CN106656293B - Physical layer secure communication method based on frequency control array beam forming - Google Patents

Physical layer secure communication method based on frequency control array beam forming Download PDF

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CN106656293B
CN106656293B CN201611191654.2A CN201611191654A CN106656293B CN 106656293 B CN106656293 B CN 106656293B CN 201611191654 A CN201611191654 A CN 201611191654A CN 106656293 B CN106656293 B CN 106656293B
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林静然
杨金泰
利强
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University of Electronic Science and Technology of China
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
    • H04W12/02—Protecting privacy or anonymity, e.g. protecting personally identifiable information [PII]

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Abstract

The invention relates to a physical layer safety communication method based on frequency control array beam forming, which comprises the following steps: (1) setting initialization parameters; (2) calculating the optimal frequency offset under the constraint of a certain frequency offset range according to the initialization parameters to obtain an antenna transmitting frequency vector; (3) and calculating the optimal array transmission beam vector by utilizing a matrix decomposition technology according to the antenna transmission frequency vector, and calculating the safety rate of the system. The invention adopts any frequency offset scheme, namely only the frequency offset range of each antenna is specified, and the change rule of the frequency offset among the antennas is not limited.

Description

Physical layer secure communication method based on frequency control array beam forming
Technical Field
The invention relates to the field of secret communication, which is different from the traditional scheme based on encryption and coding.
Background
Physical layer security technology has gained increasing attention and research as an effective means for securing wireless communications. Unlike the conventional strategy of ensuring communication security through encoding and encryption technologies, the physical layer security technology utilizes a physical layer method to ensure communication security by optimizing the difference in transmission rate (i.e., security rate) between a target user and an eavesdropper.
Currently, common methods for increasing the security rate include an artificial noise method, a beam forming method, and the like. However, these conventional methods are based on an important assumption that the channel state information of both the target user and the eavesdropper are irrelevant. However, in a millimeter wave communication system of the new generation, because millimeter waves have the characteristic of directional propagation, when the transmission directions of a target user and an eavesdropper are aligned, the assumption that channels are uncorrelated is difficult to establish, and thus traditional methods such as beam forming and artificial noise are ineffective.
In the frequency-controlled array communication technology, frequency offset is applied to carrier frequency of each antenna, so that array transmission beams have distance resolution capability, target users and eavesdroppers located in the same transmission direction and different transmission distances can be distinguished, and the limitation of a traditional physical layer communication security method (such as beam forming, artificial noise and the like) is overcome.
At present, a frequency control array secure communication method based on a linear incremental frequency offset strategy is adopted by some people, each antenna of the array adopts the linear incremental frequency offset strategy, and the maximization of the secure rate is realized by jointly optimizing frequency offset parameters and transmission beams. The linear increasing frequency offset strategy can reach the theoretical optimal value of the safe rate, but has certain limitation. For example, to avoid frequency decorrelation effects of the target response, the upper limit of the transmission frequency deviation of each antenna is typically limited. Whereas in the linearly increasing frequency offset scheme, the optimal frequency offset value between adjacent antennas is inversely proportional to the difference in transmission distance between the target user and the eavesdropper. Then, when the target user is very close to the eavesdropper, and the frequency offset value between adjacent antennas is large, the cumulative value of the linearly increasing frequency offsets may exceed the upper limit of the frequency offsets tolerated by the array, so that the expected effect cannot be achieved, and the performance of the physical layer security is affected.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a method for jointly optimizing the frequency offset and transmission beam of each antenna under any frequency offset strategy.
The technical scheme for solving the technical problems is as follows:
a physical layer safety communication method based on frequency control array beam forming comprises the following steps:
(1) setting initialization parameters;
(2) calculating the optimal frequency offset under the constraint of a preset frequency offset range according to the initialization parameters to obtain an antenna transmitting frequency vector;
(3) and calculating the optimal array transmission beam vector by utilizing a matrix decomposition technology according to the antenna transmission frequency vector, and calculating the safety rate of the system.
