阅读说明：本技术 基于射频指纹的无线设备身份认证方法及其装置 (Wireless equipment identity authentication method and device based on radio frequency fingerprint ) 是由 林云 王森 郭星昊 窦峥 涂涯 于 2020-05-12 设计创作，主要内容包括：本发明提供一种基于射频指纹的无线设备身份认证方法及其装置,该方法包括：获取授权设备的射频指纹；根据所获取的射频指纹为相应授权设备建立高斯混合模型；获取待认证设备的射频指纹；调用k近邻查找器,并在授权设备的射频指纹中查找距离待认证设备的射频指纹最近的至少两种射频指纹；将待认证设备的射频指纹输入到查找到的至少两种射频指纹所对应的授权设备的高斯混合模型中,计算出至少两种射频指纹所对应的授权设备的高斯混合模型的条件概率,并将计算出的条件概率中的最大值与预先设定的阈值进行比较,以判定待认证设备的身份。本申请的认证方法能够利用不同无线设备之间的硬件细微差异对其进行准确的身份认证。(The invention provides a wireless equipment identity authentication method and a device based on radio frequency fingerprints, wherein the method comprises the following steps: acquiring a radio frequency fingerprint of an authorized device; establishing a Gaussian mixture model for the corresponding authorization equipment according to the acquired radio frequency fingerprint; acquiring a radio frequency fingerprint of equipment to be authenticated; calling a k neighbor finder, and finding at least two radio frequency fingerprints closest to the radio frequency fingerprint of the equipment to be authenticated in the radio frequency fingerprints of the authorization equipment; inputting the radio frequency fingerprints of the equipment to be authenticated into the Gaussian mixture models of the authorization equipment corresponding to the at least two found radio frequency fingerprints, calculating the conditional probabilities of the Gaussian mixture models of the authorization equipment corresponding to the at least two found radio frequency fingerprints, and comparing the maximum value in the calculated conditional probabilities with a preset threshold value to judge the identity of the equipment to be authenticated. The authentication method can utilize the hardware subtle difference between different wireless devices to carry out accurate identity authentication.)

1. A wireless equipment identity authentication method based on radio frequency fingerprint is characterized by comprising the following steps:

acquiring a radio frequency fingerprint of an authorized device;

establishing a Gaussian mixture model for the corresponding authorization equipment according to the acquired radio frequency fingerprint;

acquiring a radio frequency fingerprint of equipment to be authenticated;

calling a k neighbor finder, and finding at least two radio frequency fingerprints closest to the radio frequency fingerprint of the equipment to be authenticated in the radio frequency fingerprints of the authorization equipment;

inputting the radio frequency fingerprints of the equipment to be authenticated into the Gaussian mixture models of the authorization equipment corresponding to the at least two found radio frequency fingerprints, calculating the conditional probabilities of the Gaussian mixture models of the authorization equipment corresponding to the at least two found radio frequency fingerprints, and comparing the maximum value of the calculated conditional probabilities with a preset threshold value to judge the identity of the equipment to be authenticated.

2. The method of claim 1, wherein the establishing a gaussian mixture model for the corresponding authorized device according to the obtained rf fingerprint comprises:

and respectively establishing a Gaussian mixture model according to the acquired radio frequency fingerprint of each authorization device.

3. The method of claim 2, wherein obtaining the rf fingerprint of the authorized device comprises:

collecting communication signals of the authorization equipment for multiple times, and carrying out preprocessing and interception of a steady-state signal segment;

and solving the bispectrum value of the steady-state signal segment by adopting a bispectrum estimation algorithm.

4. The method of claim 3, wherein obtaining the RF fingerprint of the authorized device further comprises:

and performing rectangular integral bispectrum transformation on the solved bispectrum value.

5. The method of claim 4, wherein obtaining the RF fingerprint of the authorized device further comprises:

and calling a preset dimensionality reduction matrix to perform characteristic dimensionality reduction on the bispectrum value subjected to the square integral bispectrum transformation.

6. The method of claim 1, wherein the establishing a gaussian mixture model for the corresponding authorized device according to the obtained rf fingerprint comprises:

the radio frequency fingerprint features from the same authorized device are used as a data set for training the gaussian mixture model.

