CN117768886A - Physical layer authentication method based on dynamic super-surface antenna multipath estimation - Google Patents
Physical layer authentication method based on dynamic super-surface antenna multipath estimation Download PDFInfo
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Abstract
The invention provides a physical layer authentication method based on dynamic subsurface antenna multipath estimation, which comprises the following steps: firstly, constructing a communication system model, wherein the communication system model comprises a base station Alice and a user Bob, and a plurality of barriers exist between Alice and Bob; wherein Alice adopts a super-surface antenna, bob adopts a common omni-directional antenna, and a signal sent by Bob reaches the super-surface antenna through a multipath channel; secondly, the super-surface antenna rapidly changes in a symbol period, and a receiving direction diagram is changed to obtain sampling data; performing DOA estimation on the sampled data by adopting an atomic norm minimization algorithm to obtain corresponding multipath channel information; and finally, performing physical layer authentication according to the obtained multipath channel information, and judging whether the received signal is legal or not. The invention realizes high-freedom signal receiving at the front end of the radio frequency by utilizing the super-surface antenna, and can avoid multipath channel information loss caused by multipath superposition by rapidly reconstructing the antenna pattern and constructing a high-order projection space.
Description
Technical Field
The invention relates to the technical field of communication safety, in particular to a physical layer authentication method based on dynamic super-surface antenna multipath estimation, which can accurately estimate multipath channel information through the characteristic of quick change of a dynamic super-surface antenna, and carries out physical layer authentication according to the estimated multipath channel information to judge whether a received signal is legal or not, if so, the received signal is processed, otherwise, the received signal is directly discarded.
Background
The wireless channel is an important component of the wireless communication link, and communication performance can be effectively improved only if the signal processing process is matched with the channel characteristics. In the existing MIMO system, channel detection is realized by sending reference signals such as pilot frequency, and channel estimation is completed by processing the pilot frequency signals at a receiving end, and because the channel estimation process is realized by adopting a digital processing means at a radio frequency rear end, the observed channel is already superposition of multipath, and multipath information loss is necessarily caused in the superposition process. Traditional wireless communications are limited by the lack of "fine" awareness of "differentiated" wireless environments, and can only passively adapt to wireless environments. Conventional antennas are fixed, static, and "fool" in observing the electromagnetic environment. A single antenna cannot distinguish between multipath and more so between signal and interference. The traditional array is isomorphic, the aliased signals are distinguished based on array elements, and information loss cannot be recovered.
The antenna/array pattern reflects the directional reception capability of the antenna for signals in different directions, and in the traditional antenna/array design, the amplitude pattern of the antenna is mainly focused, so that maximum energy reception at a specific angle is realized, and side lobe gain suppression is realized as much as possible in other directions. However, due to the existence of openness of electromagnetic wave propagation, the signal will form multipath in the air, and multipath parameters (angle, complex gain, etc.) will change with natural environment, so that the conventional electromagnetic performance solidification structure antenna/array cannot realize the matching reception of multipath signals on the interface, especially in the extremely simple single antenna scene, the conventional antenna pattern has fixed pointing angle, and cannot separate multipath.
Disclosure of Invention
Aiming at the technical problems that the prior art cannot accurately estimate the multipath channel and causes information loss, the invention provides a physical layer authentication method based on the multipath estimation of a dynamic super-surface antenna, and the multipath channel estimated by the dynamic super-surface antenna is a separable multipath channel among sub-channels due to the characteristic that the dynamic super-surface antenna can rapidly change in one symbol period; because the dynamic super-surface antenna can change the self-direction diagram, when the physical layer authentication is carried out based on the channels, the sub-channels are independently received, so that the obtained effect is better.