The invention has the beneficial effects that:
1. the invention provides a scheme of any frequency offset, so that the frequency offset is set more flexibly, and good safe communication performance can be achieved even in a very limited frequency offset range;
2. under the condition that the distance between a target user and an eavesdropper is close enough, the traditional linear increasing frequency offset scheme cannot reach the expected safety rate under the constraint of a certain frequency offset range, and the safety performance of a physical layer is influenced;
3. the invention uses the method of jointly optimizing the frequency deviation and the transmission wave beam of each antenna to further optimize the transmission wave beam of the antenna, thereby further improving the safety rate of the system.
On the basis of the technical scheme, the invention can be further improved as follows.
Further, setting the initialization parameters includes: initialization parameter ru,re,θuAnd thetaeWherein r isu,reRepresenting the spatial distance, theta, between the target user and the eavesdropper and the source antenna, respectivelyuAnd thetaeRespectively representing the included angles between a connecting line between the target user and the eavesdropper as well as between the target user and the information source antenna and the due north direction;
initializing the number M of information source antennas; the maximum frequency offset of each antenna is delta F, and the signal reference carrier frequency is Fc；
According to the formula
Figure BDA0001187169110000031
Initializing a distance between the array antennas, wherein c represents the propagation speed of the electromagnetic waves;
initializing the upper limit P of the total power of the system and the variance σ of the noise in the communication system2。
Further, the step (2) includes the steps of:
(21) initializing the iteration number k as 0, and M as (k mod M) +1, wherein (k mod M) represents the remainder of k divided by M; initializing feasible points
Figure BDA0001187169110000032
So that the vector f(k)Each component f ofi (k)(i ═ 1, 2.., M) are all at [ f ·c,fc+ΔF]Within the range; the initialization algorithm iteratively calculates the precision, among which
Figure BDA0001187169110000033
(221) Initializing n-1;
(222) if n is m, then
Figure BDA0001187169110000034
Wherein κ is a slope parameter, ζ is a center point parameter, and is an offset parameter, and performing step (225); otherwise, performing step (223);
(223) calculating a slope parameter
Figure BDA0001187169110000035
(224) Determination
Figure BDA0001187169110000041
Whether or not, if so, then
Figure BDA0001187169110000042
Wherein, the [ alpha ], [ beta ]m,n]+＝max{0,m,n}；
Otherwise, if
Figure BDA0001187169110000043
Then
Figure BDA0001187169110000044
Wherein
Figure BDA0001187169110000045
Respectively indicating that omega is integer in positive direction and integer in negative direction;
(225) if n is equal to M, go to step (226); otherwise, making n equal to n +1, and returning to the step (222);
(226) updating
Figure BDA0001187169110000046
Judgment of
Figure BDA0001187169110000047
If true, then order
Figure BDA0001187169110000048
Judgment of
Figure BDA0001187169110000049
If true, then order
Figure BDA00011871691100000410
(23) Order to
Figure BDA00011871691100000411
Using updated frequency vectors
Figure BDA00011871691100000412
Computing
Figure BDA00011871691100000413
(24) Judgment of
Figure BDA00011871691100000414
Whether or not to be established, and if so,
then k is k +1, M is (k mod M) +1, and the procedure returns to step (22);
otherwise, outputting the optimal solution
Figure BDA00011871691100000415
Wherein f is*＝f(k+1)。
The beneficial effect of adopting the further scheme is that the frequency deviation mode enables the frequency deviation to be set more flexibly, and the good safety communication performance can be achieved even in a very limited frequency deviation range.
