Multi-feature fusion method for wireless device RF fingerprint extraction based on attention mechanism

Abstract

The present invention relates to a multi-feature fusion wireless device radio frequency fingerprint extraction method based on an attention mechanism, comprising the following steps: step 1: extracting signal features caused by three different hardware defects of a wireless transmitter, namely, carrier frequency offset, nonlinearity and frequency response distortion, to obtain radio frequency fingerprints in three dimensions; step 2: using a single-dimensional feature extraction module to respectively extract carrier frequency offset features, nonlinear features and frequency response distortion features, to obtain three single-dimensional radio frequency fingerprint extraction features; step 3: using a multi-feature fusion module to process the three single-dimensional radio frequency fingerprint extraction features to obtain a radio frequency fingerprint with multi-feature fusion; step 4: for the radio frequency fingerprint with multi-feature fusion, obtaining a classification of the wireless device through a fully connected layer, and completing the training of a neural network; step 5: extracting the signal features to be identified based on step 1, obtaining a radio frequency fingerprint, using the trained neural network to identify the radio frequency fingerprint, and completing the classification of the wireless transmitter.

Description

Technical Field

[0001] The present invention relates to the field of communication and information security, and in particular to a method for extracting radio frequency fingerprints of wireless devices using multi-feature fusion based on an attention mechanism. Background Art

[0002] Since there is always a certain deviation between the actual parameters of the electronic components of the equipment and the nominal values, even if the electronic components are produced by the same manufacturer and the same batch, there will still be distinguishable differences in the transmitter itself. Specifically, the frequency offset of the local oscillator, phase noise, digital-to-analog converter, mixer, nonlinearity of the power amplifier and various influencing factors related to the filter characteristics jointly form an RF fingerprint with individual distinguishing characteristics. Figure 1 The RF front end of a typical wireless signal transmitter is shown. It can be seen that the baseband signal enters the signal modulation link after digital signal processing. The signal modulation is completed by analog circuits such as digital / analog converters, orthogonal modulators, up-converters, power amplifiers, and RF oscillators, and finally the RF signal is transmitted through the antenna. In the above process, the parameter error of the analog signal processing device is the source of the RF fingerprint feature.

[0003] Reference [1] adopted a scheme of composite RF fingerprint features for device classification and identification, combined with multiple modulation features for fusion, used four features such as frequency offset, cluster center, constellation offset, and I / Q offset, and used the K-means clustering algorithm to evaluate the device identification performance.

[0004] Most of the existing radio frequency fingerprint extraction technologies are based on a single hardware defect and have insufficient representation capabilities, resulting in the need to improve the differentiation of their fingerprint features.

[0005] The existing RF fingerprint extraction method based on multiple signal features is relatively simple in its comprehensive method for multiple signal features. It does not comprehensively consider the key information of each feature itself, nor does it consider the differences in the importance of different features. As a result, the existing RF fingerprint extraction method based on multiple signal features is not robust and the recognition accuracy needs to be improved.

[0006] The purpose of this invention is to propose a multi-feature fusion RF fingerprint extraction method based on attention mechanism, which can integrate signal features caused by various hardware defects, strengthen the key features in the signal features, and consider the differences in the importance of features in different dimensions, thereby improving the discrimination of RF fingerprints and improving the accuracy of device identity recognition. Summary of the invention

[0007] With the rapid development of wireless network technology represented by 5G, a large number of wireless devices need to access the network. Wireless networks have open communication characteristics and face information security threats that cannot be ignored. Current wireless networks use traditional identity recognition mechanisms based on high-level cryptographic protocols. Once the user's identity information is stolen, the network will face disguised attacks from malicious users. Radio frequency fingerprint technology is one of the user identification methods that is not easily vulnerable to disguised attacks in the current wireless network security protection. It can uniquely determine the transmitter identity of the signal by analyzing the features carried in the wireless signal that can reflect the inherent defects of the transmitter hardware. However, the existing method of feature extraction for a single hardware defect has the problem of insufficient representation capability and the recognition accuracy is not high enough. The present invention proposes a multi-feature fusion radio frequency fingerprint extraction method based on an attention mechanism. The present invention integrates the signal features caused by multiple hardware defects, expands the feature dimension of the radio frequency fingerprint, and uses the attention mechanism to strengthen the key features in the signal features, thereby improving the accuracy of device identity recognition.

[0008] In order to achieve the above purpose, the technical solution adopted by the present invention is:

[0009] A multi-feature fusion wireless device radio frequency fingerprint extraction method based on an attention mechanism specifically includes the following steps:

[0010] Step 1: Extract the signal features of the wireless transmitter caused by three different hardware defects: carrier frequency offset, nonlinearity, and frequency response distortion, and obtain a three-dimensional RF fingerprint. The three-dimensional RF fingerprint and the corresponding wireless transmitter label constitute the data set for training the neural network;

[0011] Step 2: Based on the three-dimensional RF fingerprint obtained in step 1, three single-dimensional feature extraction modules are used to respectively extract carrier frequency offset features, nonlinear features, and frequency response distortion features to obtain three single-dimensional RF fingerprint extraction features;

[0012] Step 3: The three single-dimensional radio frequency fingerprint extraction features obtained in step 2 are processed using a multi-feature fusion module to obtain a radio frequency fingerprint with multi-feature fusion;

[0013] Step 4: Based on the multi-feature fused RF fingerprint obtained in step 3, the classification of the wireless transmitter is obtained through the fully connected layer to complete the training of the neural network;

[0014] Step 5: Based on step 1, the signal characteristics of the wireless transmitter to be identified due to three different hardware defects, namely, carrier frequency offset, nonlinearity and frequency response distortion, are extracted to obtain a three-dimensional RF fingerprint; further, the RF fingerprint is identified using the neural network trained in step 4 to complete the classification of the wireless transmitter.

[0015] Based on the above scheme, step 1 specifically includes:

[0016] Step 1.1: Extraction of carrier frequency offset features based on differential. During the communication process of wireless devices, the receiver performs differential operations on the received signals and obtains the RF fingerprint of the carrier frequency offset dimension after visualization. The differential operation is specifically expressed as follows:

[0017] Step 1.1.1 The signal transmitted by the transmitter is expressed as:

[0018]

[0019] Among them, S(t) represents the transmitted signal, X(t) is the transmitter baseband signal, is the imaginary unit, f cTx is the carrier frequency of the transmitter;

[0020] Step 1.1.2: For the sake of clarity, the influence of factors such as channel and noise is ignored, and the signal received by the receiver is represented as R(t), R(t)=S(t);

[0021] The receiver performs down-conversion to obtain the baseband signal expressed as:

[0022]

[0023] Among them, f cRx is the carrier frequency of the receiver, It is the phase error when the receiver receives the signal;

[0024] When f cRx ≠f cTx When , the baseband signal obtained by the receiver down-conversion is expressed as:

[0025]

[0026] Where θ = f cRx -f cTx , which is the difference between the carrier frequency of the receiver and the carrier frequency of the transmitter.

