CN115103365A

CN115103365A - Mobile communication terminal identification method based on polarization fingerprint

Info

Publication number: CN115103365A
Application number: CN202210678782.9A
Authority: CN
Inventors: 张萌; 魏冬; 徐锦龙; 石志鑫; 王中方; 李静; 张巧遇; 付婧雯; 高星; 翁腾凡
Original assignee: Institute of Information Engineering of CAS
Current assignee: Institute of Information Engineering of CAS
Priority date: 2022-06-15
Filing date: 2022-06-15
Publication date: 2022-09-23

Abstract

The invention discloses a mobile communication terminal identification method based on polarization fingerprints, which belongs to the field of information communication. The invention solves the problems of high IMSI extraction difficulty of the mobile communication terminal and low fingerprint stability and high application difficulty of the current radio frequency fingerprint.

Description

Mobile communication terminal identification method based on polarization fingerprint

Technical Field

The invention belongs to the field of information communication, and particularly relates to a mobile communication terminal identification method based on polarized fingerprints.

Background

The mobile communication terminal identification technology is a technology for identifying the individual identity of a mobile communication terminal through specific characteristics, and is widely applied to the fields of electronic countermeasure, personnel search and rescue, medical first aid, road flow monitoring, technical detection and capture, confidential control and the like of important sensitive places. Currently, the mobile communication terminal identification technology can be divided into two types, one is based on the IMSI ^[1-2] (International Mobile Subscriber Identification Number, International Mobile Subscriber identity) based Mobile communication terminal Identification technology, and the other is based on radio frequency fingerprint ^[3-5] Mobile communication terminal identification technology. The IMSI based identification technology can be further classified into a pseudo base station based identification technology and an uplink mobile communication signal measurement based identification technology. The identification technology based on the pseudo base station utilizes the weakness that a GSM system has no bidirectional authentication or the signaling of a part NAS (Non-Access Stratum) of an LTE system has no safety protection, the mobile communication terminal is tricked into the pseudo base station, the IMSI which uniquely identifies the identity of the mobile communication terminal in a mobile communication network is obtained, and then the identification and tracking of the mobile communication terminal are realized. The identification technology based on the measurement of the uplink mobile communication signal acquires the IMSI of the mobile communication terminal by capturing the uplink mobile communication signal of the terminal and analyzing the signaling content related to the IMSI according to a protocol, thereby achieving the aim of identifying and tracking the mobile communication terminal. The mobile communication terminal identification technology based on radio frequency fingerprint is radiation source individual identification technology based on physical layer, that is, the characteristics extracted from the basic electromagnetic properties of power, frequency, phase and the like of the signal, which can be used for identifying the identity of the equipment sending the signal, include transient characteristics and steady-state characteristics, and the identity characteristics are used for identifying the mobile communication terminal based on the radio frequency fingerprintAnd (4) mobile communication terminal individuals.

The pseudo base station based mobile communication terminal identification technique relies in principle on "terminal reselecting cell" and (quasi) synchronization with the base station. The former theoretically hardly achieves a "adsorption rate" of 100%, and is ineffective for mobile communication terminals in a connected state; the latter, due to implementation limitations, causes many products to lose synchronization with the base station after a period of time after being turned on, thereby greatly reducing the "adsorption rate". Meanwhile, there are also such as: the equipment price is high, the method is only applicable to partial systems, the interference effect is limited by the adsorption rate, a plurality of novel terminals support the function of the anti-counterfeiting base station, and the potential information safety hazard and the like can exist. In addition, in 4G and 5G Mobile communication networks, IMSI encryption transmission is generally used when network access authentication and TMSI (Temporary Mobile Subscriber Identity) update fails. In view of the security of IMSI, in order to avoid IMSI transmission on the air interface as much as possible, for signaling interaction under general conditions, the system adopts TMSI to temporarily replace IMSI, preventing illegal individuals or groups from stealing and tracking mobile communication terminals by intercepting mobile communication signals. Therefore, there is a limitation in IMSI acquisition regardless of the pseudo base station-based identification technique or the uplink mobile communication signal measurement-based identification technique. A mobile communication terminal identification technology based on Radio Frequency Fingerprint (RFF), for example, a system and a method for identifying and positioning an object based on device physical Fingerprint features disclosed in patent CN107368732A, where the extracted physical layer Fingerprint includes transient physical layer Fingerprint features, steady physical layer Fingerprint features, and spectrum physical layer Fingerprint features, which depend on basic electromagnetic properties such as signal power, Frequency, phase, etc., and are susceptible to the influence of signal pilot sequence, modulation mode, channel fading, multipath effect, and noise, and the stability is not high.