The technical scheme of the invention is realized as follows:
a physical layer authentication method based on dynamic super-surface antenna multipath estimation comprises the following steps:
step one: constructing a communication system model, wherein the communication system model comprises a base station Alice and a user Bob, and various barriers exist between the base station Alice and the user Bob; the base station Alice adopts a super-surface antenna, the user Bob adopts a common omni-directional antenna, and a signal sent by the user Bob reaches the super-surface antenna through a multipath channel;
step two: the super-surface antenna rapidly changes in a symbol period, and changes a receiving direction diagram to obtain sampling data; performing DOA estimation on the sampled data by adopting an atomic norm minimization algorithm to obtain corresponding multipath channel information;
step three: and carrying out physical layer authentication according to the obtained multipath channel information, judging whether the received signal is legal or not, if so, carrying out processing, otherwise, directly discarding.
The specific transmission method for the signal sent by the user Bob to reach the super-surface antenna through the multipath channel comprises the following steps:
user Bob sends K pilot frequency to make channel estimation, in every pilot frequency symbol period, inputs signalNumber s k The super-surface antenna pattern is changed M times, and then in the duration of the kth pilot symbol, the received signal expression is:
wherein,pilot signal transmitted for Bob, +.>Representing the channel between base station Alice and user Bob, n k ＝[n k1 ,...,n ki ,...,n km ] T Represents noise generated by M times of agility of the super-surface antenna, n ki ～N(0,σ 2 )；Representing multipath channel information pre-stored by the super-surface antenna, wherein L is the number of multipath channels; />Array popularity matrix representing uniform linear array, a (θ) = [ a (θ) 1 ),...,a(θ L )]，/>d represents the spacing between the units of the super-surface antenna, lambda represents the wavelength of the received signal, theta represents the angle of the signal reaching the super-surface antenna, and N represents the number of the units of the super-surface antenna; />Representing t m Super-surface antenna state parameter v during time sampling m ＝[v m1 ,...v mn ,v mN ] T ，/>A mn Representation superrepresentationWeighting coefficient of each element in the surface antenna to the amplitude of the incident signal, Φ mn Representing the weighting coefficients of each element in the subsurface antenna to the phase of the incident signal.
In the second step, the method for obtaining multipath channel information includes:
at the receiving end, LS channel estimation algorithm is utilized to obtain
Wherein Y= [ Y ] 1 ,...,y K ]，Represents data obtained by sampling K pilots respectively M times, s= [ s ] 1 ,...,s K ] T Representing K pilot sequences s * Representing taking the conjugate of s; />Representing channel information estimated using an LS channel estimation algorithm;
performing multipath channel parameter estimation by using an atomic norm minimization algorithm, and converting the formula (2) into:
wherein,representing residual noise; v is determined by the state of each unit in the super-surface antenna, and V is a Hadamard matrix; defining an atom set with a column vector of a (θ):
set a is a wireless dictionary indexed by a continuously varying parameter θ, then the atomic norm b of a is expressed as:
wherein c k Is the non-negative coefficient of the kth selected atom,is the corresponding phase;
removal ofAnd the estimated angle, the expression (3) is written as:
wherein ε>0 is a parameter related to noise level, ε=262.6e -0.1327SNR The method comprises the steps of carrying out a first treatment on the surface of the Formula (6) may be written as follows:
formula (7) is equivalent to:
solving the formula (8) by CVX to obtain an optimal solutionFrom a dual polynomial->The peak value of the constructed frequency spectrum is found out L peak values by searching the spectrum peak value, namelyDOA estimation; inverse determination of multipath channel from (6)Namely:
wherein the method comprises the steps ofIs the violation.
The physical layer authentication method according to the obtained multipath channel information comprises the following steps:
separating multipath channels when physical layer authentication is carried out, and respectively carrying out physical layer authentication, namely:
wherein h is BR And (theta) represents multipath channel information pre-stored by the super surface antenna.
Compared with the prior art, the invention has the beneficial effects that:
1) The dynamic super-surface antenna can rapidly and flexibly regulate and control the amplitude, phase and direction of electromagnetic waves by arranging a plurality of digital programmable metamaterial units on the substrate; the invention can realize high-degree-of-freedom signal reception at the front end of the radio frequency by utilizing the super-surface antenna, multipath reception is equivalent to projection on an antenna pattern function, and the high-position projection space is constructed by rapidly reconstructing the antenna pattern, so that multipath channel information loss caused by multipath superposition can be avoided.
