CN106374980A - Safe transmission method in MIMO Y eavesdropping network based on real interference alignment - Google Patents

Abstract

The invention discloses a safe transmission method in an MIMO Y eavesdropping network based on real interference alignment. According to the method, through utilization of a real interference alignment technology and an artificial noise technology, through construction of useful signal precoding matrixes and interference suppression matrixes, inter-user interference signals at legal user positions are located in null spaces of receiving suppression matrixes; and noise signals are completely eliminated through linear combination. Moreover, through construction of a noise signal coding matrix at a relay position, the noise signals are completely aligned to receiving signal spaces of eavesdropping users, so the eavesdropping users cannot eavesdrop the signals and the whole multi-user eavesdropping network can obtain multiple safe communication channels.

Description

Secure transmission method in MIMO Y-eavesdropping network based on real interference alignment

Technical Field

The invention belongs to the field of physical layer security in wireless communication, and particularly relates to a secure transmission method in a MIMOY eavesdropping network based on real interference alignment.

Background

In recent years, security issues in wireless communications have become a focus of research. The traditional encryption algorithm is mainly applied to an upper network, and information is encrypted by using a secret key at a transmitting end to convert a plaintext into a ciphertext; at the receiving end, the information is decrypted by using the key, and the ciphertext is converted into the plaintext. An eavesdropper would analyze the plaintext based on the received ciphertext. Therefore, cryptographic algorithms need to be continuously improved and the length of keys increased to cope with the ever increasing computing power of computers. Physical layer security techniques have been gradually applied to wireless networks and ad hoc networks as a complement to encryption techniques. The core idea is to utilize different physical characteristics between the legal channel and the eavesdropping channel to realize secure transmission. At present, many researches are concentrated on physical layer security technology, wiener proves that both legal communication parties can still obtain perfect security communication under the condition of no shared key for the first time, and simultaneously points out that under a discrete memoryless channel model, the security rate is the difference value between the legal channel rate and the eavesdropping channel rate, and a wiener eavesdropping channel model is provided, which lays a foundation for future researches, and the same security rate formula is obtained by popularizing the wiener eavesdropping channel model to a Gaussian channel model and a broadcast channel model by existing documents.

In a multi-user eavesdropping network, the problems of reliability and safety of information transmission exist simultaneously. The transmission process of the system is inevitably affected by the interference between users, thereby reducing the number of data streams, i.e., the degree of freedom (DOF), that the system can transmit. Therefore, in order to attenuate the inter-user interference, the interference alignment technique has attracted a wide attention. The basic principle of interference alignment is to compress the interference vector into a smaller interference space, where the desired signal is independent, and then recover the desired signal by simply forcing zeros so that many users can communicate simultaneously in a low-dimensional signal space. The prior art proposes interference alignment algorithms requiring a small number of antennas, which can achieve the same degree of freedom as the conventional interference alignment algorithms. Notably, we have found that cooperative scrambling techniques are not as mentally desirable as interference alignment techniques. As one of the key technologies in physical layer security, the cooperative scrambling technology generally places a transmitted noise signal in a null space of a channel, so that the transmitted noise signal does not interfere with a useful signal, and only weakens a received signal-to-noise ratio of an eavesdropping end; interference alignment is also desirable to separate the desired signal and the interfering signal at the receiving end. Therefore, researchers have studied to implement secure communication in a multi-user eavesdropping network using interference alignment techniques. As in the prior art, the authors implement the number of non-zero secure data streams, i.e. (privacy degrees of freedom), of K user gaussian interference channels using interference alignment in combination with network coding techniques.

For multi-user eavesdropping networks with relays, it is indicated that interference alignment techniques can be used to achieve secure communication throughout the system. X.he and a.yener investigated the problem of privacy freedom in a two-hop eavesdropping network with unreliable relays. However, at present, the study on the security degree of freedom of the multi-path relay eavesdropping network is still lacked. A typical K-user multi-hop relay eavesdropping network is a MIMO Y eavesdropping channel, in which all users are multi-antenna nodes, each user desires to communicate with all other users through a relay, and since its communication model is shaped like the letter "Y" and its communication mode is in a one-to-many manner, it is named "Y model". The communication process mainly comprises a Multiple Access (MAC) stage and a Broadcast (BC) stage. In the MAC stage, each user sends K-1 signals to the relay, and simultaneously, signal alignment is carried out at the relay; in the BC stage, the relay broadcasts the aligned K (K-1)/2 signals to all users, and each user can obtain a desired signal through self-interference cancellation. In the invention, a safe communication scheme based on a real interference alignment technology is provided, and the safe communication of a multi-user eavesdropping system with relays is realized by designing a pre-coding matrix, an interference suppression matrix and an artificial noise coding matrix.

Disclosure of Invention

The invention aims to overcome the defects and provide a secure transmission method in a MIMO Y eavesdropping network based on real interference alignment.