7. The method of claim 6, wherein the establishing a Gaussian mixture model for the corresponding authorized device according to the obtained RF fingerprint comprises:

the gaussian mixture model is trained using the expectation maximization algorithm.

8. A wireless device identity authentication device based on radio frequency fingerprint, characterized in that the authentication device comprises:

the acquisition module is used for acquiring the radio frequency fingerprints of the authorization equipment and the equipment to be authenticated;

the model establishing module is used for establishing a Gaussian mixture model for the corresponding authorization equipment according to the acquired radio frequency fingerprint;

the searching module calls a k neighbor searcher and searches at least two radio frequency fingerprints closest to the radio frequency fingerprint of the equipment to be authenticated in the radio frequency fingerprints of the authorization equipment; and

and the identity judgment module is used for inputting the radio frequency fingerprints of the equipment to be authenticated into the Gaussian mixture models of the authorization equipment corresponding to the at least two searched radio frequency fingerprints, calculating the conditional probabilities of the Gaussian mixture models of the authorization equipment corresponding to the at least two radio frequency fingerprints, and comparing the maximum value in the calculated conditional probabilities with a preset threshold value so as to judge the identity of the equipment to be authenticated.

9. A computer device comprising a memory and a processor, the memory having stored thereon a computer program operable on the processor, wherein the processor, when executing the computer program, performs the steps of the method of any of claims 1 to 7.

10. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the method of any one of claims 1 to 7.

Technical Field

The invention relates to the field of wireless equipment identity authentication, in particular to a wireless equipment identity authentication method and a wireless equipment identity authentication device based on radio frequency fingerprints.

Background

The traditional identity authentication mechanism of the internet of things is based on password security, and the security of the identity authentication mechanism is only related to the length of a secret key. With the rapid development of computer software and hardware, equipment in hands of ordinary users also has strong computing power, and password breaking is not very difficult, so that the authentication mechanism of the internet of things based on the password is not reliable any more. Password-based authentication mechanisms can only increase the security of the authentication mechanism by increasing the length of the password. However, due to the limited computing power of the internet of things device, the computing load of the internet of things device will be exceeded by the excessively complex password computation.

Aiming at the defect of the authentication mechanism based on the password, students develop a lightweight Internet of things security authentication mechanism based on non-password authentication at home and abroad successively. Since the hardware feature of the physical layer is not easily imitated and forged, and it can solve the deficiency of the authentication mechanism based on the password, the research on enhancing the security of the wireless network by using the hardware feature of the physical layer of the wireless device is receiving more and more attention. The following are some representative patents and their deficiencies in the aspect of radio frequency fingerprint authentication in China:

chinese patent document No. CN105162778A, published as 2015-12-16, describes a cross-layer authentication method based on radio frequency fingerprints, which is to determine the similarity between the radio frequency fingerprint of an authorized device and the radio frequency fingerprint of a device to be authenticated by comparison, but the method requires cross-layer acquisition of authentication information.

Chinese patent document with publication number CN110087233A and publication number 2019-08-02 describes an unmanned aerial vehicle identity authentication method based on radio frequency fingerprints, which extracts Haar-like features of DCTF of unmanned aerial vehicle communication signals and uses an SVM classifier for identity recognition, but the patent does not have defense capability for unauthorized unmanned aerial vehicles.

Chinese patent document No. CN107612949A, published as 2018-01-19, describes a method and system for access authentication of a wireless intelligent terminal based on radio frequency fingerprint, and the method proposes to combine a radio frequency fingerprint technology with an authentication protocol, and use the radio frequency fingerprint to complete bidirectional authentication between a wireless device and a server. However, the method does not refer to a specific radio frequency fingerprint extraction method and a radio frequency fingerprint authentication method.

Therefore, research and development of an authentication method based on a physical layer are urgently needed, and identity authentication of equipment to be authenticated can be independently completed on the premise that authentication information of other layers does not need to be acquired.

Disclosure of Invention

In order to solve the above problems, the present invention provides a method for authenticating an identity of a wireless device based on a radio frequency fingerprint, which can independently complete the identity authentication of a device to be authenticated without acquiring authentication information of other layers.