In order to make up for the deficiency of natural RFF, artificial injection of radio frequency signal fingerprint MeRFFI is proposed aiming at expanding the difference of radio frequency signal fingerprints and enhancing the stability and the continuity of the radio frequency fingerprints ^[6] . The MeRFFI adjusts the power and phase change of different frequency components in the radio frequency signal through the controllable reflecting surface, so that the aim of artificially injecting RFF is fulfilled. Although it is not limited toThus, the MeRFFI scheme inevitably fluctuates in the same scale in the time-frequency domain of the information-bearing signal while artificially expanding the radio frequency fingerprint, which undoubtedly reduces the signal quality. Therefore, the source of the transient RFF, the steady RFF or the artificially injected radio frequency fingerprint is the characteristic which is hidden in the radio frequency signal time-frequency domain and can represent the identity of the radiation source. In fact, the signal has polarization properties as an electromagnetic wave, and the polarization is independent of the time-frequency domain. Polarization is the time-varying trajectory of the electric field vector of an electromagnetic wave across its propagation cross-section. A common communication system does not modulate the Polarization of a signal to carry information, so that a Polarization Fingerprint (PF) has a potential to solve the problem of insufficient research on the existing radio frequency Fingerprint in some scenarios.

Disclosure of Invention

The invention aims to provide a mobile communication terminal identification method of polarization fingerprints, which is used for constructing a polarization fingerprint mathematical model, extracting the signal polarization fingerprints of a mobile communication terminal, identifying the individual mobile communication terminal by utilizing the polarization fingerprint characteristics of the mobile communication terminal, and has good anti-noise performance and higher identification efficiency. The invention solves the problems of high IMSI extraction difficulty of the mobile communication terminal and low fingerprint stability and high application difficulty of the current radio frequency fingerprint.

In order to realize the purpose, the invention adopts the following technical scheme:

a mobile communication terminal identification method based on polarized fingerprint comprises the following steps:

a polarized fingerprint mathematical model construction step: constructing a mathematical model of the polarization fingerprint based on the polarization states of the circularly polarized patch single radiation element antenna and the multi-radiation element antenna, wherein the mathematical model provides a relation for solving the polarization fingerprint through signal frequency, an antenna hardware parameter vector and a hardware defect vector;

a polarized fingerprint extraction step: calculating the minimum frequency interval of the signal according to the signal frequency range of the antenna; sampling the received signal to obtain a polarization phase at a sampling point; calculating the frequency of the sampling point according to the minimum frequency interval; calculating the polarization fingerprints at the sampling points by using a mathematical model of the polarization fingerprints according to the polarization phases and the frequencies of the sampling points, and extracting the polarization fingerprints of each frequency component;

the method comprises the following steps of constructing a population-individual characteristic template polarization fingerprint database: collecting antenna signals by using known mobile communication terminals of various models, extracting polarization fingerprints of the mobile communication terminals through the polarization fingerprint extraction step, classifying according to group characteristics and individual characteristics of the polarization fingerprints, and constructing a group-individual characteristic template polarization fingerprint database;

mobile communication terminal identification: for the mobile communication terminal to be identified, the polarized fingerprint is extracted through the polarized fingerprint extraction step, then the polarized fingerprint is compared with the polarized fingerprint in the group-individual characteristic template polarized fingerprint library, firstly, the group characteristics are compared, whether the mobile communication terminal belongs to a known model is judged, if not, the mobile communication terminal is directly judged to be unknown in identity, otherwise, the individual characteristics are continuously compared, and whether the mobile communication terminal belongs to a certain known device is judged.

