CN110752865A - Multi-user MIMO communication secrecy method under relay cooperation network - Google Patents

Multi-user MIMO communication secrecy method under relay cooperation network Download PDF

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CN110752865A
CN110752865A CN201910986813.5A CN201910986813A CN110752865A CN 110752865 A CN110752865 A CN 110752865A CN 201910986813 A CN201910986813 A CN 201910986813A CN 110752865 A CN110752865 A CN 110752865A
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relay
interference
eavesdropping
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matrix
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CN110752865B (en
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孙惜媛
解志斌
翁志辉
任彦玲
徐桧
田雨波
张贞凯
王彪
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Jiangsu University of Science and Technology
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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
    • H04B7/0413—MIMO systems
    • H04B7/0452—Multi-user MIMO systems
    • 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
    • H04B7/022—Site diversity; Macro-diversity
    • H04B7/024—Co-operative use of antennas of several sites, e.g. in co-ordinated multipoint or co-operative multiple-input multiple-output [MIMO] systems
    • 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
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/14—Relay systems
    • H04B7/15—Active relay systems
    • H04B7/155—Ground-based stations
    • H04B7/15564—Relay station antennae loop interference reduction
    • H04B7/15585—Relay station antennae loop interference reduction by interference cancellation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04K—SECRET COMMUNICATION; JAMMING OF COMMUNICATION
    • H04K3/00—Jamming of communication; Counter-measures
    • H04K3/80—Jamming or countermeasure characterized by its function
    • H04K3/82—Jamming or countermeasure characterized by its function related to preventing surveillance, interception or detection
    • H04K3/825—Jamming or countermeasure characterized by its function related to preventing surveillance, interception or detection by jamming
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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Abstract

The invention discloses a multi-user MIMO communication security method under a relay cooperative network, which considers a more comprehensive application scene in the relay cooperative network, provides a security communication implementation method under the condition that an eavesdropping terminal is configured with different antennas, utilizes a relay to send artificial noise to interfere the eavesdropping terminal to steal useful signals, and eliminates multi-user interference and artificial noise interference based on a distributed interference alignment algorithm. Compared with other methods of transmitting artificial noise by using a transmitting end and a receiving end, the method has the advantages of reducing implementation complexity of the transmitting and receiving ends, and improving system safety while not reducing transmission rate of a main channel.

Description

Multi-user MIMO communication secrecy method under relay cooperation network
Technical Field
The invention relates to an interference alignment technology, in particular to a multi-user MIMO communication secrecy method under a relay cooperation network, and belongs to the technical field of wireless communication.
Background
In modern information society, it is becoming increasingly important to securely exchange encrypted information in wireless networks. In addition to or instead of the upper layer encryption method, the physical layer safely utilizes the characteristics of multipath, reciprocity, space uniqueness and the like of a channel to improve the safety of the wireless communication system at the bottom layer. With the explosive growth of mobile devices and data traffic, interference management becomes a critical issue in modern wireless communications. By combining the physical layer security and the interference alignment technology, the problems of secure communication and user interference when a user is intercepted in a Multiple-Input Multiple-Output (MIMO) network can be solved, and therefore the effectiveness and the reliability of the system are improved.
Physical Layer Security (PLS) technical research is mainly developed from aspects of information theory, transmission optimization, power resource allocation and the like. The information theory mainly researches the privacy capacity theory of the system; the transmission optimization and power resource allocation mainly research Artificial Noise (AN), beamforming, security coding and other physical layer security technologies that utilize channel characteristics. Cooperative communication is used as a key technology of next-generation wireless communication, and spatial diversity and significant performance benefits are achieved by using relay forwarding information in the aspects of link stability, spectrum benefits, system capacity, transmission range and the like.
Most of the conventional interference control methods adopt the channel orthogonalization principle. The Interference Alignment (IA) technique reduces the influence of aggregation interference by aligning information sent by multiple source nodes to a low-dimensional subspace at a receiving end. The closed-form solution to interference alignment is difficult to solve, especially when there are a large number of users in the network. Therefore, several iterative algorithms are provided to solve the interference alignment problem, and the complexity of solving a closed interference alignment solution process is reduced. These iterative algorithms are based primarily on a minimum interference leakage criterion, a minimum mean square error criterion, a maximum signal-to-interference-and-noise ratio criterion, and a maximum total rate criterion.
Chinese patent CN 106059705 a discloses a relay physical layer secure transmission method, which analyzes a scheme of relay sending artificial noise interference interception under the condition of only one group of users, and the relay adopts a decoding-forwarding full duplex mode, and can simultaneously send a mixed signal of an expected signal and artificial noise to a destination node while receiving information from a source node. Chinese patent CN 108429708A introduces a green secret communication method for multi-user interference alignment network, which is based on MIMO interference alignment network to transmit artificial noise at the receiving end and perform energy collection at the same time, but increases the energy consumption at the receiving end to affect the quality of the received signal. "Transactions on Wireless Communications" volume 15, No. 8 "Anti-Eave dropping Schemes for Interference Alignment (IA) -Based Wireless networks" proposes an MIMO network Based on Interference Alignment, and a transmitting end sends artificial noise to interfere with an Eavesdropping user, but the method increases the energy consumption of the transmitting end. In signal processing, volume 28, phase 9, physical layer security technology and security area analysis based on receiver artificial noise, a method for transmitting artificial noise by a receiving end is provided, and a new concept of a security area is provided, wherein traversal security capacity analysis is performed on positions of different eavesdroppers, but only the situation of one group of users is discussed in the document. In Chongqing post and telecommunications university newspaper 26, No. 4, DOF (degree of freedom) analysis of two-user relay auxiliary channel based on actual interference alignment technology, a two-user relay auxiliary interference channel model is discussed, and an interference signal is transmitted by a relay to improve the confidentiality rate. Therefore, it is necessary to solve the problems of network security including eavesdropping end among multiple users, energy consumption reduction at the receiving and transmitting points, and communication quality improvement.
Disclosure of Invention
The invention aims to provide a multi-user MIMO communication secrecy method under a relay cooperation network, which ensures the reliability and effectiveness of communication. Aiming at the situation that only one group of users or two groups of users are discussed in the prior art and the defect of large energy consumption of a transmitting and receiving end, the invention provides a method for simultaneously solving the wireless communication safety problem and the MIMO technology interference problem. The method for the safe communication under the two antenna conditions is provided, one condition is that the number of the antennas of the eavesdropping end is smaller than that of the transmitting end and the relay end, the transmitting end and the eavesdropping end have null space at the moment, the relay end does not need to transmit artificial noise, and only the interference from other users is eliminated at the receiving end by utilizing the interference alignment technology. The other situation is that the number of the antennas of the eavesdropping end is larger than that of the transmitting end and the relay end, no null space exists between the transmitting end and the eavesdropping end, the relay end needs to transmit artificial noise to interfere with the eavesdropping user, and the receiving end needs to eliminate interference from other users and interference of the artificial noise.