In order to achieve the above object, the present invention comprises the steps of:

before starting to transmit signals, each user needs to select a useful signal from a PAM constellation, and a noise signal sent by a relay is also taken from one PAM constellation;

step two, according to the known global channel state information, each sending user designs a relevant pre-coding matrix according to the interference alignment condition;

step three, assuming that all users and nodes are in a full duplex mode, all users send coded signals to the relay, and the relay sends first artificial noise signals;

step four, the relay broadcasts the artificial noise and the amplified useful signal to all users at the same time;

and step five, after each user receives the signals twice, eliminating artificial noise signals sent by the relay through linear combination, and demodulating useful signals by using a receiving suppression matrix meeting certain limiting conditions, so that the whole system obtains a certain communication rate.

The specific method of the first step is as follows:

all channels are real channel matrix using real interference alignment technique, and user U is assumed_iTo user U_jSignal s of_ijTaken from the PAM constellation C (a) defined below_U,Q_U) I.e. by

C(a_U,Q_U)＝a_U{-Q_U,-Q_U+1,...,Q_U-1,Q_U}

In the formula:

Q_U-a number of users K and a transmission power per user P_iThe associated positive values, for > 0,

a_U-real numbers such that the transmit signal of each user satisfies the transmit power limit, for γ > 0,

in the above description, each user U_iTransmitted signal s_i＝[s_i1,s_i2,...,s_iK]^T∈R^(K-1)×1Is subject to a precoding matrix V_i∈R^M×(K-1)Encoded signal X_i∈R^M×1I.e. bySo that the transmission power is limited toThus, Q_UAnd in the expression_UGamma in the expression takes any one of a plurality of groups of values which meet the power limiting condition;

relaying the transmitted interference noise b in the MBWC MIMO Y model_i∈R^K(K-1)×1Contains K (K-1) symbols, which are taken from another PAM constellation C (a)_R,Q_R) I.e. by

C(a_R,Q_R)＝a_R{-Q_R,-Q_R+1,...,Q_R-1,Q_R}

In the formula:

Q_R-a positive value relating to the number K of users and the secondary transmission power P, for > 0,

a_Ra real number such that the transmitted signal at the relay satisfies the transmit power limit, for γ > 0,

in sending b_iIt needs to be coded before, and the coding matrix is T_i∈R^N×K(K-1)(ii) a Thus, the artificial noise transmitted by the relay isLimit of transmitted signal powerTo be E [ tr (zz)^H)]β P is less than or equal to, therefore, Q_RAnd in the expression_Rγ in the expression takes any one of a plurality of sets of values that satisfy the power limitation condition.

The specific method of the second step is as follows:

in order to eliminate the interference between users generated when K users communicate with each other and demodulate the signals from other K-1 users, a precoding matrix V needs to be designed for each user_i，Which consists of K-1 precoding vectors v of dimension M × 1_ijComposition of each precoding vector v_ijWill be for each signal s_jiPerforming linear precoding, i.e. v_ijs_ij(ii) a When the dimension of the space opened by N antennas at the relay is less than K (K-1) symbol numbers, part of signals are subjected to aliasing at the relay, in order to avoid the situation, an interference alignment technology is adopted, and when the number of antennas at each node meets the requirementWhen all paired signals are like s_ijAnd s_jiAligned to the same dimension of the relay, in which case K (K-1) useful signals can be included in the relayIn dimensional space, i.e. the following equation needs to be satisfied:

wherein, the equivalent vector of the same dimension after passing through the channel is marked as U_i,j，K is user U ═ 1,2_iTo the relay, to the user U_iThe real channel matrix of (a); at this point, no aliasing will occur between the signals at the relay;

at the relay, to ensure that the desired legitimate signal can not be eavesdropped, when the GCSI is known, the precoding matrix T of the artificial noise signal is designed_iSo that it satisfiesNamely, it is

Wherein,i 1,2, K denotes a real channel matrix between the eavesdropping peer and the user, and between the eavesdropping peer and the relay, respectively, G_iEquivalent vectors of the same dimensionality after the channel is intercepted; the encoded artificial noise signal is represented as

The concrete method of the third step is as follows:

all users will encode the signal X_iAnd sending the signals to the relay node, wherein the signals received by the relay are as follows:

in the formula:

n_rlocal white gaussian noise at the relay;

when all users send to the relayWhen transmitting signal, the relay broadcasts the artificial noise with power of β P to the user and the eavesdropping end at the same time, at this time, the signal received by the user at this stage is

In the formula:

beta-the artificial noise power distribution coefficient at the relay.