[0027] Step 1.1.3 The difference processing process is expressed as:

[0028]

[0029] Where D(t) is the difference result, Y * To take the conjugate value, d is the difference interval;

[0030] After differential processing, the phase rotation factor e in the differential result D(t) -i2πθnIt is a fixed value that is only related to the differential interval and will not change with time.

[0031] Step 1.1.4 plots the differential signal directly on the complex plane, discretizes the complex plane into a series of pixel points, and uses different RGB values ​​to represent the number of differential operation results falling into a certain pixel area, thus obtaining a visualized differential constellation trajectory diagram, i.e., the RF fingerprint in the carrier frequency offset dimension;

[0032] Step 1.2 is based on nonlinear feature extraction in the dual spectrum domain to obtain a nonlinear RF fingerprint, which specifically includes:

[0033] Step 1.2.1 Signal data segmentation:

[0034] The captured signal data {r(0), r(1), ... r(N-1)} of length N is divided into K segments, each segment has M observation samples, then N = KM, and the sample mean of each segment is subtracted from the M observation samples in each segment, and the value is expressed as r (k) (n) represents the nth observed sample of the kth segment of signal data, n = 0, 1, ..., M-1, k = 1, 2, ..., K;

[0035] Step 1.2.2 Calculate the discrete Fourier transform coefficients:

[0036]

[0037] Wherein, λ represents a discrete frequency variable, λ=0,1,…,M / 2; on this basis, the discrete Fourier transform coefficients are obtained;

[0038] Step 1.2.3 calculates the triple correlation of the discrete Fourier transform coefficients and performs frequency domain smoothing on ±L1 frequency components around the frequency sampling point:

[0039]

[0040] Among them, λ1,λ2 are discrete frequency variables in the bispectral domain, 0≤λ2≤λ1,λ1+λ2≤f s / 2;f s is the sampling frequency; △0 represents the frequency sampling interval in the dual spectrum domain, △0=f s / N0; N0 is the total number of frequency samples; i1, i2 are variables used to traverse the neighborhood frequency components during accumulation; let N1 = 2L1 + 1, which represents the length of the bispectrum smoothing over the adjacent frequencies, and the values ​​of N0 and N1 satisfy M = N0·N1;

[0041] Step 1.2.4: Use ω1 and ω2 to represent the angular frequency in the dual spectrum domain. Substituting into equation (6), we get the bispectral density estimation of the k-th segment signal data: Then the bispectral density estimates of K segments are averaged to obtain the bispectral density estimate of the entire process:

[0042]

[0043] Among them, the sampling frequency f s Set to 1.

[0044] Step 1.2.5: Convert the bispectral density estimation value obtained in step 1.2.4 into different RGB values ​​and plot the bispectrum to obtain the RF fingerprint in nonlinear dimension;

[0045] Step 1.3 extracts the frequency response distortion feature based on short-time Fourier transform to obtain the RF fingerprint of the frequency response distortion dimension;

[0046] For the time domain signal f(t) received by the receiver, it is first multiplied by the time window function g(t-τ) to intercept the time domain signal near time τ to obtain a local signal. Then, the obtained local signal is subjected to Fourier transform to obtain the formula of short-time Fourier transform, as shown in formula (8):

[0047]

[0048] Where ω is the angular frequency, e -jωt It plays a frequency limiting role; τ is the time delay. By continuously changing the value of τ, the time window determined by g(t) moves continuously on the time axis, and the time domain signal f(t) is gradually intercepted to obtain the Fourier transform at different times.

[0049] The result of the short-time Fourier transform F(τ,ω) is a two-dimensional function of time τ and angular frequency ω.

[0050] Similar to the bispectrum, the value of F(τ,ω) is converted into different RGB value representations, and the short-time Fourier transform time-frequency diagram is plotted to obtain the RF fingerprint of the frequency response distortion dimension.

[0051] Based on the above scheme, the single-dimensional feature extraction module described in step 2 includes: a convolution block, a channel attention module, a spatial attention module and a fully connected layer.

[0052] Based on the above scheme, the convolution block includes three convolution layers, the number of input channels of the first convolution layer is 3, the number of output channels of the three convolution layers are 32, 64, and 64 respectively, the convolution kernel sizes of the three convolution layers are all 3×3, and the padding values ​​are all 1; each convolution layer is followed by a ReLU activation function, a maximum pooling layer, a regularization layer, and a Dropout layer; the sliding window size of the maximum pooling layer is 2×2; the regularization layer is used to standardize the data, and the discard rate of the Dropout layer is 0.2.

[0053] Based on the above scheme, the channel attention module includes: a maximum pooling layer, an average pooling layer, a multi-layer perceptron and a Sigmoid activation function. The specific processing process of the channel attention module includes:

[0054] The preliminary features F output by the convolution block are input into the maximum pooling layer and the average pooling layer respectively, and the maximum pooling and average pooling are performed. The results of the maximum pooling and the average pooling are input into the multi-layer perceptron respectively to obtain two features. After adding the two features, the channel attention map M is obtained by using the Sigmoid activation function to activate them. C ;

[0055] The multi-layer perceptron consists of two two-dimensional convolutional layers, the convolution kernel size is 1×1, the number of output channels is 4 and 64 respectively, the ReLU activation function is used after the first convolutional layer, and the Sigmoid activation function is used after the second convolutional layer;

[0056] Based on the above scheme, the spatial attention module includes: an average pooling layer, a maximum pooling layer, a convolution layer and a Sigmoid function; the specific processing process of the spatial attention module includes:

[0057] The feature F′ is input into the maximum pooling layer and the average pooling layer respectively to calculate the average and maximum values ​​in the channel dimension. The average pooling and maximum pooling results are concatenated in the channel dimension and then input into a convolution layer. The convolution kernel size is set to 7×7 in the convolution operation.

[0058] The padding value is set to 3, the number of input and output channels is 2 and 1 respectively, and finally the Sigmoid activation function is used to activate and obtain the result of spatial attention mapping M S .