Further, the step (3) includes the steps of:
(31) calculating the wave beam vector of the frequency control array,
Figure BDA0001187169110000051
respectively expressed as frequency control array transmission channel vectors corresponding to a target user and an eavesdropper according to formulas
Figure BDA0001187169110000052
Figure BDA0001187169110000053
Calculating the mth component of the target user and eavesdropper channel vector, wherein M is 1, 2.. M;
(32) according to formulas of target user and eavesdropper respectively
Figure BDA0001187169110000054
Figure BDA0001187169110000055
Calculating a channel covariance matrix of the target user and the eavesdropper, wherein
Figure BDA0001187169110000056
Respectively represent hu,heThe conjugate of the transposed vector of (a),
calculating an intermediate variable matrix according to a formula
Figure BDA0001187169110000057
Figure BDA0001187169110000058
Wherein, IM×MIs an identity matrix of size M × M;
(33) calculating an optimal beamforming weighting vector according to a formula
Figure BDA0001187169110000059
Calculating a frequency-steering array beam-forming vector of a target user and an eavesdropper, wherein w*A vector of M × 1, the M-th component of which is
Figure BDA00011871691100000510
Wherein
Figure BDA00011871691100000511
Figure BDA00011871691100000512
Represents the conjugate transpose vector of vector ξ, and λΣAnd vΣRespectively the maximum eigenvalue of the matrix sigma and the eigenvector corresponding to the maximum eigenvalue; sgn { lambdaΣIs a sign function ifΣRespectively taking positive number, zero and negative number, sgn { lambdaΣThe values of which take 1, 0 and-1 respectively,
[sgn{λΣ}]+＝max{0,sgn{λΣ}}
(34) when the carrier frequency takes the optimum value
Figure BDA0001187169110000061
Frequency control array beam forming weighting vector obtaining optimal value
Figure BDA0001187169110000062
According to the formula
Rs＝log(1+λΣ[sgn(λΣ)]+)
The secure rate of the system is calculated.
The beneficial effect of adopting the above further scheme is that the beam forming technology is adopted to optimize the beam, so that the safety rate is further improved by the system.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The principles and features of this invention are described below in conjunction with the following drawings, which are set forth by way of illustration only and are not intended to limit the scope of the invention.
As shown in fig. 1, the present invention relates to the field of secure communication, and unlike the conventional scheme based on encryption and encoding, the present invention uses a physical layer secure communication method based on frequency controlled array beamforming to optimize the secure transmission rate between a user and an eavesdropper in the same transmission direction and at different transmission distances, which includes the following steps.
(1) Setting initialization parameters which comprise ru,re,θuAnd thetaeWherein r isu,reIs divided intouRespectively representing the spatial distances ru, r, e, theta between the target user and the eavesdropper and source antennauAnd thetaeRespectively representing the included angles between a connecting line between the target user and the eavesdropper as well as between the target user and the information source antenna and the due north direction;
initializing the number M of information source antennas; the maximum frequency offset of each antenna is delta F, and the signal reference carrier frequency is Fc；
According to the formula
Figure BDA0001187169110000063
Initializing a distance between the array antennas, wherein c represents the propagation speed of the electromagnetic waves;
initializing the upper limit P of the total power of the system and the variance σ of the noise in the communication system2；
(2) Calculating the optimal frequency offset under the constraint of a certain frequency offset range according to the initialization parameters to obtain an antenna transmitting frequency vector; which comprises the following steps:
(21) initializing the iteration number k as 0, and M as (k mod M) +1, wherein (k mod M) represents the remainder of k divided by M; initializing feasible points
Figure BDA0001187169110000071
So that the vector f(k)Each component f ofi (k)(i ═ 1, 2.., M) are all at [ f ·c,fc+ΔF]Within the range; the initialization algorithm iteratively calculates the precision, among which
Figure BDA0001187169110000072
(221) Initializing n-1;
(222) if n is m, then
Figure BDA0001187169110000073
Wherein κ is a slope parameter, ζ is a center point parameter, and is an offset parameter, and performing step (225); otherwise, performing step (223);
(223) calculating a slope parameter
