CN115510924B - Radio frequency fingerprint identification method based on improved variational modal decomposition - Google Patents

Radio frequency fingerprint identification method based on improved variational modal decomposition Download PDF

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CN115510924B
CN115510924B CN202211460835.6A CN202211460835A CN115510924B CN 115510924 B CN115510924 B CN 115510924B CN 202211460835 A CN202211460835 A CN 202211460835A CN 115510924 B CN115510924 B CN 115510924B
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CN115510924A (en
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王鹏
张琰祥
文璐
惠鏸
邓彬
薛东
叶安君
陈礼云
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China Railway First Survey and Design Institute Group Ltd
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Abstract

The invention relates to a radio frequency fingerprint identification method based on improved variational modal decomposition. The existing variational modal decomposition method is used for identifying the problems of modal aliasing and over-decomposition of the radio frequency fingerprint of the signal. The method comprises the steps of acquiring signals of wireless communication equipment; initializing a decomposition mode number and a punishment factor, and setting a confusion threshold and an energy ratio threshold; carrying out variation modal decomposition on the signal to obtain the maximum value of correlation coefficients of each mode and the minimum value of energy ratio of each mode; obtaining qualified decomposition mode number and qualified punishment factors in an iteration mode; calculating to obtain a reconstructed signal as a radio frequency fingerprint of the signal; and inputting the reconstructed signal into a long-term and short-term memory network for classification and identification. The method judges whether modal aliasing occurs in the decomposition process by using the maximum value of the correlation coefficient of each mode after decomposition, judges whether the decomposition process has an over-decomposition problem by using the minimum value of the energy ratio of each mode, and can effectively extract the radio frequency fingerprint of the equipment.

Description

Radio frequency fingerprint identification method based on improved variational modal decomposition
Technical Field
The invention relates to the technical field of radio frequency fingerprint identification, in particular to a radio frequency fingerprint identification method based on improved variational modal decomposition.
Background
Due to the openness of wireless communication networks, security issues are of paramount importance. To secure wireless communications, access security of the wireless communication device is first guaranteed. The existing wireless communication equipment identity authentication method usually adopts an MAC/IP address and key authentication mode, and is easy to be tampered or attacked by illegal users. The radio frequency fingerprint comes from hardware difference inside the wireless equipment, has uniqueness and is difficult to tamper, and can be used as a basis for identifying different wireless equipment. Therefore, the method for identifying the identity of the equipment through the radio frequency fingerprint of the wireless transmitting equipment is a valuable security authentication technology.
In the field of radio frequency fingerprint identification, the radio frequency fingerprint capable of representing the essential characteristics of equipment is effectively extracted, and the key effect is played on improving the identification accuracy of wireless communication equipment. The variation modal decomposition method can adaptively decompose the signal into narrow-band components with different center frequencies, so as to obtain the fingerprint characteristics of the equipment. However, this method requires the prior selection of the decomposition parameter, decomposition mode number
Figure 973551DEST_PATH_IMAGE001
And a penalty factor pick>
Figure 931668DEST_PATH_IMAGE002
When the decomposition parameter setting is not accurate, the problems of modal aliasing and over-decomposition and the like of the variational modal decomposition can be caused, so that the identification accuracy is reduced.
Disclosure of Invention
The invention aims to provide a radio frequency fingerprint identification method based on improved variational modal decomposition, which solves the problems of modal aliasing and over-decomposition possibly occurring in the variational modal decomposition and effectively improves the identification accuracy of equipment.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a radio frequency fingerprint identification method based on improved variational modal decomposition comprises the following steps:
acquiring a signal of a wireless communication device;
initializing decomposition mode number and punishment factors, and setting a confusion threshold and an energy ratio threshold;
taking the initialized decomposition modal number and the initialized penalty factor as decomposition parameters, and carrying out variation modal decomposition on the signal to obtain the maximum value of correlation coefficients of each mode and the minimum value of energy proportion of each mode;
obtaining qualified decomposition mode number and qualified punishment factor through an iteration mode;
calculating to obtain a reconstructed signal as a radio frequency fingerprint of the signal according to the qualified decomposition mode number and the qualified punishment factor;
and inputting the reconstructed signal into a long-term and short-term memory network for classification and identification.