[0059] Based on the above solution, step 2 specifically includes the following steps:

[0060] Step 2.1 Preliminary feature extraction using convolutional blocks

[0061] For the single-dimensional RF fingerprint extracted in step 1, a convolution block is used to perform preliminary feature extraction. The RF fingerprint is an image. The image of the single-dimensional RF fingerprint is obtained by a convolution block to obtain a preliminary feature F. The preliminary feature F contains four dimensions B×C×H×W, where B represents the number of samples in each batch, C represents the number of channels, H represents the height of the feature map, and W represents the width of the feature map;

[0062] Step 2.2 Use channel attention module and spatial attention module to enhance the key information in the preliminary features

[0063] Step 2.2.1 Preliminary feature F is used to obtain channel attention map M through the channel attention moduleC , the channel attention map M C The feature F′ is obtained by point multiplication with the unprocessed preliminary feature F, thereby highlighting the key information on the channel component;

[0064] The channel attention mapping is shown in formula (9):

[0065] M C (F)=σ(MLP(AvgPool(F))+MLP(MaxPool(F))) (9)

[0066] Among them, σ represents the Sigmoid function, AvgPool represents average pooling, and MaxPool represents maximum pooling. MLP is a multi-layer perceptron with hidden layers.

[0067] Step 2.2.2 Feature F′ obtains the spatial attention map M through the spatial attention module S , and the unprocessed feature F′ is multiplied to obtain the feature F″, highlighting the key information in the spatial area;

[0068] The implementation principle of spatial attention mapping is shown in formula (10):

[0069] M S (F)=σ(f([AvgPool(F);MaxPool(F)])) (10)

[0070] Among them, M S (F) represents the formed spatial attention map, σ represents the Sigmoid function, and f represents the convolution operation. AvgPool represents average pooling, MaxPool represents maximum pooling, and [] represents the concatenation operation.

[0071] Therefore, the overall attention mechanism is expressed as:

[0072] F′=M C (F)⊙F (11)

[0073] F"=M S (F')⊙F' (12)

[0074] Among them, F represents the preliminary features, M C (F) represents the channel attention map, M S (F′) represents the spatial attention map, the ⊙ symbol represents the element-wise multiplication, and F″ is the final output; the feature F″ still contains four dimensions of B×C×H×W;

[0075] Step 2.3 Further extract features based on the fully connected layer

[0076] Expand the last three dimensions C×H×W of feature F″ into one dimension, convert it into a two-dimensional tensor of B×L, input it into a fully connected layer, and the output dimension is 256, so as to obtain a one-dimensional feature representation of B radio frequency fingerprints from the single-dimensional radio frequency fingerprint source;

[0077] Step 2.4 finally uses three one-dimensional feature extraction modules to obtain the features of one-dimensional RF fingerprint extraction based on three dimensions of carrier frequency offset features, nonlinear features and frequency response distortion features.

[0078] Based on the above scheme, the size of the image in step 2.1 is adjusted according to different application scenarios and complexity requirements, including 32×32, 64×64, 128×128, 256×256 pixels, etc.

[0079] Based on the above scheme, the multi-feature fusion module described in step 3 includes: a self-attention module, and the self-attention module includes: a layer of Tanh activation function, a layer of fully connected layer with a size of 256×1, and a layer of Sigmoid activation function.

[0080] Based on the above solution, step 3 specifically includes the following steps:

[0081] Step 3.1: Perform dimension-increasing splicing on the three single-dimensional RF fingerprint extracted features obtained in step 2, increase the multi-feature dimension S, and obtain a feature M containing three dimensions of B×S×L;

[0082] Step 3.2: Pass the feature M through the self-attention module to obtain the self-attention map M A ;

[0083] Step 3.3: Transform the feature dimension of feature M. The specific operation of the feature dimension transformation is: swap the last two dimensions to obtain a new dimension of B×L×S.

[0084] Step 3.4: Perform tensor matrix multiplication on the processing results of feature M in step 3.2 and step 3.3 to complete the extraction of multi-feature fusion RF fingerprint.

[0085] Based on the above solution, step 4 specifically includes:

[0086] The data set is divided into a training set and a validation set in a certain ratio. The RF fingerprints in the training set are input into the neural network in batches. The loss function is calculated based on the output of the neural network and the label of the RF fingerprint. The parameters of the neural network are updated using the back propagation algorithm. In the process of continuously updating the parameters of the neural network, the recognition performance of the neural network is verified using the validation set.

[0087] When the recognition performance of the neural network on the validation set no longer improves, the training of the neural network is completed, and a neural network for extracting radio frequency fingerprints of wireless devices by multi-feature fusion is obtained;

[0088] Beneficial effects of the present invention:

[0089] The present invention comprehensively extracts the signal features caused by three different hardware defects of the wireless transmitter to form a radio frequency fingerprint, including carrier frequency offset, nonlinearity, frequency response distortion, etc. The present invention strengthens the key feature area of ​​the single-dimensional signal feature source of the radio frequency fingerprint of the wireless device based on the channel attention and spatial attention mechanisms, and assigns different weights to the signal features from different sources based on the self-attention mechanism, thereby expanding the dimension of the radio frequency fingerprint and forming richer feature information of the radio frequency fingerprint, so that the radio frequency fingerprint sources of different dimensions can complement each other's advantages and integrate information, so as to achieve the construction of an efficient and robust radio frequency fingerprint with multi-feature fusion, so that the wireless device identification has better robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] The present invention has the following accompanying drawings:

[0091] Figure 1 Schematic diagram of the RF front end of a wireless signal transmitter;

[0092] Figure 2 Differential constellation trajectory diagrams of different samples from different wireless devices;

[0093] Figure 3 Schematic diagram of dual spectra of different samples from different wireless devices;

[0094] Figure 4 Short-time Fourier transform time-frequency diagrams of different samples from different wireless devices;

[0095] Figure 5 Flow chart of the method for extracting radio frequency fingerprint of wireless devices by fusion of multiple features based on attention mechanism;

[0096] Figure 6 Schematic diagram of the performance results of a single feature network with attention mechanism added;

[0097] Figure 7 Schematic diagram of the performance comparison between multi-feature fusion and single feature. DETAILED DESCRIPTION

[0098] The following is combined with Figures 2 to 7 The present invention is described in further detail.

[0099] The present invention proposes a multi-feature fusion RF fingerprint extraction method based on attention mechanism. Firstly, signal features related to three hardware defects are selected, and a deep neural network combined with attention mechanism is used to extract RF fingerprint as a whole. The extracted RF fingerprint is applied to wireless device identity recognition.

[0100] Step 1: Extract signal features caused by three hardware defects to form RF fingerprints.

[0101] The signal features of the wireless transmitter caused by three different hardware defects, namely carrier frequency offset, nonlinearity and frequency response distortion, are extracted to obtain a three-dimensional RF fingerprint. The three-dimensional RF fingerprint and the corresponding wireless transmitter label constitute a data set for training the neural network.

