Radio frequency fingerprint identification method based on fractal trajectory

Abstract

The invention discloses a radio frequency fingerprint identification method based on a fractal track, and the method comprises the following steps: obtaining original radio frequency signals of N radio frequency devices to be identified, and carrying out the preprocessing of the original radio frequency signals; performing transient detection based on the preprocessed original radio frequency signal to obtain a target signal, and obtaining a fractal trajectory corresponding to the target signal by adopting a dynamic sliding window; extracting features of the N radio frequency devices based on the fractal trajectory, and constructing a radio frequency fingerprint feature vector based on the features of the N radio frequency devices; the radio frequency fingerprint feature vectors are input into a support vector machine, identities of N radio frequency devices are recognized, through the method, fractal track characteristics of transient signals are deeply analyzed, the radio frequency fingerprint recognition method based on the fractal track is designed, and the radio frequency fingerprint recognition method based on the fractal track can be achieved no matter which modulation mode the signals are received. The optimal target signal interval can be selected for radio frequency fingerprint extraction and identification without other priori knowledge.

Description

Technical Field

[0001] The invention belongs to the field of signal analysis and relates to a radio frequency fingerprint recognition method based on fractal trajectory. Background Art

[0002] With the rapid evolution of wireless communication network technology, many constraints of traditional wired networks have been broken, allowing information to be transmitted wirelessly, which has greatly eliminated the barriers of time and space. Although wireless communication networks have improved the portability of communication, they also have various vulnerabilities that seriously threaten their security. Wireless communication networks mainly replace the original cables with electromagnetic waves as the carrier of information transmission, which provides opportunities for malicious attackers. Wireless networks have many forms of attacks, among which counterfeit attacks are the most important and threatening. Attackers can deceive devices by copying most of the information. Therefore, new mechanisms need to be innovated to prevent attacks and threats caused by the outside world. Since the tolerance effect of electronic components in wireless devices is the main reason for the generation of RF fingerprints, RF fingerprints are difficult to clone and are unique, thus becoming a new paradigm for wireless device identity authentication.

[0003] According to the differences in the selected target signal types, RF fingerprint recognition technology can be divided into two major research paths: based on transient signals and based on steady-state signals. Among them, the steady-state signal segment refers to the signal generated when the transmitter is started and enters a stable operating state. It is expressed in the form of a modulated waveform and carries the actual communication content, ensuring that the subsequent signal information to be identified is fully retained. However, it requires more prior knowledge based on the modulation method and code design of the target signal, and its versatility is not good. The transient signal segment refers to the instantaneous generation when the transmitter is started or shut down. Although it does not carry valid data content, it contains the unique properties of the hardware circuit of the transmitting source, and does not need to rely on the modulation domain information of the signal. It has a wider range of applications, so it can be used to effectively construct a set of RF fingerprint features. Summary of the invention

[0004] In order to solve the above problems, the technical solution adopted by the present invention is: a radio frequency fingerprint recognition method based on fractal trajectory, comprising the following steps:

[0005] Obtaining original radio frequency signals of N radio frequency devices to be identified, and preprocessing the original radio frequency signals;

[0006] Based on the preprocessed original RF signal, transient detection is performed to obtain the target signal, and the fractal trajectory corresponding to the target signal is obtained using a dynamic sliding window;

[0007] Extracting features of N radio frequency devices based on fractal trajectories, and constructing radio frequency fingerprint feature vectors based on the features of the N radio frequency devices;

[0008] The RF fingerprint feature vector is input into the support vector machine to identify the identities of N RF devices.

[0009] Further: the process of using the dynamic sliding window to obtain the fractal trajectory corresponding to the target signal is as follows:

[0010] The target signal x(n) with a total length of N discrete is segmented using a sliding window with a length of L. When the starting index of the sliding window moves to i, the corresponding truncated signal is defined as x d (i);

[0011] The Higuchi algorithm is used to calculate the fractal dimension of the truncated time series. As the starting point of the sliding window moves, the fractal trajectory corresponding to the signal is obtained.

