A cross-receiver radio frequency fingerprinting method, system and terminal device

Abstract

This invention discloses a cross-receiver radio frequency fingerprinting method, system, and terminal device, relating to the field of wireless communication security technology. The invention estimates the carrier frequency offset of the received IQ signal by decoupling the transmitter and receiver carrier frequency offsets; extracts the slope and curvature of the frequency domain phase as domain-invariant features; constrains the consistency of features of the same device across different receivers based on contrastive learning; employs optimal transmission alignment of the spectral envelope distribution of different receivers to reduce inter-domain offset; and achieves cross-receiver device identification through joint optimization of invariant features. By estimating the carrier frequency offset and decoupling the transmitter and receiver frequency offsets, extracting the frequency domain phase slope and curvature as domain-invariant features, and combining contrastive learning to constrain the consistency of features of the same device across receivers with optimal transmission alignment of the spectral envelope distribution of different receivers, this invention achieves reliable device access authentication and identification under receiver-less conditions, improving the model's generalization ability and stability.

Description

Technical Field

[0001] This invention relates to the field of wireless communication security technology, specifically to a cross-receiver radio frequency fingerprinting method, system, and terminal device. Background Technology

[0002] With the rapid development of technologies such as the Internet of Things (IoT), 5G / 6G, low-Earth orbit satellite communication, and smart manufacturing, various wireless terminal devices are being deployed on a large scale in scenarios such as smart cities, industrial control, vehicle networking, and drone management. Wireless device identification and access authentication are crucial foundational links for ensuring network security and business trustworthiness. Their goal is to accurately distinguish legitimate devices in complex and open wireless channels and to promptly detect and block attacks such as impersonation, spoofing, and replay attacks. Current network layer or application layer authentication typically relies on device identifiers such as MAC addresses and serial numbers, as well as cryptographic credentials such as keys and certificates. However, in real-world engineering environments, these identifiers are easily copied or forged, key management and updates are costly, and deploying strong cryptographic algorithms on resource-constrained terminals can impose burdens on computing power, power consumption, and latency. Therefore, there is an urgent need to uncover deeper, more difficult-to-forge authentication criteria from the wireless signal itself.

[0003] Radio frequency (RF) fingerprinting, as a physical layer authentication technology, utilizes the unavoidable non-ideal characteristics of wireless transmission link hardware caused by differences in manufacturing processes, device aging, and operating conditions to achieve inherent device identification. Typical sources of RF fingerprints include carrier frequency offset, sampling clock deviation, phase noise, IQ imbalance, power amplifier nonlinearity, modulation error, and transient startup characteristics. These features are often difficult to clone and are therefore considered to have high security value. In actual deployments, RF data is usually collected by different receivers. Differences in analog front-end filtering, mixers, amplifiers, analog-to-digital converters, and clock sources between different receivers introduce receiver-specific characteristics, causing the same device's transmitted signal to exhibit different data distributions on different receivers. Carrier frequency offset is one of the key factors causing domain offset. The observed frequency offset in the received signal is often a superposition of the transmitter and receiver frequency offsets. If only frequency offset compensation or direct use of frequency offset as a fingerprint feature is used for identification, the model easily learns receiver-related features, leading to poor performance across receivers. Furthermore, receiver differences also cause changes in the spectral envelope shape and statistical distribution shifts, making it difficult to guarantee cross-domain consistency using existing deep learning techniques alone. Summary of the Invention

[0004] The purpose of this invention is to provide a cross-receiver radio frequency fingerprinting method, system, and terminal device. By estimating and decoupling the transmitter and receiver frequency offsets, the frequency domain phase slope and phase curvature are extracted as domain-invariant features. Combined with contrastive learning constraints on the consistency of cross-receiver features of the same device and optimal transmission alignment with the spectral envelope distribution of different receivers, reliable device access authentication and identity recognition are achieved under receiver-less conditions, thereby improving the model's generalization ability and stability.

[0005] 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 cross-receiver radio frequency fingerprint recognition method, comprising the following steps: The system receives IQ signals acquired from multiple receivers and performs normalization preprocessing. Utilizing the symbol repetition structure in the preamble of the processed IQ signals, it estimates the observed carrier frequency offset. This observed carrier frequency offset is then input into a pre-trained carrier frequency offset decoupling network to decouple the transmitter and receiver carrier frequency offsets. The carrier frequency offset decoupling network is constructed using multiple one-dimensional convolutional modules and multiple fully connected layers. The preprocessed IQ signal is subjected to a fast Fourier transform to obtain a complex spectrum in the frequency domain. The frequency domain phase sequence of the complex spectrum is calculated and phase expansion and smoothing are performed. The processed frequency domain phase sequence is subjected to first-order and second-order difference to obtain phase slope features and phase curvature features, respectively. The phase slope features and phase curvature features constitute frequency domain invariant features that are insensitive to changes in the receiver domain. The frequency domain complex spectrum, phase slope features, and phase curvature features are fused and input into a pre-trained feature extraction network to output a feature representation vector. The feature representation vector is then fused with the decoupled transmitter carrier frequency offset and input into a classifier consisting of three linear layers for device classification, resulting in device identity classification results and device identity classification loss. The feature extraction network includes multiple consecutively stacked complex convolutional modules and linear classification layers. The complex convolutional modules include complex one-dimensional convolutional layers, Leaky ReLU activation layers, batch normalization layers, and max pooling layers. Based on the extraction of spectral envelopes from the frequency domain complex spectrum, the spectral envelopes of different receiver domains are regarded as probability distributions of different domains. The optimal transmission method is used to calculate the Wasserstein distance between different receiver domains. By minimizing the Wasserstein distance between domains, the alignment of the spectral envelope distributions of different receivers is achieved, and the optimal transmission alignment loss is obtained. The obtained optimal transmission alignment loss and device identity classification loss are weighted and combined with the pre-constructed contrast loss function to form a joint loss function. This joint loss function is then used to jointly optimize and train the feature extraction network, resulting in a cross-receiver RF fingerprint recognition model. The trained recognition model is then used to identify the device identity of the IQ signal from an unknown receiver.