The purpose of the invention is realized by the following technical scheme:
a multi-user MIMO communication security method in a relay cooperation network comprises K sending ends T, a relay end R, K receiving ends R and an eavesdropping end E, wherein the sending ends are provided with M antennas, the relay ends are provided with S antennas, the receiving ends are provided with N antennas, and the eavesdropping end is provided with L antennas. The number of the antennas of all the nodes is not less than one. The relay terminal R adopts a full duplex amplification forwarding mode, and the data stream d sent by the sending terminal T and the artificial noise data stream d sent by the relay terminal RanAre both smaller than the smaller value of the transmitting end antenna M and the receiving end antenna N. The sending end T and the relay end R know the information of the eavesdropping end E so as to judge whether the eavesdropping channel has a null space or not, thereby determining whether artificial noise needs to be sent to interfere the eavesdropping rate or not and ensuring safe communication.
The multi-user MIMO communication secrecy method under the relay cooperation network comprises the following steps:
the method comprises the following steps: initializing a two-hop MIMO relay network with eavesdropping users, wherein the number of antennas of each node is not less than 1.
Step two: and adopting different secret communication methods according to the comparison of the number of the eavesdropping end, the sending end and the relay antenna.
1) When L < M and L < R, the transmitting end T has a null space to the eavesdropping end E, information can be directly transmitted in the null space of the eavesdropping channel, the eavesdropping end E cannot hear a target signal, and the relay end R does not need to transmit artificial noise at the moment.
In the first time slot, a sending end T broadcasts signals, a relay end R and a receiving end R receive the signals, and an eavesdropping end E eavesdrops the signals.
The signal received by the relay terminal R is:
Figure BDA0002236942330000031
the signal received by the receiving end r is:
Figure BDA0002236942330000032
the signal received by the eavesdropping terminal E is as follows:
Figure BDA0002236942330000033
in the formula PiIndicating the transmitting end TiPower of transmission, E [ | x[i](1)||2]＝Pi。
Figure BDA0002236942330000034
For the transmitting end TiThe channel coefficients to the relay peer R,
Figure BDA0002236942330000035
for the transmitting end TiThe channel coefficients to the receiving end r,
Figure BDA0002236942330000036
for the transmitting end TiChannel coefficients to the eavesdropping end E. x is the number of[i](1) To representSending terminal TiA target signal transmitted in a first time slot. n is[R],n[r],n[E]The noise vectors of the relay terminal R, the receiving terminal R and the eavesdropping terminal E respectively have a mean value of 0 and a variance of
Figure BDA0002236942330000037
Independent and identically distributed complex Gaussian random variables.
2) When L is larger than or equal to M and L is larger than or equal to R, the transmitting end T has no null space to the eavesdropping end E, and the relay end R needs to transmit artificial noise to interfere the eavesdropping of the eavesdropping end E.
In the first time slot, the sending terminal T sends a signal, and the relay terminal R adopts SiThe root antenna receiving the useful signal, SjThe root antenna receives a self-interference signal, SRThe root antenna transmits the artificial noise.
The relay terminal R receives the signal:
in the formula
Figure BDA0002236942330000042
For the channel coefficient from relay R to relay R, z[R](1) Indicates the relay terminal R with power PRTransmitted in the first time slot and containing danA target signal of the data stream.
The signals at the receiving end are:
Figure BDA0002236942330000043
the signal received by the eavesdropping terminal is as follows:
Figure BDA0002236942330000044
in the formula
Figure BDA0002236942330000045
Is the channel coefficient from the relay end R to the eavesdropping end E.
Step three: 1) and when L is less than M and L is less than R, in the second time slot, the sending end T sends the signal again, the relay end R forwards the signal, the receiving end R receives the signal, and the eavesdropping end E eavesdrops the signal.
The signal received by the receiving end r is:
Figure BDA0002236942330000046
in the formula x[i](2) Indicating the transmitting end TiThe target signal transmitted in the second time slot,
Figure BDA0002236942330000047
for the channel coefficient, P, from the relay R to the receiver RRFor the transmission power of the relay terminal R, x[R](2)＝βyR(1) For the signal forwarded by the relay R β is an amplified forwarding factor.
The signal received by the eavesdropping terminal E is:
Figure BDA0002236942330000048
in the formulaIs the channel coefficient from the relay end R to the eavesdropping end E.
2) And when L is larger than or equal to M and L is larger than or equal to R, the transmitting end T transmits the signal again in the second time slot, the relay end R transmits the secret data stream by adopting d antennas, the rest (s-d) antennas are used for transmitting artificial noise, and the relay end R does not receive the signal at the moment.
The receiving end r receives signals as follows:
Figure BDA0002236942330000052
where ρ ∈ (0,1) is the power division factor.
The signal received by the eavesdropping terminal E is as follows:
Figure BDA0002236942330000053
step four: 1) when L < M and L < R, the receiving end can eliminate the interference of other users when the following conditions are satisfied:
Figure BDA0002236942330000054
in the formula
Figure BDA0002236942330000055
A unit precoding matrix representing the ith user transmission target signal and satisfying
Figure BDA0002236942330000056
A unit precoding matrix representing the target signal transmitted by the kth user and satisfying
Figure BDA0002236942330000057
A unit interference suppression matrix representing the reception target signal of the kth user and satisfying
Figure BDA0002236942330000058
Is expressed as U [ 2 ]k]The conjugate transpose matrix of (2). Equivalent channel:a channel matrix representing the ith transmitting terminal T to the kth receiving terminal r,
Figure BDA00022369423300000510
represents the channel matrix from the ith sender T to the relay R,
Figure BDA00022369423300000511
representing the channel matrix from the relay terminal R to the kth receiver terminal R.A channel matrix representing the k-th transmitting terminal T to the k-th receiving terminal r,is shown ask transmit terminal T to relay terminal R channel matrices,
Figure BDA0002236942330000061
representing the channel matrix from the relay terminal R to the kth receiver terminal R. And independent equal distribution (i.i.d) is satisfied between each channel. The interference of other users received by the receiving end r can be realized by a distributed interference alignment algorithm based on a minimum interference leakage criterion, the minimum interference leakage criterion is improved by the invention, and the specific implementation method is as follows:
step1 initializing the precoding matrix
Figure BDA0002236942330000062
To satisfy
Step2 the iteration starts.
Step3 calculation of interference covariance matrix for downlink k users
Figure BDA0002236942330000064
In the formula Q[k](1),Q[k](2) Can be obtained by the following equation:
Figure BDA0002236942330000065
step4 calculation of the downlink k-user interference suppression matrix
Figure BDA0002236942330000066
In the formula of U[k](1),U[k](2) Can be obtained by the following formula
Figure BDA0002236942330000067
The above formula represents U[k]Is equal to Q[k]D ofkAnd the characteristic vectors corresponding to the minimum characteristic values form a matrix.
Step5 reversing the communication direction to order
Figure BDA0002236942330000068
Computing a precoding matrix for an uplink
Figure BDA0002236942330000069
Step6 calculating the uplink k user interference covariance matrix
Figure BDA00022369423300000610
In the formula
Figure BDA00022369423300000611
Can be obtained by the following equation:
Figure BDA00022369423300000612
in the formula
Figure BDA00022369423300000613
A transmit-side precoding matrix representing the reverse link,
Figure BDA00022369423300000614
a channel matrix representing the reverse link.