[0012] Further: the extracting of features of N radio frequency devices based on fractal trajectories includes:

[0013] The skewness of the fractal trajectory, the spectral energy of the fractal trajectory, the constant term fitting coefficient of the fractal trajectory, the coefficient of variation of the fractal trajectory and the Hurst exponent of the fractal trajectory.

[0014] Further: the target signal x(n) with a total length of N discrete is segmented using a sliding window with a length of L. When the starting index of the sliding window moves to i, the corresponding truncated signal is defined as x d (i);

[0015] The fractal dimension of the truncated time series is calculated using the Higuchi algorithm. As the starting point of the sliding window moves, the fractal trajectory corresponding to the signal is obtained as follows:

[0016] Create a subset of samples from the original signal:

[0017]

[0018] Among them, m is the initial time and starting time of each subset, k is the time interval, and determines the number of subsets. m and k are integers.

[0019] Among them, the curve length of each subset X(m,k) defined by Higuchi is as follows:

[0020]

[0021] In the above formula, (N-1) / [(Nm) / k]k is the normalization factor of the curve length;

[0022] Plot L with k as the horizontal axis on a log-log scale m (k) curve, when k changes from N to 0, Lm (k) Data should fall on one axis;

[0023] Use the least squares method to calculate the point (L m (k)) is fitted, and the slope of the curve obtained by fitting can be used as the estimated value of the fractal dimension;

[0024] Finally, as the starting point of the sliding window moves, the fractal trajectory corresponding to the target signal is obtained.

[0025] Further: the expression of the skewness γ of the fractal trajectory is as follows:

[0026]

[0027] Among them, σ d is the standard deviation of the fractal trajectory d, N d represents the length of the fractal trajectory d, represents the average of the fractal trajectories d;

[0028] The expression of the spectrum energy E of the fractal trajectory is as follows:

[0029]

[0030] Among them, |D(f) 2 is the square of the modulus of the spectral density of the fractal trajectory;

[0031] The expression of the fractal trajectory using the polynomial function p(x) is as follows:

[0032]

[0033] Where j represents the order of the polynomial function, a j is the coefficient of the polynomial function of order j. When N=2, binomial fitting is performed on the fractal trajectory, and the constant fitting coefficient is selected as the feature;

[0034] The expression of the coefficient of variation cv of the fractal trajectory is as follows:

[0035]

[0036] Among them, σ d is the standard deviation of the fractal trajectory, is the mean of the fractal trajectory, and the standard deviation σ d and average The calculation formula is as follows.

[0037]

[0038] Further: the calculation steps of the Hurst exponent of the fractal trajectory are as follows:

[0039] The fractal trajectory sequence d = {d(i), i = 1, 2, 3, ..., N} is divided into K data groups of length m. For each divided subgroup, its mean is defined as The maximum cumulative value of the absolute deviation from the mean within the subgroup is recorded as Z max :

[0040]

[0041] The minimum cumulative value of the absolute value of the deviation from the mean within the subgroup is recorded as Z min :

[0042]

[0043] The range within each group is recorded as R(m):

[0044] R(m)=Z max -Z min

[0045] The sample standard deviation of each group is recorded as:

[0046]

[0047] R, S, and m satisfy the following general relationship:

[0048] R(m) / S(m)=cm H

[0049] Where c is a constant, R(m) / S(m) is the rescaled range, and H is the Hurst index. According to the equation:

[0050] log(R / S) m =log(c)+Hlog(m)

[0051] Taking the log(m) sequence as the independent variable, the corresponding log(R / S) m The sequence is the dependent variable, and the least squares regression method is introduced to perform a straight-line fitting analysis on the data. The slope satisfies k=H, and the H value is the estimated result of the Hurst exponent.

[0052] Furthermore: the RF fingerprint feature vector is input into a support vector machine to identify the identities of N RF devices; principal component analysis is used to reduce the dimension of the obtained feature vector; the reduced features are randomly divided into training sets and test sets in a certain proportion, and input into a support vector machine (SVM) for classification; the label results output by the trained model are compared with the actual labels to obtain the classification accuracy.