[0006] Furthermore, by utilizing the symbol repetition structure in the preamble segment of the preprocessed IQ signal, the observed carrier frequency offset is estimated, as follows: Short training symbols with repetitive structures are extracted from the IQ signal to obtain sequence segments for carrier frequency estimation. Perform delayed autocorrelation on the preamble of each receiver: in, This represents the time-delay autocorrelation between any two sequences. D Let the time delay be between any two short training symbols. L Indicates the sample length, the first... The carrier frequency offset observed by each receiver is: In the formula, Indicates the first Each receiver observes the carrier frequency offset.

[0007] Furthermore, the training process of the carrier frequency offset decoupling network is as follows: The input WiFi device time-domain dataset is represented as follows: The input WiFi radio frequency data is normalized using the root mean square (RMS) method, and the IQ signal is divided by the RMS of the input samples to ensure that the signal amplitude is within the range specified in the original text. The RMS normalization calculation process is as follows: in, It is a complex value after RMS normalization. It is the input IQ signal data. It is the square of the amplitude of the input IQ signal data. It is the sample size; The normalized IQ signal data is converted into a frequency domain representation using the Fast Fourier Transform (FFT): in, It is the transformed frequency domain data. It is the normalized IQ signal data at time point The value at that location, It is the number of normalized IQ samples. It is the discrete angular frequency, describing the frequency components in the frequency domain. It is a frequency index, with a value of ; frequency domain data The input carrier frequency offset decoupling network consists of a one-dimensional convolutional module, each of which includes a one-dimensional convolutional layer, a Leaky ReLU activation layer, a batch normalization layer, and a max pooling layer. The feature extraction process is as follows: in, It is the first The output features of each convolutional module, i.e. , Represents one-dimensional convolution. This represents the LeakyReLU activation function. Indicates the batch normalization layer. Indicates the max pooling layer; Output features The data is sequentially input into the fully connected layer, first mapped to 512-dimensional features, then to 256-dimensional features. These 256-dimensional features serve as the domain-invariant features output by the teacher network. Subsequently, they are further mapped to 128-dimensional features, and the final device category is output. The classification process is as follows: in, It is the output feature of each linear layer. This is the final network output, and the loss is calculated as follows: .

[0008] Furthermore, a Fast Fourier Transform is performed on the preprocessed IQ signal to obtain a frequency domain complex spectrum. The frequency domain phase sequence of the frequency domain complex spectrum is calculated and subjected to phase expansion and smoothing denoising. First-order and second-order differences are performed on the processed frequency domain phase sequence to obtain phase slope features and phase curvature features, respectively. The phase slope features and phase curvature features constitute frequency domain invariant features that are insensitive to changes in the receiver domain, as detailed below: The normalized IQ data is converted into a frequency domain graph using Fast Fourier Transform: in, It uses the frequency domain characteristics after Fourier transform to represent the normalized IQ signal in time. n The value at that location, N It is the number of normalized IQ signal samples. k It is a frequency index, with values... ; Extracting frequency domain data phase sequence As shown below: in, It is a phase sequence. and They represent the frequency domain components respectively. The imaginary and real parts; The phase slope feature is extracted by performing a first-order difference along the frequency direction on the phase sequence. The phase slope feature is shown below: The phase curvature characteristics are calculated by performing a second-order difference on the phase sequence, as shown below: in, and Representing frequency index and Phase slope characteristics at that point Frequency index The phase curvature characteristics at that location.

[0009] Furthermore, the frequency domain complex spectrum, phase slope features, and phase curvature features are fused and input into a pre-trained feature extraction network to output a feature representation vector. This feature representation vector is then fused with the decoupled transmitter carrier frequency offset and input into a classifier for device classification, yielding the device identity classification result and the device identity classification loss, as detailed below: in, It is the first Features output by a complex convolutional module ; Indicates a splicing operation; Represents complex convolution; This represents the Leaky ReLU activation function; Indicates the batch normalization layer; Indicates the max pooling layer; The complex convolution module is configured with four modules, whose output channels are as follows: All convolutional kernels have a size of 3, a stride of 1, and padding of 1. The kernel size of the max pooling layer is 2. The features output from the convolution are flattened and then sequentially input into the fully connected layer, where they are first mapped to 512-dimensional features. These 512-dimensional features serve as the total feature representation vector extracted by the feature extraction network. Next, the feature representation vector The carrier frequency offset obtained from decoupling is then spliced ​​and fused with the specific carrier frequency offset obtained from the transmitter. in Feature Representation Vector With transmitter carrier frequency offset The spliced ​​and merged features are used for the final device category; The concatenated features are input into the classifier, and the final classification output is the device identity classification result: in, This indicates the output by category. Represents a linear classification layer; Calculate the device identity classification loss using the device identity classification results: In the formula, This indicates the output by category. This represents a linear classification layer.

[0010] Furthermore, during the feature extraction network training phase, sample features collected from the same Wi-Fi device by different receivers are constructed as positive sample pairs, and sample features collected from different Wi-Fi devices are constructed as negative sample pairs. A contrastive learning loss is constructed to constrain positive sample pairs to be closer in the feature space and negative sample pairs to be farther apart. The contrastive learning loss is specifically represented as follows: in, Indicates comparative loss, Indicates batch size, Indicates the sample index. Indicates a positive sample pair. Indicates negative sample pairs, Represents a plotted view. This represents a view that differs from the plotted point. Indicates the first The feature vector of each sample in the anchor point view. Indicates the first The normalized feature vector of each sample in the view This represents the exponential similarity between positive sample pairs. This represents the sum of the exponential similarities over all negative sample pairs. Indicates a positive sample pair. This represents a negative sample pair.

