A robust and secure transmission method for wireless relay communication under cooperative interference

Abstract

The present invention discloses a method for robust secure transmission of wireless relay communication under cooperative interference, which comprises the following steps: firstly, a wireless cooperative relay eavesdropping channel model is established; when a channel state information error occurs, the optimization problem is to satisfy the mean mean square error (MSE) constraint of the legal target node and the power constraint of each relay node within the given legal link channel state information error obeying Gaussian distribution, and at the same time consider eliminating the influence of the interference signal sent by the cooperative interference node on the legal target node; then, the optimization problem is relaxed by using the "3σ principle" of Gaussian distribution and the triangle inequality, and the optimization problem is converted into an optimization problem on the real number domain by using orthogonal transformation; finally, the optimization problem is solved by using a double-layer optimization method. The present invention reduces the sensitivity of the wireless cooperative relay system to CSI errors and improves the reliability and confidentiality of the system.

Description

Technical Field

[0001] The present invention relates to the technical field of information communication network, and in particular to a method for robust and secure transmission of wireless relay communication under coordinated interference. Background Art

[0002] In recent years, the demand for miniaturization and low power consumption of wireless communication terminals has become increasingly high, and wireless communication systems are developing in the direction of multi-node and distributed. Making full use of the cooperation between nodes can not only improve the utilization efficiency of wireless resources, but also enhance the security of information transmission.

[0003] According to the different cooperation modes, relay nodes are divided into two modes: cooperative forwarding and cooperative interference. Cooperative forwarding means that the relay node directly forwards the received signal to the target node; cooperative interference does not receive the signal sent by the source node, but only provides interference signals to reduce the receiving performance of the eavesdropping node, that is, by introducing friendly helper nodes to improve the confidentiality transmission performance of the system.

[0004] In practical applications, when the eavesdropping node is located near the relay node, it can detect the signals sent by the source node and the relay node. In this case, the system needs to take into account the security performance of the two transmission stages. Cooperative interference technology can be used to improve the security transmission performance of the first stage, that is, in the first stage of transmission, a part of the relay is used to send interference signals to interfere with the eavesdropping node, and the other part of the relay receives the signal and uses distributed beamforming technology to forward the useful signal. In actual wireless relay communications, channel state information estimation and quantization will cause non-ideal channel state information, making the channel state information of these two transmission stages destined to have errors. Therefore, how to improve the robustness of the physical layer security transmission of the wireless cooperative relay system under cooperative interference is a key problem that needs to be solved. Summary of the invention

[0005] The purpose of the present invention is to provide a physical layer security transmission method for a wireless cooperative relay system that can reduce information leakage, deteriorate the reception quality of eavesdropping nodes while ensuring the reception performance of legitimate target nodes, and realize safe and reliable transmission of information.

[0006] The technical solution to achieve the purpose of the present invention is: a method for robust and secure transmission of wireless relay communication under cooperative interference, comprising the following steps:

[0007] Step 1: Establish a wireless cooperative relay eavesdropping channel model, calculate the signals obtained by the legitimate target node and the eavesdropping node, then send artificial noise through the relay node to interfere with the eavesdropping of the eavesdropping node, calculate the estimated signals obtained by the legitimate target node and the eavesdropping node after interference, and finally calculate the mean square error of the legitimate target node and the minimum mean square error of the eavesdropping node when the artificial noise generated by the relay node is located in the null space of the legitimate channel;

[0008] Step 2: When a channel state information error occurs, the optimization problem is to meet the mean mean square error (MSE) constraint of the legal target node and the power constraint of each relay node within the given legal link channel state information error that obeys the Gaussian distribution, while considering eliminating the influence of the interference signal sent by the cooperative interference node on the legal target node;

[0009] Step 3: Use the "3σ principle" of Gaussian distribution and the triangle inequality to relax the optimization problem;

[0010] Step 4: Use orthogonal transformation to transform the optimization problem into an optimization problem in the real number domain;

[0011] Step 5: Use the two-layer optimization method to solve the optimization problem.