Further, if two degenerate modes of two orthogonal polarization states obtained simultaneously when the single-radiating-element antenna is fed through a feed point are horizontal modes E _H And vertical mode E _V Then, the polarization state of the single radiating element antenna is expressed as:

wherein, | E _H /E _V I is the modulus of the polarization state p, argE _H /E _V Is E _H /E _V I.e. the phase angle of the polarization state p; .

Furthermore, if the multi-radiating element antenna is a two-radiating element antenna, it contains 3 resistors R ₁ 、R ₂ 、R ₃ Then, the polarization state of the two radiating element antennas is expressed as:

wherein, C ₁ F is the signal frequency, which is the capacitance in the circuit.

Further, the mathematical model of the polarization fingerprint is represented as:

where the expression of the function P (·) is determined by the structure of the antenna, f is the frequency of the signal,

is a vector of parameters of the hardware that,

is a hardware defect vector.

Further, the method for calculating the minimum frequency interval of the signal comprises the following steps: firstly, determining the minimum value and the maximum value of the signal frequency of an antenna; then receiving the horizontal and vertical components of the signal over a continuous period of time; then, sampling the horizontal component and the vertical component to obtain two finite length sequences under discrete time, wherein the sequence length is N; the minimum frequency spacing is equal to the ratio of the difference between the maximum and minimum of the signal frequency to N-1.

Further, the method for obtaining the polarization phase at the sampling point comprises the following steps: performing discrete Fourier transform on the two finite length sequences to obtain two corresponding frequency spectrums; the polarization phase at the sampling point is determined from the two spectra.

Further, the expression for calculating the frequency of the sampling point according to the minimum frequency interval is:

f _k ＝f _L +(k-1)Δf；

wherein f is _L Is the minimum value of the signal frequency, Δ f is the minimum frequency interval, and k is the sampling point.

Further, the method for extracting the polarization fingerprint of each frequency component comprises the following steps: representing the polarization state of the signal at the frequency as a repolarization ratio according to the polarization phase and the frequency at the sampling point; and calculating the polarized fingerprint formed by the polarization states of the frequency components according to the mathematical model of the polarized fingerprint, wherein the frequency components are sampled at the minimum frequency interval.

Further, the method for acquiring the group characteristics and the individual characteristics of the polarization fingerprint comprises the following steps: firstly, obtaining a model vector of a mobile communication terminal, an individual vector of the mobile communication terminal and a polarization fingerprint set corresponding to the individual vector of the mobile communication terminal; then, obtaining the group characteristics of the polarized fingerprints by calculating the average polarized fingerprints of the polarized fingerprint set; finally, the group characteristics are subtracted from the polarization fingerprints to extract the individual characteristics.

Further, in the mobile communication terminal identification step, threshold values of group characteristics and individual characteristic judgment are set, and the difference between two group characteristics or two individual characteristics is represented by Euclidean geometric distance; when polarization fingerprint comparison is carried out, the model or the equipment of the mobile communication terminal is determined through the magnitude relation between the Euclidean geometric distance between two group characteristics or two individual characteristics and a threshold value, if the Euclidean geometric distance is smaller than the corresponding threshold value, the mobile communication terminal is judged to belong to the known model or the known equipment, otherwise, the mobile communication terminal does not belong to the known model or the known equipment.

The invention has the following advantages:

(1) the polarization fingerprint provided by the invention describes the change relation of the signal polarization state along with the frequency, is irrelevant to the signal modulation mode and the existence time, can be acquired and stably and continuously exist in any time period, and ensures that the extracted polarization fingerprint characteristics of the mobile communication terminal have higher stability. The mobile communication terminal identification scheme based on the polarized fingerprint provided by the invention realizes the characteristic extraction and identification of the individual mobile communication terminal under the condition of not extracting the IMSI of the mobile communication terminal.

