CN114286336A - Multi-cell network secure transmission method based on artificial noise - Google Patents
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Abstract
The invention belongs to the technical field of wireless communication, and particularly relates to a multi-cell network safe transmission method based on artificial noise; the method comprises the following steps: the base station sends information to the user side, wherein the information comprises AN information and safety information; the user side processes the received information by adopting AN AN alternative minimized interference alignment algorithm to obtain a beam forming vector and a receiving vector of the signal; obtaining a recovery signal according to the output receiving vector and the beamforming vector; the interference alignment algorithm of the invention reduces the channel quality of the eavesdropping node by using artificial noise, and does not introduce additional interference to the legal transmission of the multi-cell wireless network; by alternately iterating and interfering the matrix and the subspace at the receiving end, the interference is projected into a lower-dimensionality signal space, and the remaining interference-free signal space is used for transmitting useful signals, so that interference alignment is realized, the safety performance of the system is further enhanced, the safety performance of the system is improved, and the method has wider application scenes.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a multi-cell network secure transmission method based on artificial noise.
Background
Due to the broadcast nature and the open nature of wireless communications, security of information transmission is a challenging issue in wireless networks, and physical layer security is becoming increasingly important. The generation of the interception model and the definition of the security capacity lay a foundation for the research work of the later physical layer security. If the reliability of the main channel is higher than that of the eavesdropping channel, the legitimate user can achieve correct decoding, and the eavesdropping node cannot perform correct decoding.
In a multi-cell wireless network, interference can seriously affect the transmission rate of users, and the safety performance of the system is reduced. In contrast to this conventional view, in an Interference network, Interference Alignment (IA) is a very effective Interference management method, in which precoding matrices of all users are cooperatively designed to limit Interference in the same subspace, and useful information is transmitted using the remaining Interference-free space. To realize the secure transmission of the secret information, the information flow can be cached in the noise of the interception channel by using the thought of random coding and the characteristic of the wireless channel, so that the interception node can not obtain the information of the main channel, and the security of the system can be improved to a certain extent.
Physical layer security techniques mainly used to realize secure transmission of information include Artificial Noise (AN), beamforming, and phase rotation. Among the various methods, AN is AN intuitive and effective way to implement secure communications. For example, a multi-user interference alignment network ensures the safety of transmission by introducing artificial noise, and the scheme utilizes a distributed interference alignment iterative algorithm to design a precoding matrix and an interference suppression matrix at a transceiving end. However, the solution needs to assume the reciprocity of the wireless network, which limits the application of the algorithm in practice. There is a scheme for securing transmission using artificial noise in AN interference alignment-based wireless network, but the scheme fixes power allocation between a security signal and AN signal, and cannot adapt to dynamic changes of the wireless network.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a multi-cell network safe transmission method based on artificial noise, which comprises the following steps: the base station sends information to the user side, wherein the information comprises AN information and safety information; the user side processes the received information by adopting AN AN alternative minimized interference alignment algorithm to obtain a beam forming vector and a receiving vector of the signal; obtaining a recovery signal according to the output receiving vector and the beamforming vector;
the process of processing the received information by adopting the AN alternation minimized interference alignment algorithm comprises the following steps:
s1: initializing a wave beam forming vector and an artificial noise pre-coding matrix of a transmitting end; setting iteration times;
s2: calculating a set of standard orthogonal bases of a receiving interference matrix and a receiving interference subspace according to the wave beam forming vector of the transmitting end and the artificial noise pre-coding matrix;
s3: calculating a signal space projection matrix and a receiving vector of a receiving end according to the standard orthogonal basis;
s4: calculating a system interference leakage value according to the wave beam forming vector of the transmitting end, the artificial noise pre-coding matrix and the standard orthogonal base;
s5: judging whether the iteration times meet or whether the system interference leakage value is converged, and if the iteration times meet or the system interference leakage value is converged, outputting a receiving vector and a beam forming vector; if the iteration times are not met or the system interference leakage value is not converged, executing step S6;
s6: calculating an emission interference matrix according to the projection matrix;
s7: and updating the beamforming vector and the artificial noise precoding matrix at the transmitting end according to the transmitting interference matrix and returning to the step S2.