[0011] Furthermore, based on the extraction of spectral envelopes from the frequency domain complex spectrum, the spectral envelopes of different receiver domains are regarded as probability distributions of different domains. The optimal transmission method is used to calculate the Wasserstein distance between different receiver domains. By minimizing the inter-domain Wasserstein distance, the alignment of the spectral envelope distributions of different receivers is achieved, resulting in the optimal transmission alignment loss, as detailed below: Extracting the frequency domain complex spectrum from the frequency domain complex spectrum Calculate amplitude Further calculation of the envelope The envelope is non-negatively normalized to construct the receiver. discrete probability distribution The details are as follows: Define the transmission cost matrix between different receiver domains Then we have: in, Indicates the first The value corresponding to each frequency bin Indicates the first Let T be the optimal transmission value corresponding to each frequency bin. Solve the following optimal transmission problem: in, , It is a vector consisting entirely of 1s; Thus, the domain is obtained. and First-order Wasserstein distance : in, and These represent the distribution of different receivers; minimize Make the receiver and Alignment of the frequency domain envelope probability distribution.

[0012] Furthermore, the joint loss function is as follows: in, and These are comparative losses Distance from Wasserstein The weighting coefficients.

[0013] According to a second aspect of the present invention, the present invention provides a cross-receiver radio frequency fingerprint recognition system for implementing the cross-receiver radio frequency fingerprint recognition method described in the first aspect, comprising: The carrier frequency offset decoupling module is used to receive IQ signals collected by multiple receivers and perform normalization preprocessing. It uses the symbol repetition structure in the preamble of the processed IQ signal to estimate the carrier frequency offset and obtain the observed carrier frequency offset. The obtained observed carrier frequency offset is then input into a pre-trained carrier frequency offset decoupling network to decouple the transmitter carrier frequency offset and the receiver carrier frequency offset. The frequency domain invariant feature generation module is used to perform a fast Fourier transform on the preprocessed IQ signal to obtain a frequency domain complex spectrum, calculate the frequency domain phase sequence of the frequency domain complex spectrum and perform phase expansion and smoothing denoising, and perform first-order and second-order difference on the processed frequency domain phase sequence to obtain phase slope features and phase curvature features respectively. The phase slope features and phase curvature features constitute frequency domain invariant features that are insensitive to changes in the receiver domain. The feature extraction and device classification module is used to fuse the frequency domain complex spectrum, phase slope features and phase curvature features into a pre-trained feature extraction network, output a feature representation vector, and fuse the feature representation vector with the decoupled transmitter carrier frequency offset and input it into a classifier for device classification, thereby obtaining the device identity classification result and the device identity classification loss. The optimal transmission alignment loss production module is used to extract the spectral envelope based on the frequency domain complex spectrum, treating the spectral envelopes of different receiver domains as probability distributions of different domains; it uses the optimal transmission method to calculate the Wasserstein distance between different receiver domains, and achieves alignment of the spectral envelope distributions of different receivers by minimizing the inter-domain Wasserstein distance, thus obtaining the optimal transmission alignment loss. The loss function construction and model training module is used to weight and combine the obtained optimal transmission alignment loss and device identity classification loss with the pre-constructed contrast loss function to form a joint loss function. This joint loss function is then used to jointly optimize and train the feature extraction network to obtain a cross-receiver radio frequency fingerprint recognition model. The trained recognition model is then used to identify the device identity of the IQ signal of an unknown receiver.

[0014] According to a third aspect of the present invention, a terminal device is provided, 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, and when the processor loads and executes the computer program, it employs the cross-receiver radio frequency fingerprinting method described in the first aspect.

[0015] This invention has at least the following beneficial effects: 1. This invention constructs a carrier frequency offset decoupling network to jointly decouple the superimposed frequency offsets observed by multiple receivers into a unique transmitter carrier frequency offset and a receiver carrier frequency offset corresponding to each receiver. This effectively separates the inherent frequency offset characteristics of the transmit link from the frequency offset interference introduced by the receiver. This decoupling method avoids the problem of loss of transmitter intrinsic information caused by directly using the observed frequency offset as a fingerprint feature or discarding it after simple compensation in traditional methods. This allows the subsequently extracted features to truly reflect the hardware differences of the transmitting equipment, fundamentally suppressing the interference of receiver frequency offset on fingerprint recognition, and laying the foundation for stable recognition in cross-receiver scenarios.

[0016] 2. This invention constructs a robust fingerprint representation that is insensitive to changes in the receiver domain by extracting the slope and curvature features of the frequency domain phase as domain-invariant features. The phase slope characterizes the overall trend of the frequency domain phase as a function of frequency, while the phase curvature characterizes the local nonlinear details of the phase change. Both originate from the inherent non-ideal characteristics of the transmit link hardware and exhibit good robustness to differences in the receiver front-end. Compared to directly using the original frequency domain phase or using only a single differential feature, this invention integrates global trends and local details, significantly reducing sensitivity to receiver model, status, and channel environment while preserving the intrinsic information of the transmitter hardware.

[0017] 3. This invention introduces a contrastive learning mechanism in the feature learning stage. Features from the same transmitting device under different receivers are constructed as positive sample pairs, and features from different devices are constructed as negative sample pairs. Contrastive loss constrains positive sample pairs to cluster tightly in the feature space, while negative sample pairs are kept far apart. This mechanism forces the feature extraction network to ignore receiver-related domain offset information and focus on learning the inherent, cross-receiver consistent fingerprint features of the transmitting device. This effectively enhances the consistency and separability of feature representations of the same device under different receiver conditions, improving the model's generalization ability to unseen receivers.