(2) The method comprises the steps of constructing a two-stage characteristic template polarization fingerprint database by utilizing two aspects of group characteristics and individual characteristics, judging accurate model information of the mobile communication terminal based on the group characteristics, locking the identity information of the mobile communication terminal to be identified in a certain range, and then identifying and judging the individual of the mobile communication terminal based on the individual characteristics. Compared with the existing identification scheme based on the radio frequency fingerprint, the method has the advantages that the identification efficiency is higher when the large-scale system is faced, and meanwhile, the accuracy is higher under the condition of low signal to noise ratio.

(3) The more the number of sampling points is, the lower the false alarm rate is, the longer the sampling time is, the more the points are collected by the identification equipment, and the wider the frequency range covered by the formed polarization fingerprint at the moment, so that the contained identity information is richer. The polarized fingerprint can stably and continuously exist, so that the design scheme of the invention has the capability of increasing the sampling quantity, thereby improving the identification false alarm rate under the condition of low signal-to-noise ratio.

Drawings

Fig. 1 is a schematic diagram of a typical rectangular patch antenna.

Fig. 2 is an equivalent circuit diagram of a rectangular patch antenna.

Fig. 3 is a schematic diagram of a two-element patch antenna.

Fig. 4 is a phase lead feed circuit diagram.

FIG. 5 is a diagram of a two-level feature template polarization fingerprint library.

Fig. 6 is a polarization fingerprint diagram in a polar coordinate system.

FIG. 7 is a population characteristic map of a polarized fingerprint.

FIG. 8 is an individual feature map of a polarized fingerprint.

FIG. 9 is a graph comparing a polarized fingerprint to a radio frequency fingerprint.

Detailed Description

In order to make the aforementioned and other features and advantages of the invention more comprehensible, embodiments accompanied with figures are described in detail below.

The embodiment discloses a mobile communication terminal identification method based on polarized fingerprints. For the sake of clarity of the method, the formation of the polarization state will first be described. Polarization fingerprints are derived from the characteristics of signal polarization containing identity information left by structural and hardware imperfections of the antenna, which appear as frequency dependence of the signal polarization state. The invention mainly aims at the common circularly polarized antenna of the mobile communication terminal equipment to carry out polarized fingerprint modeling. This embodiment discusses two different circularly polarized antennas: the single-radiating element antenna and the multi-radiating element antenna are specifically as follows.

1) Single radiating element antenna

A classical single-element antenna is composed of a rectangular patch and a feed point F, and as shown in fig. 1 (a), the length and width of the patch are equal. According to the cavity mode theory of patch antennas ^[7] At this time, two degenerate modes with two orthogonal polarization states can be obtained simultaneously through F-point feeding, and the horizontal mode is recorded as E _H Vertical mode is denoted as E _V And the resonant frequencies of the two degenerate modes are both f _r And the amplitudes are equal and the phase difference is zero. Then the rectangular patch antenna will now radiate a linearly polarized wave of +45 deg..

In order to radiate a circularly polarized state, E needs to be changed _H And E _V The phase difference between them. A classical approach is to vary E by adding a degenerate mode-separating element Δ s to the patch, for example the corner cut shown in FIG. 1 (b) _H And E _V The equivalent impedance phase angle in between. According to the theory of cavity modes ^[7] At this time E _H And E _V Will be given by f _r Respectively become f _H And f _V 。

It can be seen that the degenerate mode-separating unit Δ s is _H And E _V Are separated. The frequency f of the signal exciting the antenna is selected to be f _H And f _V In between, i.e. f _H <f<f _V . Since the difference between the signal frequency and the two resonant frequencies is positive and negative, one can determine that the equivalent impedance phase angle for one mode is leading and the equivalent impedance phase angle for the other mode is lagging. By controlling the degenerate mode separation unit and the operating frequency, the required amplitude ratio and phase difference can be formed, thus creating the desired polarization state.