Preferably, the formulas for calculating the received interference matrix and the orthonormal basis are respectively as follows:
Ck＝xl[Qk],l＝1,...,Nk-1 and k ═ 1,2,3
wherein ,QkRepresenting the received interference matrix, HkjRepresenting the channel matrix from base station j to user k, j representing the base station transmitting the useful signal, p representing the base station transmitting the safety signal, HkpRepresenting the channel matrix, v, from base station p to user kjRepresenting the transmit beamforming vector, w, of base station jpRepresenting an artificial noise precoding matrix, CkDenotes the orthonormal base, xl[Qk]Representation matrix QkEigenvector corresponding to the ith largest eigenvalue, NkRepresenting the number of receive antennas for user k.
Preferably, the formulas for calculating the signal space projection matrix and the receiving vector of the receiving end are respectively as follows:
wherein ,FkA signal space projection matrix, C, representing the user kkDenotes the orthonormal base, ukA reception vector at the receiving end is represented,
representation matrix
The null space of (a).
Preferably, the formula for calculating the system interference leakage value is as follows:
wherein ,IkRepresenting the interference leakage value, v, of user kjRepresents the transmit beamforming vector, H, of base station jkjRepresenting the channel matrix from base station j to user k, CkRepresenting an orthonormal basis.
Preferably, the formula for calculating the transmission interference matrix is as follows:
wherein ,
a first transmit interference matrix is represented,
representing a second transmitted interference matrix, k representing the kth user, q representing a user eavesdropped by an eavesdropper, HkjRepresenting the channel matrix, H, from base station j to user kqjRepresenting the channel matrix, F, from base station j to user qkA signal space projection matrix, F, representing a user kqA signal space projection matrix representing user q.
Preferably, the formula for updating the beamforming vector and the artificial noise precoding matrix at the transmitting end is as follows:
wherein ,vjRepresents the transmit beamforming vector for base station j,
representation matrix
Eigenvectors, w, corresponding to the smallest eigenvaluesqRepresenting an artificial noise pre-coding matrix and,
representation matrix
D is the eigenvector corresponding to the d-th minimum eigenvalue, d represents the number of independent data streams to be transmitted, danIndicating the number of transmitting ANs.
Preferably, obtaining the recovered signal according to the output reception vector and beamforming vector includes: initializing a power distribution ratio, and calculating a signal-to-noise ratio of a recovery signal according to the receiving vector, the beam forming vector and the power distribution ratio; calculating the signal-to-interference-and-noise ratio of the signal received by the eavesdropper according to the power distribution ratio and the signal-to-noise ratio of the recovered signal; constructing a safe speed target function according to the signal-to-interference-and-noise ratio of a signal received by an eavesdropper; solving the maximum value of the safe rate objective function to obtain the optimal power distribution ratio; and calculating a recovery signal according to the optimal power distribution ratio.
Further, the formula for calculating the signal-to-noise ratio of the recovered signal is:
wherein ,
representing the signal-to-interference-and-noise ratio, P, of the recovered signalpTo representSignal transmission power at the transmitting end, phi denotes the power distribution ratio, HpqRepresenting the channel matrix, v, from base station p to user qpRepresenting the transmit beamforming vector for base station p,
representing the transpose of the received vector.
Further, the safe rate objective function is:
wherein ,RSDenotes the base station safe transmission rate, phi denotes the power allocation ratio, gamma denotes the effective snr of the received signal of user q, mu denotes the threshold,
representing the signal to interference plus noise ratio of the signal received by the eavesdropper and epsilon representing the maximum allowed probability of security disruption.