In order to achieve the above object, the present application provides a wireless device identity authentication method based on a radio frequency fingerprint, where the authentication method includes: acquiring a radio frequency fingerprint of an authorized device; establishing a Gaussian mixture model for the corresponding authorization equipment according to the acquired radio frequency fingerprint; acquiring a radio frequency fingerprint of equipment to be authenticated; calling a k neighbor finder, and finding at least two radio frequency fingerprints closest to the radio frequency fingerprint of the equipment to be authenticated in the radio frequency fingerprints of the authorization equipment; and inputting the radio frequency fingerprints of the equipment to be authenticated into the Gaussian mixture models of the authorization equipment corresponding to the at least two searched radio frequency fingerprints, calculating the conditional probabilities of the Gaussian mixture models of the authorization equipment corresponding to the at least two radio frequency fingerprints, and comparing the maximum value in the calculated conditional probabilities with a preset threshold value to judge the identity of the equipment to be authenticated.

Further, establishing a gaussian mixture model for the corresponding authorized device according to the acquired radio frequency fingerprint comprises: and respectively establishing a Gaussian mixture model according to the acquired radio frequency fingerprint of each authorization device.

Further, acquiring the radio frequency fingerprint of the authorized device comprises: collecting communication signals of the authorization equipment for multiple times, and carrying out preprocessing and interception of a steady-state signal segment; and solving the bispectrum value of the steady-state signal segment by adopting a bispectrum estimation algorithm.

Further, acquiring the radio frequency fingerprint of the authorized device further comprises: and performing rectangular integral bispectrum transformation on the solved bispectrum value.

Further, acquiring the radio frequency fingerprint of the authorized device further comprises: and calling a preset dimensionality reduction matrix to perform characteristic dimensionality reduction on the bispectrum value subjected to the square integral bispectrum transformation.

Further, establishing a gaussian mixture model for the corresponding authorized device according to the acquired radio frequency fingerprint comprises: the radio frequency fingerprint features from the same authorized device are used as a data set for training the gaussian mixture model.

Further, establishing a gaussian mixture model for the corresponding authorized device according to the acquired radio frequency fingerprint comprises: the gaussian mixture model is trained using the expectation maximization algorithm.

According to another aspect of the present application, there is provided a wireless device identity authentication apparatus based on a radio frequency fingerprint, the authentication apparatus including: the acquisition module is used for acquiring the radio frequency fingerprints of the authorization equipment and the equipment to be authenticated; the model establishing module is used for establishing a Gaussian mixture model for the corresponding authorization equipment according to the acquired radio frequency fingerprint; the searching module calls a k neighbor searcher and searches at least two radio frequency fingerprints closest to the radio frequency fingerprint of the equipment to be authenticated in the radio frequency fingerprints of the authorization equipment; and the identity judgment module is used for inputting the radio frequency fingerprints of the equipment to be authenticated into the Gaussian mixture models of the authorization equipment corresponding to the at least two searched radio frequency fingerprints, calculating the conditional probabilities of the Gaussian mixture models of the authorization equipment corresponding to the at least two radio frequency fingerprints, and comparing the maximum value in the calculated conditional probabilities with a preset threshold value to judge the identity of the equipment to be authenticated.

According to yet another aspect of the present application, there is provided a computer device, comprising a memory and a processor, wherein the memory stores a computer program that can be executed on the processor, and the processor implements the steps of the above-mentioned wireless device identity authentication method based on radio frequency fingerprint when executing the computer program.

According to yet another aspect of the present application, there is provided a computer readable storage medium, on which a computer program is stored, which, when being executed by a processor, implements the steps of the above-mentioned method for authenticating an identity of a wireless device based on a radio frequency fingerprint.

The wireless equipment identity authentication method based on the radio frequency fingerprint can utilize hardware subtle differences among different wireless equipment to carry out accurate identity authentication on the wireless equipment.