-user U_jLocal white Gaussian noise at MAC stage with a noise variance of

The concrete method of the fourth step is as follows:

after K (K-1) signals are received in a relay way, the signals are amplified and forwarded to all users, and the forwarded signals are X_r＝αY_rWhere α is the amplification factor at the relay, the power limit for transmitting the desired signal isAt the same time, the artificial noise signal is transmitted again, which is the same as the MAC stage, and the received signal of each user at this stage is

In the formula:

-user U_jLocal white Gaussian noise in BC stage with noise variance of

The concrete method of the step five is as follows:

firstly, weighting and combining the signals received twice by the legal receiving end and the eavesdropping end to obtain combined signals:

note that:thus, Y_jThe method does not contain artificial noise z, so that a legal user cannot be influenced by an artificial noise interference signal;

after alignment by said disturbances Y is aligned_jRe-expressed as a superimposed version of two sets of paired signals:

in the formula:

-an interference alignment matrix;

the dimension relays the pair of signals to the dimension,

for user U_jIn which the received signal is divided into two parts, the desired useful signalInterfering signals with other users

Secondly, designing a receiving suppression matrix of each user; after spatial signal alignment, user U_jIt is further required to use (K-1) × M dimension reception rejection matrix F_i＝[f_1if_2i...f_i-1,if_i+1,i...f_Ki]^TFor Y_jPerform interference zero forcing, and receive effective signal, i.e. using F_jLeft times Y_j，

In the formula:

a dimension equivalent reception rejection matrix;

equivalent reception rejection matrix P_jIs selected according to the principle that

Wherein Null { A } represents the Null space of matrix A; the two formulas represent P_jIs taken fromAnd is a null space of_jIs out of positionIn the null space of (a);

in order to select a matrix P that meets the above-mentioned criteria_jFirst, it is necessary to make explicit whether such a matrix exists; assuming that each legitimate node knows CSI, the above equation is equivalent toTo satisfy this condition, the number of antennas at the relay must be satisfiedWhich is already included in the feasibility of disturbing the alignment, i.e.Therefore, it must be true when the interference alignment condition is satisfied; in order to ensure that there is a presence,is shown inAn N × N- (K-1) -dimensional null space exists in the matrix, denoted as Q, and Q is assumed to be composed of a series of N × 1 order null vectors Q, i.e., Q isP_jWriting in the form of column vectors, P_j＝[p_j,1p_j,2...p_j,K-1](ii) a At this time, if and only if the matrix a exists, it is such that a ═ p is satisfied_j,1p_j,2...p_j,K-1q_j]When rank (a) is K, this indicates that P is selected_jIs independent of null space, i.e.In summary, the reception suppression matrix P at the user is_jOr F_jAlways present;

therefore, in any case, the reception suppression matrix meeting the conditions is selected, and then self-interference elimination is carried out, so that the user U_jDemodulate the received signal, i.e.

In the formula:

-user U_jLegally receiving the signal;

-user U_jA precoding matrix of the legitimate signal of (a);

the third step: detecting a signal using a maximum likelihood detection scheme;

at user U_jRecord the estimated signal asWhen the received signal is knownUsing maximum likelihood detection method to obtainThe estimated signal is obtained and used as the estimation signal,

wherein,

chi is-is S_jThe obtained set has (2Q)_U+1)^K-1Seed growing;

argmin||A||²the minimum of the two norms of the matrix a.

Compared with the prior art, the method utilizes the real interference alignment technology and the artificial noise technology, and realizes that the interference signals among the users are positioned at the zero space of the receiving inhibition matrix at the legal user by constructing the useful signal pre-coding matrix and the interference inhibition matrix, and the noise signals are linearly combined and completely eliminated; in addition, a noise signal coding matrix is constructed at the relay, and noise signals are completely aligned to a receiving signal space of an eavesdropping user, so that the purpose that the eavesdropping user cannot eavesdrop the signals is achieved, and the whole multi-user eavesdropping network can obtain a plurality of secure communication channels.

Drawings

FIG. 1 is a diagram illustrating the MAC stage of the eavesdropping model according to the present invention;

FIG. 2 is a diagram illustrating a BC stage of the eavesdropping model according to the present invention;

FIG. 3 is a block flow diagram of the present invention.

Detailed Description

The invention is further described below with reference to the accompanying drawings.

The invention provides a physical layer security scheme adopting a real interference alignment technology and cooperative scrambling, which adopts an amplification forwarding protocol, carries out precoding at a user based on a multi-user-relay-multi-user physical channel, sends artificial noise at a relay, and the noise interferes with an external eavesdropping node under the condition of not interfering the user, and obtains all secure communication channels under the condition of limiting the power of each user node.