[0102] Step 1.1 Carrier frequency offset feature extraction based on differential

[0103] Based on the fact that the transmitter and the receiver have different carrier frequencies, the present invention uses the carrier frequency offset as one of the radio frequency fingerprint features of the wireless device.

[0104] During the communication process of the wireless device, the receiver performs a "differential" operation on the received signal to obtain a visualized differential constellation trace figure (DCTF), which is the RF fingerprint of the carrier frequency offset dimension.

[0105] The specific expression of the difference operation is as follows:

[0106] Step 1.1.1 The signal transmitted by the transmitter is expressed as:

[0107]

[0108] Among them, S(t) represents the transmitted signal, X(t) is the transmitter baseband signal, is the imaginary unit, f cTx is the carrier frequency of the transmitter.

[0109] Step 1.1.2 For the sake of clarity, the influence of factors such as channel and noise is ignored, and the signal received by the receiver is expressed as R(t), R(t) = S(t);

[0110] The receiver performs down-conversion to obtain the baseband signal expressed as:

[0111]

[0112] Among them, f cRx is the carrier frequency of the receiver, It is the phase error when the receiver receives the signal;

[0113] When f cRx ≠f cTx When , the baseband signal obtained by the receiver down-conversion is expressed as:

[0114]

[0115] Where θ = f cRx -f cTx , which is the difference between the carrier frequency of the receiver and the carrier frequency of the transmitter.

[0116] Step 1.1.3 The difference processing process is expressed as:

[0117]

[0118] Where D(t) is the difference result, Y * To take the conjugate value, d is the difference interval.

[0119] After differential processing, the phase rotation factor e in the differential result D(t) -i2πθn It is a fixed value, which is only related to the differential interval and will not change with time. Therefore, the differential processing operation compensates for the rotation effect of the constellation diagram to obtain a fixed constellation trajectory diagram to reflect the individual differences between devices, and this is used as one of the sources for extracting the RF fingerprint features of wireless devices.

[0120] Step 1.1.4 Plot the differential signal directly on the complex plane, discretize the complex plane into a series of pixels, and use different RGB values ​​to represent the number of differential operation results falling into a certain pixel area. [3] , and obtain the differential constellation trajectory diagram after visualization, such as Figure 2 As shown, it reflects the statistical characteristics of the difference operation results on the complex plane. The change of color in the figure indicates the density of the constellation trajectory points. The darker the color, the denser the distribution of the constellation trajectory points. [4] Based on this, the carrier frequency offset can be visualized to intuitively represent the degree of phase rotation on the constellation trajectory diagram.

[0121] Step 1.2 Nonlinear feature extraction based on bispectral domain

[0122] Based on the differences in the internal structure of transmitter devices, the present invention introduces nonlinear features extracted based on bispectral transformation as one of the RF fingerprint features of wireless devices. After the receiver obtains the received signal, the estimation of the signal bispectrum is completed based on finite observation values. The bispectrum estimation is mainly performed through non-parametric methods to obtain the RF fingerprint of nonlinear dimension, which specifically includes the following steps:

[0123] Step 1.2.1 Signal data segmentation

[0124] Divide the captured signal data {r(0), r(1), ... r(N-1)} of length N into K segments, each segment has M observation samples, that is, N = KM, and subtract the sample mean of each segment from the M observation samples in the segment. (k) (n) represents the nth observed sample of the kth segment of signal data, n = 0, 1, L, M-1, k = 1, 2, …, K.

[0125] Step 1.2.2 Calculate the discrete Fourier transform coefficients

[0126]

[0127] Among them, λ=0,1,…,M / 2, which represents a discrete frequency variable.

[0128] On this basis, the discrete Fourier transform (DFT) coefficients are obtained.

[0129] Step 1.2.3 calculates the triple correlation of the discrete Fourier transform coefficients and performs frequency domain smoothing on ±L1 frequency components around the frequency sampling point:

[0130]

[0131] Among them, λ1,λ2 are discrete frequency variables in the bispectral domain, 0≤λ2≤λ1,λ1+λ2≤f s / 2;f s is the sampling frequency; △0 represents the frequency sampling interval in the dual spectrum domain, △0=f s / N0; N0 is the total number of frequency samples. i1, i2 are variables used to traverse the neighborhood frequency components during accumulation. Let N1 = 2L1 + 1, which represents the length of the bispectrum smoothing over the adjacent frequencies. The values ​​of N0 and N1 must satisfy M = N0·N1.

[0132] Step 1.2.4: Use ω1 and ω2 to represent the angular frequency in the two-dimensional frequency domain. Substituting into equation (6), we get the bispectral density estimation of the k-th segment signal data: Then the bispectral density estimates of K segments are averaged to obtain the bispectral density estimate of the entire process:

[0133]

[0134] Among them, the sampling frequency f s Set to 1;

[0135] Step 1.2.5: Through the above calculation process, the bispectral characteristics of the signals transmitted by each wireless device can be obtained. Further, the bispectral density estimation value is used to draw the bispectral in a visual form, that is, the bispectral density estimation value is converted into different RGB values ​​to present, and the RF fingerprint of the nonlinear dimension is obtained.

[0136] like Figure 3 , which is a visualization of the bi-spectra of different samples of different wireless devices.

[0137] Step 1.3 Frequency response distortion feature extraction based on short-time Fourier transform

[0138] In order to take into account both the spectrum density distribution in the frequency domain and the local temporal information in the time domain, the present invention uses the information embodied after performing short-time Fourier transform (STFT) on the received signal as one of the sources for extracting the radio frequency fingerprint features of the wireless device.

[0139] Specifically, for the time domain signal f(t) received by the receiver, it is first multiplied by the time window function g(t-τ) to intercept the time domain signal near the time τ to obtain a local signal, and then the obtained local signal is subjected to Fourier transform to obtain the short-time Fourier transform as follows:

[0140]

[0141] Where ω is the angular frequency, e -jωt It plays a frequency limiting role; τ is the time delay. By continuously changing the value of τ, the time window determined by g(t) continuously moves on the time axis, and the time domain signal f(t) is gradually intercepted to obtain the Fourier transform at different times. The result of the short-time Fourier transform F(τ,ω) is a two-dimensional function of time τ and angular frequency ω. Similar to the bispectrum, the value of F(τ,ω) is converted into different RGB values ​​to draw the STFT time-frequency diagram and obtain the RF fingerprint of the frequency response distortion dimension.

[0142] STFT can simultaneously reflect the time domain and frequency domain information of the signal under study. Figure 4 The STFT time-frequency diagrams of different wireless devices are shown, which have a certain degree of distinction.