Further, with the initialized decomposition mode number and the initialized penalty factor as decomposition parameters, performing variational mode decomposition on the signal, including:
the signal of the wireless communication device is
Figure 361381DEST_PATH_IMAGE003
Initialized resolution mode number ^>
Figure 351202DEST_PATH_IMAGE004
Initialized penalty factor of &>
Figure 476678DEST_PATH_IMAGE005
；
By initialized decomposed mode numbers
Figure 450319DEST_PATH_IMAGE006
And an initialized penalty factor +>
Figure 840980DEST_PATH_IMAGE007
For resolving the parameter, the signal is asserted>
Figure 530981DEST_PATH_IMAGE008
Make and/or>
Figure 637477DEST_PATH_IMAGE009
Order-variation modeDecomposed to get->
Figure 160731DEST_PATH_IMAGE010
An intrinsic mode function->
Figure 10875DEST_PATH_IMAGE011
，/>
Figure 521096DEST_PATH_IMAGE012
。
Further, obtaining a maximum value of the correlation coefficient of each mode includes:
will be provided with
Figure 126390DEST_PATH_IMAGE010
An intrinsic mode function->
Figure 730415DEST_PATH_IMAGE013
Respectively discretized to obtain->
Figure 56355DEST_PATH_IMAGE010
A discretized eigenmode function->
Figure 206101DEST_PATH_IMAGE014
；/>
Calculating any pair of discretized eigenmode functions
Figure 372509DEST_PATH_IMAGE015
And/or>
Figure 935602DEST_PATH_IMAGE016
Is greater than or equal to>
Figure 48920DEST_PATH_IMAGE017
Defining a maximum value for each modal correlation coefficient as->
Figure 332134DEST_PATH_IMAGE018
，/>
Figure 269DEST_PATH_IMAGE019
，/>
Figure 329619DEST_PATH_IMAGE020
，/>
Figure 246628DEST_PATH_IMAGE021
；
Figure 703456DEST_PATH_IMAGE023
Wherein:
Figure 431240DEST_PATH_IMAGE024
，/>
Figure 44624DEST_PATH_IMAGE025
respectively representing a discretized eigenmode function->
Figure 296483DEST_PATH_IMAGE026
And/or>
Figure 72065DEST_PATH_IMAGE027
The two variables correspond to the number of pairs of cooperation numbers and pairs of non-cooperation numbers in the element data pairs.
Further, obtaining the minimum value of the energy ratio of each mode comprises:
computing eigenmode functions
Figure 344653DEST_PATH_IMAGE028
Is based on the energy->
Figure 789540DEST_PATH_IMAGE029
And pick up the signal>
Figure 192227DEST_PATH_IMAGE030
Is expressed as
Figure 694753DEST_PATH_IMAGE031
The energy of each eigenmode function/>
Figure 498761DEST_PATH_IMAGE032
In the total energy of the signal->
Figure 70425DEST_PATH_IMAGE033
The ratio of (b) can be expressed as:
Figure 745645DEST_PATH_IMAGE034
defining the minimum value of the energy ratio of each mode as
Figure 978043DEST_PATH_IMAGE035
。
Further, obtaining qualified decomposition mode number and qualified punishment factor by an iteration mode, including:
setting a confusion threshold as
Figure 530116DEST_PATH_IMAGE036
Setting an energy ratio threshold as->
Figure 744670DEST_PATH_IMAGE037
；
If it is not
Figure 955072DEST_PATH_IMAGE038
And->
Figure 776397DEST_PATH_IMAGE039
If the mode aliasing phenomenon occurs but the over-decomposition problem does not exist, increasing the number of decomposition modes and returning; otherwise, carrying out the next step;
if it is not
Figure 561689DEST_PATH_IMAGE040
And->
Figure 468465DEST_PATH_IMAGE041
Adding penalty if modal aliasing occurs and there is over-resolution problemFactor and return; otherwise, carrying out the next step;
if it is not
Figure 751066DEST_PATH_IMAGE042
And->
Figure 551532DEST_PATH_IMAGE043
If the mode aliasing phenomenon does not occur and the excessive decomposition problem exists, reducing the number of the decomposition modes and returning, otherwise, carrying out the next step;
if it is used
Figure 117511DEST_PATH_IMAGE044
And->
Figure 370638DEST_PATH_IMAGE045
The judgment result shows that no mode aliasing phenomenon occurs and no over-decomposition problem exists, the decomposition result meets the requirement, and the qualified decomposition mode number is output>
Figure 925772DEST_PATH_IMAGE046
And a qualifying penalty factor->
Figure 970957DEST_PATH_IMAGE047
。
Further, according to the qualified decomposition mode number and the qualified penalty factor, a reconstructed signal is calculated and obtained to serve as a radio frequency fingerprint of the signal, and the method comprises the following steps:
according to qualified decomposition mode number
Figure 317625DEST_PATH_IMAGE048
And a qualifying penalty factor>
Figure 58048DEST_PATH_IMAGE049
Calculating a reconstructed signal->
Figure 479189DEST_PATH_IMAGE050
The process is as follows:
Figure 582143DEST_PATH_IMAGE051
。