The invention considers a MIMO Y eavesdropping model, there are K users totally, each user has M antennas, there are N antennas in the relay, realize the intercommunication among a plurality of users through an AF relay, the system contains an eavesdropping node, the power that each user sends the signal is P_iThe sum of the transmission power of all users is P, the power of the artificial noise signal transmitted by the relay is β P, the power of the retransmission legal signal is (1- β) P, wherein β is the power distribution coefficient of the relay, and 0 < β < 1. the whole transmission process is described as follows:

as shown in fig. 1, fig. 2 and fig. 3, the present invention provides a physical layer secure transmission method in a K-user MIMO Y eavesdropping system based on a real interference alignment technique and a cooperative interference technique, including the following steps:

1) before starting to transmit signals, each user needs to select a useful signal from a PAM constellation, and a noise signal sent by a relay is also taken from one PAM constellation;

in the following analysis, to employ a real interference alignment technique, all channels are real channel matrices, and it is assumed that user U_iTo user U_jSignal s of_ijTaken from the PAM constellation C (a) defined below_U,Q_U) I.e. by

C(a_U,Q_U)＝a_U{-Q_U,-Q_U+1,...,Q_U-1,Q_U}

In the formula:

Q_U-a number of users K and a transmission power per user P_iThe associated positive values, for > 0,

a_U-real numbers such that the transmit signal of each user satisfies the transmit power limit, for γ > 0,in the above description, each user U_iTransmitted signal s_i＝[s_i1,s_i2,...,s_iK]^T∈R^(K-1)×1Is subject to a precoding matrix V_i∈R^M×(K-1)Encoded signal X_i∈R^M×1I.e. bySo that the transmission power is limited toThus, Q_UAnd in the expression_Uγ in the expression may take any one of a plurality of sets of values that satisfy the power limitation condition.

Relaying the transmitted interference noise b in the MBWC MIMO Y model_i∈R^K(K-1)×1Contains K (K-1) symbols, which are taken from another PAM constellation C (a)_R,Q_R) I.e. by

C(a_R,Q_R)＝a_R{-Q_R,-Q_R+1,...,Q_R-1,Q_R}

In the formula:

Q_R-a positive value relating to the number K of users and the secondary transmission power P, for > 0,

a_Ra real number such that the transmitted signal at the relay satisfies the transmit power limit, for γ > 0,in sending b_iIt needs to be coded before, and the coding matrix is T_i∈R^N×K(K-1)Later we need to do with T_iAnd (5) designing. Thus, the artificial noise transmitted by the relay isIts transmit signal power is limited to E tr (zz)^H)]β P. ltoreq. therefore, Q_RAnd in the expression_Rγ in the expression may take any one of a plurality of sets of values that satisfy the power limitation condition.

2) According to the known global channel state information, each sending user needs to design a relevant precoding matrix according to the interference alignment condition; an artificial noise coding matrix also needs to be designed at the relay, and the specific method is as follows:

in order to eliminate the interference between users generated when K users communicate with each other and demodulate the signals from other K-1 users, a precoding matrix V needs to be designed for each user_i，Which consists of K-1 precoding vectors v of dimension M × 1_ijComposition of each precoding vector v_ijWill be for each signal s_jiPerforming linear precoding, i.e. v_ijs_ij. When the dimension of a space opened by N antennas at a relay is smaller than K (K-1) symbol numbers, aliasing occurs to partial signals at the relay, and in order to avoid the situation, an interference alignment technology is adopted, and when the number of antennas at each node meets the requirementWhen all paired signals are like s_ijAnd s_jiAligned to the same dimension of the relay, in which case K (K-1) useful signals can be included in the relayIn dimensional space, i.e. the following equation needs to be satisfied

Wherein, the equivalent vector of the same dimension after passing through the channel is marked as U_i,j，K is user U ═ 1,2_iTo the relay, to the user U_iThe real channel matrix of (a). At this point, no aliasing will occur between the signals at the relay.

At the relay, to ensure that the desired legitimate signal can not be eavesdropped, when the GCSI is known, we design the precoding matrix T of the artificial noise signal_iSo that it satisfiesNamely, it is

Wherein,i 1,2, K denotes a real channel matrix between the eavesdropping peer and the user, and between the eavesdropping peer and the relay, respectively, G_iIs an equivalent vector of the same dimension after the channel is intercepted. The encoded artificial noise signal is represented as

3) Assuming that all users and nodes are in a full duplex mode, in the first stage, all users send coded signals to a relay, and the relay sends artificial noise signals for the first time; in the second stage, the relay broadcasts the artificial noise and the amplified useful signal to all users simultaneously;

the specific communication process is divided into the following steps:

step 1(MAC stage): all users will encode the signal X_iAnd sending the signals to the relay node, wherein the signals received by the relay are as follows:

in the formula:

n_rlocal white gaussian noise at the relay.