[0143] Step 2: Extraction of single-dimensional RF fingerprint features of wireless devices based on channel attention and spatial attention mechanisms

[0144] Based on the three-dimensional RF fingerprint obtained in step 1, three single-dimensional feature extraction modules are used to respectively extract carrier frequency offset features, nonlinear features, and frequency response distortion features to obtain three single-dimensional RF fingerprint extraction features;

[0145] The network structure of the single-dimensional radio frequency fingerprint feature extraction of the present invention is as follows Figure 5 As shown in the “single-dimensional feature extraction module” in .

[0146] Specifically, it includes three parts: preliminary feature extraction, channel attention and spatial attention focusing on the key information in the preliminary features, and further extracting features based on the fully connected layer.

[0147] Step 2.1 Preliminary feature extraction using convolutional blocks

[0148] For the single-dimensional RF fingerprint obtained in step 1, a convolution block is used to perform preliminary feature extraction. The RF fingerprint is an image, and the size of the image is adjusted according to different application scenarios and complexity requirements. The size of the image includes 32×32, 64×64, 128×128, and 256×256 pixels.

[0149] The convolution block contains three convolution layers. The number of input channels of the first convolution layer is 3, and the number of output channels of the three convolution layers are 32, 64, and 64 respectively. The convolution kernel size of the three convolution layers is 3×3, and the padding value is 1. Each convolution layer is followed by a ReLU activation function, a maximum pooling layer, a regularization layer, and a Dropout layer.

[0150] The sliding window size of the maximum pooling layer is 2×2; the regularization layer is used to standardize the data, and the dropout rate of the Dropout layer is 0.2.

[0151] The sample is passed through the convolution block to obtain a preliminary feature F, which contains four dimensions B×C×H×W, where B represents the number of samples in each batch, C represents the number of channels, H represents the height of the feature map, and W represents the width of the feature map;

[0152] Step 2.2 Use channel attention module and spatial attention module to enhance the key information in the preliminary features

[0153] Step 2.2.1 Preliminary feature F is used to obtain channel attention map M through the channel attention module C , the channel attention map M C The feature F′ is obtained by point multiplication with the unprocessed preliminary feature F, thereby highlighting the key information on the channel component;

[0154] The channel attention mapping can be shown as formula (9):

[0155] M C (F)=σ(MLP(AvgPool(F))+MLP(MaxPool(F))) (9)

[0156] Among them, σ represents the Sigmoid function, AvgPool represents average pooling, and MaxPool represents maximum pooling. MLP is a multi-layer perceptron with hidden layers.

[0157] The specific network structure is as follows Figure 5As shown in the “Channel Attention Module” in the figure. The channel attention module includes: average pooling layer, maximum pooling layer, multi-layer perceptron and Sigmoid activation function;

[0158] The preliminary features F output by the convolution block are input into the maximum pooling layer and the average pooling layer respectively, and the maximum pooling and average pooling are performed. The results of the maximum pooling and the average pooling are input into the multi-layer perceptron respectively to obtain two features. After adding the two features, the channel attention map M is obtained by using the Sigmoid activation function to activate them. C ;

[0159] The specific implementation of average pooling and maximum pooling uses an adaptive method. When setting the code parameters, the output size "output_size" is set to 1, that is, the size of the feature map is set to 1.

[0160] ×1.

[0161] The multi-layer perceptron is implemented using two layers of two-dimensional convolutional layers. The convolution kernel size is 1×1, and the number of output channels is 4 and 64 respectively. The ReLU activation function is used after the first convolutional layer, and the Sigmoid activation function is used after the second convolutional layer.

[0162] Step 2.2.2 Feature F′ obtains the spatial attention map M through the spatial attention module S , and the point product with the unprocessed feature F′ is obtained to obtain the feature F″, highlighting the key information in the spatial area.

[0163] The implementation principle of spatial attention mapping is shown in formula (10):

[0164] M S (F)=σ(f([AvgPool(F);MaxPool(F)])) (10)

[0165] Among them, M S (F) represents the formed spatial attention map, σ represents the Sigmoid function, and f represents the convolution operation. AvgPool represents average pooling, MaxPool represents maximum pooling, and [] represents the concatenation operation.

[0166] The specific network structure is as follows Figure 5 As shown in the “Spatial Attention Module” in the figure, the spatial attention module includes: an average pooling layer, a maximum pooling layer, a convolutional layer and a Sigmoid function;

[0167] The feature F′ is subjected to average pooling and maximum pooling in the channel dimension, that is, the average and maximum values ​​in the channel dimension are calculated, and the number of channels of the obtained results is 1; the average pooling and maximum pooling results are concatenated in the channel dimension and then input into a convolution layer. In the convolution operation, the convolution kernel size is set to 7×7, the padding value is set to 3, the input and output channel numbers are 2 and 1 respectively, and finally the Sigmoid function is used as the activation function to obtain the result of spatial attention mapping M S .

[0168] Therefore, the overall attention mechanism is expressed as:

[0169] F'=M C (F)⊙F (11)

[0170] F"=M S (F')⊙F' (12)

[0171] Among them, F represents the preliminary features, M C (F) represents the channel attention map, M S (F′) represents the spatial attention map, the ⊙ symbol represents the element-wise multiplication, and F″ is the final output; the feature F″ still contains four dimensions B×C×H×W.

[0172] Step 2.3 Further extract features based on the fully connected layer

[0173] Furthermore, the last three dimensions C×H×W of the feature F″ are expanded into one dimension and converted into a two-dimensional tensor of B×L. It is input into a fully connected layer with an output dimension of 256, and a one-dimensional feature representation of B radio frequency fingerprints from a single-dimensional radio frequency fingerprint source is obtained.

[0174] Step 2.4 uses three one-dimensional feature extraction modules to obtain the features of one-dimensional RF fingerprint extraction based on three dimensions of carrier frequency offset feature, nonlinear feature and frequency response distortion feature.

[0175] Step 3: Multi-feature fusion based on self-attention mechanism

[0176] Step 3 completes the multi-feature fusion of three-dimensional RF fingerprints based on the self-attention mechanism. The specific network structure is as follows: Figure 5 As shown in the “Multi-feature fusion module”.

[0177] In the multi-feature fusion module, the features extracted from the three-dimensional single-dimensional RF fingerprint obtained in step 2 are first dimensionalized and spliced ​​to increase the multi-feature dimension S to obtain a feature M containing three dimensions of B × S × L. On the one hand, the feature M obtains a self-attention map M through the self-attention module. AOn the other hand, M is transformed in feature dimension. The specific operation of the feature dimension transformation is as follows: the last two dimensions are exchanged, that is, the feature dimension is converted into B×L×S.