According to the theory of cavity modes ^[7] At this time, E can be calculated by an equivalent circuit as shown in FIG. 2 _H And E _V 。E _H And E _V Working in fundamental mode TM respectively ₀₁ And TM ₁₀ . Since the other higher order modes L 'are small compared to the two fundamental modes, the effect of the other higher order modes L' can be neglected. Then the input impedance of the fundamental mode at this time is:

and:

where m and n are the order of the modes in two orthogonal directions, G is the equivalent circuit of the typical rectangular patch antenna of fig. 2 _mn Is an equivalent resistance, C _mn Is an equivalent capacitance, L _mn For equivalent inductance, ω is angular frequency, tan δ _eff Is the resistance correction factor, x ₀ Is the x-axis coordinate, y, of the feed point ₀ Is the y-axis coordinate of the feed point, h is the thickness of the patch, epsilon ₀ Is the relative dielectric constant, epsilon, of the patch medium _r Is the relative dielectric constant of the feed point, d ₀ Is the equivalent current element at the feed point, l is the length of the patch, j ₀ Is the Sinc function, and the eigenfunctions of the patch are:

because the feed signal has a frequency f, and TM ₀₁ And TM ₁₀ Respectively at a resonant frequency of f _H And f _V Then the ratio of the voltages of the two modes is:

wherein:

wherein, Q is the quality factor of the equivalent circuit. The polarization state parameters formed by the single-radiating-element antenna are expressed as vectors

The polarization state at this time can be expressed by equation (6):

wherein, | E _H /E _V I is the modulus of the polarization state p, argE _H /E _V Is E _H /E _V I.e. the phase angle of the polarization state p.

2) Multi-radiation element antenna

The multi-radiation element antenna can form a circular polarization state through the combination of a plurality of linear polarization radiation elements ^[8] As shown in fig. 3. The two radiating elements have the same physical size and are arranged in orthogonal directions, and the circularly polarized state can be coupled out in a far field only by controlling the phase difference of the feeding signals of the two radiating elements to be pi/2. Because the radio frequency front end only outputs one feed signal, an extra feed circuit is needed in the antenna to divide one feed signal into two feed signals with equal power and pi/2 phase difference. If a phase-lead RC phase shift circuit is used as the feed circuit, as shown in fig. 4.

At the moment, two feed signals u _H 、u _V Respectively as follows:

wherein R is ₁ ，R ₂ ，R ₃ 3 resistors, C, respectively, of the circuit of FIG. 4 ₁ Is a capacitance in a circuit, u _i For the input feed signal, f is the signal frequency. The polarization state parameter formed by the two-radiating-element antenna is expressed as a vector

The polarization state at this time can be expressed by equation (8):

based on the above description of two different circularly polarized antennas, a method for identifying a mobile communication terminal based on polarized fingerprints disclosed in this embodiment is described as follows, specifically comprising the following steps:

s1: mathematical modeling of polarized fingerprints

The polarization states formed by the antennas are frequency dependent, and the mathematical expressions for the polarization states formed by different antenna structures are different from each other. Different antennas also have unique hardware drawbacks

Which in turn creates a unique signal polarization. The composition of the antenna forming polarization states is thus abstracted as p, i.e. the polarization fingerprint.

Wherein, the concrete expression of the function P (-) is determined by the structure of the antenna, f is the frequency of the signal, and the hardware parameter vector

A design parameter, a hardware defect vector, for an ideal state

A unique hardware deficiency introduced in the manufacturing process for each antenna.

According to the polarization fingerprint model, as shown in equation (10), a polarization fingerprint is a curve of polarization state with respect to frequency. Since the concrete expression of equation (10) is determined by the antenna structure, the overall shape of the curve is also determined by the antenna structure, and the local fluctuation of the curve is determined by hardware imperfections.