When all users send signals to the relay, the relay simultaneously broadcasts the artificial noise z-direction user with power of β P and the eavesdropping terminal, and at the moment, the signals received by the users at the stage are

In the formula:

-user U_jLocal white Gaussian noise at MAC stage with a noise variance of

Step 2(BC stage): when relayingAfter receiving K (K-1) signals, amplifying and transmitting the signals to all users, wherein the transmitted signals are X_r＝αY_rWhere α is the amplification factor at the relay, the power limit for transmitting the desired signal isAt the same time, the artificial noise signal is transmitted again, which is the same as the MAC stage, and the received signal of each user at this stage is

In the formula:

-user U_jLocal white Gaussian noise in BC stage with noise variance of ${{\mathrm{\&sigma;}}_j}^2.$

4) After each user receives the signals twice, artificial noise signals sent by the relay are eliminated through linear combination, and useful signals are demodulated by using a receiving suppression matrix meeting a certain limiting condition, so that the whole system obtains a certain communication rate. The method comprises the following specific steps:

step 1: the signals received twice by the legal receiving end and the eavesdropping end are weighted and combined, and the combined signals are obtained as follows:

note that:thus, Y_jThe legal user is not influenced by the artificial noise interference signal because the artificial noise z is not contained in the system.

After alignment by said disturbances Y can be aligned_jRe-expressed as a superimposed version of two sets of paired signals:

in the formula:

-an interference alignment matrix;

the dimension relays the pair of signals to the dimension,

for user U_jIn which the received signal is divided into two parts, the desired useful signalInterfering signals with other users

Step 2: and designing a receiving suppression matrix of each user. After spatial signal alignment, user U_jIt is further required to use (K-1) × M dimension reception rejection matrix F_i＝[f_1if_2i...f_i-1,if_i+1,i...f_Ki]^TFor Y_jPerform interference zero forcing to receive effective signal, i.e. using F_jLeft times Y_j，

In the formula:

- (K-1) × N-dimensional equivalent reception suppression matrix.

Equivalent reception rejection matrix P_jIs selected according to the principle that

Where Null { A } represents the Null space of matrix A. The two formulas represent P_jIs taken fromAnd is a null space of_jIs out of positionIn the null space of (a).

In order to select a matrix P that meets the above-mentioned criteria_jFirst it needs to be made clear whether such a matrix is present or not. Assuming that each legitimate node knows CSI, the above equation is equivalent toTo satisfy this condition, the number of antennas at the relay must be satisfiedWhich is already included in the feasibility of disturbing the alignment, i.e.Therefore, the interference alignment condition is necessarily satisfied. To ensure presence, we note thatThis is shown inThere exists a null space of dimension N × N- (K-1), denoted Q, in the matrix, assuming Q is made up of a series of null vectors Q of order N × 1, i.e., Q is theP_jCan be written in the form of a column vector, P_j＝[p_j,1p_j,2...p_j,K-1]. At this time, if and only if the matrix a exists, it is such that a ═ p is satisfied_j,1p_j,2...p_j,K-1q_j]When rank (a) is K, this indicates that P is selected_jIs independent of null space, i.e.In summary, the reception suppression matrix P at the user is_jOr F_jWill always be present.

Therefore, in any case, we can select the reception suppression matrix meeting the condition, and then eliminate by self-interference, the user U_jCan demodulate the received signal, i.e.

In the formula:

-user U_jA signal is legally received.

-user U_jOf the legitimate signal.

And step 3: the signal is detected using a maximum likelihood detection scheme.

At user U_jRecord the estimated signal asWhen the received signal is knownThen, the estimated signal is obtained by utilizing a maximum likelihood detection method,

wherein,

chi is-is S_jThe obtained set has (2Q)_U+1)^K-1Seed growing;

argmin||A||²the minimum of the two norms of the matrix a.

In summary, the whole multi-user relay eavesdropping network can realize the secure communication.

5) In order to verify the performance of the present invention, we will analyze the number of secure data streams that can be obtained by the system under this scheme from the viewpoint of information theory, i.e. derive the security freedom of the whole system. When the number of secure data streams is greater than zero, the entire system is securely communicable. The method comprises the following specific steps:

step 1: the number of data streams communicated by a legitimate user is first derived. The information rate obtained by each user is:

in the formula:

i (A, B) -mutual information of two random variables A and B;

h (-) -information entropy.

Wherein, due to S_jThe K-1 symbols in (A) are equally likely to be from the PAM constellation C (a)_U,Q_U) Thus H (S)_j)＝log(2Q_U+1)^K-1. In addition, we use Markov chainsRestricted by the Ferno inequalityThe upper bound of the error probability is:

in the formula η_γ-and P_iAn irrelevant positive value. Herein, we assume P_iP/K, so the sum rate of legitimate users is expressed asNamely, it is

R_sum≥K log(2Q_U+1)^K-1-K-K Pr_U(e)log(2Q_U+1)^K-1

We are right to R_sumThe value of (A) is limited under the condition of high signal-to-noise ratio, namely the legal data flow number of the whole system can be obtained,

this means that when each user transmits K-1 data, the legal number of data streams for K users of the entire system is K (K-1).