Further, the formula for calculating the recovery signal is:
wherein ,
represents a recovered signal, PpDenotes a signal transmission power of a transmitting end, phi denotes a power distribution ratio,
a transposed matrix representing the received vector, HpqRepresenting the channel matrix, v, from base station p to user qpRepresenting the transmit beamforming vector, x, of base station ppRepresenting data symbols transmitted by base station p, nqRepresenting an additive white gaussian noise vector received by user q.
The invention has the beneficial effects that: the interference alignment algorithm of the invention reduces the channel quality of the eavesdropping node by using artificial noise, and does not introduce additional interference to the legal transmission of the multi-cell wireless network; by alternately iterating and interfering the matrix and the subspace at the receiving end, the interference is projected into a signal space with lower dimensionality, and the remaining non-interference signal space is used for transmitting useful signals, so that interference alignment is realized; the algorithm designs AN alternative minimized interference alignment algorithm with AN to update the interference subspace of each transceiving end, can work in a time division duplex system and a frequency division duplex system, and does not need to assume the reciprocity of channels, the distribution of antennas or AN information transmission mode between two iteration steps, so the algorithm is more suitable for researching the solution of interference alignment; the channel quality of the eavesdropping node is reduced by utilizing artificial noise, and meanwhile, no extra interference is introduced to the legal transmission of the multi-cell network, so that the reliability of secret message transmission is improved; in addition, only if the statistical CSI of the eavesdropping node is known, the dynamic power distribution between the confidential signal and the AN signal is considered on the basis of interference alignment, the power distribution between the confidential signal and the AN signal can be dynamically adjusted, the safety performance of the system is further enhanced, the safety performance of the system is improved, and the application scene is wider.
Drawings
Fig. 1 is a system model diagram of a three-cell interference alignment network according to the present invention;
FIG. 2 is a flowchart of AN alternative AN minimization interference alignment algorithm according to the present invention;
FIG. 3 is a flow chart of the numerical analysis power allocation ratio of the present invention;
FIG. 4 is a diagram illustrating the relationship between the interference leakage value of a user and the number of iterations;
FIG. 5 is a schematic diagram illustrating the variation of the allocation ratio of different transmission powers and the optimal power of the base station when the interference is aligned according to the present invention;
fig. 6 is a diagram illustrating the result of the safety rate when the interference is aligned according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a multi-cell network secure transmission method based on artificial noise, as shown in fig. 2, the method comprises the following steps: the base station sends information to the user side, wherein the information comprises AN information and safety information; the user side processes the received information by adopting AN AN alternative minimized interference alignment algorithm to obtain a beam forming vector and a receiving vector of the signal; obtaining a recovery signal according to the output receiving vector and the beamforming vector;
the process of processing the received information by adopting the AN alternation minimized interference alignment algorithm comprises the following steps:
s1: initializing a wave beam forming vector and an artificial noise pre-coding matrix of a transmitting end; setting iteration times;
s2: calculating a set of standard orthogonal bases of a receiving interference matrix and a receiving interference subspace according to the wave beam forming vector of the transmitting end and the artificial noise pre-coding matrix;
s3: calculating a signal space projection matrix and a receiving vector of a receiving end according to the standard orthogonal basis;
s4: calculating a system interference leakage value according to the wave beam forming vector of the transmitting end, the artificial noise pre-coding matrix and the standard orthogonal base;
s5: judging whether the iteration times meet or whether the system interference leakage value is converged, and if the iteration times meet or the system interference leakage value is converged, outputting a receiving vector and a beam forming vector; if the iteration times are not met or the system interference leakage value is not converged, executing step S6;
s6: calculating an emission interference matrix according to the projection matrix;
s7: and updating the beamforming vector and the artificial noise precoding matrix at the transmitting end according to the transmitting interference matrix and returning to the step S2.