[0178] The self-attention module includes a layer of Tanh activation function, a layer of fully connected layer with a size of 256×1, and a layer of Sigmoid activation function;

[0179] Finally, the results of the two-step processing of feature M are multiplied by tensor matrices to complete the extraction of multi-feature fusion RF fingerprint.

[0180] It should be noted that when comparing performance, if you choose not to use the self-attention module, you need to change the feature dimension transformation operation to a summation operation on multiple feature dimensions S.

[0181] Step 4: Based on the multi-feature fusion RF fingerprint obtained in step 3, a fully connected layer is used to classify the wireless device. The output dimension of the fully connected layer is the number of categories of the wireless device, and the training of the neural network is completed.

[0182] Based on the above scheme, the carrier frequency offset △f reflected by the differential constellation trajectory diagram and the nonlinear characteristics n reflected by the bispectrum o And the influence of frequency response distortion represented by short-time Fourier transform When performing feature-level fusion, as shown in formula (13):

[0183]

[0184] A neural network is trained using a labeled dataset, which uses a supervised objective function. The dataset is represented as: {(m (1) ,y (1) ),…,(m (i) ,y (i) )},m (i) represents the combination of three-dimensional RF fingerprints extracted from the i-th sample of the same device based on carrier frequency offset characteristics, nonlinear characteristics, and frequency response distortion characteristics, y (i) Represents the label of the i-th sample, that is, its corresponding device identity.

[0185] The data set is divided into a training set and a validation set in a certain ratio. The RF fingerprints in the training set are input into the neural network in batches. The loss function is calculated based on the output of the neural network and the label of the RF fingerprint. The parameters of the neural network are updated using the back propagation algorithm. In the process of continuously updating the parameters of the neural network, the recognition performance of the neural network is verified using the validation set. When the recognition performance of the neural network on the validation set is no longer improved, the training of the neural network is completed, and a neural network for extracting RF fingerprints of wireless devices with multi-feature fusion can be obtained.

[0186] The trained neural network can be used to extract the radio frequency fingerprint of wireless devices with multi-feature fusion, and complete the classification of wireless devices based on the radio frequency fingerprint with multi-feature fusion.

[0187] Step 5: Based on step 1, the signal characteristics of the wireless transmitter to be identified due to three different hardware defects, namely carrier frequency offset, nonlinearity and frequency response distortion, are extracted to obtain a three-dimensional RF fingerprint. The RF fingerprint is identified using the neural network trained in step 4 to complete the classification of the wireless transmitter.

[0188] In this application, the channel attention module, spatial attention module and self-attention module are all lightweight modules, which have plug-and-play characteristics in the overall neural network. You can choose whether to use a certain module without changing the overall network structure. For example, when comparing the performance of multi-feature fusion with or without adding the attention mechanism, you only need to choose whether to use the attention mechanism module.

[0189] The feature extraction method based on convolutional neural network (convolutional block) used in the scheme can also be implemented using other convolution-based deep neural networks (such as VGG, GoogLeNet, etc.), or deep residual network (Deep residual network, ResNet) and its latest improvement, dense connection network (Dense Convolutional Network, DenseNet) and other neural networks.

[0190] The input image size used in the solution can be adjusted according to the application scenario and system complexity requirements. Common sizes include, but are not limited to, 32×32, 64×64, 128×128, 256×256 pixels, etc.

[0191] The present invention extracts the signal characteristics caused by three different hardware defects of the wireless transmitter, namely carrier frequency offset, nonlinearity and frequency response distortion, to obtain a three-dimensional radio frequency fingerprint. The present invention strengthens the key feature area of ​​the single-dimensional radio frequency fingerprint of the wireless device based on the channel attention and spatial attention mechanisms, and assigns different weights to the radio frequency fingerprint features of different dimensions based on the self-attention mechanism, forming a richer feature information of the radio frequency fingerprint, so that the radio frequency fingerprints of different dimensions can complement each other's advantages and integrate information, and construct an efficient and robust radio frequency fingerprint with multiple features, so that the wireless device identification has better robustness.

[0192] 1. Single feature recognition performance with attention mechanism

[0193] The performance of the selected single signal features that represent different hardware defects is verified. Based on the single features extracted from the wireless device, the recognition results of the wireless device are first obtained on a general convolutional neural network that only contains convolutional blocks and fully connected layers. The recognition results of the wireless device are further obtained in the convolutional neural network that adds the channel attention module and the spatial attention module. Figure 6 The accuracy of identifying different wireless devices based on a single signal feature on a convolutional neural network before and after the introduction of the attention mechanism (channel attention and spatial attention) is demonstrated.

[0194] In the figure, the horizontal axis represents different signal-to-noise ratio levels, and the vertical axis represents the accuracy of the recognition results. DCTF stands for differential constellation trajectory diagram. The results based on each feature are distinguished using curves of different line types. The dotted line represents the recognition performance of the general convolutional neural network for wireless devices, and the solid line represents the recognition performance after the introduction of the attention mechanism (channel attention and spatial attention). From the observation results, it can be seen that in the comparison of single signal features, the recognition performance of the differential constellation trajectory diagram is the best. At the same time, the recognition accuracy of a single feature with the introduction of the attention mechanism has been improved to a certain extent compared with that without the introduction of the attention mechanism, indicating that the attention mechanism can strengthen the key features of a single feature, thereby improving the recognition performance of a single feature.

[0195] 2. Recognition performance of multi-feature fusion with attention mechanism

[0196] Furthermore, in order to verify the robustness of the RF fingerprint extraction method based on the multi-feature fusion of the attention mechanism, the performance of the neural network under different signal-to-noise ratios is tested. The present invention simulates the sampling data under different signal-to-noise ratios by adding artificial noise to the original data. After analysis, it can be seen that the signal-to-noise ratio of the original sampling signal is 35-40dB. Therefore, this experiment uses a step size of 5dB to further add noise to the original signal, and finally forms an amplified data set with a signal-to-noise ratio ranging from 0dB to 40dB. Figure 7 The experimental performance of the multi-feature fusion scheme with or without the introduction of the attention mechanism is compared with other schemes that introduce the attention mechanism for a single feature.

[0197] In the figure, the horizontal axis represents the change in signal-to-noise ratio, and the vertical axis corresponds to the recognition accuracy. It can be found that the recognition accuracy of the radio frequency fingerprint extraction method based on the multi-feature fusion of attention mechanism proposed in the present invention is higher than the scheme of introducing attention mechanism for each single feature. At the same time, under the condition of low signal-to-noise ratio, the accuracy of the radio frequency fingerprint extraction method based on the multi-feature fusion of attention mechanism proposed in the present invention can still reach more than 90%. In addition, the radio frequency fingerprint extraction method based on the multi-feature fusion of attention mechanism has a small fluctuation range of accuracy within the range of the entire signal-to-noise ratio, can stably identify the identity of the device, and with the increase of the signal-to-noise ratio, its recognition accuracy gradually increases, and can reach 99.998% accuracy, and can eventually tend to achieve a completely correct classification result.