2) Along with the increase of the signal-to-noise ratio, the estimated angle is more and more accurate, and the multipath channel information is more and more accurate; because the dynamic super-surface antenna can adjust the receiving direction diagram and can respectively receive signals from different directions, the physical layer authentication is performed by the channel information which is finely estimated by the multipath, and the physical layer authentication effect is better than that of the receiving of the mixed multipath channel information.
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In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a system model diagram of the present invention.
Fig. 2 is a schematic diagram of a data frame structure according to the present invention.
Fig. 3 is a graph of NMSE for estimating the angle of arrival of the DOA according to the present invention.
Fig. 4 is a graph of NMSE for estimating multipath information complex gain in accordance with the present invention.
Fig. 5 is a graph of fine multipath information estimation and hybrid multipath information estimation physical layer authentication ROC.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without any inventive effort, are intended to be within the scope of the invention.
The embodiment of the invention provides a physical layer authentication method based on dynamic super-surface antenna multipath estimation, which comprises the following specific steps:
step one: constructing a communication system model, as shown in fig. 1, wherein the communication system model comprises a base station Alice and a user Bob, and various barriers exist between the base station Alice and the user Bob; the user Bob transmitting the signal is a single-antenna user, and the dynamic super-surface antenna is used as a base station Alice and consists of N units. As shown in fig. 2, it is assumed that only K pilots are transmitted for channel estimation, and in each pilot symbol period, the input signal s k The pattern of the super-surface antenna is changed M times, and the pilot symbol is held at the kthIn the continuous time, the expression of the received signal is:
wherein,the pilot signal transmitted by Bob is a known signal. />Representing the channel between base station Alice and user Bob, n k ＝[n k1 ,...,n ki ,...,n km ] T Represents noise generated by M times of agility of the super-surface antenna, n ki ～N(0,σ 2 )；/>Representing multipath channel information pre-stored by the super-surface antenna, wherein L is the number of multipath channels; />Array popularity matrix representing uniform linear array, a (θ) = [ a (θ) 1 ),...,a(θ L )]，/>d represents the spacing between the units of the super-surface antenna, lambda represents the wavelength of the received signal, theta represents the angle of the signal reaching the super-surface antenna, and N represents the number of the units of the super-surface antenna; v= [ V 1 ,...v m ...,v M ]，/>Representing t m Super-surface antenna state parameter v during time sampling m ＝[v m1 ,...v mn ,v mN ] T ，/>A mn Representing a subsurface antennaWeighting coefficient of each unit of (a) to the amplitude of the incident signal, phi mn Representing the weighting coefficients of each element in the subsurface antenna to the phase of the incident signal. Since the super-surface antenna in this embodiment is a 1bit encoded super-surface antenna, Φ mn Is 1 or-1, and defaults to a herein mn =1, i.e. the amplitude of the signal is not changed.
Step two: the super-surface antenna rapidly changes in a symbol period, and changes a receiving direction diagram to obtain sampling data; performing DOA estimation on the sampled data by adopting an atomic norm minimization algorithm to obtain corresponding multipath channel information;
at the receiving end, LS channel estimation algorithm is utilized to obtainThe channel estimation result is obtained by the following formula:
wherein Y= [ Y ] 1 ,...,y K ]，Represents data obtained by sampling K pilots respectively M times, s= [ s ] 1 ,...,s K ] T Representing K pilot sequences s * Representing taking the conjugate of s; />Channel information estimated using the LS channel estimation algorithm.
The influence of noise is removed as much as possible through the above formula, the space domain multidimensional sampling information is obtained, and the atomic norm minimization algorithm is utilized to estimate the multipath channel parameters. The conversion of formula (2) to:
wherein,representing residual noise; v is determined by the state of each unit in the super-surface antenna, and the embodiment adopts a 1bit coding super-surface antenna, wherein the elements in the matrix are +/-1, and V can be directly made into a Hadamard matrix.