[0018] 4. This invention employs optimal transmission theory to align the spectral envelope distributions of different receivers. By calculating and minimizing the Wasserstein distance between receiver domains, it accurately matches the differences in spectral morphology and statistical structure caused by different receivers. Compared to traditional adversarial domain adaptation methods, optimal transmission alignment offers stronger geometric interpretation and distribution matching accuracy. It effectively suppresses spectral envelope drift caused by differences in analog circuits such as receiver front-end filtering, amplification, and mixing while preserving frequency domain fingerprint discrimination information, further enhancing the stability of features across receiver scenarios.

[0019] 5. This invention constructs a joint optimization framework comprising device identity classification loss, contrastive learning loss, and optimal transmission alignment loss. Through multi-task collaborative training, the feature extraction network simultaneously satisfies cross-receiver feature consistency constraints and spectral distribution alignment constraints under the constraint of classification accuracy. The three losses work synergistically and complement each other: the classification loss ensures the discriminativeness of features, the contrastive loss strengthens cross-domain consistency, and the optimal transmission alignment reduces inter-domain distribution offset. This joint optimization strategy enables the fingerprint recognition capability learned by the trained model on the source domain receiver to be effectively transferred to the unseen target domain receiver, significantly improving the generalization performance and engineering practicality of RF fingerprint recognition in heterogeneous receiver deployment environments.

[0020] 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

[0021] 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.

[0022] Figure 1 This is a flowchart illustrating the identification method described in this invention; Detailed Implementation 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.

[0023] Example 1: Specific definitions of terms in this embodiment: Wasserstein distance, also known as bulldozer distance or Earth Mover's Distance, is a distance metric between probability distributions defined based on optimal transport theory. It measures the minimum "transportation" cost required to transform one distribution into another.

[0024] Fast Fourier Transform (FFT): An efficient algorithm for computing the Discrete Fourier Transform (DFT) and its inverse transform. It can quickly convert time-domain signals into frequency-domain signals and is widely used in signal processing, image analysis, and data compression.

[0025] WIFI radio frequency signal data: refers to the high-frequency electromagnetic waves used for Wi-Fi communication. In essence, it is a radio frequency (RF) signal that operates in a specific frequency band (such as 2.4GHz or 5GHz) and transmits data wirelessly.

[0026] IQ signal data refers to the digital representation of a radio frequency or baseband signal in a communication system, which decomposes the signal into two orthogonal components: I (in-phase component) and Q (quadrature component). It fully preserves the amplitude, phase, and frequency information of the original signal and is the core foundation of modern wireless communication, radar, and signal analysis. IQ signal data belongs to radio frequency signal data.

[0027] Complex-Valued Convolutional Neural Network (CVCNN): This is a class of deep learning models that perform operations directly on the complex domain. Specifically, it includes complex convolutional layers, complex activation functions, and complex batch normalization layers. It can not only process the amplitude information of data, but also preserve and utilize phase information, demonstrating superior expressive power compared to traditional real-valued networks in fields such as speech, radar, and medical imaging.

[0028] Please see Figure 1 This invention provides a technical solution: a cross-receiver radio frequency fingerprint recognition method, comprising the following steps: Step 1: Normalize and preprocess the WiFi RF signals collected by multiple receivers to reduce the impact of power differences. Based on this, utilize the symbol repetition structure in the WiFi preamble and employ delayed autocorrelation to estimate the carrier frequency offset, obtaining the observed carrier frequency offset. Under the condition that multiple receivers simultaneously receive the same WiFi data packet, design a carrier frequency offset decoupling network. Use the observed frequency offset of each receiver as input and output the estimated frequency offset of the transmitter and each receiver, as detailed below: The carrier frequency offset decoupling network consists of three one-dimensional convolutional modules and four fully connected layers. Each one-dimensional convolutional module includes a one-dimensional convolutional layer, a Leaky ReLU activation layer, a batch normalization layer, and a max pooling layer. The number of output channels of the three one-dimensional convolutional layers are respectively, the kernel size is 3, the stride is 1, and the padding is 1. The pooling kernel size of the max pooling layer is 2. Step 1-1: Input the WiFi device time-domain dataset as follows: The input WiFi RF data is normalized using the root mean square (RMS) method, and the IQ data is divided by the RMS of the input samples to ensure that the signal amplitude is within the range specified in the standard. The RMS normalization calculation process is as follows: in, It is a complex value after RMS normalization. It is the input IQ signal data. It is the square of the amplitude of the input IQ signal data. It is the sample size; This processing method can eliminate the difference in the amplitude of the input signal, make the feature data of different scales comparable, improve the stability of the numerical value, speed up the convergence of the model, and facilitate subsequent signal analysis and processing. Steps 1-2: Extract short training symbols with repetitive structures from the normalized IQ signal to obtain sequence segments for carrier frequency estimation. Perform delayed autocorrelation on the preamble of each receiver: in, This represents the time-delay autocorrelation between any two sequences. D Let the time delay be between any two short training symbols. L Indicates the sample length, the first... The carrier frequency offset observed by each receiver is: Steps 1-3: Constructing a carrier frequency offset decoupling network The observed carrier frequency offset Decoupling is the transmitter carrier frequency offset and receiver carrier frequency offset The details are as follows: The input WiFi device time-domain dataset can be represented as: Next, the input WiFi RF data is normalized using the root mean square (RMS) method, dividing the IQ data by the input sample RMS to ensure the signal amplitude is within a certain range. This processing method can eliminate differences in the amplitude of the input signal, making feature data at different scales comparable, improving numerical stability, accelerating model convergence, and facilitating subsequent signal analysis and processing. The RMS normalization calculation process is as follows: in, It is a complex value after RMS normalization. It is the input IQ data. It is the square of the input IQ data amplitude. It refers to the number of samples.