[0053] Further: the process of reducing the dimension of the obtained feature vector by principal component analysis is as follows:

[0054] 1) Extract the RF fingerprint feature vector feature set X∈R n*m To de-mean the sample features in, for each feature of the sample, use the value of the current feature minus the mean of the feature in the sample set, that is,

[0055] 2) Calculate the covariance matrix XX of the sample T ;

[0056] 3) Perform eigenvalue decomposition on the covariance matrix to obtain the eigenvalues ​​and eigenvectors of the covariance matrix;

[0057] 4) Select the eigenvectors corresponding to the largest first k eigenvalues ​​and transform them into P;

[0058] 5) Y=PX is the k-dimensional feature matrix obtained after dimensionality reduction.

[0059] The present invention provides a radio frequency fingerprint recognition method based on fractal trajectories, which is a method for wireless device identity authentication based on transient radio frequency fingerprints. The method proposes a radio frequency fingerprint recognition method based on fractal trajectories based on energy-limited signals. The radio frequency fingerprint recognition method utilizes the differences in the self-similarity and complexity of the fractal trajectories of different devices in time to achieve effective extraction of multi-dimensional features, and applies these features to the identity authentication process of the device. Taking into account the influence of the algorithm's time complexity, the feature vector is constructed by extracting five different statistics of the fractal trajectory, namely the skewness, spectral energy, coefficient of variation, constant term fitting coefficient, and Hurst exponent, thereby improving the recognition accuracy of different devices. The authentication method of the present application can utilize the subtle differences in hardware between different devices to accurately authenticate them.

[0060] Compared with the prior art, the present invention has the following significant advantages: through the method of the present invention, the fractal trajectory characteristics of transient signals are deeply analyzed, and a radio frequency fingerprint recognition method based on fractal trajectory is designed, which can realize that no matter what modulation mode the received signal is, the best target signal interval can be selected for radio frequency fingerprint extraction and recognition, and no other prior knowledge is required. Through experiments, it can be obtained that the use of the present invention can effectively identify different devices, and the recognition accuracy rate is 98.7%. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0062] Figure 1 is a flow chart of the method;

[0063] Figure 2 is the original feature classification confusion matrix;

[0064] Figure 3 It is a PCA-3D feature visualization diagram. DETAILED DESCRIPTION

[0065] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0066] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is by no means intended to limit the present invention and its application or use. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0067] Figure 1 is a flow chart of the method;

[0068] A radio frequency fingerprint recognition method based on fractal trajectory comprises the following steps:

[0069] S1: Obtain original radio frequency signals of N radio frequency devices to be identified, and pre-process the original radio frequency signals;

[0070] S2: Perform transient detection based on the preprocessed original RF signal to obtain a transient signal segment, acquire the target signal, and use a dynamic sliding window to obtain a fractal trajectory corresponding to the target signal;

[0071] S3: extracting features of N radio frequency devices based on the fractal trajectory, and constructing a radio frequency fingerprint feature vector based on the features of the N radio frequency devices;

[0072] S4: Input the RF fingerprint feature vector into the support vector machine to identify the identities of N RF devices.

[0073] Steps S1 / S2 / S3 / S4 are executed sequentially;

[0074] The preprocessing of the original radio frequency signal includes filtering and normalization;

[0075] The process of using a dynamic sliding window to obtain the fractal trajectory corresponding to the target signal is as follows:

[0076] The target signal x(n) with a total length of N discrete is segmented using a sliding window with a length of L. When the starting index of the sliding window moves to i, the corresponding truncated signal is defined as x d (i);

[0077] The Higuchi algorithm is used to calculate the fractal dimension of the truncated time series. As the starting point of the sliding window moves, the fractal trajectory corresponding to the signal is obtained.

[0078] The extracting of features of N radio frequency devices based on fractal trajectories includes:

[0079] The skewness of the fractal trajectory, the spectral energy of the fractal trajectory, the constant term fitting coefficient of the fractal trajectory, the coefficient of variation of the fractal trajectory and the Hurst exponent of the fractal trajectory.

[0080] The target signal x(n) with a total length of N discrete is segmented using a sliding window with a length of L. When the starting index of the sliding window moves to i, the corresponding truncated signal is defined as x d (i);

[0081] The fractal dimension of the truncated time series is calculated using the Higuchi algorithm. As the starting point of the sliding window moves, the fractal trajectory corresponding to the signal is obtained as follows:

[0082] Create a subset of samples from the original signal:

[0083]

[0084] Among them, m is the initial time and starting time of each subset, k is the time interval, and determines the number of subsets. m and k are integers.