Step7 calculating the uplink k-user interference suppression matrix
Figure BDA0002236942330000071
In the formula
Figure BDA0002236942330000072
Can be obtained by the following formula
Figure BDA0002236942330000073
The above formula represents
Figure BDA0002236942330000074
Is equal to
Figure BDA0002236942330000075
D ofkAnd the characteristic vectors corresponding to the minimum characteristic values form a matrix.
Step8 reversing the communication direction to order
Step9, continue iteration, update U[k]And calculating the interference leakage value until the interference leakage value is smaller than a given threshold value, namely converging, and ending the iteration.
Step10 output V[k],U[k]。
Step11 otherwise, returning to Step 3.
V to be output[k],U[k]Substituting:
Figure BDA0002236942330000077
the objective function for minimizing interference leakage is:
Figure BDA0002236942330000078
at this time, the matrix form of the received signal at the receiving end r is:
Figure BDA0002236942330000079
in the formula X[k]Containing d indicating the transmission of the Kth user[k]Signal vectors for each data stream.
Figure BDA00022369423300000710
Represents an Additive White Gaussian Noise (AWGN) vector received by the kth user.
The transmission rate of the kth user is:
Figure BDA00022369423300000711
the interception rate of the interception end is as follows:
Figure BDA0002236942330000081
the system security rate is:
Figure BDA0002236942330000082
in the formulaIndicating that the greater of x and 0 is taken. Defining a channel matrix
Figure BDA0002236942330000084
2) When L is larger than or equal to M and L is larger than or equal to R, the self-interference problem of the relay terminal R can be eliminated by methods such as antenna interference elimination, radio frequency interference elimination and digital interference elimination. When the following conditions are met, the receiving end can eliminate the interference of other users and artificial noise:
Figure BDA0002236942330000086
in the formula
Figure BDA0002236942330000087
The unit precoding matrix representing the artificial noise transmitted by the relay terminal R and meeting the requirementEquivalent channel:
Figure BDA0002236942330000089
other users and artifacts received at the receiver rThe interference can be realized by a distributed interference alignment algorithm based on a minimum interference leakage criterion, the minimum interference leakage criterion is improved by the invention, and the specific implementation method is as follows:
step1 initializing the precoding matrixTo satisfy
Figure BDA00022369423300000811
Figure BDA00022369423300000812
To satisfy
Figure BDA00022369423300000813
Step2 the iteration starts.
Step3 calculation of interference covariance matrix for downlink k users
Figure BDA00022369423300000814
In the formula Q[k](1),Q[k](2) Can be obtained by the following equation:
Figure BDA0002236942330000091
in the formula PanSending artificial noise power for relay terminal R and satisfying Pan＝(1-ρ)PR。W[R]A precoding matrix representing the relay transmission noise.
Step4 calculation of the downlink k-user interference suppression matrix
Figure BDA0002236942330000092
In the formula of U[k](1),U[k](2) Can be obtained by the following formula
Figure BDA0002236942330000093
The above formula represents U[k]Is equal to Q[k]D ofkAnd the characteristic vectors corresponding to the minimum characteristic values form a matrix.
Step5 reversing the communication direction to order
Figure BDA0002236942330000094
Computing a precoding matrix for an uplink
Figure BDA0002236942330000095
Step6 calculating the uplink k user interference covariance matrix
Figure BDA0002236942330000096
In the formula
Figure BDA0002236942330000097
Can be obtained by the following equation:
Figure BDA0002236942330000098
Figure BDA0002236942330000099
step7 calculating the uplink k-user interference suppression matrix
Figure BDA00022369423300000910
Interference rejection matrix for artificial noise
Figure BDA00022369423300000911
In the formula
Figure BDA00022369423300000912
Can be obtained by the following equation:
Figure BDA00022369423300000913
Figure BDA0002236942330000101
the above formula represents U[k]，
Figure BDA0002236942330000102
Is equal to Q[k]，
Figure BDA0002236942330000103
D ofkAnd the characteristic vectors corresponding to the minimum characteristic values form a matrix.
Step8 reversing the communication direction to order
Figure BDA0002236942330000104
Step9, continue iteration, update U[k]、
Figure BDA0002236942330000105
And calculating the interference leakage value until the interference leakage value is smaller than a given threshold value, namely converging, and ending the iteration.
Step10 output V[k]、U[k]、W[k]。
Step11 otherwise, returning to Step 3.
V to be output[k]、U[k]、W[k]Substituting:
Figure BDA0002236942330000106
Figure BDA0002236942330000107
the objective function for minimizing interference leakage is:
Figure BDA0002236942330000108
at this time, the matrix form of the received signal at the receiving end r is:
Figure BDA0002236942330000109
the transmission rate of the kth user is:
Figure BDA00022369423300001010
the interception rate of the interception end is as follows:
Figure BDA00022369423300001011
the safe rate of the system is:
Figure BDA0002236942330000111
in which a channel matrix is defined
Figure BDA0002236942330000112
The object of the invention can be further achieved by the following technical measures:
the multi-user MIMO communication security method under the relay cooperation network comprises the following parameter ranges in the first step: k1, 2, N1, 2, S1, 2, L1, 2, 1.
Figure BDA0002236942330000113
M+N-(K+1)d≥0。
In the multi-user MIMO communication confidentiality method under the relay cooperative network, the design criterion of the amplification forwarding factor in the third step is to meet the relay transmission power P while maximizing the strength of the transmitted informationRThe constraint of (2):
Figure BDA0002236942330000114
the multi-user MIMO communication security method in the relay cooperative network comprises the step three that when the eavesdropping channel has no null space, the signal is transmittedThe second time slot relay terminal R of (1) has power rho PRForwarding the signal at the transmitting end with a power (1-P) PRGenerating artificial noise.
In the fourth step, a matrix form of signals received by the eavesdropping terminal under different conditions is given according to the relation between the number of the E antennas of the eavesdropping terminal, the number of users and data streams sent by the sending terminal T.
1) When L < M, L < R, the eavesdropping channel has a null space.
(1) M is more than L and less than or equal to dK-d +1, and R is more than L and less than or equal to dK-d + 1. At this time, the eavesdropping terminal E cannot eliminate the interference of other users.
At this time, the eavesdropping end E receives a signal matrix form:
Figure BDA0002236942330000115
in the formula
Figure BDA0002236942330000116
A unit interference suppression matrix for representing the target signal intercepted by the interception end E and satisfies
Figure BDA0002236942330000121
Represents U[k]The conjugate transpose matrix of (2). Equivalent channel:a channel matrix representing the kth transmitting end to the eavesdropping end E,
Figure BDA0002236942330000123
representing the channel matrix from the relay peer R to the eavesdropping peer E.
Figure BDA0002236942330000124
And representing the channel matrix from the ith transmitting terminal T to the eavesdropping terminal E.
(2) M + N ═ d (K +1), dK-d + 1. ltoreq.L < M, dK-d + 1. ltoreq.L < R. The eavesdropping end E is provided with at least (dK-d +1) antennas to eliminate other user interference, but the interference of the main channel information data stream still exists.