Drawings

The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:

FIG. 1 illustrates a flow chart of a method for wireless device identity authentication based on radio frequency fingerprints according to the present application;

FIG. 2 illustrates a flow chart for performing a signal bispectrum calculation in accordance with a preferred embodiment of the present application;

FIG. 3 illustrates an integration path of a rectangular-integrated bispectrum employed in accordance with a preferred embodiment of the present application;

FIG. 4 illustrates a flow chart for training a Gaussian Mixture Model (GMM) by an expectation maximization algorithm (EM) according to a preferred embodiment of the present application;

FIG. 5 shows a block diagram of a Multi-GMM authentication model in accordance with a preferred embodiment of the present application;

FIG. 6 illustrates a detailed flow chart of a method for wireless device identity authentication based on radio frequency fingerprints according to the present application;

fig. 7 shows a wireless device identity authentication apparatus based on radio frequency fingerprint according to a preferred embodiment of the present application.

Detailed Description

In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.

According to the application, a wireless equipment identity authentication method based on radio frequency fingerprint is provided, and the authentication method comprises the following steps: acquiring a radio frequency fingerprint of an authorized device; establishing a Gaussian mixture model for the corresponding authorization equipment according to the acquired radio frequency fingerprint; acquiring a radio frequency fingerprint of equipment to be authenticated; calling a k neighbor finder, and finding at least two radio frequency fingerprints closest to the radio frequency fingerprint of the equipment to be authenticated in the radio frequency fingerprints of the authorization equipment; inputting the radio frequency fingerprints of the equipment to be authenticated into the Gaussian mixture models of the authorization equipment corresponding to the at least two found radio frequency fingerprints, calculating the conditional probabilities of the Gaussian mixture models of the authorization equipment corresponding to the at least two found radio frequency fingerprints, and comparing the maximum value in the calculated conditional probabilities with a preset threshold value to judge the identity of the equipment to be authenticated.

The method and the device can independently complete the identity authentication of the equipment to be authenticated by extracting the difference information of the physical layer hardware of different authorization equipment to form the radio frequency fingerprint without acquiring the authentication information of other layers.

As shown in fig. 1, according to the present application, a method for authenticating an identity of a wireless device based on a radio frequency fingerprint includes:

s101: a radio frequency fingerprint of an authorized device is obtained.

According to a preferred embodiment of the present application, the approximate estimation of the bispectrum of the signal is obtained by using a method of bispectrum estimation, and more particularly, the bispectrum estimation is calculated by using a direct method. The direct method has great advantages in the aspects of bispectral resolution and computational efficiency, is simple and direct, and can obtain better resolution when the sample length is enough.

Briefly described below for calculating a signal bispectrum value by direct methods, fig. 2 shows a flow chart for performing a signal bispectrum calculation according to a preferred embodiment of the present application.

As shown in fig. 2, the obtaining the bispectrum value of the stationary signal segment by using the bispectrum estimation algorithm may include the following steps:

s1012, segmenting the original signal sequence, assuming that the number of segments is K, each segment includes M sample points, that is, N is KM, and centering the data segments.

S1013, the DFT coefficients are calculated for each segment:

wherein, λ ═ 0,1 ·, M/2, i ═ 0,1 ·, K, y⁽ⁱ⁾(n) is the ith data.

S1014, calculating the third-order correlation of DFT coefficients:

s1015, averaging the K-segment bispectrum estimates obtained in step S1014, so as to obtain a bispectrum estimate of the original signal:

wherein, ω is₁＝(2πf_s/N₀)λ₁，ω₂＝(2πf_s/N₀)λ₂。

The bispectrum values of the original signal can be obtained by the above steps.

And then, acquiring the radio frequency fingerprint characteristics of the communication signal according to the obtained dual-spectrum values of the original signal.

According to another preferred embodiment of the present application, the radio frequency fingerprint of the communication signal of the authorized device is obtained by using a Square Integrated Bispectrum (SIB) method among the contour Integrated bispectrum methods. That is, the rectangular integral bispectrum transformation is performed on the bispectrum values of the original signal obtained by the above method. The rectangular integral bispectrum is obtained by performing integral operation by taking each side of a series of rectangles which take a bispectrum origin as a center on a bispectrum plane as an integral path, wherein the specific integral path is shown in fig. 3.