[0085] Among them, the curve length of each subset X(m,k) defined by Higuchi is as follows:

[0086]

[0087] In the above formula, (N-1) / [(Nm) / k]k is the normalization factor of the curve length;

[0088] The second step is to plot L with abscissa k on a log-log scale. m (k) curve, when k changes from N to 0, L m (k) Data should fall on one axis;

[0089] Use the least squares method to calculate the point (L m (k)) is fitted, and the slope of the curve obtained by fitting can be used as the estimated value of the fractal dimension;

[0090] Finally, as the starting point of the sliding window moves, the fractal trajectory corresponding to the target signal is obtained. The expression of the skewness γ of the fractal trajectory is as follows:

[0091]

[0092] Among them, σ d is the standard deviation of the fractal trajectory d, N d represents the length of the fractal trajectory d, represents the average of the fractal trajectories d;

[0093] The expression of the spectrum energy E of the fractal trajectory is as follows:

[0094]

[0095] Among them, |D(f) 2 is the square of the modulus of the spectral density of the fractal trajectory;

[0096] The expression of the fractal trajectory using the polynomial function p(x) is as follows:

[0097]

[0098] Where j represents the order of the polynomial function, a j is the coefficient of the polynomial function of order j. When N=2, binomial fitting is performed on the fractal trajectory, and the constant fitting coefficient is selected as the feature;

[0099] The expression of the coefficient of variation cv of the fractal trajectory is as follows:

[0100]

[0101] Among them, σ d is the standard deviation of the fractal trajectory, is the mean of the fractal trajectory, standard deviation σ d and average The calculation formula is as follows.

[0102]

[0103] The calculation steps of the Hurst exponent of the fractal trajectory are as follows:

[0104] The fractal trajectory sequence d = {d(i), i = 1, 2, 3, ..., N} is divided into K data groups of length m. For each divided subgroup, its mean is defined as The maximum cumulative value of the absolute deviation from the mean within the subgroup is recorded as Z max :

[0105]

[0106] The minimum cumulative value of the absolute value of the deviation from the mean within the subgroup is recorded as Z min :

[0107]

[0108] The range within each group is recorded as R(m):

[0109] R(m)=Z max -Z min

[0110] The sample standard deviation of each group is recorded as:

[0111]

[0112] R, S, and m satisfy the following general relationship:

[0113] R(m) / S(m)=cm H

[0114] Where c is a constant, R(m) / S(m) is the rescaled range, and H is the Hurst index. According to the equation:

[0115] log(R / S) m =log(c)+Hlog(m)

[0116] Taking the log(m) sequence as the independent variable, the corresponding log(R / S) m The sequence is the dependent variable, and the least squares regression method is introduced to perform a straight-line fitting analysis on the data. The slope satisfies k=H, and these H values ​​are the estimated results of the Hurst exponent.

[0117] The RF fingerprint feature vector is input into the support vector machine to identify the identities of N RF devices. The principal component analysis is used to reduce the dimension of the obtained feature vector. The reduced features are randomly divided into training set and test set in a certain ratio, such as 7:3, and input into the support vector machine SVM for classification. The label results output by the trained model are compared with the actual labels to obtain the classification accuracy.

[0118] The process of reducing the dimension of the obtained feature vector by principal component analysis is as follows:

[0119] 1) Extract the RF fingerprint feature vector feature set X∈R n*m To de-mean the sample features in, for each feature of the sample, use the value of the current feature minus the mean of the feature in the sample set, that is,

[0120] 2) Calculate the covariance matrix XX of the sample T ;

[0121] 3) Perform eigenvalue decomposition on the covariance matrix to obtain the eigenvalues ​​and eigenvectors of the covariance matrix;

[0122] 4) Select the eigenvectors corresponding to the largest first k eigenvalues ​​and transform them into P;

[0123] 5) Y=PX is the k-dimensional feature matrix obtained after dimensionality reduction.