At this time, the eavesdropping end E receives a signal matrix form:
Figure BDA0002236942330000125
2) when L is larger than or equal to M and L is larger than or equal to R, no null space exists in the eavesdropping channel.
(1) And L is more than or equal to M and less than dK-d +1, and R is more than or equal to L and less than dK-d +1, so that the eavesdropping end cannot eliminate the interference of other users and artificial noise.
At this time, the eavesdropping end E receives a signal matrix form:
Figure BDA0002236942330000126
in the formula Z[R]Meaning that the relay R transmits
Figure BDA0002236942330000127
Signal vectors for each data stream. Equivalent channel
(2) M + N ═ d (K +1), M ≦ dK-d +1 ≦ L, R ≦ dK-d +1 ≦ L, at this time, the eavesdropping user may eliminate the interference of other users, but cannot eliminate the interference between the main channel information data streams and the interference of artificial noise.
At this time, the eavesdropping end E receives a signal matrix form:
Figure BDA0002236942330000129
in the multi-user MIMO communication security method in the relay cooperative network, self-interference in step four can adopt a Zero Forcing (ZF) precoding cancellation method in digital interference cancellation, and the main idea of Zero Forcing precoding is to select a non-Zero matrix T at a relayiSatisfy HiiTiWhen 0, the residual self-interference is 0. The ZF precoding scheme has the capability of completely eliminating residual self-interference. Precoding matrix TiMust be aZero matrix, otherwise no signal is transmitted. In order to obtain a non-zero precoding matrix, it should be ensured that the total number of transmit antennas is greater than the sum of receive antennas for the desired signal and receive antennas for the self-interference signal, which is expressed by the following formula:
SR>Si+Sj(41)
at this time, the signal received by the relay terminal R is:
Figure BDA0002236942330000131
under the sufficient condition, a non-zero space HiiSingular Value Decomposition (SVD):
Figure BDA0002236942330000132
in the formula
Figure BDA0002236942330000133
nii＝SR-SiAnd V isiiIf the middle column vectors are orthogonal to each other, the precoding matrix can be represented as:
T[i]＝V[ii]A[ii](44)
in the formula AiiIs non-zero niiThe x L zero forcing precoding matrix (L denotes an average transmitted data symbol).
Compared with the prior art, the method has the advantages that the relays are used for sending the artificial noise to interfere the eavesdropping of the useful signals by the eavesdropping end, and compared with a method for sending the artificial noise by the sending end and the receiving end, the method reduces the energy consumption of the sending end and the receiving end and improves the reliability of the system. By adopting the relay-added cooperative communication, the remote communication quality can be improved. Interference among users in the MIMO communication network can be eliminated by utilizing the interference alignment technology. The invention is more practical, considers more comprehensive conditions and provides a method for safe communication under different antenna numbers.
Drawings
Fig. 1 is a system model diagram of a relay cooperative network of the present invention;
FIG. 2 is a flow chart of a multi-user MIMO communication privacy method in a relay cooperative network;
FIG. 3 is a flow chart of a distributed interference alignment algorithm for eavesdropping on channels with nulls;
fig. 4 is a flow chart of a distributed interference alignment algorithm for eavesdropping channels without nulls.
Detailed Description
The invention is further described with reference to the following figures and specific examples.
As shown in fig. 1, the present invention is a system model diagram of a relay cooperative network.
A relay cooperation network comprises K sending ends T, a relay end R, K receiving ends R and an eavesdropping end E, wherein the sending ends are provided with M antennas, the relay end is provided with S antennas, the receiving ends are provided with N antennas, and the eavesdropping end is provided with L antennas. The number of the antennas of all the nodes is not less than one. The relay terminal R adopts a full duplex amplification forwarding mode, and the data stream d sent by the sending terminal T and the artificial noise data stream d sent by the relay terminal RanAre both smaller than the smaller value of the transmitting end antenna M and the receiving end antenna N. The sending end T and the relay end R know the information of the eavesdropping end E so as to judge whether the eavesdropping channel has a null space or not, thereby determining whether artificial noise needs to be sent to interfere the eavesdropping rate or not and ensuring safe communication.
The invention discloses a multi-user MIMO communication secrecy method under a relay cooperation network, which is shown in figure 2:
the method comprises the following steps: initializing a two-hop MIMO relay network with a wiretap user, wherein the number of antennas of each node is not less than 1, and the values of each parameter are as follows: k-5, M-9, N-8, R-10, d-2, dan＝1。
Step two: and adopting different secret communication methods according to the comparison of the number of the eavesdropping end, the sending end and the relay antenna.
1) When L < M and L < R, the transmitting end T has a null space to the eavesdropping end E, information can be directly transmitted in the null space of the eavesdropping channel, the eavesdropping end E cannot hear a target signal, and the relay end R does not need to transmit artificial noise at the moment.
In the first time slot, a sending end T broadcasts signals, a relay end R and a receiving end R receive the signals, and an eavesdropping end E eavesdrops the signals.
The signal received by the relay terminal R is:
Figure BDA0002236942330000141
the signal received by the receiving end r is:
Figure BDA0002236942330000142
the signal received by the eavesdropping terminal E is as follows:
Figure BDA0002236942330000143
in the formula PiIndicating the transmitting end TiPower of transmission, E [ | x[i](1)||2]＝Pi。
Figure BDA0002236942330000144
For the transmitting end TiThe channel coefficients to the relay peer R,
Figure BDA0002236942330000151
for the transmitting end TiThe channel coefficients to the receiving end r,
Figure BDA0002236942330000152
for the transmitting end TiChannel coefficients to the eavesdropping end E. x is the number of[i](1) Indicating the transmitting end TiA target signal transmitted in a first time slot. n is[R],n[r],n[E]The noise vectors of the relay terminal R, the receiving terminal R and the eavesdropping terminal E respectively have a mean value of 0 and a variance ofIndependent and identically distributed complex Gaussian random variables.
2) When L is larger than or equal to M and L is larger than or equal to R, the transmitting end T has no null space to the eavesdropping end E, and the relay end R needs to transmit artificial noise to interfere the eavesdropping of the eavesdropping end E.
In the first time slot, the sending terminal T sends a signal, and the relay terminal R adopts SiThe root antenna receiving the useful signal, SjThe root antenna receives a self-interference signal, SRThe root antenna transmits the artificial noise.
The relay terminal R receives the signal:
Figure BDA0002236942330000154
in the formula
Figure BDA0002236942330000155
For the channel coefficient from relay R to relay R, z[R](1) Indicates the relay terminal R with power PRTransmitted in the first time slot and containing danA target signal of the data stream.
The signals at the receiving end are:
Figure BDA0002236942330000156
the signal received by the eavesdropping terminal is as follows:
Figure BDA0002236942330000157
in the formula
Figure BDA0002236942330000158
Is the channel coefficient from the relay end R to the eavesdropping end E.
Step three: 1) and when L is less than M and L is less than R, in the second time slot, the sending end T sends the signal again, the relay end R forwards the signal, the receiving end R receives the signal, and the eavesdropping end E eavesdrops the signal.