One preferred embodiment of the present invention is as follows:
as shown in FIG. 1, assume that there is a base station BS in a cell1、BS2 and BS3To 3 legal users R in the cell1、R2 and R3Sending information, user k, k e {1,2,3} respectively representing user R1、R2 and R3(ii) a Wherein, the base station BS3To the user R3Transmitting a secure message, a passive eavesdropping node eavesdropping the message, a BS3To R3The artificial noise AN is also transmitted to interfere the eavesdropping node while the safety message is transmitted; base stations BS of two other cells1And BS2Only the useful signal is transmitted and no additional interference is introduced to the legitimate transmissions in the network. Suppose that three base stations are equipped with M number of transmitting antennas1,M2,M3The number of receiving antennas equipped by three legal users is N1,N2,N3And the eavesdropping node only has a single receiving antenna. Each base station transmits an independent data stream, and the BS simultaneously3Also send the number of ANs as dan。
BS3To the user R3Transmitting a security signal and AN AN signal, and a BS1And BS2Only useful signals are transmitted, and the signals recovered by the legal user and the eavesdropping node are as follows:
wherein ,
representing a channel matrix from a base station j to a user k, wherein k, j belongs to {1,2,3}, and the requirement that quasi-static flat attenuation and drop are independent is met, and the channel state information can be obtained by assuming cooperation between the base stations;
and
respectively represent a beam forming vector, a receiving vector and an artificial noise precoding matrix which respectively satisfy
And
base station BS1、BS2And BS3Respectively, is P1、P2And P3；xjJ is 1,2,3 represents data symbol transmitted by jth base station;
represents BS3The AN vector sent;
representing an additive white gaussian noise vector received by the kth legal user; phi is more than or equal to 0 and less than or equal to 1 represents BS3The proportion of power allocated to the security signal; the channel from the base station to the eavesdropping node is represented as
Assuming that only the statistical CSI of the eavesdropping node is known, in particular, channel he1,he2,he3Independent of each other, all obey the cyclic symmetrical complex Gaussian distribution of the unit variance of zero mean.
One specific implementation of processing the received information by using AN alternative minimized interference alignment algorithm is as follows:
initializing transmit beamforming vectors vjAnd artificial noise precoding matrix w3J is 1,2,3, and the iteration number is set;
calculating a receiving interference matrix Q according to a wave beam forming vector and an artificial noise precoding matrix of a transmitting endkAnd receiving a set of orthonormal bases C of the interference subspacekSatisfy the following requirements
Ck＝xl[Qk],l＝1,...,Nk-1 and k ═ 1,2,3
wherein ,QkRepresenting the received interference matrix, HkjRepresenting the channel matrix, H, from base station j to user kk3Representing the base station BS3Channel matrix to user k, vjRepresenting the transmit beamforming vector, w, of base station j3Representing an artificial noise precoding matrix, CkDenotes the orthonormal base, xl[Qk]Representation matrix QkEigenvector corresponding to the ith largest eigenvalue, NkRepresenting the number of receive antennas for user k.
Computing a signal space projection matrix F from orthonormal basiskWith the receiving vector u of the receiving endkAnd k is 1,2, and 3, and the formulas of the spatial projection matrix and the receiving vector of the receiving end are respectively as follows:
wherein ,FkA signal space projection matrix, C, representing the user kkDenotes the orthonormal base, ukA reception vector at the receiving end is represented,
representation matrix
The null space of (a).
Calculating the system interference leakage value according to the wave beam forming vector of the transmitting end, the artificial noise pre-coding matrix and the standard orthogonal base, wherein the interference leakage value of the user k is as follows:
the system interference leakage value is:
wherein ,IkRepresenting the interference leakage value, H, of user kkjRepresenting the channel matrix for base station j to user k.
Judging whether the iteration times meet or whether the system interference leakage value converges, if not, calculating an emission interference matrix according to the projection matrix, wherein the formula is as follows:
wherein ,
a first transmit interference matrix is represented,
representing a second transmit interference matrix, H3jRepresenting base station j to user R3Of the channel matrix, F3Represents a user R3The signal space projection matrix of (a).