compared with the prior art, the invention has the following beneficial effects:
the method judges whether modal aliasing occurs between the modes in the decomposition process by using the correlation coefficient between the modes after decomposition, judges whether the over-decomposition problem occurs in the decomposition process by using the ratio of energy of each mode in the total energy of the signal, and can adaptively extract qualified decomposition parameters aiming at the received radio frequency signal
Figure 834133DEST_PATH_IMAGE052
And &>
Figure 452065DEST_PATH_IMAGE053
Therefore, the problems of mode aliasing and over-decomposition which possibly occur in the variation mode decomposition are avoided, and the radio frequency fingerprint of the equipment can be effectively extracted, so that the identification accuracy of the wireless transmitting equipment is improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings of the embodiments can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a graph of the spectrum of each eigenmode function of the method of the present invention.
Fig. 3 is an exploded waveform diagram of the method of the present invention. In the figure, a) is a simulation signal time domain waveform diagram, and b) is a simulation signal frequency domain waveform diagram.
FIG. 4 is a graph of recognition accuracy for the method of the present invention.
Detailed Description
To facilitate an understanding of the invention, the invention will now be described more fully with reference to the accompanying drawings. Preferred embodiments of the present invention are shown in the drawings. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.
It should be noted that like reference numerals and letters refer to like items and, thus, once an item is defined in one embodiment, it need not be further defined and explained in subsequent embodiments. Furthermore, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
It should also be noted that although a method description refers to a sequence of steps, in some cases it may be performed in a different order than here and should not be construed as a limitation on the sequence of steps.
The invention provides a radio frequency fingerprint identification method based on improved variational modal decomposition, which comprises the steps of initializing parameters, calculating correlation coefficients and energy ratios, selecting qualified decomposition parameters, calculating reconstruction signals and classifying and identifying as shown in figure 1. The method specifically comprises the following steps:
s1: acquiring a signal from a wireless communication device
Figure 602862DEST_PATH_IMAGE054
。
S2: and initializing decomposition mode number and penalty factor, and setting a confusion threshold and an energy ratio threshold.
Number of decomposition modes initialized to
Figure 107793DEST_PATH_IMAGE055
Initialized penalty factor of &>
Figure 593001DEST_PATH_IMAGE056
Setting a confusion threshold as>
Figure 760546DEST_PATH_IMAGE057
Setting an energy ratio threshold as>
Figure 333609DEST_PATH_IMAGE058
。
S3: and performing variation modal decomposition on the signal by taking the initialized decomposition modal number and the initialized penalty factor as decomposition parameters to obtain the maximum value of correlation coefficients of each mode and the minimum value of energy proportion of each mode. The method specifically comprises the following steps:
s301: by initialized decomposed mode numbers
Figure 804298DEST_PATH_IMAGE059
And an initialized penalty factor +>
Figure 663670DEST_PATH_IMAGE060
For resolving the parameter, the signal is asserted>
Figure 459457DEST_PATH_IMAGE061
Make a->
Figure 760512DEST_PATH_IMAGE055
Staged modal decomposition to get >>
Figure 833511DEST_PATH_IMAGE055
Characteristic mode function>
Figure 519576DEST_PATH_IMAGE062
，/>
Figure 209183DEST_PATH_IMAGE063
。
Intrinsic mode function
Figure 454875DEST_PATH_IMAGE064
Is concerned with a time variable>
Figure 303751DEST_PATH_IMAGE065
As a function of (c). Penalty factor pick>
Figure 36084DEST_PATH_IMAGE066
The bandwidth of the frequency domain of each eigenmode function is controlled by a parameter, and the bandwidth of the frequency domain of the eigenmode function can be changed.
S302: and calculating the maximum value of the correlation coefficient of each mode. The method specifically comprises the following steps:
the method selects Kendall correlation coefficient as the basis for measuring the correlation between two variables.