The signal received by the receiving end r is:
in the formula x[i](2) Indicating the transmitting end TiThe target signal transmitted in the second time slot,
Figure BDA0002236942330000161
for the channel coefficient, P, from the relay R to the receiver RRFor the transmission power of the relay terminal R, x[R](2)＝βyR(1) β is an amplification forwarding factor for the signal forwarded by the relay terminal R, and the design rule of the amplification forwarding factor is to satisfy the relay transmission power P while maximizing the strength of the transmitted informationRThe constraint of (2):
Figure BDA0002236942330000162
the signal received by the eavesdropping terminal E is:
Figure BDA0002236942330000163
2) and when L is larger than or equal to M and L is larger than or equal to R, the transmitting end T transmits the signal again in the second time slot, the relay end R transmits the secret data stream by adopting d antennas, the rest (s-d) antennas are used for transmitting artificial noise, and the relay end R does not receive the signal at the moment.
The receiving end r receives signals as follows:
Figure BDA0002236942330000164
where ρ ∈ (0,1) is the power division factor.
The signal received by the eavesdropping terminal E is as follows:
Figure BDA0002236942330000165
step four: 1) when L < M and L < R, the receiving end can eliminate the interference of other users when the following conditions are satisfied:
Figure BDA0002236942330000166
in the formula
Figure BDA0002236942330000167
A unit precoding matrix representing the ith user transmission target signal and satisfying
Figure BDA0002236942330000168
A unit precoding matrix representing the target signal transmitted by the kth user and satisfyingA unit interference suppression matrix representing the reception target signal of the kth user and satisfying
Figure BDA0002236942330000171
Represents U[k]The conjugate transpose matrix of (2). Equivalent channel:
Figure BDA0002236942330000172
a channel matrix representing the ith transmitting terminal T to the kth receiving terminal r,
Figure BDA0002236942330000173
represents the channel matrix from the ith sender T to the relay R,representing the channel matrix from the relay terminal R to the kth receiver terminal R.
Figure BDA0002236942330000175
A channel matrix representing the k-th transmitting terminal T to the k-th receiving terminal r,
Figure BDA0002236942330000176
represents the channel matrix from the kth sender T to the relay R,
Figure BDA0002236942330000177
representing the channel matrix from the relay terminal R to the kth receiver terminal R. And independent equal distribution (i.i.d) is satisfied between each channel.
The interference of other users can be eliminated at the receiving end by a distributed interference alignment algorithm, and is implemented by adopting an improved minimum interference leakage criterion, and the specific implementation process is shown in fig. 3:
step1 initializing the precoding matrix
Figure BDA0002236942330000178
To satisfy
Figure BDA0002236942330000179
Step2 the iteration starts.
Step3 calculation of interference covariance matrix for downlink k users
Figure BDA00022369423300001710
In the formula Q[k](1),Q[k](2) Can be obtained by the following equation:
Figure BDA00022369423300001711
step4 calculation of the downlink k-user interference suppression matrix
Figure BDA00022369423300001712
In the formula of U[k](1),U[k](2) Can be obtained by the following formula
Figure BDA00022369423300001713
The above formula represents U[k]Is equal to Q[k]D ofkAnd the characteristic vectors corresponding to the minimum characteristic values form a matrix.
Step5 reversing the communication direction to order
Figure BDA00022369423300001714
Computing a precoding matrix for an uplink
Figure BDA0002236942330000181
Step6 calculating the uplink k user interference covariance matrix
Figure BDA0002236942330000182
In the formula
Figure BDA0002236942330000183
Can be obtained by the following equation:
Figure BDA0002236942330000184
in the formula
Figure BDA0002236942330000185
A transmit-side precoding matrix representing the reverse link,
Figure BDA0002236942330000186
a channel matrix representing the reverse link.
Step7 calculating the uplink k-user interference suppression matrix
Figure BDA0002236942330000187
In the formula
Figure BDA0002236942330000188
Can be obtained by the following formula
The above formula represents
Figure BDA00022369423300001810
Is equal toD ofkAnd the characteristic vectors corresponding to the minimum characteristic values form a matrix.
Step8 reversing the communication direction to order
Figure BDA00022369423300001812
Step9, continue iteration, update U[k]And calculating the interference leakage value until the interference leakage value is smaller than a given threshold value, namely converging, and ending the iteration.
Step10 output V[k],U[k]。
Step11 otherwise, returning to Step 3.
V to be output[k],U[k]Substituting:
Figure BDA00022369423300001813
the objective function for minimizing interference leakage is:
Figure BDA00022369423300001814
at this time, the matrix form of the received signal at the receiving end r is:
in the formula X[k]Containing d indicating the transmission of the Kth user[k]Signal vectors for each data stream.
Figure BDA0002236942330000192
Represents an Additive White Gaussian Noise (AWGN) vector received by the kth user.
And giving a matrix form of signals received by the eavesdropping terminal E under different conditions according to the relationship between the number of the eavesdropping terminal E antennas and the number of users and the data stream transmitted by the transmitting terminal T.
(1) M is more than L and less than or equal to dK-d +1, and R is more than L and less than or equal to dK-d + 1. At this time, the eavesdropping terminal E cannot eliminate the interference of other users.
At this time, the eavesdropping end E receives a signal matrix form:
Figure BDA0002236942330000193
in the formula
Figure BDA0002236942330000194
A unit interference suppression matrix for representing the target signal intercepted by the interception end E and satisfies
Figure BDA0002236942330000195
Represents U[E]The conjugate transpose matrix of (2). Equivalent channel:a channel matrix representing the kth transmitting end to the eavesdropping end E,
Figure BDA0002236942330000197
representing the channel matrix from the relay peer R to the eavesdropping peer E.And representing the channel matrix from the ith transmitting terminal T to the eavesdropping terminal E.
(2) M + N ═ d (K +1), dK-d + 1. ltoreq.L < M, dK-d + 1. ltoreq.L < R. The eavesdropping end E is provided with at least (dK-d +1) antennas to eliminate other user interference, but the interference of the main channel information data stream still exists.
At this time, the eavesdropping end E receives a signal matrix form:
the transmission rate of the kth user is:
Figure BDA0002236942330000201
the interception rate of the interception end is as follows:
Figure BDA0002236942330000202
the system security rate is:
Figure BDA0002236942330000203
in the formula
Figure BDA0002236942330000204
Indicating that the greater of x and 0 is taken. Defining a channel matrix
Figure BDA0002236942330000205
2) When L is larger than or equal to M and L is larger than or equal to R, the self-interference problem of the relay terminal R can be eliminated by methods such as antenna interference elimination, radio frequency interference elimination and digital interference elimination. Taking Zero Forcing (ZF) precoding cancellation method in digital interference cancellation as an example, the main idea of Zero Forcing precoding is to select a non-Zero matrix T at the relayiSatisfy HiiTiWhen 0, the residual self-interference is 0. The ZF precoding scheme has the capability of completely eliminating residual self-interference. Precoding matrix TiA non-zero matrix is necessary, otherwise no signal is transmitted. In order to obtain a non-zero precoding matrix, it should be ensured that the total number of transmit antennas is greater than the sum of receive antennas for the desired signal and receive antennas for the self-interference signal, which is expressed by the following formula:
SR>Si+Sj(25)
at this time, the signal received by the relay terminal R is:
Figure BDA0002236942330000207
under the sufficient condition, a non-zero space HiiSingular Value Decomposition (SVD):
Figure BDA0002236942330000208
in the formula
Figure BDA0002236942330000211
nii＝SR-SiAnd V isiiIf the middle column vectors are orthogonal to each other, the precoding matrix can be represented as:
T[i]＝V[ii]A[ii](28)
in the formula AiiIs non-zero niiThe x L zero forcing precoding matrix (L denotes an average transmitted data symbol).