[0012] Compared with the prior art, the present invention has the following significant advantages: (1) it can effectively reduce information leakage and ensure the receiving performance of legitimate target nodes in the case of unknown eavesdropping link CSI; (2) it deteriorates the receiving quality of the eavesdropping node and improves the security and reliability of information transmission. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 The system model diagram is a method for robust and secure transmission of wireless relay communications under cooperative interference. DETAILED DESCRIPTION

[0014] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0015] Combination Figure 1 The present invention provides a method for robust and secure transmission of wireless relay communication under cooperative interference, comprising the following steps:

[0016] Step 1: Establish a wireless cooperative relay eavesdropping channel model, calculate the signals obtained by the legitimate target node and the eavesdropping node, then send artificial noise through the relay node to interfere with the eavesdropping of the eavesdropping node, calculate the estimated signals obtained by the legitimate target node and the eavesdropping node after interference, and finally calculate the mean square error of the legitimate target node and the minimum mean square error of the eavesdropping node when the artificial noise generated by the relay node is located in the null space of the legitimate channel;

[0017] Step 2: When a channel state information error occurs, the optimization problem is to meet the mean mean square error (MSE) constraint of the legal target node and the power constraint of each relay node within the given legal link channel state information error that obeys the Gaussian distribution, while considering eliminating the influence of the interference signal sent by the cooperative interference node on the legal target node;

[0018] Step 3: Use the "3σ principle" of Gaussian distribution and the triangle inequality to relax the optimization problem;

[0019] Step 4: Use orthogonal transformation to transform the optimization problem into an optimization problem in the real number domain;

[0020] Step 5: Use the two-layer optimization method to solve the optimization problem.

[0021] Furthermore, in step 1, a wireless cooperative relay eavesdropping channel model is established, the signals obtained by the legitimate target node and the eavesdropping node are calculated, and then artificial noise is sent through the relay node to interfere with the eavesdropping of the eavesdropping node, and the estimated signals obtained by the legitimate target node and the eavesdropping node after the interference are calculated. Finally, when the artificial noise generated by the relay node is located in the null space of the legitimate channel, the mean square error of the legitimate target node and the minimum mean square error of the eavesdropping node are calculated, as follows:

[0022] Step 1.1: Establish a wireless cooperative relay eavesdropping channel model, as follows:

[0023] Figure 1 The wireless cooperative relay eavesdropping channel model shown in the figure consists of a sending node S, n relay nodes {R1,…,R n}, a legitimate target node D, a friendly cooperative interference node J and an eavesdropping node E, where the number of relay nodes n>1, the source node, relay node and legitimate target node are all equipped with a single antenna, n>1, and the relay node is set to adopt the amplification and forwarding protocol;

[0024] At a certain moment, the source node communicates with the relay node, and its friendly cooperative interference node J cooperates to enhance the security performance of the system. Assume that all nodes use half-duplex mode, and because the distance between the source node and the legitimate target node is very far, there is no direct link between the source node and the legitimate target node, and the signal must be forwarded through the relay node, that is, the signal reaches the target node after two stages of transmission; Figure 1 In the figure, Phase I represents the transmission process of the first phase of the signal, Phase II represents the transmission process of the second phase of the signal, the solid line represents the transmission of the legitimate link, and the dotted line represents the transmission of the eavesdropping link; it is assumed that the top eavesdropping node is near the relay node, and can intercept the signals sent by the source node and the relay node; in the process of signal transmission, the relay node cooperates to forward the signal sent by the source node, and the friendly cooperative interference node sends interference signals to interfere with the signal reception of the eavesdropping node;

[0025] use represents the complex channel gain from the source node to all relay nodes, represents the complex channel gain from all relay nodes to the legitimate target node, represents the complex channel gain from the cooperative interference node to all relay nodes; it is assumed that the eavesdropping node is also equipped with a single antenna, so represents the channel gain from all relay nodes to the eavesdropping node, represents the channel gain from the cooperative interference node to the eavesdropping node, represents the channel gain from the source node to the eavesdropping node; h sr 、h rd 、h e 、h se and h je Each element in is an independent and identically distributed complex Gaussian random variable.

[0026] Step 1.2: Calculate the signals obtained by the legitimate target node and the eavesdropping node, as follows:

[0027] Suppose the source node sends a secret signal s to the legitimate target node through the relay node, and the signal is sent to meet The signal sent by the source node must go through two stages of transmission to reach the legitimate target node; in the first transmission stage, the source node sends a signal to the relay node in the form of broadcasting. Since there is no direct link between the source node and the legitimate target node, the legitimate target node cannot receive the signal sent by the source node; since the eavesdropping node is near the relay node, the eavesdropping node can intercept the signal sent by the source node; at the same time, in this stage, the cooperative interference node J sends an interference signal z to deteriorate the receiving performance of the eavesdropping node. Therefore, in the first stage of transmission, the signal x received by the relay node r =(x r,1 ,…,x r,n ) T for:

[0028]

[0029] Among them, P s is the signal transmission power, P j is the transmission power of the cooperative interference signal, z is the interference signal sent by the cooperative interference node J at this stage, and after normalization, it satisfies The covariance matrix is Zero-mean Gaussian additive white noise vector, I n is the n×n identity matrix;

[0030] At the same time, the eavesdropping node receives the signal x e for:

[0031]

[0032] in, Variance Zero-mean additive white Gaussian noise;

[0033] In the second stage of transmission, n relay nodes amplify the received signal and forward it to the legitimate target node. In this stage, the eavesdropping node can also intercept the signal forwarded by the relay node. The relay node uses distributed beamforming technology, that is, multiplying the signal by the transmit beamforming matrix before sending it. For the received signal vector x r weighting;

[0034] Set the maximum transmission power of each relay node to P i ,i=1,…,n, the power consumption of the relay node to send useful signals P t for:

[0035]

[0036] Where w=(w1,…,w n ) T , R sr =diag(|h sr,1 | 2 ,···,|h sr,n | 2 ), R jr =diag(|h jr,1 | 2 ,···,|h jr,n | 2 );

[0037] The legitimate target node receives the signal y d for:

[0038]

[0039] in, The variance is Zero-mean additive white Gaussian noise;

[0040] At the same time, the eavesdropping node can also eavesdrop on the signal of the second phase, and the signal y e for:

[0041]

[0042] in, The variance is Zero-mean additive white Gaussian noise.

[0043] Step 1.3: The relay node sends artificial noise to interfere with the eavesdropping node, and calculates the estimated signal obtained by the legitimate target node and the eavesdropping node after interference, as follows:

[0044] The present invention designs a physical layer security technology in the case of unknown eavesdropping link CSI. The first transmission stage adopts cooperative interference technology, and the second transmission stage adopts masked beamforming technology. In view of the situation that there are errors in the CSI from the source node to all relay nodes and the CSI from all relay nodes to the legitimate target nodes, a robust security transmission scheme is designed, and an optimization algorithm is designed using a double-layer optimization method.

[0045] In the case of unknown eavesdropper channel state information, the confidentiality rate cannot be optimized directly. Therefore, in addition to using cooperative interference technology in the first stage, in the second stage of transmission, the relay node not only considers using distributed beamforming technology, but also uses artificial noise strategies to interfere with potential eavesdroppers.

[0046] Therefore, in the second stage of transmission, the relay node must both receive the signal vector x r Using the beamforming matrix W b After weighted forwarding, artificial noise must also be sent Then, the signal y sent by the relay node r =(y r,1 ,…,y r,n ) T for:

[0047] y r =W b x r +n an (6)

[0048] Among them, the power of each relay node satisfies represents the artificial noise power;

[0049] Considering artificial noise, the received signal y of the legitimate target node d becomes:

[0050]

[0051] Set the legal target node to use a linear receiving filter To process the received signal y d , thus obtaining an estimate of its expected sign, where β is a positive scalar;

[0052] Then the estimated symbol obtained by the legal target node is for:

[0053]

[0054] The signal y received by the eavesdropping node e becomes:

[0055]

[0056] Step 1.4: Calculate the mean square error of the legitimate target node and the minimum mean square error of the eavesdropping node when the artificial noise generated by the relay node is located in the null space of the legitimate channel, as follows:

[0057] In the second stage of transmission, it can be seen from formula (7) that artificial noise interferes with the reception of the legitimate target node, so corresponding processing must be performed; in order to prevent artificial noise from interfering with the reception performance of the legitimate target node, the artificial noise n generated by the relay node is an Must be on a legal channel rd The null space of So, we can get:

[0058] n an =Πv a (10)

[0059] Where Π is h rd A set of orthogonal bases of the null space that satisfies ΠΠ H =I n , v a is zero mean and has a variance of iid Gaussian random vector;

[0060] According to formula (10), the mean square errors of the legal target nodes are obtained as follows:

[0061]

[0062] Among them, r h1 =(h sr,1 h rd,1 ,…,h sr,n h rd,n ) T , r h2 =(h jr,1 h rd,1 ,…,h jr,n h rd,n ) T , Re(·) represents the real part of the complex number, R rd =diag(|h rd,1 | 2 ,···,|h rd,n | 2 );

[0063] Combining formula (2) and formula (9), the signal model of the eavesdropping node in the two-stage transmission process is:

[0064] y e =H e x+ne (12)

[0065] Among them, y e =(x e ,y e ) T , x=(s,z) T ,

[0066] Assuming that the eavesdropping node knows the transmit beamforming matrix and artificial noise covariance matrix of the relay node, the minimum mean square error of the eavesdropping node is:

[0067]

[0068] in, G e,1 Represents G e The first row of elements in .