Updating transmit side beamforming vector vjAnd artificial noise precoding matrix w3The formula of (1) is:
wherein ,
representation matrix
Eigenvectors, w, corresponding to the smallest eigenvalues3Representing an artificial noise pre-coding matrix and,
representation matrix
D is the eigenvector corresponding to the d-th minimum eigenvalue, d represents the number of independent data streams to be transmitted, danIndicating the number of transmitting ANs.
If the iteration times or the system interference leakage value is converged, outputting a receiving vector and a beam forming vector; according to the receiving vector and the beam forming vector, a recovery signal after the interference of other users is eliminated can be obtained; the convergence of the interference alignment algorithm is shown in FIG. 4, with 3 iterations increasingThe interference leakage values of the users are all reduced and finally converge to 10-15Left and right, indicating that the last disturbs have been aligned.
Since only the statistical CSI of the eavesdropping node is known, a security interruption cannot be avoided; the invention considers maximizing the safe rate under the constraint of the interruption probability. Reconfiguring a user R3The recovered signal of (a) is:
wherein ,
representing the signal-to-interference-and-noise ratio, P, of the recovered signal3Denotes the signal transmission power of the transmitting end, [ phi ] denotes the power distribution ratio, H33Representing the base station BS3To the user R3V of the channel matrix3Representing the base station BS3The transmit beamforming vector of (a) is,
representing the transpose of the received vector.
For an eavesdropping node, the received signal is as follows:
calculating the signal-to-noise ratio of the recovered signal according to the output receiving vector, the beamforming vector and the power distribution ratio, wherein the formula is as follows:
calculating the signal-to-interference-and-noise ratio of the signal received by the eavesdropper according to the power distribution ratio and the signal-to-noise ratio of the recovered signal, wherein the formula is as follows:
wherein M represents a base station BS3The number of equipped transmit antennas.
In order to realize the maximization of the safety rate under the constraint of the safety interruption probability, a safety rate objective function is constructed according to the signal-to-interference-and-noise ratio of a signal received by an eavesdropper, wherein the safety rate objective function is as follows:
wherein ,RSIndicating the safe transmission rate of the base station,
represents R3The effective signal-to-noise ratio of the received signal,
a threshold value is indicated that is related to the probability of interruption,
representing the signal to interference plus noise ratio of the signal received by the eavesdropper and epsilon representing the maximum allowed probability of security disruption.
Optimize phi, order
The objective function can be written as:
solving the above objective function, as shown in fig. 3, the solving process is as follows:
to RS(phi) derivation
Due to R'S(φ) is a monotonically decreasing function of φ, and thus R ″, can be derivedS(phi) < 0. According to a second order condition in convex optimization, RSAnd (phi) is a strict concave-up function. If R'S(1) When R is not less than 0S(phi) is a strictly increasing function when R'S(0) When the ratio is less than or equal to 0, RS(φ) is a strict decreasing function; the original optimization problem is solved by adopting a numerical method, and the specific steps are as follows:
1) by bringing phi-1 into R'S(phi) function, calculate R'S(1)；
2) R 'is'S(1)≥0，RS(phi) is a strict increasing function on (0,1), so that the optimal power distribution ratio phi can be obtained*1 and maximum safe rate
Otherwise, carrying out the next step;
3) bringing phi-0 into R'S(phi) function, calculate R'S(0)；
4) R 'is'S(0)≤0，RS(phi) is a strict decreasing function on (0,1), so that the optimal power distribution ratio phi can be obtained*0 and maximum safe rate
Otherwise, carrying out the next step;
5) r's'SThe function (phi) is equal to 0, i.e. R'SWhen (phi) is 0, the equation is solved to obtain the optimal power distribution proportion phi*And a safe speedRate of change
The variation of the allocation ratio of different transmission powers of the base station to the optimal power when the interference is aligned is shown in fig. 5; when the base station BS1And base station BS2Is 20dB, all power is allocated to the useful signal, but with the base station BS3The probability of information leakage is increased due to the increase of the transmitting power; for example, when P3Greater than 15dB, the generation of AN reduces the eavesdropper's reception quality, with P3The optimal power allocation ratios for all schemes converge to the same value.