Wherein, calculation of SIB is:

wherein S is_lThe integration path of the rectangular integrated bispectrum of fig. 3 is shown. As known from the calculation process of the SIB, the SIB can fully utilize the characteristic information in the dual-spectrum plane, and the omission and repeated calculation of points can not occur. And obtaining the radio frequency fingerprint characteristics of the communication signals after rectangular integral bispectrum transformation.

As described above, acquiring the radio frequency fingerprint of the authorized device may be obtained by:

collecting communication signals of the authorization equipment for multiple times, and carrying out preprocessing and interception of a steady-state signal segment;

obtaining a bispectrum value of the steady-state signal segment by adopting a bispectrum estimation algorithm;

and performing rectangular integral bispectrum transformation on the solved bispectrum value.

The steady state signal is preferably used in this application because the steady state signal segments are easily accessible and contain a large amount of identifiable information.

In addition, in the method, the bispectrum value of the original signal is calculated by adopting a direct method, and the radio frequency fingerprint characteristic of the communication signal is obtained by adopting the rectangular integral bispectrum, so that the operation of obtaining the radio frequency fingerprint characteristic of the communication signal is simple and easy.

According to another embodiment of the present application, a preset dimensionality reduction matrix (the dimensionality reduction matrix used herein may be obtained by a conventional dimensionality reduction method) is called to perform feature dimensionality reduction on the bispectrum values subjected to the square integral bispectrum transformation, so as to obtain a radio frequency fingerprint of a signal, and the radio frequency fingerprint and the dimensionality reduction matrix of the authorized device are saved.

S102: and establishing a Gaussian Mixture Model (GMM) for the corresponding authorized device according to the acquired radio frequency fingerprint.

Through the steps, a Gaussian mixture model can be established for each authorization device, and the radio frequency fingerprint and the GMM data of the corresponding authorization device are uploaded to background data for storage. That is, each authorized device and its radio frequency model correspond to a unique GMM.

Preferably, a gaussian mixture model is respectively established according to the acquired radio frequency fingerprint of each authorized device. Multiple GMM models are formed by building a GMM for each authorized device. These GMM models are formed with k-nearest neighbors lookup as will be described below as a combined authentication model-Multi-GMM model. By establishing a GMM for each authorized device, the lookup can be made more accurate and the degree of matching can be made higher.

Specifically, using the radio frequency fingerprint features from the same authorized device as the data set for training the GMM, the specific calculation flow is as follows:

the gaussian mixture model is constructed by finding a gaussian joint distribution for different clusters of signal samples of a device, and then using a set of weight vectors ω ═ ω { ω ═ ω where the sum is unity₁，ω₂，...，ω_N-adding the previously found gaussian joint distributions to a combined distribution and using the combined distribution to fit the distribution of the signal samples in the feature space. The GMM is obtained by adding N Gaussian joint distributions according to weights. N is the number of gaussian distributions of the GMM model. The GMM model of order N is essentially a multi-bit probability distribution function whose probability density function is as follows:

in the above formula, N is the order of the GMM model, X is an M-dimensional random variable, and ω ═ ω { [ ω ] } ω₁，ω₂，…，ω_NIs a weight coefficient, and should satisfy the following relationship:

each gaussian sub-distribution p_i(X) is a Gaussian joint distribution of M dimensions, and the expression is as follows:

wherein mu_iMean vector of Gaussian distribution, Sigma_iIs a covariance matrix.

In summary, the feature distribution of the signal samples of a wireless device can be calculated by N gaussian joint distribution models according to the weight ω ═ ω { ω ═ ω }₁，ω₂，…，ω_NAnd adding the obtained GMM model for fitting. Wherein the parameters to be determined have a mean vector mu_iCovariance matrix ∑_iAnd the weight vector ω ═ ω₁，ω₂，…，ω_NDetermining the parameters determines a GMM model. Based on the above, one GMM model can be denoted as ξ ═ (N, ω)_i，μ_i,Σ_i）,i＝1，…，N (8)

That is, establishing a GMM is an estimation and optimization of several parameters. According to the present application, the expected maximum algorithm (EM) is employed to estimate the parameters of the GMM. The expectation maximization algorithm is an iterative algorithm, and the iteration of the EM algorithm is divided into two steps: firstly, solving a rough value of a parameter to be estimated; the second step maximizes the likelihood function using the values of the first step. FIG. 4 shows a flow diagram for training a Gaussian Mixture Model (GMM) by an expectation maximization algorithm (EM) according to a preferred embodiment of the present application.