[0124] Embodiment 1:

[0125] (1) Obtain the original RF signal of the RF device to be identified, and perform preprocessing and normalization;

[0126] In this embodiment, the Bluetooth wireless signals of 9 different devices are selected as targets and numbered 1-9, and 140 data are collected for each device. Since the Bluetooth signal operates in the ISM2400 frequency band, according to the Nyquist sampling theorem, the sampling frequency needs to be at least 4.8Gsps. The sampling rates of the selected data are 5Gsps, 10Gsps, and 20Gsps, and the signal duration is about 3μs. The real signal is directly captured by a high sampling rate oscilloscope and a low-resolution analog-to-digital converter. During the signal acquisition process, since the oscilloscope generates some unnecessary spurious signals, a bandpass filter is added in the preprocessing part to filter out the spurious signals.

[0127] (2) Perform transient detection based on the preprocessed original RF signal to obtain the target signal, and use a dynamic sliding window to obtain the fractal trajectory corresponding to the target signal;

[0128] First, transient detection is performed to obtain the transient signal segment, that is, the target signal. Further, a sliding window is used to obtain the fractal trajectory corresponding to the transient signal segment:

[0129] The target signal x(n) with a total length of N discrete is segmented using a sliding window with a length of L. When the starting index of the sliding window moves to i, the corresponding truncated signal is defined as x d(i). Subsequently, the fractal dimension of the obtained truncated time series is accurately calculated using the Higuchi algorithm. The specific principle is as follows. First, a sample subset of the original signal is created according to the following method.

[0130]

[0131] Where m is the initial time and starting moment of each subset, k is the time interval and determines the number of subsets. m and k are integers. Therefore, for example, setting k = 3, N = 100, m = 1, 2, 3 will generate the following three subsets:

[0132] X(1,3):X(1),X(4),...,X(100),

[0133] X(2,3):X(2),X(5),...,X(98),

[0134] X(3,3):X(3),X(6),...,X(99).

[0135] Among them, the curve length of each subset X(m,k) defined by Higuchi is as follows:

[0136]

[0137] In the above formula, (N-1) / [(Nm) / k]k is the normalization factor for the curve length.

[0138] The second step is to plot L with abscissa k on a log-log scale. m (k) curve, when k varies from N to 0, the data should fall on one axis.

[0139] Next, use the least squares method to calculate the point (L m (k)) is fitted, and the slope of the curve obtained by fitting can be used as the estimated value of the fractal dimension. Finally, as the starting point of the sliding window moves, the fractal trajectory corresponding to the signal is obtained.

[0140] (3) extracting the features of N RF devices based on the fractal trajectory, and constructing a RF fingerprint feature vector based on the features of the N RF devices;

[0141] (3.1) Calculate the skewness of the fractal trajectory of each device as a feature;

[0142]

[0143] Among them, σ d is the standard deviation of the fractal trajectory d, N d represents the length of the fractal trajectory d, represents the average of the fractal trajectories d;

[0144] (3.2) Calculate the spectral energy of the fractal trajectory as a feature

[0145]

[0146] where |D(f)| 2 is the square of the modulus of the spectral density of the fractal trajectory;

[0147] (3.3) Calculate the constant fitting coefficient of the fractal trajectory as the feature

[0148] The fractal trajectory is fitted with an N-order polynomial by the least squares method, namely:

[0149] X(t)=b1+b2t+b3t 2 +…b N+1 t N

[0150] When N=2 is selected, binomial fitting is performed on the fractal trajectory, and the constant term fitting coefficient is selected as the feature;

[0151] (3.4) Calculate the coefficient of variation of the fractal trajectory as a feature

[0152]

[0153] Among them, σ d is the standard deviation of the fractal trajectory, is the average of the fractal trajectory. Standard deviation σ d and average The calculation formula is as follows:

[0154]

[0155] (3.5) Calculate the Hurst index of the fractal trajectory as a feature;

[0156] The rescaled range method is usually used to calculate the Hurst index, and its calculation steps are as follows:

[0157] The fractal trajectory sequence d = {d(i), i = 1, 2, 3, ..., N} is divided into K data groups of length m. For each divided subgroup, its mean is defined as The maximum cumulative value of the absolute deviation from the mean within the subgroup is recorded as Z max :