[0198] It can be concluded that the multi-feature fusion wireless device RF fingerprint extraction method based on the attention mechanism proposed in the present invention can stably identify devices even under low signal-to-noise ratio conditions, making the wireless device RF fingerprint more discriminative and improving the accuracy of wireless device identity recognition.

[0199] [1]Peng L, Hu A, Zhang, J, et al. Design of a Hybrid RF FingerprintExtraction and Device Classification Scheme [J]. IEEE Internet of ThingsJournal, 2019, 6(1): 349-360.

[0200] [2]Peng L, Zhang J, Liu M and Hu A.Deep Learning Based RF FingerprintIdentification Using Differential Constellation Trace Figure[J]. IEEETransactions on Vehicular Technology, 2020, 69(1):1091–1095.

[0201] [3] Liu Ming, Liu Nian, Han Xiaoyi, Peng Lining, Fu Hua, Chen Yicong. A method for identifying power IoT devices based on radio frequency fingerprint[J]. China Electric Power, 2021, 54(03): 80-88.

[0202] [4] Peng Lining, Hu Aiqun, Zhu Changming, Jiang Yu. Radio frequency fingerprint extraction method based on constellation trajectory graph[J]. Journal of Information Security, 2016, 1(01): 50-58.

[0203] Differential Constellation Trace Figure (DCTF)

[0204] Short Time Fourier Transform (STFT)

[0205] Fourier Transform (FT)

[0206] The contents not described in detail in this specification belong to the prior art known to professional and technical personnel in this field.

