sample; This represents the normalized input amplitude; Indicates complex baseband sample The phase angle; express The model; Defined by carrier frequency offset Frequency operator of parameters It applies a deterministic carrier frequency offset according to the following formula, expressed as: in The carrier frequency offset normalized to the sampling rate; Defined by the standard deviation of phase jitter Phase operator with parameters Its Gaussian phase jitter is superimposed according to the following formula, and is expressed as: in The standard deviation of phase jitter, Indicates the first Phase jitter superimposed on each sampling point; This indicates that the mean is 0 and the variance is 0. Gaussian distribution; This indicates that each sampling point independently and identically distributed follows this distribution; Define the target signal-to-noise ratio noise operator with parameters Additive white noise is introduced into the I / Q signal samples according to the following formula, expressed as: in Indicates the first A two-dimensional additive Gaussian white noise vector added to each sampling point; Represents a 2×2 identity matrix; The average signal power, The target signal-to-noise ratio.

5. The tagless performance estimation method for radio frequency fingerprint recognition based on multi-temperature energy regression according to claim 4, characterized in that: The source domain dataset is perturbed according to the perturbation parameters in the controllable perturbation parameter space to generate multiple enhanced replica datasets that retain the source domain labels, as follows: The controllable disturbance parameter space is parameterized using a parameter set, which is represented as follows: in, , , and These represent the disturbance parameters corresponding to amplitude nonlinear disturbance, carrier frequency offset disturbance, phase jitter disturbance, and additive noise disturbance, respectively. The perturbation parameters in the parameter set are enumerated on a predefined parameter grid, and the source domain dataset is processed using the amplitude operator, frequency operator, phase operator, and noise operator with different perturbation levels to obtain... One enhanced replica dataset: Among them, the Enhanced replica dataset The samples in the database inherit the device identity tags of the corresponding source domain samples; The identification category of each enhanced replica sample is determined based on the logit vector output by the radio frequency fingerprint classifier. The identification category is compared with the corresponding device identity label, and the proportion of the number of samples with the same identification category and device identity label to the total number of samples in the corresponding enhanced replica dataset is determined as the true accuracy of the enhanced replica dataset.

6. The tagless performance estimation method for radio frequency fingerprint recognition based on multi-temperature energy regression according to claim 1, characterized in that: Each enhanced replica dataset is input into the radio frequency fingerprint classifier to obtain the logit vector corresponding to each sample in each enhanced replica dataset. Based on the logit vector and a predefined temperature set, the sample-level energy of each sample at different temperatures is calculated. The sample-level energies at the same temperature in the same enhanced replica dataset are averaged to obtain the average sample-level energy corresponding to each temperature. The average sample-level energies corresponding to each temperature are stacked to obtain the multi-temperature energy index corresponding to each enhanced replica dataset, as detailed below: The radio frequency fingerprint classifier Input sample Mapping to include The logit vector of each component: For any temperature in the predefined set of temperatures The sample-level energy is calculated based on the logit vector according to the following formula: In the formula, Indicates sample At temperature The sample-level energy below, Represents the temperature parameter, and ; This represents the c-th logit component output by the radio frequency fingerprint classifier; c represents the number of device categories. Represents the natural logarithm; This represents an exponential function with the natural constant e as its base. The predefined temperature set is represented as: For the Enhanced replica dataset and the first in the predefined temperature set Temperature The average sample-level energy is calculated using the following formula: in, Indicates the first The first enhanced replica dataset One sample; This indicates the number of samples contained in each augmented replica dataset; The first The average sample-level energy of each enhanced replica dataset at various temperatures is stacked in temperature order to obtain the first... Multi-temperature energy metrics corresponding to each enhanced replica dataset: in, This indicates the number of temperatures included in the predefined temperature set.