[0158]

[0159] The minimum cumulative value of the absolute value of the deviation from the mean within the subgroup is recorded as Z min :

[0160]

[0161] The range within each group is recorded as R(m):

[0162] R(m)=Z max -Z min

[0163] The sample standard deviation of each group is recorded as:

[0164]

[0165] Hurst found that R, S, and m satisfy the following general relationship:

[0166] R(m) / S(m)=cm H

[0167] Where c is a constant, R(m) / S(m) is the rescaled range, and H is the Hurst index. According to the equation:

[0168] log(R / S) m =log(c)+Hlog(m)

[0169] Taking the log(m) sequence as the independent variable, the corresponding log(R / S) m The sequence is the dependent variable, and the least squares regression method is introduced to perform a straight line fitting analysis on the data. The slope satisfies k=H, and these values ​​are the estimation results of the Hurst exponent.

[0170] (3.6) The five-dimensional statistics of the fractal trajectory calculated above, namely, skewness, spectrum energy, coefficient of variation, constant term fitting coefficient, and Hurst exponent, are used to construct the RF fingerprint feature vector.

[0171] (4) Inputting the RF fingerprint feature vector into a support vector machine to identify the identities of N RF devices;

[0172] The 140 samples of each device are divided into training set and test set in a ratio of 7:3. The principal component analysis is used to reduce the dimension of the obtained five-dimensional vector. The processing flow of the principal component analysis is as follows:

[0173] 1) For the feature set X∈R n*m For each feature of the sample, use the value of the current feature minus the mean of the feature in the sample set, that is,

[0174] 2) Calculate the covariance matrix XX of the sample T .

[0175] 3) Perform eigenvalue decomposition on the covariance matrix and find the eigenvalues ​​and eigenvectors of the covariance matrix.

[0176] 4) Select the eigenvectors corresponding to the largest first k eigenvalues ​​and transform them into P.

[0177] 5) Y=PX is the k-dimensional feature matrix obtained after dimensionality reduction.

[0178] The reduced feature vector is used as input into the support vector machine (SVM) and the linear kernel function is used to learn and train the model. The classification accuracy of the model is 98.68% and 97.39% on the training set and test set respectively.

[0179] Figure 2 is the original feature classification confusion matrix;

[0180] Figure 3 It is a PCA-3D feature visualization diagram.

[0181] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A radio frequency fingerprint recognition method based on fractal trajectory, characterized in that: The following steps are involved: Obtaining original radio frequency signals of N radio frequency devices to be identified, and preprocessing the original radio frequency signals; Based on the preprocessed original RF signal, transient detection is performed to obtain the target signal, and the fractal trajectory corresponding to the target signal is obtained using a dynamic sliding window; Extracting features of N radio frequency devices based on fractal trajectories, and constructing radio frequency fingerprint feature vectors based on the features of the N radio frequency devices; The RF fingerprint feature vector is input into the support vector machine to identify the identities of N RF devices.

2. The radio frequency fingerprint recognition method based on fractal trajectory according to claim 1 is characterized in that: The process of using a dynamic sliding window to obtain the fractal trajectory corresponding to the target signal is as follows: The target signal x(n) with a total length of N discrete is segmented using a sliding window with a length of L. When the starting index of the sliding window moves to i, the corresponding truncated signal is defined as x d (i); The Higuchi algorithm is used to calculate the fractal dimension of the truncated time series. As the starting point of the sliding window moves, the fractal trajectory corresponding to the signal is obtained.

3. The method for radio frequency fingerprint recognition based on fractal trajectory according to claim 1, characterized in that: The extracting of features of N radio frequency devices based on fractal trajectories includes: The skewness of the fractal trajectory, the spectral energy of the fractal trajectory, the constant term fitting coefficient of the fractal trajectory, the coefficient of variation of the fractal trajectory and the Hurst exponent of the fractal trajectory.