When the following conditions are met, the receiving end can eliminate the interference of other users and artificial noise:
Figure BDA0002236942330000212
in the formula
Figure BDA0002236942330000213
The unit precoding matrix representing the artificial noise transmitted by the relay terminal R and meeting the requirement
Figure BDA0002236942330000214
Equivalent channel:
Figure BDA0002236942330000215
the interference of other users and artificial noise can be eliminated at the receiving end by a distributed interference alignment algorithm, and the implementation is realized by adopting an improved minimum interference leakage criterion, and the specific implementation process is shown in fig. 4:
step1 initializing the precoding matrix
Figure BDA0002236942330000216
To satisfy
Figure BDA0002236942330000217
Figure BDA0002236942330000218
To satisfy
Figure BDA0002236942330000219
Step2 the iteration starts.
Step3 calculation of interference covariance matrix for downlink k users
Figure BDA00022369423300002110
In the formula Q[k](1),Q[k](2) Can be obtained by the following equation:
Figure BDA00022369423300002111
in the formula PanSending artificial noise power for relay terminal R and satisfying Pan＝(1-ρ)PR。W[R]A precoding matrix representing the relay transmission noise.
Step4 calculation of the downlink k-user interference suppression matrix
In the formula of U[k](1),U[k](2) Can be obtained by the following formula
Figure BDA0002236942330000221
The above formula represents U[k]Is equal to Q[k]D ofkAnd the characteristic vectors corresponding to the minimum characteristic values form a matrix.
Step5 reversing the communication direction to order
Figure BDA0002236942330000222
Computing a precoding matrix for an uplink
Figure BDA0002236942330000223
Step6 calculating the uplink k user interference covariance matrixIn the formula
Figure BDA0002236942330000225
Can be obtained by the following equation:
Figure BDA0002236942330000226
Figure BDA0002236942330000227
step7 calculating the uplink k-user interference suppression matrix
Figure BDA0002236942330000228
Interference rejection matrix for artificial noise
Figure BDA0002236942330000229
In the formula
Figure BDA00022369423300002210
Can be obtained by the following equation:
Figure BDA00022369423300002211
Figure BDA00022369423300002212
the above formula represents U[k]，
Figure BDA00022369423300002213
Is equal to Q[k]，D ofkAnd the characteristic vectors corresponding to the minimum characteristic values form a matrix.
Step8 reversing the communication direction to order
Figure BDA00022369423300002215
Step9, continue iteration, update U[k]、
Figure BDA00022369423300002216
And calculating the interference leakage value until the interference leakage value is smaller than a given threshold value, namely converging, and ending the iteration.
Step10 output V[k]、U[k]、W[k]。
Step11 otherwise, returning to Step 3.
V to be output[k]、U[k]、W[k]Substituting:
Figure BDA0002236942330000231
Figure BDA0002236942330000232
the objective function for minimizing interference leakage is:
Figure BDA0002236942330000233
at this time, the matrix form of the received signal at the receiving end r is:
Figure BDA0002236942330000234
and giving a matrix form of signals received by the eavesdropping terminal E under different conditions according to the relation between the eavesdropping terminal E antenna and the number of users and the data stream transmitted by the transmitting terminal T.
(1) L is more than or equal to M and less than dK-d +1, R is more than or equal to L and less than dK-d +1, and the eavesdropping end E cannot eliminate the interference of other users and artificial noise.
At this time, the eavesdropping end E receives a signal matrix form:
in the formula Z[R]Meaning that the relay R transmits
Figure BDA0002236942330000236
Signal vectors for each data stream. Equivalent channel
Figure BDA0002236942330000237
(2) M + N ═ d (K +1), M ≦ dK-d +1 ≦ L, R ≦ dK-d +1 ≦ L, and the eavesdropping peer E may eliminate the interference of other users, but cannot eliminate the interference between the main channel information data streams and the interference of artificial noise.
At this time, the eavesdropping end E receives a signal matrix form:
Figure BDA0002236942330000238
the transmission rate of the kth user is:
Figure BDA0002236942330000241
the interception rate of the interception end is as follows:
Figure BDA0002236942330000242
the safe rate of the system is:
Figure BDA0002236942330000243
in which a channel matrix is defined
Figure BDA0002236942330000244
In addition to the above embodiments, the present invention may have other embodiments, and any technical solutions formed by equivalent substitutions or equivalent transformations fall within the scope of the claims of the present invention.

Claims (6)

1. A multi-user MIMO communication secrecy method under a relay cooperation network comprises K sending terminals T and a relay terminalR, K receiving terminals R, a wiretap terminal E, a sending terminal equipped with M antennas, a relay terminal equipped with S antennas, a receiving terminal equipped with N antennas, a wiretap terminal equipped with L antennas, the number of antennas of all nodes is not less than one, the relay terminal R adopts a full duplex amplification forwarding mode, a data stream d sent by a sending terminal T and an artificial noise data stream d sent by the relay terminal RanAll be less than the less value in sending end antenna M, the receiving end antenna N, sending end T and relay R are known to eavesdrop end E's information to this judges to eavesdrop the channel and whether have the null space, thereby decides whether to send artificial noise and disturb its eavesdrop rate, guarantees the safety communication, its characterized in that, relay cooperation network following multiuser MIMO communication secret method contains the following step:
the method comprises the following steps: initializing a two-hop MIMO relay network with eavesdropping users, wherein the number of antennas of each node is not less than 1;
step two: adopting different secret communication methods according to the comparison of the number of the eavesdropping end with the number of the sending end and the relay antenna;
1) when L < M and L < R, the transmitting end T has null space to the eavesdropping end E, the information can be directly transmitted in the null space of the eavesdropping channel, the eavesdropping end E can not hear the target signal, and the relay end R does not need to transmit artificial noise,
in the first time slot, the sending terminal T broadcasts signals, the relay terminal R and the receiving terminal R receive the signals, the interception terminal E intercepts the signals,
the signal received by the relay terminal R is:
Figure FDA0002236942300000011
the signal received by the receiving end r is:
Figure FDA0002236942300000012
the signal received by the eavesdropping terminal E is as follows:
Figure FDA0002236942300000013
in the formula PiIndicating the transmitting end TiPower of transmission, E [ | x[i](1)||2]＝Pi。
Figure FDA0002236942300000014
For the transmitting end TiThe channel coefficients to the relay peer R,
Figure FDA0002236942300000021
for the transmitting end TiThe channel coefficients to the receiving end r,
Figure FDA0002236942300000022
for the transmitting end TiChannel coefficient, x, to eavesdropping end E[i](1) Indicating the transmitting end TiTarget signal, n, transmitted in a first time slot[R],n[r],n[E]The noise vectors of the relay terminal R, the receiving terminal R and the eavesdropping terminal E respectively have a mean value of 0 and a variance of
Figure FDA0002236942300000023
Independent and identically distributed complex Gaussian random variables;