Figure BDA0001187169110000074
(224) Determination
Figure BDA0001187169110000075
Whether or not, if so, then
Figure BDA0001187169110000076
Wherein, the [ alpha ], [ beta ]m,n]+＝max{0,m,n}；
Otherwise, if
Figure BDA0001187169110000077
Then
Figure BDA0001187169110000081
Wherein
Figure BDA0001187169110000082
Respectively indicating that omega takes integers in positive and negative directions;
(225) if n is equal to M, go to step (226); otherwise, making n equal to n +1, and returning to the step (222);
(226) updating
Figure BDA0001187169110000083
Judgment of
Figure BDA0001187169110000084
If true, then order
Figure BDA0001187169110000085
Judgment of
Figure BDA0001187169110000086
If true, then order
Figure BDA0001187169110000087
(23) Order to
Figure BDA0001187169110000088
Using updated frequency vectors
Figure BDA0001187169110000089
Computing
Figure BDA00011871691100000810
(25) Judgment of
Figure BDA00011871691100000811
Whether or not to be established, and if so,
then k is k +1, M is (k mod M) +1, and the procedure returns to step (22);
otherwise, outputting the optimal solution
Figure BDA00011871691100000812
Wherein f is*＝f(k+1)。
(3) Calculating an optimal array transmission beam vector by using a matrix decomposition technology according to the antenna transmission frequency vector, and calculating the safety rate of the system;
which comprises the following steps:
(31) calculating the wave beam vector of the frequency control array,
Figure BDA0001187169110000091
respectively expressed as frequency control array transmission channel vectors corresponding to a target user and an eavesdropper according to formulas
Figure BDA0001187169110000092
Figure BDA0001187169110000093
Calculating the mth component of the target user and eavesdropper channel vector, wherein M is 1, 2.. M;
(32) according to formulas of target user and eavesdropper respectively
Figure BDA0001187169110000094
Figure BDA0001187169110000095
Calculating a channel covariance matrix of the target user and the eavesdropper, wherein
Figure BDA0001187169110000096
Respectively represent hu,heThe conjugate of the transposed vector of (a),
calculating an intermediate variable matrix according to a formula
Figure BDA0001187169110000097
Figure BDA0001187169110000098
Wherein, IM×MIs an identity matrix of size M × M,
(33) calculating an optimal beamforming weighting vector according to a formula
Figure BDA0001187169110000099
Calculating a frequency-steering array beam-forming vector of a target user and an eavesdropper, wherein w*A vector of M × 1, the M-th component of which is
Figure BDA00011871691100000910
It is composed of
Figure BDA00011871691100000911
In (1),
Figure BDA00011871691100000912
represents the conjugate transpose vector of vector ξ, and λΣAnd vΣRespectively the maximum eigenvalue of the matrix sigma and the eigenvector corresponding to the maximum eigenvalue; sgn { lambdaΣIs a sign function ifΣRespectively taking positive number, zero and negative number, sgn { lambdaΣThe values of which take 1, 0 and-1 respectively,
[sgn{λΣ}]+＝max{0,sgn{λΣ}}
(34) when carrier frequency is takenObtaining the optimum value
Figure BDA00011871691100000913
Frequency control array beam forming weighting vector obtaining optimal value
Figure BDA00011871691100000914
According to the formula Rs＝log(1+λΣ[sgn(λΣ)]+) And calculating the safety rate of the system.
The invention adopts any frequency offset scheme, namely only the frequency offset range of each antenna is specified, and the change rule of the frequency offset among the antennas is not limited.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (3)

1. A physical layer safety communication method based on frequency control array beam forming is characterized by comprising the following steps:
(1) setting initialization parameters;
(2) calculating the optimal frequency offset under the constraint of a preset frequency offset range according to the initialization parameters to obtain an antenna transmitting frequency vector;
(3) calculating an optimal array transmission beam vector by using a matrix decomposition technology according to the antenna transmission frequency vector, and calculating the safety rate of the system;
setting initialization parameters includes:
initialization parameter ru,re,θuAnd thetaeWherein r isu,reRepresenting the spatial distance, theta, between the target user and the eavesdropper and the source antenna, respectivelyuAnd thetaeRespectively representing the connection between target user and eavesdropper and source antennaAn included angle in the due north direction;
initializing the number M of information source antennas; the maximum frequency offset of each information source antenna is delta F, and the signal reference carrier frequency is Fc；