S30201: will be provided with
Figure 88354DEST_PATH_IMAGE067
An intrinsic mode function->
Figure 742382DEST_PATH_IMAGE068
Respectively discretizing to obtain->
Figure 55551DEST_PATH_IMAGE069
A discretized post-eigenmode function
Figure 834151DEST_PATH_IMAGE070
；
S30202: calculating any pair of discretized eigenmode functions
Figure 950881DEST_PATH_IMAGE070
And/or>
Figure 866272DEST_PATH_IMAGE071
Is greater than or equal to>
Figure 174893DEST_PATH_IMAGE072
Kendall correlation coefficient, defines the maximum value of each modal correlation coefficient as ≥ ->
Figure 514608DEST_PATH_IMAGE073
，/>
Figure 525158DEST_PATH_IMAGE074
，
Figure 178993DEST_PATH_IMAGE075
，/>
Figure 453373DEST_PATH_IMAGE076
；
Figure 573776DEST_PATH_IMAGE077
Wherein:
Figure 743726DEST_PATH_IMAGE078
，/>
Figure 935673DEST_PATH_IMAGE079
respectively representing a discretized eigenmode function>
Figure 720352DEST_PATH_IMAGE080
And/or>
Figure 277235DEST_PATH_IMAGE081
The two variables correspond to the number of pairs of cooperation numbers and pairs of non-cooperation numbers in the element data pairs.
Discretizing any pair of variables of the eigenmode function
Figure 137744DEST_PATH_IMAGE082
，/>
Figure 921330DEST_PATH_IMAGE083
Constitutes a data pair->
Figure 59050DEST_PATH_IMAGE084
，/>
Figure 426315DEST_PATH_IMAGE085
，…，/>
Figure 508541DEST_PATH_IMAGE086
. If +>
Figure 979974DEST_PATH_IMAGE087
，/>
Figure 365343DEST_PATH_IMAGE088
，
Figure 998450DEST_PATH_IMAGE089
Indicates that the data pair->
Figure 817239DEST_PATH_IMAGE090
And/or>
Figure 154679DEST_PATH_IMAGE091
The variation directions are consistent, and the variation directions are called as cooperative number pairs. Otherwise, the direction of change is opposite, and the two are called as an uncoordinated number pair.
S303: and calculating the minimum value of the energy ratio of each mode. The method specifically comprises the following steps:
computing eigenmode functions
Figure 50348DEST_PATH_IMAGE092
Is based on the energy->
Figure 369202DEST_PATH_IMAGE093
And combine the signal>
Figure 691599DEST_PATH_IMAGE094
Is expressed as
Figure 632398DEST_PATH_IMAGE095
Then the energy of the respective eigenmode function->
Figure 599217DEST_PATH_IMAGE096
In the total energy of the signal->
Figure 698760DEST_PATH_IMAGE097
The ratio of (b) can be expressed as:
Figure 898666DEST_PATH_IMAGE098
defining the minimum value of each modal energy ratio as
Figure 982770DEST_PATH_IMAGE099
。
S4: and obtaining qualified decomposition mode number and qualified punishment factor through an iteration mode. The method specifically comprises the following steps:
if it is not
Figure 538517DEST_PATH_IMAGE100
And->
Figure 651704DEST_PATH_IMAGE101
If there is no over-resolution problem but mode aliasing is present, the number of resolution modes is increased and can be expressed as ^ greater than or equal to>
Figure 420464DEST_PATH_IMAGE102
And returning to S3; otherwise, S4 is carried out;
if it is not
Figure 841081DEST_PATH_IMAGE103
And->
Figure 156394DEST_PATH_IMAGE104
If there is a modal aliasing and over-resolution problem, a penalty factor is added which can be expressed as->
Figure 410789DEST_PATH_IMAGE105
And returning to S3; otherwise, S4 is carried out; wherein it is present>
Figure 54129DEST_PATH_IMAGE106
Is based on each time>
Figure 874842DEST_PATH_IMAGE107
In an increasing amount, i.e. [ alpha ] ->
Figure 670759DEST_PATH_IMAGE108
Each step size of (a); />
If it is not
Figure 814165DEST_PATH_IMAGE109
And->
Figure 679221DEST_PATH_IMAGE110
If there is no modal aliasing and there is over-resolution, the number of resolution modes is reduced and can be expressed as->
Figure 300696DEST_PATH_IMAGE111
And returning to S3; otherwise, S4 is carried out;
if it is not
Figure 406579DEST_PATH_IMAGE112
And->
Figure 704574DEST_PATH_IMAGE113
The judgment result is in accordance with the requirement, the decomposition mode number and the penalty factor are qualified at the moment, and the output qualified decomposition mode number is recorded as ^ greater than or equal to>