S2: construction of two-stage characteristic template polarization fingerprint library

Because the difference degree of the antenna structure is far greater than the hardware defect, the polarization fingerprint also has two difference degrees. Polarized fingerprints from the same structure antenna often have similar overall shapes, and polarized fingerprints from different structure antennas have obvious differences, so that the polarized fingerprints have group characteristics and belong to the expression of polarized fingerprints on large difference. Due to the uniqueness of hardware defects introduced by different individual antennas with the same structure, the local fluctuation of the polarized fingerprint has obvious difference, which is called as the individual characteristic of the polarized fingerprint and belongs to the expression of small difference degree of the polarized fingerprint.

In order to extract the polarization state of the signal, the receiver needs to adopt an orthogonal dual-polarized antenna, which is assumed to be a horizontal and vertical linear polarization base (H, V). The signal range is (f) _L ,f _H ) Wherein f is _L Is the minimum value of the signal frequency, f _H Is the maximum value of the signal frequency; the horizontal component of the received signal in the case of a continuous time t is r _H (t) the vertical component of the received signal is r _V (t)，0<t<+∞。r _H (t) and r _V (t) obtaining a finite-length sequence r at discrete time n after sampling _H [n]And r _V [n]And the sequence length is N, N is 0,1. Then the minimum frequency interval is at this time deltaf.

Then for the sequence r _H [n]And r _V [n]Performing Discrete Fourier Transform (DFT) to obtain frequency spectrum H [ n ]]And V [ n ]]。

Because H [ n ] and V [ n ] contain the amplitude and phase information at sampling point k, the polarization phase descriptor at sampling point k is:

(arctan|H[k]/V[k],argH[k]-argV[k]) (13)

the frequency corresponding to the sampling point k is f _k 。

f _k ＝f _L +(k-1)Δf (14)

Then the frequency f _k The polarization state of the signal can be expressed as:

p[f _k ]＝|H[k]/V[k]|e ^{j(argH[k]-argV[k])} (15)

the polarization fingerprint composed of the polarization states of the respective frequency components at this time can be expressed as:

equation (16) corresponds to sampling equation (10) at the minimum frequency interval Δ f.

In the above formula, p [ f ] _k ]For different signal frequencies f _k The value of the following equation (10). Structural differences of the devices

And

the abstract representation is a vector, and a concrete representation is not needed and can be obtained in a concrete example in a real measurement mode. The value of the polarization state including structural differences

And

information, such as the polarization fingerprint of the device 1, can be represented as: → p ₁ ＝{p(f ₁ ),p(f ₂ ),...p(f _N ) }; the polarization fingerprint of the device 2 can be expressed as: → p ₂ ＝{p(f ₁ ),p(f ₂ ),...p(f _N )}。→p ₁ And → p ₂ The difference is the structural difference of the equipment 1 and the equipment 2

And

the method comprises the steps that a polarization fingerprint library is established by utilizing a mobile communication terminal with a known model, the group characteristics of different antenna structures in the polarization fingerprint library and the individual characteristics of the same antenna structure are known, when other terminals to be detected are judged subsequently, whether the polarization fingerprint in the polarization fingerprint library is matched with the group characteristics of the different antenna structures and the individual characteristics of the same antenna structure are judged, and if the polarization fingerprint in the polarization fingerprint library is matched with the group characteristics of the different antenna structures, which type of equipment or which type of equipment in the same type of equipment can be determined. Specifically, assuming that there are N types of mobile communication terminals in the system, a mobile communication terminal model vector is formed

Representing all mobile communication terminals belonging to model n. If K mobile communication terminals belong to the model n, then the individual vectors of the mobile communication terminals

D _nk Representing a device k belonging to model n. And with

Corresponding sets of polarized fingerprints

Wherein

Indicating a mobile communication terminal D _nk The polarized fingerprint of (1).