Claims

1. A multi-feature fusion wireless device radio frequency fingerprint extraction method based on attention mechanism, characterized in that: The specific steps include: Step 1: Extract the signal features of the wireless transmitter caused by three different hardware defects: carrier frequency offset, nonlinearity, and frequency response distortion, and obtain a three-dimensional RF fingerprint. The three-dimensional RF fingerprint and the corresponding wireless transmitter label constitute the data set for training the neural network; Step 2: Based on the three-dimensional RF fingerprint obtained in step 1, three single-dimensional feature extraction modules are used to respectively extract carrier frequency offset features, nonlinear features, and frequency response distortion features to obtain three single-dimensional RF fingerprint extraction features; Step 3: The three single-dimensional radio frequency fingerprint extraction features obtained in step 2 are processed using a multi-feature fusion module to obtain a radio frequency fingerprint with multi-feature fusion; Step 4: Based on the multi-feature fused RF fingerprint obtained in step 3, the classification of the wireless transmitter is obtained through the fully connected layer to complete the training of the neural network; Step 5: Based on step 1, the signal characteristics of the wireless transmitter to be identified due to three different hardware defects, namely, carrier frequency offset, nonlinearity and frequency response distortion, are extracted to obtain a three-dimensional RF fingerprint; further, the RF fingerprint is identified using the neural network trained in step 4 to complete the classification of the wireless transmitter; Step 1 specifically includes: Step 1.1: Extraction of carrier frequency offset features based on differential. During the communication process of wireless devices, the receiver performs differential operations on the received signals and obtains the RF fingerprint of the carrier frequency offset dimension after visualization. The differential operation is specifically expressed as follows: Step 1.1.1 The signal transmitted by the transmitter is expressed as: Among them, S(t) represents the transmitted signal, X(t) is the transmitter baseband signal, is the imaginary unit, f cTx is the carrier frequency of the transmitter; Step 1.1.2 Ignore the influence of channel and noise factors, and the signal received by the receiver is expressed as R(t), R(t) = S(t); The receiver performs down-conversion to obtain the baseband signal expressed as: Among them, f cRx is the carrier frequency of the receiver, It is the phase error when the receiver receives the signal; When f cRx ≠f cTx When the receiver down-converts, the baseband signal obtained is expressed as: Where θ = f cRx -f cTx , is the difference between the carrier frequency of the receiver and the carrier frequency of the transmitter; Step 1.1.3 The difference processing process is expressed as: Where D(t) is the difference result, Y * To take the conjugate value, d is the difference interval; Step 1.1.4 plots the differential signal directly on the complex plane, discretizes the complex plane into a series of pixel points, and uses different RGB values ​​to represent the number of differential operation results falling into a certain pixel area, thereby obtaining the RF fingerprint of the carrier frequency offset dimension; Step 1.2 is based on nonlinear feature extraction in the dual spectrum domain to obtain a nonlinear RF fingerprint, which specifically includes: Step 1.2.1 Signal data segmentation: The captured signal data {r(0), r(1), ···r(N-1)} of length N is divided into K segments, each segment has M observation samples, then N = KM, and the sample mean of each segment is subtracted from the M observation samples in each segment, and the value is expressed as r (k) (n) represents the nth observed sample of the kth segment of signal data, n=0,1,···,M-1, k=1,2,···,K; Step 1.2.2 Calculate the discrete Fourier transform coefficients: Wherein, λ represents a discrete frequency variable, λ=0,1,···,M / 2; on this basis, the discrete Fourier transform coefficients are obtained; Step 1.2.3 calculates the triple correlation of the discrete Fourier transform coefficients and performs frequency domain smoothing on ±L1 frequency components around the frequency sampling point: Among them, λ1,λ2 are discrete frequency variables in the bispectral domain, 0≤λ2≤λ1,λ1+λ2≤f s / 2;f s is the sampling frequency; Δ0 represents the frequency sampling interval in the dual spectrum domain, Δ0 = f s / N0; N0 is the total number of frequency samples; i1, i2 are variables used to traverse the neighborhood frequency components during accumulation; let N1 = 2L1 + 1, which represents the length of the bispectrum smoothing over the adjacent frequencies, and the values ​​of N0 and N1 satisfy M = N0·N1; Step 1.2.4: Use ω1 and ω2 to represent the angular frequency in the dual spectrum domain. Substituting into equation (6), we get the bispectral density estimation of the k-th segment signal data: Then the bispectral density estimates of K segments are averaged to obtain the bispectral density estimate of the entire process: Among them, the sampling frequency f s Set to 1; Step 1.2.5: Convert the bispectral density estimation value obtained in step 1.2.4 into different RGB values ​​and plot the bispectrum to obtain the RF fingerprint in nonlinear dimension; Step 1.3 extracts the frequency response distortion feature based on short-time Fourier transform to obtain the RF fingerprint of the frequency response distortion dimension; For the time domain signal f(t) received by the receiver, it is first multiplied by the time window function g(t-τ) to intercept the time domain signal near time τ to obtain a local signal. Then, the obtained local signal is subjected to Fourier transform to obtain the formula of short-time Fourier transform, as shown in formula (8): Where ω is the angular frequency, e -jωt It plays a frequency limiting role; τ is the time delay. By continuously changing the value of τ, the time window determined by g(t) continuously moves on the time axis, gradually intercepting the time domain signal f(t), and obtaining the Fourier transform at different times; The result of the short-time Fourier transform F(τ,ω) is a two-dimensional function of time τ and angular frequency ω; Convert the value of F(τ,ω) into different RGB values, draw the short-time Fourier transform time-frequency diagram, and obtain the RF fingerprint of the frequency response distortion dimension; The single-dimensional feature extraction module described in step 2 includes: a convolution block, a channel attention module, a spatial attention module and a fully connected layer; The convolution block includes three convolution layers, the number of input channels of the first convolution layer is 3, the number of output channels of the three convolution layers are 32, 64, and 64 respectively, the convolution kernel size of the three convolution layers is 3×3, and the padding value is 1; each convolution layer is followed by a ReLU activation function, a maximum pooling layer, a regularization layer, and a Dropout layer; the sliding window size of the maximum pooling layer is 2×2; the regularization layer is used to standardize the data, and the dropout rate of the Dropout layer is 0.2; The channel attention module includes: a maximum pooling layer, an average pooling layer, a multi-layer perceptron and a Sigmoid activation function; The specific processing process of the channel attention module includes: The preliminary features F output by the convolution block are input into the maximum pooling layer and the average pooling layer respectively, and the maximum pooling and average pooling are performed. The results of the maximum pooling and the average pooling are input into the multi-layer perceptron respectively to obtain two features. After adding the two features, the channel attention map M is obtained by using the Sigmoid activation function to activate them. C ; The multi-layer perceptron consists of two two-dimensional convolutional layers, the convolution kernel size is 1×1, the number of output channels is 4 and 64 respectively, the ReLU activation function is used after the first convolutional layer, and the Sigmoid activation function is used after the second convolutional layer; The spatial attention module includes: an average pooling layer, a maximum pooling layer, a convolutional layer and a Sigmoid function; The specific processing process of the spatial attention module includes: The feature F′ is input into the maximum pooling layer and the average pooling layer respectively to calculate the average and maximum values ​​in the channel dimension. The average pooling and maximum pooling results are concatenated in the channel dimension and then input into a convolution layer. In the convolution operation, the convolution kernel size is set to 7×7, the padding value is set to 3, the number of input and output channels is 2 and 1 respectively, and finally the Sigmoid activation function is used to activate the spatial attention mapping result M. S ; Step 2 specifically includes the following steps: Step 2.1: Use convolutional blocks for preliminary feature extraction; For the single-dimensional RF fingerprint obtained in step 1, a convolution block is used to perform preliminary feature extraction. The RF fingerprint is an image. The image of the single-dimensional RF fingerprint is obtained by a convolution block to obtain a preliminary feature F. The preliminary feature F contains four dimensions B×C×H×W, where B represents the number of samples in each batch, C represents the number of channels, H represents the height of the feature map, and W represents the width of the feature map; Step 2.2 uses the channel attention module and the spatial attention module to enhance the key information in the preliminary features; Step 2.2.1 Preliminary feature F is passed through the channel attention module to obtain the channel attention map M C , the channel attention map M C The feature F′ is obtained by point multiplication with the unprocessed preliminary feature F, thereby highlighting the key information on the channel component; The channel attention mapping is shown in formula (9): M C (F)=σ(MLP(AvgPool(F))+MLP(MaxPool(F))) (9) Among them, σ represents the Sigmoid function, AvgPool represents average pooling, and MaxPool represents maximum pooling. MLP is a multi-layer perceptron with hidden layers; Step 2.2.2 Feature F′ obtains the spatial attention map M through the spatial attention module S , and the unprocessed feature F′ is multiplied to obtain the feature F″, highlighting the key information in the spatial area; The implementation principle of spatial attention mapping is shown in formula (10): M S (F)=σ(f([AvgPool(F);MaxPool(F)])) (10) Among them, M S (F) represents the formed spatial attention map, σ represents the Sigmoid function, and f represents the convolution operation; AvgPool represents average pooling, MaxPool represents maximum pooling, and [ ] represents the concatenation operation; Therefore, the overall attention mechanism is expressed as: F′=M C (F)⊙F (11) F″=M S (F′)⊙F′ (12) Among them, F represents the preliminary features, M C (F) represents the channel attention map, M S (F′) represents the spatial attention map, the e symbol represents the element-wise multiplication, and F″ is the final output; the feature F″ still contains four dimensions of B×C×H×W; Step 2.3 further extracts features based on the fully connected layer; Expand the last three dimensions C×H×W of feature F″ into one dimension, convert it into a two-dimensional tensor of B×L, input it into a fully connected layer, and the output dimension is 256, so as to obtain a one-dimensional feature representation of B radio frequency fingerprints from the single-dimensional radio frequency fingerprint source; Step 2.4 finally uses three one-dimensional feature extraction modules to obtain the features of one-dimensional RF fingerprint extraction based on three dimensions of carrier frequency offset feature, nonlinear feature and frequency response distortion feature; The multi-feature fusion module described in step 3 includes: a self-attention module, and the self-attention module includes: a layer of Tanh activation function, a layer of fully connected layer with a size of 256×1, and a layer of Sigmoid activation function; Step 3 specifically includes the following steps: Step 3.1: Perform dimension-increasing splicing on the three single-dimensional RF fingerprint extracted features obtained in step 2, increase the multi-feature dimension S, and obtain a feature M containing three dimensions of B×S×L; Step 3.2: Pass the feature M through the self-attention module to obtain the self-attention map M A ; Step 3.3: Transform the feature dimension of feature M. The specific operation of the feature dimension transformation is: swap the last two dimensions to obtain a new dimension of B×L×S; Step 3.4: Perform tensor matrix multiplication on the processing results of feature M in step 3.2 and step 3.3 to complete the extraction of multi-feature fusion RF fingerprint; Step 4 specifically includes: The data set is divided into a training set and a validation set in a certain ratio. The RF fingerprints in the training set are input into the neural network in batches. The loss function is calculated based on the output of the neural network and the label of the RF fingerprint. The parameters of the neural network are updated using the back propagation algorithm. In the process of continuously updating the parameters of the neural network, the recognition performance of the neural network is verified using the validation set. When the recognition performance of the neural network on the validation set no longer improves, the training of the neural network is completed, and a neural network for extracting radio frequency fingerprints of wireless devices using multi-feature fusion is obtained.

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