Step 2: and analyzing the number of data streams which can be overheard by the eavesdropping end. The signal received twice by the eavesdropping peer is first analyzed. In the MAC phase, the signal received by the eavesdropping peer is:

wherein:

-local noise at the eavesdropping end when the signal is received for the first time, the variance of the noise being

In the BC phase, the signal received by the eavesdropping terminal for the second time is:

wherein:

-local noise at the eavesdropping end on the second reception of the signal, with a noise variance of

For the eavesdropping end, we cannot know the eavesdropping method used by the eavesdropping end, so in the invention, the eavesdropping end is assumed to adopt a method which is most beneficial to eavesdropping, namely, the eavesdropping end linearly combines the received two signals. Assuming that an eavesdropper can utilize the receiving matrixCombining the two eavesdropped signals to obtain the maximum eavesdropped signal-to-noise ratio, i.e.The demodulated signal of the eavesdropping terminal is represented as

In the formula:

S_i-the transmission signal of each user,

N_ethe eavesdropping-side equivalent local noise, i.e.

When in useWhen the signal received by the eavesdropping terminal can be re-expressed as

The first term in the above equation represents the effect of the interfering signal on each user signal. We align the signal and the interference to one dimension, so that the eavesdropping end cannot distinguish the useful signal and cannot eavesdrop. At this time, the wiretap information rate is

When W is₁≠0,W₂≠0，Can be expressed as

At this time:

for eavesdropping end, orderThe number of eavesdropping channels is equivalently expressed as:

this means that the eavesdropping end can eavesdrop at mostA data stream of symbolsIndicating a rounding down.

And step 3: and the intercepted data stream is removed from the legal data stream, the rest data stream is the number of the safe and confidential data streams, and when the safe data stream exists in the whole system, the whole system can carry out safe communication. Thus, the minimum value of the number of secure data streams for the K-user MBWC model is

This indicates that when the number of users is greater than three, the system can obtain a minimum number of data streamsWherein the symbolsIndicating rounding up. The data flow number is always positive value, namely the data flow of the safety communication exists in the whole system, and the safety of the system is ensured.

The scheme of the safe communication based on the real interference alignment technology and the cooperative scrambling technology in the K user MIMO Y eavesdropping channel provided by the invention has the following advantages:

the scheme is suitable for the multi-user multi-directional relay eavesdropping network, the safety communication of the whole system is realized by designing the pre-coding matrix, the noise coding matrix and the receiving inhibiting matrix aiming at different users and designing the sending method under the full-duplex communication mode, and the system safety vacancy in the relay network is made up.

From the above proof of performance, the number of secure channels obtained by this method is always greater than zero, which also indicates that the entire system can always achieve secure communication.

Claims (6)

1. A secure transmission method in a MIMO Y-eavesdropping network based on real interference alignment is characterized by comprising the following steps:

before starting to transmit signals, each user needs to select a useful signal from a PAM constellation, and a noise signal sent by a relay is also taken from one PAM constellation;

step two, according to the known global channel state information, each sending user designs a relevant pre-coding matrix according to the interference alignment condition;

step three, assuming that all users and nodes are in a full duplex mode, all users send coded signals to the relay, and the relay sends first artificial noise signals;

step four, the relay broadcasts the artificial noise and the amplified useful signal to all users at the same time;

and step five, after each user receives the signals twice, eliminating artificial noise signals sent by the relay through linear combination, and demodulating useful signals by using a receiving suppression matrix meeting certain limiting conditions, so that the whole system obtains a certain communication rate.

2. The method for secure transmission in a MIMO Y eavesdropping network based on real interference alignment according to claim 1, wherein the specific method of the first step is as follows:

all channels are real channel matrix using real interference alignment technique, and user U is assumed_iTo user U_jSignal s of_ijTaken from the PAM constellation C (a) defined below_U,Q_U) I.e. by

C(a_U,Q_U)＝a_U{-Q_U,-Q_U+1,...,Q_U-1,Q_U}

In the formula:

Q_U-a number of users K and a transmission power per user P_iThe associated positive values, for > 0,

a_U-real numbers such that the transmit signal of each user satisfies the transmit power limit, for γ > 0,

in the above description, each user U_iTransmitted signal s_i＝[s_i1,s_i2,...,s_iK]^T∈R^(K-1)×1Is subject to a precoding matrix V_i∈R^M×(K-1)Encoded signal X_i∈R^M×1I.e. bySo that the transmission power is limited toThus, Q_UAnd in the expression_UGamma in the expression takes any one of a plurality of groups of values which meet the power limiting condition;

relaying the transmitted interference noise b in the MBWC MIMO Y model_i∈R^K(K-1)×1Contains K (K-1) symbols, which are taken from another PAM constellation C (a)_R,Q_R) I.e. by

C(a_R,Q_R)＝a_R{-Q_R,-Q_R+1,...,Q_R-1,Q_R}

In the formula:

Q_R-a positive value relating to the number K of users and the secondary transmission power P, for > 0,

a_Ra real number such that the transmitted signal at the relay satisfies the transmit power limit, for γ > 0,

in sending b_iIt needs to be coded before, and the coding matrix is T_i∈R^N×K(K-1)(ii) a Thus, the artificial noise transmitted by the relay isIts transmit signal power is limited to E tr (zz)^H)]β P is less than or equal to, therefore, Q_RAnd in the expression_Rγ in the expression takes any one of a plurality of sets of values that satisfy the power limitation condition.