[0029] The normalized IQ data is further converted into a frequency domain representation using Fast Fourier Transform (FFT): in, It is the transformed frequency domain data. The above normalized IQ data at the specified time point The value at that location, It is the number of normalized IQ samples. It is the discrete angular frequency, describing the frequency components in the frequency domain. It is a frequency index, with a value of .

[0030] Furthermore, frequency domain data Each one-dimensional convolutional module of the input carrier frequency offset decoupling network includes a one-dimensional convolutional layer, a Leaky ReLU activation layer, a batch normalization layer, and a max pooling layer. The feature extraction process is as follows: in, It is the first The output features of each convolutional module, i.e. . Represents one-dimensional convolution. This represents the LeakyReLU activation function. Indicates the batch normalization layer. This indicates a max-pooling layer. The three one-dimensional convolutional layer modules have output channels of 32, 64, and 128, respectively, with a kernel size of 3, a stride of 1, and padding of 1. The max-pooling layer has a kernel size of 2.

[0031] The features output from the above convolution are flattened and sequentially input into the fully connected layer. First, they are mapped to 512-dimensional features, then to 256-dimensional features. These 256-dimensional features serve as the domain-invariant features output by the teacher network. Subsequently, they are mapped to 128-dimensional features, and the final device category is output. After training, the model weights are saved for learning domain-invariant features in subsequent training processes. The classification process is as follows: in, It is the output feature of each linear layer. This is the final network output, and the loss is calculated as follows: Step 2: Perform a Fast Fourier Transform on the preprocessed IQ signal to obtain the frequency domain complex spectrum. And calculate the frequency domain phase sequence After phase expansion and smoothing denoising of the phase sequence, first-order difference is used to obtain phase slope features to characterize the overall trend of phase variation with frequency; second-order difference is used to obtain phase curvature features to characterize the local nonlinearity of phase variation, thus forming a frequency-domain invariant feature representation that is relatively insensitive to changes in the receiver domain, specifically including: Step 2-1: Use Fast FFT to convert the normalized IQ data into a frequency domain graph: in, It uses the frequency domain features after FFT transformation to represent the normalized IQ data in time. n The value at that location, N It is the number of normalized IQ samples. k It is a frequency index, with values... ; It should be further noted that the Fast Fourier Transform does not change the dimension of the input data; Step 2-2: Extract frequency domain data phase components As shown below: in, It is phase sequence information. and They represent the frequency domain components respectively. The imaginary and real parts; Steps 2-3: Filter and smooth the phase sequence to improve the stability of the differential features. Further, perform first-order differential extraction along the frequency direction to extract the phase slope features, as shown below: Steps 2-4 involve performing second-order differencing on the phase sequence to calculate the phase curvature characteristics, as shown below: In the formula, and Representing frequency index and Phase slope characteristics at that point Indicates the phase curvature at the frequency index; Step 3: Construct a complex convolutional neural network as the feature extraction network to extract the complex spectrum in the frequency domain. The phase slope and curvature frequency domain invariant features obtained in step 2 are fused into the input to obtain the feature representation vector characterizing the intrinsic features of the device fingerprint. and the feature representation vector The transmitter carrier frequency offset obtained by decoupling The fused components are then input into a classifier for device classification, specifically including: Step 3-1: Construct a feature extraction network based on complex convolution to extract the spectral features of the preprocessed original radio frequency signal through Fast Fourier Transform. Phase slope characteristics Phase curvature characteristics The complex sequence, which serves as the input to the feature extraction network, is sequentially passed through a complex convolutional feature extraction module and a fully connected layer to obtain the total feature vector. The feature extraction process using complex convolution is as follows: in, It is the first The output features of each complex convolutional module, i.e. , This indicates a splicing operation. Represents complex convolution. This represents the Leaky ReLU activation function. Indicates the batch normalization layer. Indicates the max pooling layer; It should be noted that the feature extraction network includes four consecutively stacked complex convolutional modules and a linear classification layer. The complex convolutional modules include a complex one-dimensional convolutional layer, a Leaky ReLU activation layer, a batch normalization layer, and a max pooling layer. For the technical solution of this embodiment, the output channels of the four complex convolutional modules are as follows: All convolutional kernels have a size of 3, a stride of 1, and padding of 1. The kernel size of the max pooling layer is 2. Step 3-2: The features output from the convolution in Step 3-1 are flattened and then sequentially input into the fully connected layer, first mapped to 512-dimensional features. These 512-dimensional features serve as the total feature representation vector extracted by the feature extraction network. Next, the total feature representation vector The transmitter-specific carrier frequency offset obtained from step 1 is then spliced ​​and fused together. in Feature Representation Vector With transmitter carrier frequency offset The spliced ​​and merged features are used for the final device category; The concatenated features are input into the classifier, and the final classification output is the device identity classification result: in, This indicates the output by category. Represents a linear classification layer; Calculate the device identity classification loss using the device identity classification results: In the formula, This indicates a loss related to device identification classification. Represents the cross-entropy loss function; Step 3-3: During the feature extraction network training phase, positive sample pairs are constructed from the sample features collected by the same Wi-Fi device from different receivers, and negative sample pairs are constructed from the sample features collected by different Wi-Fi devices. A contrastive learning loss is constructed to constrain positive sample pairs to be closer in the feature space and negative sample pairs to be farther apart. The contrastive learning loss is specifically represented as follows: in, Indicates comparative loss, Indicates batch size, Indicates the sample index. Indicates a positive sample pair. Indicates negative sample pairs, Represents a plotted view. This represents a view that differs from the plotted point. Indicates the first The feature vector of each sample in the anchor point view. Indicates the first The normalized feature vector of each sample in the view This represents the exponential similarity between positive sample pairs. This represents the sum of the exponential similarities over all negative sample pairs. Indicates a positive sample pair. Indicates negative sample pairs; Step 4: Based on the frequency domain complex spectrum The spectral envelope is extracted, treating the spectral envelopes of different receiver domains as probability distributions of different domains. An optimal transmission method is used to calculate the transmission cost and transmission plan between receiver domains. The Wasserstein distance is used to measure the distribution difference between domains. By minimizing the Wasserstein distance between domains, the spectral envelope distributions of different receivers are aligned, thereby reducing the impact of receiver differences on the spectral morphology and statistical structure during training. Specifically, this includes: Step 4-1: Based on the frequency domain complex spectrum obtained in Step 2 Calculate amplitude Further calculation of the envelope The envelope is non-negatively normalized to construct the receiver. Discrete probability distribution: Step 4-2: Define the transmission cost matrix between different receiver domains Then we have: in, Indicates the first The value corresponding to each frequency bin Indicates the first Let T be the optimal transmission plan for each frequency bin. Solve the following optimal transmission problem: in, , It is a vector consisting entirely of 1s; Thus, the domain is obtained. and First-order Wasserstein distance: in, and These represent the distribution of different receivers; After steps 4-1 and 4-2, the minimum value is adopted. Make the receiver and Aligning the frequency domain envelope probability distribution reduces the impact of receiver front-end differences on spectral morphology and statistical structure. Step 5: The contrastive learning loss and device identity classification loss from Step 3 are weighted and jointly optimized with the optimal transmission alignment loss from Step 4 to construct a joint constraint function. This joint optimization training is then applied to the feature extraction network to obtain a cross-receiver RF fingerprint recognition model. The trained model is then used to identify the device identity of unknown receivers using their IQ signals. Specifically, this includes: In step 4, the optimal transmission alignment loss is calculated using the Wasserstein distance. This indicates that the distribution differences between different receiver domains are used to measure the overall distributional differences; therefore, the final joint constraint function is expressed as: in, and These are contrastive learning losses. Distance from Wasserstein Weighting coefficients; By updating the feature extraction network parameters through backpropagation, a cross-receiver RF fingerprint recognition model is obtained. In the inference phase, steps 1 to 2 are performed to construct features for samples collected by unseen receivers, and device identity classification is achieved through feature extraction and classification in step 3, thus realizing RF fingerprint recognition and access authentication under cross-receiver conditions.