Figure 73239DEST_PATH_IMAGE114
And outputting a qualified penalty factor to be recorded as->
Figure 755194DEST_PATH_IMAGE115
。
To sum up, first, it is determined whether modal aliasing occurs
Figure 260125DEST_PATH_IMAGE116
And without over-resolving the problem>
Figure 745333DEST_PATH_IMAGE117
At this time, the number of resolution modes should be increased. When/is>
Figure 444036DEST_PATH_IMAGE118
And->
Figure 548259DEST_PATH_IMAGE119
When this is the case, a penalty factor needs to be added. When the two points are satisfied, the decomposition mode number and the penalty factor are both large enough, and then the judgment is further made if the judgment is present>
Figure 300838DEST_PATH_IMAGE120
And->
Figure 566735DEST_PATH_IMAGE121
The number of decomposition modes needs to be reduced. The above three points are all satisfied and explained>
Figure 221576DEST_PATH_IMAGE122
And->
Figure 912845DEST_PATH_IMAGE123
And considering that the decomposition result meets the requirement, and outputting a decomposition mode number and a penalty factor.
S5: and calculating to obtain a reconstructed signal as a radio frequency fingerprint of the signal according to the qualified decomposition mode number and the qualified punishment factor. The method comprises the following steps:
according to qualified decomposition mode number
Figure 251422DEST_PATH_IMAGE124
And a qualifying penalty factor>
Figure 688220DEST_PATH_IMAGE125
Calculating a reconstructed signal->
Figure 908985DEST_PATH_IMAGE126
The process is as follows:
Figure 466262DEST_PATH_IMAGE127
。
s6: and inputting the reconstructed signal into a long-term and short-term memory network for classification and identification.
The method judges whether modal aliasing occurs in the decomposition process by using the maximum value of the correlation coefficient of each mode after decomposition, judges whether the decomposition process has the over-decomposition problem by using the minimum value of the energy ratio of each mode, and determines the qualified modal decomposition number and the penalty factor in an iteration mode. The method can adaptively acquire qualified decomposition parameters aiming at different equipment, can effectively avoid the influence of modal aliasing and over-decomposition problems on the extraction of the radio frequency fingerprint, has good adaptivity and noise robustness, and can effectively improve the identification accuracy of the equipment.
Example (b):
for the signal
Figure 65871DEST_PATH_IMAGE128
Performing the improved variational modal decomposition provided by the present invention, assuming that the signal has a magnitude of ^ in>
Figure 798203DEST_PATH_IMAGE129
At a frequency of
Figure 771844DEST_PATH_IMAGE130
，/>
Figure 959243DEST_PATH_IMAGE131
The four different frequency components are constituted:
Figure 397047DEST_PATH_IMAGE132
wherein, make
Figure 111667DEST_PATH_IMAGE133
；/>
Figure 900500DEST_PATH_IMAGE134
，/>
Figure 422748DEST_PATH_IMAGE135
，/>
Figure 590424DEST_PATH_IMAGE136
，/>
Figure 916757DEST_PATH_IMAGE137
；/>
Figure 943619DEST_PATH_IMAGE138
For additive white Gaussian noise, i.e. the signal to be decomposed is contaminated with noise, in a subsequent simulation a &>
Figure 394192DEST_PATH_IMAGE139
。
The variation modal decomposition can separate the signals
Figure 213112DEST_PATH_IMAGE140
Adaptively decomposed into a plurality of narrowband signals of different center frequencies. The decomposition process can be expressed as: />
Figure 333515DEST_PATH_IMAGE141
In the formula (I), the compound is shown in the specification,
Figure 224504DEST_PATH_IMAGE142
and &>
Figure 88555DEST_PATH_IMAGE143
Figure 230823DEST_PATH_IMAGE144
Respectively represent a signal->
Figure 522127DEST_PATH_IMAGE145
In a first or second section>
Figure 493887DEST_PATH_IMAGE146
The eigenmode functions and their corresponding center frequencies.