2) when L is more than or equal to M and L is more than or equal to R, the transmitting end T has no null space to the eavesdropping end E, the relay end R needs to transmit artificial noise to interfere the eavesdropping of the eavesdropping end E,
in the first time slot, the sending terminal T sends a signal, and the relay terminal R adopts SiThe root antenna receiving the useful signal, SjThe root antenna receives a self-interference signal, SRThe root antenna transmits the artificial noise and,
the relay terminal R receives the signal:
Figure FDA0002236942300000024
in the formula
Figure FDA0002236942300000025
For the channel coefficient from relay R to relay R, z[R](1) Indicating relayingTerminal R is supplied with power PRTransmitted in the first time slot and containing danThe target signal of the data stream is,
the signals at the receiving end are:
Figure FDA0002236942300000026
the signal received by the eavesdropping terminal is as follows:
Figure FDA0002236942300000027
in the formula
Figure FDA0002236942300000028
The channel coefficient from the relay terminal R to the eavesdropping terminal E is obtained;
step three: 1) when L < M and L < R, the transmitting end T sends the signal again, the relay end R forwards the signal, the receiving end R receives the signal, the eavesdropping end E eavesdrops the signal,
the signal received by the receiving end r is:
in the formula x[i](2) Indicating the transmitting end TiThe target signal transmitted in the second time slot,
Figure FDA0002236942300000031
for the channel coefficient, P, from the relay R to the receiver RRFor the transmission power of the relay terminal R, x[R](2)＝βyR(1) For signals forwarded by the relay peer R, β for an amplified forwarding factor,
the signal received by the eavesdropping terminal E is:
Figure FDA0002236942300000032
in the formula
Figure FDA0002236942300000033
The channel coefficient from the relay terminal R to the eavesdropping terminal E is obtained;
2) when L is larger than or equal to M and L is larger than or equal to R, the transmitting end T transmits signals again in the second time slot, the relay end R adopts d antennas to transmit the secret data stream, the rest s-d antennas are used for transmitting artificial noise, the relay end R does not receive the signals,
the receiving end r receives signals as follows:
Figure FDA0002236942300000034
where p e (0,1) is the power allocation factor,
the signal received by the eavesdropping terminal E is as follows:
step four: 1) when L < M and L < R, the receiving end can eliminate the interference of other users when the following conditions are satisfied:
Figure FDA0002236942300000036
in the formula
Figure FDA0002236942300000037
A unit precoding matrix representing the ith user transmission target signal and satisfying
Figure FDA0002236942300000038
A unit precoding matrix representing the target signal transmitted by the kth user and satisfying
Figure FDA0002236942300000039
A unit interference suppression matrix representing the reception target signal of the kth user and satisfying
Figure FDA00022369423000000310
Represents U[k]Conjugate transpose matrix of (2), equivalent channel:
Figure FDA0002236942300000041
a channel matrix representing the ith transmitting terminal T to the kth receiving terminal r,
Figure FDA0002236942300000042
represents the channel matrix from the ith sender T to the relay R,
Figure FDA0002236942300000043
representing the channel matrix from the relay terminal R to the kth receiver terminal R,
Figure FDA0002236942300000044
a channel matrix representing the k-th transmitting terminal T to the k-th receiving terminal r,
Figure FDA0002236942300000045
represents the channel matrix from the kth sender T to the relay R,the channel matrix from the relay terminal R to the kth receiving terminal R is represented, and each channel satisfies independent equal distribution (i.i.d), and the interference of other users received by the receiving terminal R can be realized by a distributed interference alignment algorithm based on a minimum interference leakage criterion, and the specific implementation method is as follows:
step1 initializing the precoding matrixTo satisfy
Figure FDA0002236942300000048
Step2, starting iteration;
step3 calculation of interference covariance matrix for downlink k users
In the formula Q[k](1),Q[k](2) Can be obtained by the following equation:
Figure FDA00022369423000000410
step4 calculation of the downlink k-user interference suppression matrix
Figure FDA00022369423000000411
In the formula of U[k](1),U[k](2) Can be obtained by the following formula
Figure FDA00022369423000000412
The above formula represents U[k]Is equal to Q[k]D ofkA matrix composed of eigenvectors corresponding to the minimum eigenvalues;
step5 reversing the communication direction to order
Figure FDA00022369423000000413
Computing a precoding matrix for an uplink
Figure FDA0002236942300000051
Step6 calculating the uplink k user interference covariance matrix
Figure FDA0002236942300000052
In the formula
Figure FDA0002236942300000053
Can be obtained by the following equation:
Figure FDA0002236942300000054
in the formula
Figure FDA0002236942300000055
A transmit-side precoding matrix representing the reverse link,a channel matrix representing a reverse link;
step7 calculating the uplink k-user interference suppression matrix
Figure FDA0002236942300000057
In the formula
Figure FDA0002236942300000058
Can be obtained by the following formula
Figure FDA0002236942300000059
The above formula represents
Figure FDA00022369423000000510
Is equal toD ofkA matrix composed of eigenvectors corresponding to the minimum eigenvalues;
step8 reversing the communication direction to order
Figure FDA00022369423000000512
Step9, continue iteration, update U[k]Calculating an interference leakage value until the interference leakage value is smaller than a given threshold value, namely converging, and ending iteration;
step10 output V[k],U[k]；
Step11 otherwise return to Step3,
v to be output[k],U[k]Substituting:
Figure FDA00022369423000000513
the objective function for minimizing interference leakage is:
Figure FDA00022369423000000514
at this time, the matrix form of the received signal at the receiving end r is:
Figure FDA0002236942300000061
in the formula X[k]Containing d indicating the transmission of the Kth user[k]The signal vectors of the individual data streams,
Figure FDA0002236942300000062
representing the additive white gaussian noise vector received by the kth user,
the transmission rate of the kth user is:
Figure FDA0002236942300000063
the interception rate of the interception end is as follows:
Figure FDA0002236942300000064
the system security rate is:
Figure FDA0002236942300000065
in the formula
Figure FDA0002236942300000066
Indicating that the greater of x and 0 is taken. Defining a channel matrix
Figure FDA0002236942300000067
Figure FDA0002236942300000068
2) When L is larger than or equal to M and L is larger than or equal to R, the self-interference problem of the relay terminal R is eliminated by an antenna interference elimination or radio frequency interference elimination or digital interference elimination method, and when the following conditions are met, the receiving terminal can eliminate the interference of other users and artificial noise:
Figure FDA0002236942300000069
in the formula
Figure FDA00022369423000000610
The unit precoding matrix representing the artificial noise transmitted by the relay terminal R and meeting the requirement
Figure FDA0002236942300000071
Equivalent channel:
Figure FDA0002236942300000072
the interference of other users and artificial noise received by the receiving end r can be realized by a distributed interference alignment algorithm based on a minimum interference leakage criterion, and the specific implementation method is as follows:
step1 initializing the precoding matrix
Figure FDA0002236942300000073
To satisfy
Figure FDA0002236942300000074
Figure FDA0002236942300000075
To satisfy
Figure FDA0002236942300000076
Step2, starting iteration;
step3 calculation of interference covariance matrix for downlink k users
Figure FDA0002236942300000077
In the formula Q[k](1),Q[k](2) Can be obtained by the following equation:
Figure FDA0002236942300000078
in the formula PanSending artificial noise power for relay terminal R and satisfying Pan＝(1-ρ)PR，W[R]A precoding matrix representing relay transmission noise;
step4 calculation of the downlink k-user interference suppression matrix
Figure FDA0002236942300000079
In the formula of U[k](1),U[k](2) Can be obtained by the following formula
Figure FDA00022369423000000710
The above formula represents U[k]Is equal to Q[k]D ofkA matrix composed of eigenvectors corresponding to the minimum eigenvalues;
step5 reversing the communication direction to order
Figure FDA00022369423000000711
Computing a precoding matrix for an uplink
Figure FDA00022369423000000712
Step6 calculating the uplink k user interference covariance matrix
Figure FDA00022369423000000713
In the formula
Figure FDA00022369423000000714
Can be obtained by the following equation:
Figure FDA0002236942300000081
step7 calculating the uplink k-user interference suppression matrix
Figure FDA0002236942300000083
Interference rejection matrix for artificial noise
Figure FDA0002236942300000084
In the formula
Figure FDA0002236942300000085
Can be obtained by the following equation:
Figure FDA0002236942300000086
the above formula represents U[k]，
Figure FDA0002236942300000088
Is equal to Q[k]，
Figure FDA0002236942300000089
D ofkA matrix composed of eigenvectors corresponding to the minimum eigenvalues;
step8 reversing the communication direction to order
Figure FDA00022369423000000810
Step9, continue iteration, update U[k]、
Figure FDA00022369423000000811
Calculating an interference leakage value until the interference leakage value is smaller than a given threshold value, namely converging, and ending iteration;
step10 output V[k]、U[k]、W[k]；
Step11 otherwise return to Step3,
v to be output[k]、U[k]、W[k]Substituting:
Figure FDA00022369423000000812
Figure FDA00022369423000000813
the objective function for minimizing interference leakage is:
Figure FDA00022369423000000814
at this time, the matrix form of the received signal at the receiving end r is:
Figure FDA0002236942300000091
the transmission rate of the kth user is:
Figure FDA0002236942300000092
the interception rate of the interception end is as follows:
Figure FDA0002236942300000093
the safe rate of the system is:
Figure FDA0002236942300000094
in which a channel matrix is defined
Figure FDA0002236942300000095
2. The method for multi-user MIMO communication privacy under a relay cooperative network as claimed in claim 1, wherein the parameter ranges in the first step are as follows:
Figure FDA0002236942300000096
Figure FDA0002236942300000097
3. the method for multi-user MIMO communication security in relay cooperative network as claimed in claim 1, wherein the design criteria of the amplify-and-forward factor in the third step is to satisfy the relay transmission power P while maximizing the transmission information strengthRThe constraint of (2):
Figure FDA0002236942300000098
4. the method as claimed in claim 1, wherein the relay peer R of the second timeslot of the transmission signal uses power pp when the eavesdropping channel has no null space in the third stepRThe signal of the transmitting terminal T is forwarded with a power (1-rho) PRGenerating artificial noise.
5. The multi-user MIMO communication security method in the relay cooperative network as claimed in claim 1, wherein in the fourth step, according to the relationship between the number of eavesdropping end E antennas, the number of users, and the data stream sent by the sending end T, a matrix form of the eavesdropping end received signal under different conditions is given:
1) when L < M, L < R, there is null space in the eavesdropping channel,
(1) m is more than L and less than or equal to dK-d +1, R is more than L and less than or equal to dK-d +1, at the moment, the eavesdropping end E can not eliminate the interference of other users,
at this time, the eavesdropping end E receives a signal matrix form:
Figure FDA0002236942300000101
in the formula
Figure FDA0002236942300000102
A unit interference suppression matrix for representing the target signal intercepted by the interception end E and satisfies
Figure FDA0002236942300000103
Figure FDA0002236942300000104
Represents U[k]Conjugate transpose matrix of (2), equivalent channel:a channel matrix representing the kth transmitting end to the eavesdropping end E,
Figure FDA0002236942300000106
a channel matrix representing the relay peer R to the eavesdropping peer E,
Figure FDA0002236942300000107
representing a channel matrix from the ith sending terminal T to the eavesdropping terminal E;
(2) m + N ═ d (K +1), dK-d +1 ≦ L < M, dK-d +1 ≦ L < R, the eavesdropping end E is equipped with at least (dK-d +1) antennas to eliminate other user interference, but the interference of the main channel information data stream still exists,
at this time, the eavesdropping end E receives a signal matrix form:
Figure FDA0002236942300000108
2) when L is more than or equal to M and L is more than or equal to R, no null space exists in the eavesdropping channel,
(1) l is more than or equal to M and less than dK-d +1, R is more than or equal to L and less than dK-d +1, at the moment, the eavesdropping end can not eliminate the interference of other users and artificial noise,
at this time, the eavesdropping end E receives a signal matrix form:
Figure FDA0002236942300000111
in the formula Z[R]Meaning that the relay R transmits
Figure FDA0002236942300000112
Signal vectors of individual data streams, equivalent channels
Figure FDA0002236942300000113
(2) M + N ≦ d (K +1), M ≦ dK-d +1 ≦ L, R ≦ dK-d +1 ≦ L, at this time, the eavesdropping user may eliminate the interference of other users, but cannot eliminate the interference between the main channel information data streams and the interference of artificial noise,
at this time, the eavesdropping end E receives a signal matrix form:
Figure FDA0002236942300000114
6. the multi-user MIMO communication security method in the relay cooperation network as claimed in claim 1, wherein the self-interference in the fourth step can be zero-forcing precoding cancellation method in digital interference cancellation, and the main idea of zero-forcing precoding is to select a non-zero matrix T at the relayiSatisfy HiiTiWhen 0, the residual self-interference is 0, the ZF precoding scheme has the capability of completely eliminating the residual self-interference, and the precoding matrix TiA non-zero matrix is required, otherwise no signal is transmitted, and in order to obtain a non-zero precoding matrix, the total number of transmitting antennas is ensured to be greater than the sum of receiving antennas of the useful signal and receiving antennas of the self-interference signal, which is expressed by the formula:
SR>Si+Sj(41)
at this time, the signal received by the relay terminal R is:
Figure FDA0002236942300000115
under the sufficient condition, a non-zero space HiiSingular Value Decomposition (SVD):
Figure FDA0002236942300000116
in the formula
Figure FDA0002236942300000117
nii＝SR-SiAnd V isiiIf the middle column vectors are orthogonal to each other, the precoding matrix can be represented as:
T[i]＝V[ii]A[ii](44)
in the formula AiiIs non-zero niiThe x L zero-forcing precoding matrix, L denotes an average transmitted data symbol.
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