[0032] In summary, this invention combines carrier frequency offset decoupling, invariant feature extraction, consistency learning, and optimal transmission alignment techniques to effectively suppress distribution drift caused by heterogeneous receivers, preserve intrinsic hardware fingerprint information, achieve accurate and reliable device identification even without a receiver, and significantly improve the model's cross-domain generalization ability. It can be applied to fields such as wireless communication security, IoT device authentication, and illegal device detection.

[0033] Example 2: This embodiment provides a cross-receiver radio frequency fingerprint recognition system for implementing the cross-receiver radio frequency fingerprint recognition method described in Embodiment 1, including: The carrier frequency offset decoupling module is used to receive IQ signals collected by multiple receivers and perform normalization preprocessing. It uses the symbol repetition structure in the preamble of the processed IQ signal to estimate the carrier frequency offset and obtain the observed carrier frequency offset. The obtained observed carrier frequency offset is then input into a pre-trained carrier frequency offset decoupling network to decouple the transmitter carrier frequency offset and the receiver carrier frequency offset. The frequency domain invariant feature generation module is used to perform a fast Fourier transform on the preprocessed IQ signal to obtain a frequency domain complex spectrum, calculate the frequency domain phase sequence of the frequency domain complex spectrum and perform phase expansion and smoothing denoising, and perform first-order and second-order difference on the processed frequency domain phase sequence to obtain phase slope features and phase curvature features respectively. The phase slope features and phase curvature features constitute frequency domain invariant features that are insensitive to changes in the receiver domain. The feature extraction and device classification module is used to fuse the frequency domain complex spectrum, phase slope features and phase curvature features into a pre-trained feature extraction network, output a feature representation vector, and fuse the feature representation vector with the decoupled transmitter carrier frequency offset and input it into a classifier for device classification, thereby obtaining the device identity classification result and the device identity classification loss. The optimal transmission alignment loss production module is used to extract the spectral envelope based on the frequency domain complex spectrum, treating the spectral envelopes of different receiver domains as probability distributions of different domains; it uses the optimal transmission method to calculate the Wasserstein distance between different receiver domains, and achieves alignment of the spectral envelope distributions of different receivers by minimizing the inter-domain Wasserstein distance, thus obtaining the optimal transmission alignment loss. The loss function construction and model training module is used to weight and combine the obtained optimal transmission alignment loss and device identity classification loss with the pre-constructed contrast loss function to form a joint loss function. This joint loss function is then used to jointly optimize and train the feature extraction network to obtain a cross-receiver radio frequency fingerprint recognition model. The trained recognition model is then used to identify the device identity of the IQ signal of an unknown receiver.

[0034] Example 3: This embodiment 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 employs the cross-receiver radio frequency fingerprinting method described in Embodiment 1.

[0035] 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.

[0036] 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.

[0037] 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 cross-receiver radio frequency fingerprinting method described in Embodiment 1.

[0038] 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.

[0039] 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.