As shown in fig. 4, the method of training the gaussian mixture model by the EM algorithm may include:

s1021, inputting observation data X ═ X₁，x₂，…，x_N}。

S1022, initializing GMM parameters, mean vector mu_κCovariance matrix ∑_kAnd a weight vector ω_k。

S1023, calculating the characteristic vector x according to the parameters of the current model_nThe probability of falling into the feature cluster i (i.e., step E in the EM algorithm).

First, X ═ X for one sample set_nThe log-likelihood function of (where n ═ 1,2, … …, T) is:

since the sum of logarithmic functions is included, it is difficult to obtain an extremum. The above formula can be rewritten as:

whereinN is the number of Gaussian distributions. The problem that the likelihood function comprises the sum of logarithmic functions can be solved by adding Y as an implicit variable into the formula (9).

According to the first step of estimating rough values of the parameters in the EM algorithm, the feature vector x is first calculated_n＝{x₁,x₂,L,x_NThe probability of falling into a feature cluster i is:

and S1024, iteratively updating the estimation value of the model according to the M steps of the EM algorithm.

The second step of the EM algorithm is to find the parameter values that maximize the likelihood function log (L (ξ | X, Y)). From equation (11), the following GMM model parameter estimation equation can be obtained:

(1) the kth weighting factor ω_kEstimation of (2):

(2) distributed by the kth Gaussian combinationMean vector mu_κEstimation of (2):

(3) estimation of covariance matrix of kth gaussian joint distribution:

s1025 determines whether the formula (10) converges, and if not, repeats steps S1023 and S1024 until the formula (10) converges, thereby ending the parameter iteration (step S1026).

According to the method described above, three important parameters of the GMM can be estimated.

The following is a brief introduction of how the single-class data description is performed by the gaussian mixture model.

After a signal sample of a device is obtained, the device is marked as xi, and the signal sample of the device can be subjected to distribution fitting through a GMM model. According to the above model building process, a GMM model is built, and when a signal sample X of the test device is received, it is input into the GMM model to obtain the following conditional probability:

p (X | ξ) represents the conditional probability that device ξ is capable of producing X. A threshold eta is preset, and whether the test sample X is generated by the equipment xi can be judged by comparing the magnitude relation between P (X | xi) and the threshold eta.

In the application, multiple single classifier models (that is, each authorization device establishes one classifier model) are established to cooperate with a k-nearest neighbor finder, so that multiple GMMs are combined into a combined authentication model, i.e., a Multi-GMM model (as shown in fig. 5).

As can be seen from fig. 5, the Multi-GMM authentication model includes a plurality of GMMs, and since the GMMs have automatic parameter optimization, the convergence speed is high, the model theory is clear and transparent, and the model effect is also ideal. The combination of a plurality of GMMs does not increase the complexity of calculation too much, and can complete the identity authentication of the wireless communication equipment, thereby avoiding the defect that the authentication category needs to be provided in advance.

S103: and acquiring the radio frequency fingerprint of the equipment to be authenticated.

The method for acquiring the radio frequency fingerprint of the authorized device acquires the radio frequency fingerprint of the device to be authenticated, and will not be described here.

S104: and calling a k neighbor finder, and finding at least two radio frequency fingerprints closest to the radio frequency fingerprint of the equipment to be authenticated in the radio frequency fingerprints of the authorization equipment.

And calling the radio frequency fingerprints of all the authorized devices at the authorized device end, and finding at least two radio frequency fingerprints closest to the device to be authenticated for the device to be authenticated through the k-nearest neighbor finder, so that the authorized device categories corresponding to the at least two radio frequency fingerprints can be further found.