The result of the safety rate values in interference alignment is shown in FIG. 6, when the transmission power of the third base station is low, the base station BS1And base station BS2The greater the transmit power of, the higher the safe rate. But as the transmit power of the third base station increases, the optimal power allocation ratios all converge to the same value, so the final safe rates are the same.
Substituting the optimal power distribution proportion obtained by solving into the user R3To obtain the user R3A received recovery signal.
The interference alignment algorithm of the invention reduces the channel quality of the eavesdropping node by using artificial noise, and does not introduce additional interference to the legal transmission of the multi-cell wireless network; by alternately iterating and interfering the matrix and the subspace at the receiving end, the interference is projected into a signal space with lower dimensionality, and the remaining non-interference signal space is used for transmitting useful signals, so that interference alignment is realized; the algorithm designs AN alternative minimized interference alignment algorithm with AN to update the interference subspace of each transceiving end, can work in a time division duplex system and a frequency division duplex system, and does not need to assume the reciprocity of channels, the distribution of antennas or AN information transmission mode between two iteration steps, so the algorithm is more suitable for researching the solution of interference alignment; the channel quality of the eavesdropping node is reduced by utilizing artificial noise, and meanwhile, no extra interference is introduced to the legal transmission of the multi-cell network, so that the reliability of secret message transmission is improved; in addition, only if the statistical CSI of the eavesdropping node is known, the dynamic power distribution between the confidential signal and the AN signal is considered on the basis of interference alignment, the power distribution between the confidential signal and the AN signal can be dynamically adjusted, the safety performance of the system is further enhanced, the safety performance of the system is improved, and the application scene is wider.
The above-mentioned embodiments, which further illustrate the objects, technical solutions and advantages of the present invention, should be understood that the above-mentioned embodiments are only preferred embodiments of the present invention, and should not be construed as limiting the present invention, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (10)
1. A multi-cell network safety transmission method based on artificial noise is characterized by comprising the following steps: the base station sends information to the user side, wherein the information comprises AN information and safety information; the user side processes the received information by adopting AN AN alternative minimized interference alignment algorithm to obtain a beam forming vector and a receiving vector of the signal; obtaining a recovery signal according to the output receiving vector and the beamforming vector;
the process of processing the received information by adopting the AN alternation minimized interference alignment algorithm comprises the following steps:
s1: initializing a wave beam forming vector and an artificial noise pre-coding matrix of a transmitting end; setting iteration times;
s2: calculating a set of standard orthogonal bases of a receiving interference matrix and a receiving interference subspace according to the wave beam forming vector of the transmitting end and the artificial noise pre-coding matrix;
s3: calculating a signal space projection matrix and a receiving vector of a receiving end according to the standard orthogonal basis;
s4: calculating a system interference leakage value according to the wave beam forming vector of the transmitting end, the artificial noise pre-coding matrix and the standard orthogonal base;
s5: judging whether the iteration times meet or whether the system interference leakage value is converged, and if the iteration times meet or the system interference leakage value is converged, outputting a receiving vector and a beam forming vector; if the iteration times are not met or the system interference leakage value is not converged, executing step S6;
s6: calculating an emission interference matrix according to the projection matrix;
s7: and updating the beamforming vector and the artificial noise precoding matrix at the transmitting end according to the transmitting interference matrix and returning to the step S2.