[0040] 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 cross-receiver radio frequency fingerprinting method, characterized in that, Includes the following steps: The system receives IQ signals acquired from multiple receivers and performs normalization preprocessing. Utilizing the symbol repetition structure in the preamble of the processed IQ signals, it estimates the observed carrier frequency offset. This observed carrier frequency offset is then input into a pre-trained carrier frequency offset decoupling network to decouple the transmitter and receiver carrier frequency offsets. The carrier frequency offset decoupling network is constructed using multiple one-dimensional convolutional modules and multiple fully connected layers. The preprocessed IQ signal is subjected to a fast Fourier transform to obtain a complex spectrum in the frequency domain. The frequency domain phase sequence of the complex spectrum is calculated and phase expansion and smoothing are performed. The processed frequency domain phase sequence is subjected to first-order and second-order difference to obtain phase slope features and phase curvature features, respectively. The phase slope features and phase curvature features constitute frequency domain invariant features that are insensitive to changes in the receiver domain. The frequency domain complex spectrum, phase slope features, and phase curvature features are fused and input into a pre-trained feature extraction network to output a feature representation vector. The feature representation vector is then fused with the decoupled transmitter carrier frequency offset and input into a classifier consisting of three linear layers for device classification, resulting in device identity classification results and device identity classification loss. The feature extraction network includes multiple consecutively stacked complex convolutional modules and linear layers. The complex convolutional modules include complex one-dimensional convolutional layers, Leaky ReLU activation layers, batch normalization layers, and max pooling layers. Based on the extraction of spectral envelopes from the frequency domain complex spectrum, the spectral envelopes of different receiver domains are regarded as probability distributions of different domains. The optimal transmission method is used to calculate the Wasserstein distance between different receiver domains. By minimizing the Wasserstein distance between domains, the alignment of the spectral envelope distributions of different receivers is achieved, and the optimal transmission alignment loss is obtained. The obtained optimal transmission alignment loss and device identity classification loss are weighted and combined with the pre-constructed contrast loss function to form a joint loss function. This joint loss function is then used to jointly optimize and train the feature extraction network, resulting in a cross-receiver RF fingerprint recognition model. The trained recognition model is then used to identify the device identity of the IQ signal from an unknown receiver.

2. The method of claim 1, wherein: By utilizing the symbol repetition structure in the preamble segment of the preprocessed IQ signal, the observed carrier frequency offset is estimated, as follows: A short training symbol with repetitive structure in the IQ signal is intercepted to obtain a sequence segment for carrier frequency estimation Performing a delay self-correlation on the preamble segment for each receiver: wherein, denotes the delay autocorrelation between any two sequences, D is the time delay between any two short training symbols, L denotes the sample length, the carrier frequency offset observed by the kthreceiver is: In the formula, represents the carrier frequency offset observed by the th receiver.

3. The method of claim 2, wherein: The training process of the carrier frequency offset decoupling network is as follows: The input WiFi device time-domain dataset is represented as follows: The input WiFi radio frequency data is normalized by using the root mean square, and the IQ signal is divided by the root mean square of the input sample, so that the signal amplitude is between 0 and 1. The RMS normalization calculation process is as follows: in, It is a complex value after RMS normalization. It is the input IQ signal data. It is the square of the amplitude of the input IQ signal data. It is the sample size; The normalized IQ signal data is converted into a frequency domain representation using the Fast Fourier Transform (FFT): in, It is the transformed frequency domain data. It is the normalized IQ signal data at time point The value at that location, It is the number of normalized IQ samples. It is the discrete angular frequency, describing the frequency components in the frequency domain. It is a frequency index, with a value of ; frequency domain data The input carrier frequency offset decoupling network consists of a one-dimensional convolutional module, each of which includes a one-dimensional convolutional layer, a Leaky ReLU activation layer, a batch normalization layer, and a max pooling layer. The feature extraction process is as follows: in, It is the first The output features of each convolutional module, i.e. , Represents one-dimensional convolution. This represents the LeakyReLU activation function. Indicates the batch normalization layer. Indicates the max pooling layer; Output features The data is sequentially input into the fully connected layer, first mapped to 512-dimensional features, then to 256-dimensional features. These 256-dimensional features serve as the domain-invariant features output by the teacher network. Subsequently, they are further mapped to 128-dimensional features, and the final device category is output. The classification process is as follows: in, It is the output feature of each linear layer. This is the final network output, and the loss is calculated as follows: 。 4. The cross-receiver radio frequency fingerprint recognition method according to claim 1, characterized in that: The preprocessed IQ signal is subjected to a Fast Fourier Transform to obtain a complex spectrum in the frequency domain. The frequency domain phase sequence of the complex spectrum is calculated and subjected to phase expansion and smoothing denoising. The processed frequency domain phase sequence is subjected to first-order and second-order differences to obtain phase slope features and phase curvature features, respectively. The phase slope features and phase curvature features constitute frequency domain invariant features that are insensitive to changes in the receiver domain, as detailed below: The normalized IQ data is converted into a frequency domain graph using Fast Fourier Transform: in, It uses the frequency domain characteristics after Fourier transform to represent the normalized IQ signal in time. n The value at that location, N It is the number of normalized IQ signal samples. k It is a frequency index, with values... ; Extracting frequency domain data phase sequence As shown below: in, It is a phase sequence. and They represent the frequency domain components respectively. The imaginary and real parts; The phase slope feature is extracted by performing a first-order difference along the frequency direction on the phase sequence. The phase slope feature is shown below: The phase curvature characteristics are calculated by performing a second-order difference on the phase sequence, as shown below: in, and Representing frequency index and Phase slope characteristics at that point Frequency index The phase curvature at that point.