The construction of the two-stage feature template polarization fingerprint library needs to be aimed at

Constructing corresponding group feature vectors

For a set of mobile communication terminals belonging to the same model

Constructing corresponding individual feature vectors

As shown in fig. 5.

To be provided with

For example, since the hardware parameter approximation of each mobile communication terminal antenna having hardware defect is a normal distribution centered on an ideal value, the polarization fingerprint curve of each mobile communication terminal is also a fluctuation of an approximate normal distribution in a part of the ideal curve, and thus, the hardware parameter approximation is performed by finding

As average polarized fingerprint of

Group characteristics of

Individual features are more subtle than population features, so it is necessary to subtract population features from the polarization fingerprint to extract individual features.

S3: two-step recognition algorithm based on group-individual characteristics

The principle of the algorithm is to extract the polarization fingerprint of the equipment to be detected and the polarization fingerprint in the polarization fingerprint library constructed by the methodMatching, if matching, determining the type or equipment; if the matching is not good, the device is judged to be unknown, and the device is confirmed through manual identification and is further moved to a library. Specifically, assume that there is an existing mobile communication terminal D to be recognized _u The collected polarized fingerprint is

The identification process based on the two-stage feature template polarization fingerprint database shown in fig. 5 is divided into two steps: first, traversing the first-level group feature vector

To judge D _u Whether it is a mobile communication terminal of a known model. If D is _u And the system does not belong to any known model, and directly judges that the identity is unknown. If D is _u Belongs to the model i, and then continuously traverses the second level individual feature vector

To judge D _u Whether it belongs to a known device. And adding new elements into the first-level group feature vector and the second-level individual feature vector respectively for equipment with unknown model, and adding new elements into the identified second-level individual feature vector only for equipment with unknown model and unknown identity. The specific process of device identity matching identification is shown in algorithm 1. In which ξ _thre1 And xi _thre2 Respectively, the threshold values for the group feature and individual feature decisions. In this algorithm the difference between two features is represented by the euclidean geometrical distance.

A specific example and experimental verification are given below to compare the method of the present invention with the conventional method:

experiments were developed based on low-cost small-size mobile communication terminal equipment. The experiment comprises an identification device and eighteen mobile communication terminal devices. The identification device is composed of an orthogonal dual-polarized antenna and a Universal Software Radio Peripheral (USRP) X310 device provided with a TwinRX Radio daughter board. The circularly polarized patch antenna provided to the mobile communication terminal device is classified into three types as shown in table 1.

TABLE 1 model number of mobile communication terminal device

As can be seen from the polarization fingerprint modeling analysis, the polarization fingerprint is a curve of the polarization state changing along with the frequency. Therefore, the communication system is set as frequency hopping signals based on OFDM, and in order to fully study the polarization fingerprint property of the antenna, the bandwidth of each hop is 500KHz, the dwell time is 1ms, the total number of frequency hopping points is 53, and the total bandwidth is 902 MHz-928 MHz. The experiment is performed in a fixed office environment and a line-of-sight channel exists between the mobile communication terminal device and the identification device.

The first is the verification of the polarized fingerprint. As shown in fig. 6, each model shows polarization fingerprints of three devices for simplicity. Through a polar coordinate system, the polarization state is represented by the repolarization ratio at this time, so that the polarization fingerprint can be visually seen to describe the property of the signal polarization state changing along with the frequency, which accords with the modeling of the polarization fingerprint, and meanwhile, the equipment provided with the antennas of the same model is found to have similar population characteristics, as shown in fig. 7. Compared with the group characteristics, there is a significant difference between the devices of the same model, which is reflected by individual differences, as shown in fig. 8.

In order to compare performance with the traditional method, the experiment firstly realizes equipment identity recognition based on polarization fingerprints, and then realizes multiple kinds of equipment identity recognition based on radio frequency fingerprints. Radio frequency fingerprints are a traditional method for equipment identity recognition based on physical layer characteristics of wireless signals. Three traditional methods are realized in the experiment, and the transient state-RFF-1 refers to a transient state RFF extracted by wavelet transformation; transient-RFF-2 refers to a transient RFF composed of transient signal time domain waveforms; Steady-RFF refers to a steady-state RFF based on a k-NN classifier and spectral features. As shown in fig. 9, compared with the three conventional methods, the polarized fingerprint-based device identification has better identification accuracy, especially in the case of low signal-to-noise ratio.