Defining an atom set with a column vector of a (θ):
set a is a wireless dictionary indexed by a continuously varying parameter θ, then the atomic norm b of a is expressed as:
wherein c k Is the non-negative coefficient of the kth selected atom,is the corresponding phase.
To removeAnd the estimated angle, the expression (3) is written as:
wherein ε>0 is a parameter related to noise level, ε=262.6e -0.1327SNR The method comprises the steps of carrying out a first treatment on the surface of the Formula (6) may be written as follows:
formula (7) is equivalent to:
solving the formula (8) by CVX to obtain an optimal solutionFrom a dual polynomial->The constructed peak value of the frequency spectrum is searched by the spectrum peak to find out L peak values, namely DOA estimated values; inverse determination of multipath channel from (6)Namely:
wherein the method comprises the steps ofIs the violation.
Step three: and carrying out physical layer authentication according to the obtained multipath channel information, judging whether the received signal is legal or not, if so, carrying out processing, otherwise, directly discarding.
From the obtainedPhysical layer authentication is performed, and as the super surface unit can rapidly switch the state of the super surface unit so that the antenna presents different patterns to receive the same group of multipaths, the multipath channels are separated when the physical layer authentication is performed, and the physical layer authentication is performed respectively, namely:
wherein h is BR (θ) represents the pre-stored multipath channel information of the super-surface antennaAnd (5) extinguishing.
Conventional antenna arrays are homogeneous and invariable, and therefore result in physical layer authentication by mixing multipath channels, namely:
simulation results show that the result of formula (10) is better.
In a specific example, according to the system model of fig. 1, both communication parties are base stations (Alice), users (Bob), where Alice uses a 1bit super-surface antenna, the number of super-surface antenna elements n=32, the cell spacing is 0.25 times of wavelength according to a uniform linear array arrangement, the super-surface antenna pattern agility times m=n=32 in one pilot symbol period, and Bob uses a common omni-directional antenna. Bob sends a pilot signal to Alice with pilot length k=16. The number of multipath channels l=3, and in the method of the present invention, the probability distribution of multipath does not affect the performance, so each multipath is assumed to follow complex gaussian distribution. The channel estimation performance is described by normalized mean square error (Normalized Mean Square Error, NMSE), which represents the degree of deviation of the estimated value from the actual value, with smaller numbers representing better performance. The NMSE of the multipath angle and gain estimate are defined as follows, respectively:
wherein,is->Each element in (E) is [ -pi, pi]Within the interval, E.]Representing the desire.
As shown in fig. 3 and 4, when the signal angle of arrival (DOA) is [ -50 °, -30 °,10 ° ], the estimated angle of arrival and NMSE of multipath information are varied with the signal-to-noise ratio, and each curve is 10000 monte carlo experimental results. As the signal-to-noise ratio increases, both of the estimated performances become more and more accurate.
When the snr=5 dB, the curves of the receiver operating characteristics (Receiver Operating Characteristic, ROC) of the fine multipath information estimation and the hybrid multipath information estimation for physical layer authentication are as shown in fig. 5, pf represents a false alarm probability, i.e., a probability of judging an illegal signal as a legal signal, pd represents a correct reception probability, i.e., a probability of judging a legal signal as a legal signal, and it can be seen that the effect of physical layer authentication by the fine multipath estimation is better than that by the hybrid multipath channel.
The invention provides a method for carrying out communication between a super-surface antenna serving as a base station and a single-antenna user, wherein signals sent by the user are reflected by various barriers, namely, the signals finally reach the super-surface antenna through multipath channels, the super-surface antenna can rapidly change in a symbol period, a receiving direction diagram is changed, DOA estimation is carried out on the received signals by adopting an atomic norm minimization algorithm, and corresponding multipath channel information is obtained. And performing physical layer authentication according to the obtained multipath channel information, and judging whether the received signal is legal or not.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements that fall within the spirit and scope of the invention.