According to the formula
Figure FDA0002517794590000011
Initializing a distance between the array antennas, wherein c represents the propagation speed of the electromagnetic waves;
initializing the upper limit P of the total power of the system and the variance σ of the noise in the communication system2。
2. The method for physical layer secure communication based on frequency controlled array beamforming according to claim 1, wherein the step (2) comprises the steps of:
(21) initializing the iteration number k as 0, M as (kmod) +1, wherein (kmod) represents the remainder of k divided by M; initializing feasible points
Figure FDA0002517794590000012
So that the vector f(k)Each component f ofi (k)(i ═ 1, 2.., M) are all at [ f ·c,fc+ΔF]Within the range; the initialization algorithm iteratively calculates the precision, wherein a preset constant is used for calculating the objective function value
Figure FDA0002517794590000013
Wherein the content of the first and second substances,
Figure FDA0002517794590000014
a phase factor for the mth antenna transmission signal;
(22) updating
Figure FDA0002517794590000015
The method specifically comprises the following steps:
(221) initializing n-1;
(222) if n is m, then
Figure FDA0002517794590000021
Wherein κ is a slope parameter, ζ is a center point parameter, and is an offset parameter, and performing step (225); otherwise, performing step (223);
(223) calculating a slope parameter
Figure FDA0002517794590000022
(224) Determination
Figure FDA0002517794590000023
Whether or not, if so, then
Figure FDA0002517794590000024
Wherein, the [ alpha ], [ beta ]m,n]+＝max{0,m,n}；
Otherwise, if
Figure FDA0002517794590000025
Then
Figure FDA0002517794590000026
Wherein
Figure FDA0002517794590000027
Respectively indicating that omega is integer in positive direction and integer in negative direction;
(225) if n is equal to M, go to step (226); otherwise, making n equal to n +1, and returning to the step (222);
(226) updating
Figure FDA0002517794590000028
Judgment of
Figure FDA0002517794590000029
If true, then order
Figure FDA00025177945900000210
Judgment of
Figure FDA0002517794590000031
If true, then order
Figure FDA0002517794590000032
(23) Order to
Figure FDA0002517794590000033
Using updated frequency vectors
Figure FDA0002517794590000034
Computing
Figure FDA0002517794590000035
(24) Judgment of
Figure FDA0002517794590000036
Whether or not to be established, and if so,
then k is k +1, m is (kmmod m) +1, and return to step (22);
otherwise, outputting the optimal solution
Figure FDA0002517794590000037
Wherein f is*＝f(k+1)。
3. The method for physical layer secure communication based on frequency controlled array beamforming according to claim 2, wherein the step (3) comprises the steps of:
(31) calculating the wave beam vector of the frequency control array,
Figure FDA0002517794590000038
respectively expressed as frequency control array transmission channel vectors corresponding to a target user and an eavesdropper according to formulas
Figure FDA0002517794590000039
Figure FDA00025177945900000310
Calculating the mth component of the target user and eavesdropper channel vector, wherein M is 1, 2.. M;
(32) according to formulas of target user and eavesdropper respectively
Figure FDA00025177945900000311
Figure FDA00025177945900000312
Calculating a channel covariance matrix of the target user and the eavesdropper, wherein
Figure FDA00025177945900000313
Respectively represent hu,heThe conjugate of the transposed vector of (a),
calculating an intermediate variable matrix according to a formula
Figure FDA00025177945900000314
Figure FDA00025177945900000315
Wherein, IM×MIs an identity matrix of size M × M;
(33) calculating an optimal beamforming weighting vector according to a formula
Figure FDA0002517794590000041
Calculating a frequency-steering array beam-forming vector of a target user and an eavesdropper, wherein w*A vector of M × 1, the M-th component of which is
Figure FDA0002517794590000042
Wherein
Figure FDA0002517794590000043
Figure FDA0002517794590000044
Represents the conjugate transpose vector of vector ξ, and λΣAnd vΣRespectively the maximum eigenvalue of the matrix sigma and the eigenvector corresponding to the maximum eigenvalue; sgn { lambda∑Is a sign function ifΣRespectively taking positive number, zero and negative number, sgn { lambdaΣThe values of which take 1, 0 and-1 respectively,
[sgn{λΣ}]+＝max{0,sgn{λΣ}}
(34) when the carrier frequency takes the optimum value
Figure FDA0002517794590000045
Frequency control array beam forming weighting vector obtaining optimal value
Figure FDA0002517794590000046
According to the formula Rs＝log(1+λΣ[sgn(λΣ)]+) And calculating the safety rate of the system.
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