Application bookThe method finally obtains a signal
Figure 551842DEST_PATH_IMAGE147
The variation mode decomposition parameter is->
Figure 955142DEST_PATH_IMAGE148
，/>
Figure 985722DEST_PATH_IMAGE149
The signal ≥ as can be seen from the spectrogram of the eigenmode functions, as can be seen in FIG. 2>
Figure 474472DEST_PATH_IMAGE150
After decomposition, modal aliasing and over-decomposition problems do not exist among the modes. The time domain waveform and the frequency spectrum waveform of each mode after decomposition by the method of the invention are shown in figure 3. The 4 eigenmode functions and ^ can be seen from FIG. 3 after decomposition>
Figure 601697DEST_PATH_IMAGE151
The original components are consistent, and the decomposition result is accurate and reliable. Compared with the original signal, the reconstructed signal formed by superposition not only has the signal characteristics, namely the complete preservation of the radio frequency fingerprint, but also has the noise suppressed to a certain degree, which shows that the invention has stronger radio frequency fingerprint extraction capability.
In order to illustrate the performance of the improved variation modal decomposition method in the actual equipment identification, the improved variation modal decomposition is carried out on the actually acquired signals of 6 different WiFi equipment in total. An experimental data set was created using the first 256I/Q signals of the signal, with 200 frames of data each, the data set divided into a 70% training set, a 10% validation set, and a 20% test set. And taking the reconstructed signal formed by each mode as the radio frequency fingerprint of the equipment, and carrying out classification and identification through a long-term and short-term memory network.
In order to compare the performances of different methods, the existing continuous variation modal decomposition method and the original variation modal decomposition method are simulated. Parameters in original variational modal decomposition method
Figure 797186DEST_PATH_IMAGE152
And &>
Figure 882822DEST_PATH_IMAGE153
Are respectively set as->
Figure 249082DEST_PATH_IMAGE154
，/>
Figure 993047DEST_PATH_IMAGE155
And
Figure 216611DEST_PATH_IMAGE156
，/>
Figure 286198DEST_PATH_IMAGE157
the experimental results are shown in fig. 4. As can be seen from fig. 4, the recognition accuracy of the device is significantly higher than that of the continuous variational modal decomposition method and the original variational modal decomposition method by applying the method of the present invention, and particularly, the present invention exhibits stronger noise robustness under a low signal-to-noise ratio. The identification accuracy difference of original variational modal decomposition under different decomposition parameters is obvious, the selection of the explanation parameters has great influence on the radio frequency fingerprint identification effect, and the original variational modal decomposition parameters are fixed and are difficult to flexibly adjust the combination value according to the characteristics of different devices>
Figure 795546DEST_PATH_IMAGE158
And &>
Figure 64241DEST_PATH_IMAGE153
The value of (c). The improved variational modal decomposition method provided by the invention can adaptively select different decomposition parameters according to different devices, thereby having stronger robustness and higher identification accuracy.
The present invention has been described in terms of specific examples, which are provided to aid understanding of the invention and are not intended to be limiting. For a person skilled in the art to which the invention pertains, several simple deductions, modifications or substitutions may be made according to the idea of the invention.

Claims (5)

1. The radio frequency fingerprint identification method based on the improved variational modal decomposition is characterized in that:
the method comprises the following steps:
acquiring a signal of a wireless communication device;
initializing decomposition mode number and punishment factors, and setting a confusion threshold and an energy ratio threshold;
taking the initialized decomposition modal number and the initialized penalty factor as decomposition parameters, and carrying out variation modal decomposition on the signal to obtain the maximum value of each modal correlation coefficient and the minimum value of each modal energy ratio;
obtaining qualified decomposition mode number and qualified punishment factor by an iteration mode, comprising the following steps:
setting a confusion threshold as
Figure DEST_PATH_IMAGE002
Setting an energy ratio threshold as->
Figure DEST_PATH_IMAGE004
；
If it is not
Figure DEST_PATH_IMAGE006
And->
Figure DEST_PATH_IMAGE008
If the mode aliasing phenomenon occurs but the over-decomposition problem does not exist, increasing the number of the decomposition modes and returning; otherwise, carrying out the next step;
if it is not
Figure DEST_PATH_IMAGE010
And->
Figure DEST_PATH_IMAGE012
If the modal aliasing phenomenon occurs and the problem of over-resolution exists, adding a penalty factor and returning; otherwise, carrying out the next step;
if it is used
Figure DEST_PATH_IMAGE014
And->
Figure DEST_PATH_IMAGE016
If the mode aliasing phenomenon does not occur and the excessive decomposition problem exists, reducing the number of the decomposition modes and returning, otherwise, carrying out the next step;
if it is not
Figure DEST_PATH_IMAGE018
And->
Figure DEST_PATH_IMAGE020
The judgment result shows that no mode aliasing phenomenon occurs and no over-decomposition problem exists, the decomposition result meets the requirement, and the qualified decomposition mode number is output>
Figure DEST_PATH_IMAGE022
And a qualifying penalty factor>
Figure DEST_PATH_IMAGE024
；
Calculating to obtain a reconstructed signal as a radio frequency fingerprint of the signal according to the qualified decomposition mode number and the qualified punishment factor;
and inputting the reconstructed signal into a long-term and short-term memory network for classification and identification.