Claims (4)
1. The physical layer authentication method based on the dynamic super-surface antenna multipath estimation is characterized by comprising the following steps:
step one: constructing a communication system model, wherein the communication system model comprises a base station Alice and a user Bob, and various barriers exist between the base station Alice and the user Bob; the base station Alice adopts a super-surface antenna, the user Bob adopts a common omni-directional antenna, and a signal sent by the user Bob reaches the super-surface antenna through a multipath channel;
step two: the super-surface antenna rapidly changes in a symbol period, and changes a receiving direction diagram to obtain sampling data; performing DOA estimation on the sampled data by adopting an atomic norm minimization algorithm to obtain corresponding multipath channel information;
step three: and carrying out physical layer authentication according to the obtained multipath channel information, judging whether the received signal is legal or not, if so, carrying out processing, otherwise, directly discarding.
2. The physical layer authentication method based on dynamic subsurface antenna multipath estimation according to claim 1, wherein the specific transmission method for the signal sent by the user Bob to reach the subsurface antenna through the multipath channel is as follows:
user Bob transmits K pilots for channel estimation, and in each pilot symbol period, inputs signal s k The super-surface antenna pattern is changed M times, and then in the duration of the kth pilot symbol, the received signal expression is:
wherein,pilot signal transmitted for Bob, +.>Representing the channel between base station Alice and user Bob, n k ＝[n k1 ,...,n ki ,...,n km ] T Represents noise generated by M times of agility of the super-surface antenna, n ki ～N(0,σ 2 )；
Representing multipath channel information pre-stored by the super-surface antenna, wherein L is the number of multipath channels; />Array popularity matrix representing uniform linear array, a (θ) = [ a (θ) 1 ),...,a(θ L )]，/>d represents the spacing between the units of the super-surface antenna, lambda represents the wavelength of the received signal, theta represents the angle of the signal reaching the super-surface antenna, and N represents the number of the units of the super-surface antenna; v= [ V 1 ,...v m ...,v M ]，/>Representing t m Super-surface antenna state parameter v during time sampling m ＝[v m1 ,...v mn ,v mN ] T ，/>A mn A weighting coefficient representing the amplitude of the incident signal for each element in the subsurface antenna, Φ mn Representing the weighting coefficients of each element in the subsurface antenna to the phase of the incident signal.
3. The physical layer authentication method based on dynamic subsurface antenna multipath estimation according to claim 2, wherein in step two, the multipath channel information obtaining method is as follows:
at the receiving end, LS channel estimation algorithm is utilized to obtain
Wherein Y= [ Y ] 1 ,...,y K ]，Represents data obtained by sampling K pilots respectively M times, s= [ s ] 1 ,...,s K ] T Representing K pilot sequences s * Representing taking the conjugate of s; />Representing channel information estimated using an LS channel estimation algorithm;
performing multipath channel parameter estimation by using an atomic norm minimization algorithm, and converting the formula (2) into:
wherein,representing residual noise; v is determined by the state of each unit in the super-surface antenna, and V is a Hadamard matrix; defining an atom set with a column vector of a (θ):
set a is a wireless dictionary indexed by a continuously varying parameter θ, then the atomic norm b of a is expressed as:
wherein c k Is the non-negative coefficient of the kth selected atom,is the corresponding phase;
removal ofAnd the estimated angle, the expression (3) is written as:
wherein ε>0 is a parameter related to noise level, ε=262.6e -0.1327SNR The method comprises the steps of carrying out a first treatment on the surface of the Formula (6) may be written as follows:
formula (7) is equivalent to:
solving the formula (8) by CVX to obtain an optimal solutionFrom a dual polynomial->The constructed peak value of the frequency spectrum is searched by the spectrum peak to find out L peak values, namely DOA estimated values; from (6) the multipath channel is inversely determined>Namely:
wherein the method comprises the steps ofIs the violation.
4. The physical layer authentication method based on dynamic subsurface antenna multipath estimation according to claim 3, wherein the physical layer authentication method based on the obtained multipath channel information is as follows:
separating multipath channels when physical layer authentication is carried out, and respectively carrying out physical layer authentication, namely:
wherein h is BR And (theta) represents multipath channel information pre-stored by the super surface antenna.
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