4. The method for radio frequency fingerprint recognition based on fractal trajectory according to claim 2 is characterized in that: The target signal x(n) with a total length of N discrete is segmented using a sliding window with a length of L. When the starting index of the sliding window moves to i, the corresponding truncated signal is defined as x d (i); The fractal dimension of the truncated time series is calculated using the Higuchi algorithm. As the starting point of the sliding window moves, the fractal trajectory corresponding to the signal is obtained as follows: Create a subset of samples from the original signal: Among them, m is the initial time and starting time of each subset, k is the time interval, and determines the number of subsets. m and k are integers. Among them, the curve length of each subset X(m,k) defined by Higuchi is as follows: In the above formula, (N-1) / [(Nm) / k]k is the normalization factor of the curve length; Plot L with k as the horizontal axis on a log-log scale m (k) curve, when k changes from N to 0, L m (k) Data should fall on one axis; Use the least squares method to calculate the point (L m (k)) is fitted, and the slope of the curve obtained by fitting can be used as the estimated value of the fractal dimension; Finally, as the starting point of the sliding window moves, the fractal trajectory corresponding to the target signal is obtained.

5. The method for radio frequency fingerprint recognition based on fractal trajectory according to claim 1, characterized in that: The expression of the skewness γ of the fractal trajectory is as follows: Among them, σ d is the standard deviation of the fractal trajectory d, N d represents the length of the fractal trajectory d, represents the average of the fractal trajectories d; The expression of the spectrum energy E of the fractal trajectory is as follows: where |D(f)| 2 is the square of the modulus of the spectral density of the fractal trajectory; The expression of the fractal trajectory using the polynomial function p(x) is as follows: Where j represents the order of the polynomial function, a j is the coefficient of the polynomial function of order j. When N=2, binomial fitting is performed on the fractal trajectory, and the constant fitting coefficient is selected as the feature; The expression of the coefficient of variation cv of the fractal trajectory is as follows: Among them, σ d is the standard deviation of the fractal trajectory, is the mean of the fractal trajectory, standard deviation σ d and average The calculation formula is as follows.

6. The method of radio frequency fingerprint recognition based on fractal trajectory according to claim 1, characterized in that: The calculation steps of the Hurst exponent of the fractal trajectory are as follows: The fractal trajectory sequence d = {d(i), i = 1, 2, 3, ..., N} is divided into K data groups of length m. For each divided subgroup, its mean is defined as The maximum cumulative value of the absolute deviation from the mean within the subgroup is recorded as Z max : The minimum cumulative value of the absolute value of the deviation from the mean within the subgroup is recorded as Z min : The range within each group is recorded as R(m): R(m)=Z max -Z min The sample standard deviation of each group is recorded as: R, S, and m satisfy the following general relationship: R(m) / S(m)=cm H Where c is a constant, R(m) / S(m) is the rescaled range, and H is the Hurst index. According to the equation: log(R / S) m =log(c)+Hlog(m) Taking the log(m) sequence as the independent variable, the corresponding log(R / S) m The sequence is the dependent variable, and the least squares regression method is introduced to perform a straight-line fitting analysis on the data. The slope satisfies k=H, and the H value is the estimated result of the Hurst exponent.

7. The method of radio frequency fingerprint recognition based on fractal trajectory according to claim 1, characterized in that: The RF fingerprint feature vector is input into the support vector machine to identify the identities of N RF devices. The principal component analysis is used to reduce the dimension of the obtained feature vector. The reduced features are randomly divided into training set and test set in a certain proportion, and input into the support vector machine SVM for classification. The label results output by the trained model are compared with the actual labels to obtain the classification accuracy.

8. The method of radio frequency fingerprint recognition based on fractal trajectory according to claim 1, characterized in that: The process of reducing the dimension of the obtained feature vector by principal component analysis is as follows: 1) Extract the RF fingerprint feature vector feature set X∈R n*m To de-mean the sample features in, for each feature of the sample, use the value of the current feature minus the mean of the feature in the sample set, that is, 2) Calculate the covariance matrix XX of the sample T ; 3) Perform eigenvalue decomposition on the covariance matrix to obtain the eigenvalues ​​and eigenvectors of the covariance matrix; 4) Select the eigenvectors corresponding to the largest first k eigenvalues ​​and transform them into P; 5) Y=PX is the k-dimensional feature matrix obtained after dimensionality reduction.

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