2. The method as claimed in claim 1, wherein the formulas for calculating the received interference matrix and the orthonormal basis are respectively:
Ck＝xl[Qk],l＝1,...,Nk-1 and k ═ 1,2,3
wherein ,QkRepresenting the received interference matrix, HkjRepresenting the channel matrix from base station j to user k, j representing the base station transmitting the useful signal, p representing the base station transmitting the safety signal, HkpRepresenting the channel matrix, v, from base station p to user kjRepresenting the transmit beamforming vector, w, of base station jpRepresenting an artificial noise precoding matrix, CkDenotes the orthonormal base, xl[Qk]Representation matrix QkEigenvector corresponding to the ith largest eigenvalue, NkRepresenting the number of receive antennas for user k.
3. The method as claimed in claim 1, wherein the formulas for calculating the signal space projection matrix and the receiving vector at the receiving end are respectively:
wherein ,FkA signal space projection matrix, C, representing the user kkDenotes the orthonormal base, ukA reception vector at the receiving end is represented,
representation matrix
The null space of (a).
4. The method of claim 1, wherein the formula for calculating the system interference leakage value is as follows:
wherein ,IkRepresenting the interference leakage value, v, of user kjRepresents the transmit beamforming vector, H, of base station jkjRepresenting the channel matrix from base station j to user k, CkRepresenting an orthonormal basis.
5. The method of claim 1, wherein the formula for calculating the transmit interference matrix is as follows:
wherein ,
a first transmit interference matrix is represented,
representing a second transmitted interference matrix, k representing the kth user, q representing a user eavesdropped by an eavesdropper, HkjRepresenting the channel matrix, H, from base station j to user kqjRepresenting the channel matrix, F, from base station j to user qkA signal space projection matrix, F, representing a user kqA signal space projection matrix representing user q.
6. The method according to claim 1, wherein the formula for updating the beamforming vector and the artificial noise precoding matrix at the transmitting end is as follows:
wherein ,vjRepresents the transmit beamforming vector for base station j,
representation matrix
Eigenvectors, w, corresponding to the smallest eigenvaluesqRepresenting an artificial noise pre-coding matrix and,
representation matrix
D is the eigenvector corresponding to the d-th minimum eigenvalue, d represents the number of independent data streams to be transmitted, danIndicating the number of transmitting ANs.
7. The method of claim 1, wherein obtaining the recovery signal according to the output received vector and beamforming vector comprises: initializing a power distribution ratio, and calculating a signal-to-noise ratio of a recovery signal according to the receiving vector, the beam forming vector and the power distribution ratio; calculating the signal-to-interference-and-noise ratio of the signal received by the eavesdropper according to the power distribution ratio and the signal-to-noise ratio of the recovered signal; constructing a safe speed target function according to the signal-to-interference-and-noise ratio of a signal received by an eavesdropper; solving the maximum value of the safe rate objective function to obtain the optimal power distribution ratio; and calculating a recovery signal according to the optimal power distribution ratio.
8. The method as claimed in claim 7, wherein the formula for calculating the snr of the recovered signal is:
wherein ,
representing the signal-to-interference-and-noise ratio, P, of the recovered signalpDenotes the signal transmission power of the transmitting end, [ phi ] denotes the power distribution ratio, HpqRepresenting the channel matrix, v, from base station p to user qpRepresenting the transmit beamforming vector for base station p,
representing the transpose of the received vector.
9. The method of claim 7, wherein the safety rate objective function is:
wherein ,RSDenotes the base station safe transmission rate, phi denotes the power allocation ratio, gamma denotes the effective snr of the received signal of user q, mu denotes the threshold,
representing the signal to interference plus noise ratio of the signal received by the eavesdropper and epsilon representing the maximum allowed probability of security disruption.
10. The method of claim 7, wherein the formula for calculating the recovery signal is:
wherein ,
represents a recovered signal, PpDenotes a signal transmission power of a transmitting end, phi denotes a power distribution ratio,
a transposed matrix representing the received vector, HpqRepresenting the channel matrix, v, from base station p to user qpRepresenting the transmit beamforming vector, x, of base station ppRepresenting the number of transmissions of the base station pAccording to the symbol, nqRepresenting an additive white gaussian noise vector received by user q.
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