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Although the present invention has been described with reference to the above embodiments, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims

1. A mobile communication terminal identification method based on polarized fingerprints is characterized by comprising the following steps:

a polarized fingerprint mathematical model construction step: constructing a mathematical model of the polarization fingerprint based on the polarization states of the circularly polarized patch single radiating element antenna and the multi-radiating element antenna, wherein the mathematical model provides a relation for solving the polarization fingerprint through signal frequency, an antenna hardware parameter vector and a hardware defect vector;

2. The method according to claim 1, wherein two degenerate modes with orthogonal polarization states obtained simultaneously when the single-element antenna is fed through a feed point are horizontal mode E _H And vertical mode E _V Then, the polarization state of the single radiating element antenna is expressed as:

wherein, | E _H /E _V I is the modulus of the polarization state p, arg E _H /E _V Is E _H /E _V I.e. the phase angle of the polarization state p; .

3. The method of claim 1, wherein if the multi-radiating-element antenna is a two-radiating-element antenna, it has 3 resistors R ₁ 、R ₂ 、R ₃ Then, the polarization state of the two radiating element antennas is expressed as:

4. The method of claim 1, wherein the mathematical model of the polarization fingerprint is represented as:

is a vector of parameters of the hardware that,

is a hardware defect vector.

5. The method of claim 1, wherein the minimum frequency spacing of the signals is calculated by: firstly, determining the minimum value and the maximum value of the signal frequency of an antenna; then receiving the horizontal component and the vertical component of the signal in a continuous period of time; then, sampling the horizontal component and the vertical component to obtain two finite length sequences under discrete time, wherein the sequence length is N; the minimum frequency spacing is equal to the ratio of the difference between the maximum and minimum of the signal frequencies to N-1.

6. The method of claim 5, wherein the polarization phase at the sampling point is obtained by: performing discrete Fourier transform on the two finite length sequences to obtain two corresponding frequency spectrums; the polarization phase at the sampling point is determined from the two spectra.

7. The method of claim 5, wherein the expression for calculating the frequency of the sampling points from the minimum frequency interval is:

f _k ＝f _L +(k-1)Δf；

8. The method of claim 1, 6 or 7, wherein the polarized fingerprints of the respective frequency components are extracted by: representing the polarization state of the signal at the frequency as a repolarization ratio according to the polarization phase and the frequency at the sampling point; and calculating the polarized fingerprint formed by the polarization states of the frequency components according to the mathematical model of the polarized fingerprint, wherein the frequency components are sampled at the minimum frequency interval.

9. The method of claim 1, wherein the population and individual features of the polarized fingerprint are obtained by: firstly, obtaining a model vector of a mobile communication terminal, an individual vector of the mobile communication terminal and a polarization fingerprint set corresponding to the individual vector of the mobile communication terminal; then, obtaining the group characteristics of the polarized fingerprints by calculating the average polarized fingerprints of the polarized fingerprint set; finally, the group characteristics are subtracted from the polarization fingerprints to extract the individual characteristics.

10. The method of claim 1, wherein in the mobile communication terminal identification step, thresholds for group feature and individual feature decision are set, and a difference between two group features or two individual features is represented by euclidean geometrical distance; when polarization fingerprint comparison is carried out, the model or the equipment of the mobile communication terminal is determined through the magnitude relation between the Euclidean geometric distance between two group characteristics or two individual characteristics and a threshold value, if the Euclidean geometric distance is smaller than the corresponding threshold value, the mobile communication terminal is judged to belong to the known model or the known equipment, otherwise, the mobile communication terminal does not belong to the known model or the known equipment.