As shown in fig. 5, the radio frequency fingerprint of each authorization device uniquely corresponds to one GMM, two sets of radio frequency fingerprint sample clusters closest to the radio frequency fingerprint of the device to be authenticated are found for the radio frequency fingerprint of the device to be authenticated through the k-nearest neighbor finder, the corresponding authorization device is found according to the radio frequency fingerprint sample clusters, and the radio frequency fingerprint of the device to be authenticated is input into the GMMs of the two authorization devices, so as to determine whether the device to be authenticated is legal, if so, the authentication is successful, and if not, the authentication is failed.

S105: inputting the radio frequency fingerprints of the equipment to be authenticated into the Gaussian mixture models of the authorization equipment corresponding to the at least two searched radio frequency fingerprints, calculating the conditional probabilities of the Gaussian mixture models of the authorization equipment corresponding to the at least two radio frequency fingerprints, and comparing the maximum value in the calculated conditional probabilities with a preset threshold value to judge the identity of the equipment to be authenticated.

That is, the radio frequency fingerprints of the device to be authenticated are input into the gaussian mixture model (i.e., formula (15)) of the authorization device corresponding to the at least two kinds of radio frequency fingerprints found in step S104, so that each found radio frequency fingerprint obtains a probability value, the maximum one of the probability values is taken to compare with a preset threshold, if the maximum value is greater than the threshold, the device to be authenticated is determined to be legal, and if the maximum value is less than the threshold, the device to be authenticated is determined to be illegal.

The method for authenticating the identity of the wireless device based on the radio frequency fingerprint according to the application is described by a specific embodiment.

Fig. 6 shows a detailed flowchart of a method for authenticating an identity of a wireless device based on a radio frequency fingerprint according to the present application.

As shown in fig. 6, the authorized device sends the communication signal multiple times, and the wireless device identity authentication method according to the present application collects the communication signal X ═ X from the authorized device multiple times₁，x₂，…，x_nPreprocessing the collected signals and intercepting the steady-state signal segment to obtain X_steady＝{x_i+1，x_i+2，…，x_i+m}。

And extracting and/or reducing dimensions of the signal features subjected to preprocessing and steady-state signal segment interception to acquire the radio frequency fingerprint of the signal. That is, as described above, the bispectrum value BD (ω) of the steady-state signal segment is found by the direct method₁，ω₂) And performing rectangular integral bispectrum transformation on the solved bispectrum value. Of course, if necessary, the communication signal after the rectangular integral bispectrum transformation is subjected to feature dimension reduction through a dimension reduction matrix (the dimension reduction matrix used herein can be obtained through a conventional dimension reduction method), and the radio frequency fingerprint R of the signal is obtained as { R ═ R₁，r₂，…，r_s}. And uploading the radio frequency fingerprints and the dimensionality reduction matrix of the obtained signals to a background database for storage.

The radio frequency fingerprint R ═ { R } of the signal to be obtained by the method described above₁，r₂，…，r_sThe parameters in the GMM are input into the GMM and iteratively optimized using a desired max algorithm (EM). And after the iteration is finished, uploading the GMM model to a background database for storage. And the background database stores the GMM model corresponding to each authorized device.

The above describes a registration process of an authorized device, and an authentication process of a device to be authenticated will be described below.

The method comprises the steps that the equipment to be authenticated sends communication signals, and the communication signals Y ═ Y { Y } from the equipment to be authenticated are collected according to the wireless equipment identity authentication method₁，y₂，…，y_nPreprocessing the acquired signals and intercepting the steady-state signal segment to obtain Y_steady＝{y_i+1，y_i+2，…，y_i+m}。

And extracting and/or reducing dimensions of the signal features subjected to preprocessing and steady-state signal segment interception to acquire the radio frequency fingerprint of the signal. That is, as described above, the bispectrum value of the steady-state signal segment is obtained by the direct method, the rectangular integral bispectrum transformation is performed on the obtained bispectrum value, and the characteristic dimension reduction is performed on the communication signal subjected to the rectangular integral bispectrum transformation through the dimension reduction matrix (the dimension reduction matrix used here can be obtained through the conventional dimension reduction method) as required to obtain the radio frequency fingerprint R of the device to be authenticated_Y＝{r₁，r₂，......，r_s}。

Calling the radio frequency fingerprints of all authorized devices in a background database, and searching the radio frequency fingerprints R which are in all the authorized devices and are far away from the device to be authenticated through a k-nearest neighbor finder_Y＝{r₁，r₂，......，r_sAnd searching for corresponding authorized equipment types in the Multi-GMM according to the found radio frequency fingerprints.