3. The method for secure transmission in a MIMO Y eavesdropping network based on real interference alignment according to claim 1, wherein the specific method in the second step is as follows:

in order to eliminate the interference between users generated when K users communicate with each other and demodulate the signals from other K-1 users, a precoding matrix V needs to be designed for each user_i，Which consists of K-1 precoding vectors v of dimension M × 1_ijComposition of each precoding vector v_ijWill be for each signal s_jiPerforming linear precoding, i.e. v_ijs_ij(ii) a When the dimension of the space opened by N antennas at the relay is less than K (K-1) symbol numbers, part of signals are subjected to aliasing at the relay, in order to avoid the situation, an interference alignment technology is adopted, and when the number of antennas at each node meets the requirementWhen M is more than or equal to K-1 and 2M is more than N, all paired signals are like s_ijAnd s_jiAligned to the same dimension of the relay, in which case K (K-1) useful signals can be included in the relayIn dimensional space, i.e. the following equation needs to be satisfied:

$H_{u_{i}r}{v}_{ij}=H_{u_{j}r}{v}_{ji}=U_{i,j},i\&NotEqual;j,i,j=1,2,...K$

wherein, the equivalent vector of the same dimension after passing through the channel is marked as U_i,j，K is user U ═ 1,2_iTo the relay, to the user U_iThe real channel matrix of (a); at this point, no aliasing will occur between the signals at the relay;

at the relay, to ensure that the desired legitimate signal can not be eavesdropped, when the GCSI is known, the precoding matrix T of the artificial noise signal is designed_iSo that it satisfiesNamely, it is

$T_i=H_{re}^H{H}_{u_{i}e}{V}_i$

Wherein,i 1,2, K denotes a real channel matrix between the eavesdropping peer and the user, and between the eavesdropping peer and the relay, respectively, G_iFor passing eavesdroppingEquivalent vectors of the same dimensionality behind the track; the encoded artificial noise signal is represented as

4. The method for secure transmission in a MIMO Y eavesdropping network based on real interference alignment according to claim 1, wherein the specific method in the third step is as follows:

all users will encode the signal X_iAnd sending the signals to the relay node, wherein the signals received by the relay are as follows:

$Y_r=\underset{i=1}{\overset{K}{\&Sigma;}}{H}_{u_{i}r}{X}_i+n_r$

in the formula:

n_rlocal white gaussian noise at the relay;

when all users send signals to the relay, the relay simultaneously broadcasts the artificial noise z-direction user with power of β P and the eavesdropping terminal, and at the moment, the signals received by the users at the stage are

$Y_j^{\&lsqb;1\&rsqb;}=H_{{\mathrm{ru}}_j}z+n_j^{\&lsqb;1\&rsqb;},i=1,2,...,K$

In the formula:

beta-the artificial noise power distribution coefficient at the relay.

-user U_jLocal white Gaussian noise at MAC stage with a noise variance of

5. The method for secure transmission in a MIMO Y eavesdropping network based on real interference alignment according to claim 1, wherein the fourth step is as follows:

after K (K-1) signals are received in a relay way, the signals are amplified and forwarded to all users, and the forwarded signals are x_r＝αY_rWhere α is the amplification factor at the relay, the power limit for transmitting the desired signal isAt the same time, the artificial noise signal is transmitted again, which is the same as the MAC stage, and the received signal of each user at this stage is

$\begin{array}{c}{Y}_j^{\&lsqb;2\&rsqb;}=H_{{\mathrm{ru}}_j}{X}_r+n_j^{\&lsqb;2\&rsqb;}\\ =H_{{\mathrm{ru}}_j}\&lsqb;\mathrm{\&alpha;}(\underset{i=1}{\overset{K}{\&Sigma;}}{H}_{u_{i}r}{X}_i+n_r)+z\&rsqb;+n_j^{\&lsqb;2\&rsqb;}\\ ={\mathrm{\&alpha;H}}_{{\mathrm{ru}}_j}\underset{i=1}{\overset{K}{\&Sigma;}}{H}_{u_{i}r}{X}_i+H_{{\mathrm{ru}}_j}z+\widetilde{\mathrm{\&alpha;}}{H}_{{\mathrm{ru}}_j}{n}_r+n_j^{\&lsqb;2\&rsqb;}\end{array}$

In the formula:

-user U_jLocal white Gaussian noise in BC stage with noise variance of

6. The method for secure transmission in a MIMO Y eavesdropping network based on real interference alignment according to claim 1, wherein the concrete method of the fifth step is as follows:

firstly, weighting and combining the signals received twice by the legal receiving end and the eavesdropping end to obtain combined signals:

$Y_j=Y_j^{\&lsqb;2\&rsqb;}-Y_j^{\&lsqb;1\&rsqb;}={\mathrm{\&alpha;H}}_{rj}\underset{i=1}{\overset{K}{\&Sigma;}}{H}_{ir}{X}_i+{\tilde{n}}_j$

note that:thus, Y_jThe method does not contain artificial noise z, so that a legal user cannot be influenced by an artificial noise interference signal;

after alignment by said disturbances Y is aligned_jRe-expressed as a superimposed version of two sets of paired signals:

$\begin{array}{c}{Y}_j={\mathrm{\&alpha;H}}_{{\mathrm{ru}}_j}{U}_r{S}_r+{\tilde{n}}_j\\ ={\mathrm{\&alpha;H}}_{{\mathrm{ru}}_j}({\tilde{U}}_j{\tilde{S}}_j+{\stackrel{\&OverBar;}{U}}_j{\stackrel{\&OverBar;}{S}}_j)+{\tilde{n}}_j\end{array}$

in the formula:

-an interference alignment matrix;

the dimension relays the pair of signals to the dimension,

for user U_jIn which the received signal is divided into two parts, the desired useful signalInterfering signals with other users

Secondly, designing a receiving suppression matrix of each user; after spatial signal alignment, user U_jFurther use of (K-1)) × M dimension reception suppression matrix F_i＝[f_1if_2i... f_i-1,if_i+1,i... f_Ki]^TFor Y_jPerform interference zero forcing, and receive effective signal, i.e. using F_jLeft times Y_j，

${\hat{Y}}_j={\mathrm{\&alpha;F}}_j{H}_{{\mathrm{ru}}_j}({\tilde{U}}_j{\tilde{S}}_j+{\stackrel{\&OverBar;}{U}}_j{\stackrel{\&OverBar;}{S}}_j)+{\tilde{n}}_j={\mathrm{\&alpha;P}}_j{\tilde{U}}_j{\tilde{S}}_j+{\mathrm{\&alpha;P}}_j{\stackrel{\&OverBar;}{U}}_j{\stackrel{\&OverBar;}{S}}_j+{\tilde{n}}_j\&CenterDot;$

In the formula:

- (K-1) × N-dimensional equivalent reception suppression matrix;

equivalent reception rejection matrix P_jIs selected according to the principle that

$P_j\&Subset;Null\left\{{\stackrel{\&OverBar;}{U}}_j\right\}$

$P_j\&NotSubset;Null\left\{{\tilde{U}}_j\right\}$

Wherein Null { A } represents the Null space of matrix A; the two formulas represent P_jIs taken fromAnd is a null space of_jIs out of positionIn the null space of (a);

in order to select a matrix P that meets the above-mentioned criteria_jFirst, it is necessary to make explicit whether such a matrix exists; assuming that each legitimate node knows CSI, the above equation is equivalent toTo satisfy this condition, the number of antennas at the relay must be satisfiedWhich is already included in the feasibility of disturbing the alignment, i.e.Therefore, it must be true when the interference alignment condition is satisfied; in order to ensure that there is a presence,is shown inAn N × N- (K-1) -dimensional null space exists in the matrix, denoted as Q, and Q is assumed to be composed of a series of N × 1 order null vectors Q, i.e., Q isP_jWriting in the form of column vectors, P_j＝[p_j,1p_j,2... p_j,K-1](ii) a At this time, if and only if the matrix a exists, it is such that a ═ p is satisfied_j,1p_j,2... p_j,K-1q_j]When rank (a) is K, this indicates that P is selected_jIs independent of null space, i.e.In summary, the reception suppression matrix P at the user is_jOr F_jAlways present;

therefore, in any case, the reception suppression matrix meeting the conditions is selected, and then self-interference elimination is carried out, so that the user U_jDemodulate the received signal, i.e.

${\hat{Y}}_j={\mathrm{\&alpha;P}}_j{\tilde{U}}_j{S}_j+{\tilde{n}}_j$

In the formula:

-user U_jLegally receiving the signal;

-user U_jA precoding matrix of the legitimate signal of (a);

the third step: detecting a signal using a maximum likelihood detection scheme;

at user U_jRecord the estimated signal asWhen the received signal is knownThen, the estimated signal is obtained by utilizing a maximum likelihood detection method,

${\hat{S}}_j=\underset{S_j\&Element;\mathrm{\&chi;}}{\mathrm{argmin}}\left|\right|{\hat{Y}}_j-{\mathrm{\&alpha;P}}_j{\tilde{U}}_j{\hat{S}}_j|{|}^2$

wherein,

chi is-is S_jThe obtained set has (2Q)_U+1)^K-1Seed growing;

argmin||A||²the minimum of the two norms of the matrix a.