5. The cross-receiver radio frequency fingerprint recognition method according to claim 4, characterized in that: The frequency domain complex spectrum, phase slope features, and phase curvature features are fused and input into a pre-trained feature extraction network to output a feature representation vector. This feature representation vector is then fused with the decoupled transmitter carrier frequency offset and input into a classifier for device classification, yielding the device identity classification result and the device identity classification loss, as detailed below: in, It is the first Features output by a complex convolutional module ; Indicates a splicing operation; Represents complex convolution; This represents the Leaky ReLU activation function; Indicates the batch normalization layer; Indicates the max pooling layer; The complex convolution module is configured with four modules, whose output channels are as follows: All convolutional kernels have a size of 3, a stride of 1, and padding of 1. The kernel size of the max pooling layer is 2. The features output from the convolution are flattened and then sequentially input into the fully connected layer, where they are first mapped to 512-dimensional features. These 512-dimensional features serve as the total feature representation vector extracted by the feature extraction network. Next, the feature representation vector The carrier frequency offset obtained from decoupling is then spliced ​​and fused with the specific carrier frequency offset obtained from the transmitter. in Feature Representation Vector With transmitter carrier frequency offset The spliced ​​and merged features are used for the final device category; The concatenated features are input into the classifier, and the final classification output is the device identity classification result: in, This indicates the output by category. Represents a linear classification layer; Calculate the device identity classification loss using the device identity classification results: In the formula, This indicates a loss related to device identification classification. This represents the cross-entropy loss function.

6. The cross-receiver radio frequency fingerprint recognition method according to claim 5, characterized in that: During the feature extraction network training phase, positive sample pairs are constructed from sample features collected by the same Wi-Fi device from different receivers, and negative sample pairs are constructed from sample features collected by different Wi-Fi devices. A contrastive learning loss is constructed to constrain positive sample pairs to be closer in the feature space and negative sample pairs to be farther apart. The contrastive learning loss is specifically represented as follows: in, Indicates comparative loss, Indicates batch size, Indicates the sample index. Indicates a positive sample pair. Indicates negative sample pairs, Represents a plotted view. This represents a view that differs from the plotted point. Indicates the first The feature vector of each sample in the anchor point view. Indicates the first A sample in view The normalized eigenvectors under the following conditions This represents the exponential similarity between positive sample pairs. This represents the summation of the exponential similarity over all negative sample pairs.

7. The cross-receiver radio frequency fingerprint recognition method according to claim 5, characterized in that: Based on frequency domain complex spectrum extraction of spectral envelopes, the spectral envelopes of different receiver domains are regarded as probability distributions of different domains. The optimal transmission method is used to calculate the Wasserstein distance between different receiver domains. By minimizing the inter-domain Wasserstein distance, the spectral envelope distributions of different receivers are aligned, and the optimal transmission alignment loss is obtained, as follows: Extracting the frequency domain complex spectrum from the frequency domain complex spectrum Calculate amplitude Further calculation of the envelope The envelope is non-negatively normalized to construct the receiver. discrete probability distribution The details are as follows: Define the transmission cost matrix between different receiver domains Then we have: in, Indicates the first The value corresponding to each frequency bin Indicates the first Given the values ​​corresponding to each frequency bin, and let T be the optimal transmission value, solve the following optimal transmission problem: in, , It is a vector consisting entirely of 1s; Thus, the domain is obtained. and First-order Wasserstein distance : in, and These represent the distribution of different receivers; minimize Make the receiver and Alignment of the frequency domain envelope probability distribution.

8. The cross-receiver radio frequency fingerprint recognition method according to claim 7, characterized in that: The joint loss function is as follows: in, and These are contrastive learning losses. Distance from Wasserstein The weighting coefficients.

9. A cross-receiver radio frequency fingerprint recognition system, used to implement the cross-receiver radio frequency fingerprint recognition method according to any one of claims 1 to 8, characterized in that, include: The carrier frequency offset decoupling module is used to receive IQ signals collected by multiple receivers and perform normalization preprocessing. It uses the symbol repetition structure in the preamble of the processed IQ signal to estimate the carrier frequency offset and obtain the observed carrier frequency offset. The obtained observed carrier frequency offset is then input into a pre-trained carrier frequency offset decoupling network to decouple the transmitter carrier frequency offset and the receiver carrier frequency offset. The frequency domain invariant feature generation module is used to perform a fast Fourier transform on the preprocessed IQ signal to obtain a frequency domain complex spectrum, calculate the frequency domain phase sequence of the frequency domain complex spectrum and perform phase expansion and smoothing denoising, and perform first-order and second-order difference on the processed frequency domain phase sequence to obtain phase slope features and phase curvature features respectively. The phase slope features and phase curvature features constitute frequency domain invariant features that are insensitive to changes in the receiver domain. The feature extraction and device classification module is used to fuse the frequency domain complex spectrum, phase slope features and phase curvature features into a pre-trained feature extraction network, output a feature representation vector, and then fuse the feature representation vector with the decoupled transmitter carrier frequency offset and input it into a classifier composed of three linear layers to classify devices, thereby obtaining the device identity classification result and the device identity classification loss. The optimal transmission alignment loss production module is used to extract the spectral envelope based on the frequency domain complex spectrum, treating the spectral envelopes of different receiver domains as probability distributions of different domains; it uses the optimal transmission method to calculate the Wasserstein distance between different receiver domains, and achieves alignment of the spectral envelope distributions of different receivers by minimizing the inter-domain Wasserstein distance, thus obtaining the optimal transmission alignment loss. The loss function construction and model training module is used to weight and combine the obtained optimal transmission alignment loss and device identity classification loss with the pre-constructed contrast loss function to form a joint loss function. This joint loss function is then used to jointly optimize and train the feature extraction network to obtain a cross-receiver radio frequency fingerprint recognition model. The trained recognition model is then used to identify the device identity of the IQ signal of an unknown receiver.

10. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, The memory stores a computer program that can run on a processor, and when the processor loads and executes the computer program, it employs any one of the methods described in 1 to 8 for cross-receiver radio frequency fingerprinting.

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