7. The tagless performance estimation method for radio frequency fingerprint recognition based on multi-temperature energy regression according to claim 1, characterized in that: Construct energy-precision training sample pairs as follows: The first Multi-temperature energy metrics corresponding to each enhanced replica dataset With true accuracy Combine and construct an energy-precision training sample set: 。 8. The tagless performance estimation method for radio frequency fingerprint recognition based on multi-temperature energy regression according to claim 1, characterized in that: Using the multi-temperature energy index as input and the corresponding true accuracy as output, the Huber loss is applied to fit the energy-accuracy training sample pairs to obtain a linear regression function from the multi-temperature energy index to the recognition accuracy, as follows: Take the linear regression function A linear regressor trained with Huber loss is represented as: Among them, parameters Solve it using the following method: Where the threshold is Huber's losses are: In the formula, Indicates the threshold is Huber loss; e represents the regression residual, which is the difference between the true accuracy and the linear regression prediction. ; This represents the threshold for Huber's loss, and This is used to distinguish between small and large residuals; This represents the absolute value of the residual e.

9. The tagless performance estimation method for radio frequency fingerprint recognition based on multi-temperature energy regression according to claim 1, characterized in that: The output shows the prediction accuracy of the radio frequency fingerprint classifier on the target domain dataset, as follows: For the first in the predefined temperature set Temperature According to the target domain dataset The target domain logit vector corresponding to each target domain sample is used to calculate the average energy of the target domain according to the following formula: in, Represents the first in the target domain dataset One target domain sample; The average energy of the target domain corresponding to each temperature is stacked in the same temperature order as when constructing the multi-temperature energy index to obtain the target domain multi-temperature energy index: The target domain multi-temperature energy index Substituting into the linear regression function, the prediction accuracy is obtained according to the following formula: In the formula, This indicates the prediction accuracy of the radio frequency fingerprint classifier on the target domain dataset; This indicates multiple temperature energy indices within the target domain; and These represent the fitted linear regression weight vector and bias term, respectively; This represents a truncation operation that restricts the value to the interval [0,1].

10. A tagless performance estimation system for radio frequency fingerprint recognition based on multi-temperature energy regression, used to implement the tagless performance estimation method for radio frequency fingerprint recognition based on multi-temperature energy regression as described in any one of claims 1 to 9, characterized in that, include: The data acquisition module is used to acquire the labeled source domain dataset, the unlabeled target domain dataset, and the radio frequency fingerprint classifier trained on the source domain dataset. The enhanced copy generation module is used to construct a controllable perturbation parameter space, including amplitude nonlinear perturbation, carrier frequency offset perturbation, phase jitter perturbation and additive noise perturbation, based on the signal distortion type formed by the wireless channel and receiver front end acting on the I / Q signal. The module then performs perturbation processing on the source domain dataset according to the perturbation parameters in the controllable perturbation parameter space to generate multiple enhanced copy datasets that retain the source domain labels. The source domain multi-temperature energy index generation module is used to input each of the enhanced replica datasets into the radio frequency fingerprint classifier to obtain the logit vector corresponding to each sample in each of the enhanced replica datasets. Based on the logit vector and the predefined temperature set, the sample-level energy of each sample at different temperatures is calculated. The sample-level energy at the same temperature in the same enhanced replica dataset is averaged to obtain the average sample-level energy corresponding to each temperature. The average sample-level energies corresponding to each temperature are stacked to obtain the multi-temperature energy index corresponding to each of the enhanced replica datasets. The training sample pair construction module is used to calculate the true precision corresponding to each of the enhanced replica datasets based on the source domain labels retained by each of the enhanced replica datasets, and to associate the multi-temperature energy index corresponding to each of the enhanced replica datasets with the true precision to construct energy-precision training sample pairs. The regression function fitting module is used to fit the energy-precision training sample pairs with the multi-temperature energy index as input and the corresponding true accuracy as output, using Huber loss to obtain a linear regression function from the multi-temperature energy index to the recognition accuracy. The target domain multi-temperature energy index generation module is used to input the target domain dataset into the radio frequency fingerprint classifier to obtain the target domain logit vector corresponding to each sample in the target domain dataset. Based on the target domain logit vector, using the same predefined temperature set as when constructing the energy-precision training sample pair, the target domain sample-level energy of each target domain sample at different temperatures is calculated. The target domain sample-level energy at the same temperature is averaged to obtain the target domain average energy corresponding to each temperature. The target domain average energies corresponding to each temperature are stacked to obtain the target domain multi-temperature energy index. The prediction accuracy generation module is used to input the target domain multi-temperature energy index into the linear regression function to obtain the prediction accuracy of the radio frequency fingerprint classifier on the target domain dataset.

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