Respectively identifying the radio frequency fingerprints R of the devices to be authenticated_Y＝{r₁，r₂，......，r_sInputting the conditional probability P (R) of the authorized devices GMM corresponding to the found radio frequency fingerprint into the GMM of the authorized devices GMM, and calculating the conditional probability P (R) of the authorized devices GMM according to the formula (15) above_Y|ξ_i) And the maximum value of the conditional probabilities is compared with a preset threshold value, so as to judge whether the equipment to be authenticated passes the authentication according to the comparison result, namely, if the maximum value is larger than the threshold value, the equipment to be authenticated is judged to be legal, such asAnd if the maximum value is smaller than the threshold value, judging that the equipment to be authenticated is illegal.

According to another aspect of the present application, there is provided an apparatus for authenticating a wireless device based on a radio frequency fingerprint, as shown in fig. 7, the apparatus including: an obtaining module 100, configured to obtain a radio frequency fingerprint of an authorization device and a device to be authenticated; the model establishing module 200 is used for establishing a Gaussian mixture model for the corresponding authorization equipment according to the acquired radio frequency fingerprint; the searching module 300 calls a k-nearest neighbor searcher and searches for at least two radio frequency fingerprints closest to the radio frequency fingerprint of the device to be authenticated in the radio frequency fingerprints of the authorization device; and an identity determination module 400, which inputs the radio frequency fingerprints of the device to be authenticated into the gaussian mixture models of the authorization devices corresponding to the at least two found radio frequency fingerprints, calculates conditional probabilities of the gaussian mixture models of the authorization devices corresponding to the at least two found radio frequency fingerprints, and compares a maximum value of the calculated conditional probabilities with a preset threshold value to determine the identity of the device to be authenticated.

In one embodiment, a computer device is provided, which includes a memory and a processor, where the memory stores a computer program that is executable on the processor, and the processor implements the steps of the above-mentioned wireless device identity authentication method based on radio frequency fingerprint when executing the computer program.

In one embodiment, a computer readable storage medium is provided, on which a computer program is stored, which when executed by a processor implements the steps of the above-described method for wireless device identity authentication based on radio frequency fingerprints. Computer-readable storage media according to the present application may include, for example, non-volatile and/or volatile memory. For example, nonvolatile memory can include Read Only Memory (ROM), Programmable ROM (PROM), Electrically Programmable ROM (EPROM), Electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM may take many forms such as static RAM (sram), dynamic RAM (dram), synchronous dram (sdram), double data rate sdram (ddrsdram), enhanced sdram (esdram), synchronous link dram (Synchlink) dram (sldram), Rambus direct RAM (rdram), direct bus dynamic RAM (drdram), and bus dynamic RAM (rdram), among others.

The application relates to a wireless equipment identity authentication method based on radio frequency fingerprints and GMM, which is used for carrying out accurate identity authentication on different wireless equipment by utilizing hardware subtle differences among the different wireless equipment.

The method comprises the steps of preprocessing collected communication signals, extracting characteristics of radio frequency fingerprints, establishing GMMs (Gaussian mixture models) for the radio frequency fingerprints from the same authorization equipment, and combining a plurality of GMM models with a k neighbor finder to form a Multi-GMM authentication model, so that accurate identity authentication is performed on equipment to be authenticated with unknown identities.

The application establishes a single classifier based on a Gaussian mixture model. The single classifier is used for describing the distribution of the radio frequency fingerprints from the same authorized device in a feature space, and the GMM model is trained by using an expected maximum algorithm, so that the GMM model is further optimized.

The application also designs a radio frequency fingerprint feature extraction method based on the contour integral bispectrum (more specifically, rectangular integral bispectrum), and extracts the bispectrum value of the signal by a direct method in a nonparametric method, so as to obtain the relatively optimized signal radio frequency fingerprint feature.

The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.