2. The method of claim 1, wherein:
taking the initialized decomposition modal number and the initialized penalty factor as decomposition parameters, and carrying out variation modal decomposition on the signal, wherein the method comprises the following steps:
the signal of the wireless communication device is
Figure DEST_PATH_IMAGE026
Initialized decomposition modality number &>
Figure DEST_PATH_IMAGE028
At the beginningA penalizing factor based on ^ n>
Figure DEST_PATH_IMAGE030
；
By initialized decomposed mode numbers
Figure DEST_PATH_IMAGE032
And an initialized penalty factor +>
Figure DEST_PATH_IMAGE034
For resolving parameters, signals are combined>
Figure DEST_PATH_IMAGE036
Make and/or>
Figure DEST_PATH_IMAGE038
The order variation mode is decomposed to obtain->
Figure DEST_PATH_IMAGE040
An intrinsic mode function->
Figure DEST_PATH_IMAGE042
，/>
Figure DEST_PATH_IMAGE044
。
3. The method of claim 2, wherein:
obtaining the maximum value of the correlation coefficient of each mode, including:
will be provided with
Figure DEST_PATH_IMAGE046
An intrinsic mode function->
Figure DEST_PATH_IMAGE048
Respectively discretizing to obtain->
Figure DEST_PATH_IMAGE050
A discretized post eigenmode function>
Figure DEST_PATH_IMAGE052
；
Calculating any pair of discretized eigenmode functions
Figure DEST_PATH_IMAGE054
And &>
Figure DEST_PATH_IMAGE056
Coefficient of correlation between>
Figure DEST_PATH_IMAGE058
Defining the maximum value of the correlation coefficient of each mode as ^ or ^>
Figure DEST_PATH_IMAGE060
，/>
Figure DEST_PATH_IMAGE062
，/>
Figure DEST_PATH_IMAGE064
，/>
Figure DEST_PATH_IMAGE066
；
Figure DEST_PATH_IMAGE068
Wherein:
Figure DEST_PATH_IMAGE070
，/>
Figure DEST_PATH_IMAGE072
respectively representing a discretized eigenmode function>
Figure DEST_PATH_IMAGE074
And &>
Figure DEST_PATH_IMAGE076
The two variables correspond to the number of pairs of cooperation numbers and pairs of non-cooperation numbers in the element data pairs.
4. The method of claim 3, wherein:
obtaining the minimum value of the energy ratio of each mode, including:
computing eigenmode functions
Figure DEST_PATH_IMAGE078
Is based on the energy->
Figure DEST_PATH_IMAGE080
And combine the signal>
Figure DEST_PATH_IMAGE082
Is expressed as total energy->
Figure DEST_PATH_IMAGE084
Then the energy of the respective eigenmode function->
Figure DEST_PATH_IMAGE086
In the total energy of the signal->
Figure DEST_PATH_IMAGE088
The ratio of (b) can be expressed as:
Figure DEST_PATH_IMAGE090
defining the minimum value of the energy ratio of each mode as
Figure DEST_PATH_IMAGE092
。
5. The method of claim 4, wherein:
according to the qualified decomposition mode number and the qualified punishment factor, a reconstruction signal is obtained through calculation and is used as a radio frequency fingerprint of the signal, and the method comprises the following steps:
according to qualified decomposition mode number
Figure DEST_PATH_IMAGE093
And a qualifying penalty factor>
Figure DEST_PATH_IMAGE094
Calculating a reconstruction signal>
Figure DEST_PATH_IMAGE096
The process is as follows:
Figure DEST_PATH_IMAGE098
。/>
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