[0069] Furthermore, in step 2, when a channel state information error occurs, the optimization problem is to satisfy the mean mean square error MSE constraint of the legal target node and the power constraint of each relay node within the given legal link channel state information error that obeys the Gaussian distribution, while considering eliminating the influence of the interference signal sent by the cooperative interference node on the legal target node, as follows:

[0070] The total power consumed by the relay node is divided into the transmission power of the useful signal and the transmission power of the artificial noise. In order to maximize the deterioration of the reception quality of the potential eavesdropper when the channel state information of the eavesdropper is unknown, this section satisfies the MSE constraint c of the legitimate target node and the power constraint P of the ith relay. i Under the condition of , the transmission power of artificial noise is maximized to interfere with potential eavesdropping nodes, thereby enhancing the physical layer security performance of the system. This problem is equivalent to minimizing the power of useful signals transmitted by relay nodes under the same constraints.

[0071] From formula (7), we can see that in order to prevent the interference signal emitted by the friendly cooperative interference node from interfering with the legitimate target node, we design the relay weight w so that On the null space of This makes the interference signal sent by the friendly cooperative interference node only interfere with the potential eavesdropping node after being forwarded by the relay node, but not the legitimate target node; when the MSE constraint c of the legitimate target node and the power constraint P of each relay node are met, i Under the condition of , the power consumption of the relay node to send useful signals is minimized. This optimization problem is expressed as follows:

[0072]

[0073] in, [·] i,i Represents the element in the i-th row and i-th column of the matrix;

[0074] The following Gaussian error model is used to represent the real channel state information in actual communication:

[0075]

[0076] Among them, h sr ,h rd and h jr Indicates the real channel state information in actual communication. and represents the estimated channel state information from the source node to the relay node, from the relay node to the legitimate target node, and from the cooperative interference node to the relay node, e sr =(e sr,1 ,…,e sr,n ) T , e rd =(e rd,1 ,…,e rd,n ) T and e jr =(e jr,1 ,…,e jr,n ) T The variances are and The zero-mean additive Gaussian error is assumed; the estimation error and channel gain are assumed to be statistically independent;

[0077] In the case of non-ideal CSI of the legal link, the average MSE of the legal target node is:

[0078]

[0079] in,

[0080]

[0081] Non-ideal channel state information will lead to a reduction in the artificial noise power received by the interfering eavesdropping node. Then, within a given channel state information error, the minimum artificial noise transmission power satisfies the following inequality constraints:

[0082]

[0083] in,

[0084] Substituting formula (17) into formula (16), we obtain the following inequality:

[0085]

[0086] The relay weight w is designed to maximize the power of artificial noise. Considering the error in the channel state information from the source node to all relay nodes and the channel state information from all relay nodes to the legitimate target node, the optimization problem of the relay node sending artificial noise power is a maximum minimization problem in mathematics, which is equivalent to the minimum maximization problem of the relay node sending useful signal power. Therefore, within the given channel state information error of the legitimate link, the average MSE constraint c of the legitimate target node and the power constraint P of each relay node are satisfied. i Under the condition of eliminating the interference signal sent by the cooperative interference node on the legitimate target node, the secure transmission scheme of non-ideal CSI under cooperative interference can be designed as the following optimization problem:

[0087]

[0088] Furthermore, in step 3, the optimization problem is relaxed by using the “3σ principle” of Gaussian distribution and the triangle inequality, as follows:

[0089] definition as well as Substituting them into the optimization problem (19), the optimization problem (19) can be transformed into:

[0090]

[0091] The "3σ principle" of Gaussian distribution means that each value generated by Gaussian distribution has a 99.74% probability of falling within the interval [-3σ, 3σ]. Using the "3σ principle" of Gaussian distribution and the triangle inequality, the following formula is obtained:

[0092]

[0093] in,

[0094] Then, using the "3σ principle" of Gaussian distribution and the triangle inequality, we get the following formula:

[0095]

[0096] in,

[0097] Using inequalities (21) and (22), we can obtain:

[0098]

[0099] Using inequalities (21), (22) and (23), the optimization problem (20) is transformed into the following optimization problem:

[0100]

[0101] Where y1=(y 1,1 ,···,y 1,n ) T , y2=(y 2,1 ,···,y 2,n ) T ,

[0102]

[0103] Substituting formula (18) into the optimization problem (24), we get the following optimization problem:

[0104]

[0105] Using the triangle inequality and variable substitution, the optimization problem (25) is transformed into the following optimization problem:

[0106]

[0107] Where u1=(u 1,1 ,···,u 1,n ) T ,u2=(u 2,1 ,···,u 2,n ) T ,u3=(u 3,1 ,···,u 3,n ) T ,

[0108]

[0109] Furthermore, the optimization problem is converted into an optimization problem in the real number domain by using orthogonal transformation as described in step 4, as follows:

[0110] The first constraint of the optimization problem (26) is a complex conjugate matrix, so there exists an orthogonal matrix Γ such that Γ H AΓ=Λ,where Γ H Γ=I n , Λ=diag(λ1,···,λ n ) is a diagonal matrix;

[0111] make Then the optimization problem (26) can be equivalently transformed into the following optimization problem on the real number field:

[0112]

[0113] in, I w,i =diag(0,···,1,1,···,0) has the 2i-1th and 2ith elements as 1.

[0114] The following equivalent problem is obtained:

[0115]

[0116] Using (28), the optimization problem (27) is transformed into:

[0117]

[0118] in, f 1,i =(0,-1,···,1,···,ξ 1,i ···,0) the 2n+ith element is -1, the 4n+ith element is 1, and the 5n+ith element is ξ 1,i ,

[0119] f 2,i =(0,-1,···,1,···,ξ 2,i ···,0) the 3n+ith element is -1, the 5n+ith element is 1, and the 6n+ith element is ξ 2,i , The 4n+ith element in is 1, The 5n+ith element in is 1, The 5n+ith element in is 1;

[0120] When the following two conditions are met, A in the first constraint of the optimization problem (26) is a Hermitian positive definite matrix:

[0121] Condition 1:

[0122]

[0123] Condition 2:

[0124]

[0125] The actual communication scenario that meets condition 1 is: the signal transmission power is greater than the noise power; the actual communication scenario that meets condition 2 is: the channel quality from the relay node to the legitimate target node is better than the channel quality from the source node to the relay node.

[0126] When A in the optimization problem (26) is a Hermitian positive definite matrix, the first constraint in the optimization problem (29) is The diagonal elements of are positive. In this case, the first constraint of problem (29) can be written in the following equivalent form:

[0127]

[0128] Using (32), the optimization problem (29) can be transformed into:

[0129]

[0130] in, υ is any variable.

[0131] Furthermore, the optimization problem is solved by using a two-layer optimization method as described in step 5, as follows:

[0132] The problem (33) is solved using a two-layer optimization method. When β is fixed, the problem (33) is a SOCP problem, which is a convex optimization problem and can be solved using the interior point method to obtain the optimal solution. When the relay weight w is fixed, β is obtained by solving the following average MSE minimization problem of the legal target nodes:

[0133]

[0134] in,

[0135]

[0136] The optimization problem (34) is convex and can be solved directly to obtain β:

[0137]

[0138] After obtaining w and β, the power consumed by the relay node to send useful signals is P t,i =[ww H ] i,i [T] i,i , the remaining power is used to send artificial noise;

[0139] It can be obtained by solving the following problem:

[0140]

[0141] in,

[0142] The optimization problem (36) is a linear programming problem, which can be solved using the interior point method to obtain the optimal value.

[0143] The above description is only a specific implementation of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention.

Claims

1. A method for robust and secure transmission of wireless relay communication under cooperative interference, characterized in that: The following steps are involved: Step 1: Establish a wireless cooperative relay eavesdropping channel model, calculate the signals obtained by the legitimate target node and the eavesdropping node, then send artificial noise through the relay node to interfere with the eavesdropping of the eavesdropping node, calculate the estimated signals obtained by the legitimate target node and the eavesdropping node after interference, and finally calculate the mean square error of the legitimate target node and the minimum mean square error of the eavesdropping node when the artificial noise generated by the relay node is located in the null space of the legitimate channel; Step 2: When a channel state information error occurs, the optimization problem is to meet the mean mean square error (MSE) constraint of the legal target node and the power constraint of each relay node within the given legal link channel state information error that obeys the Gaussian distribution, while considering eliminating the influence of the interference signal sent by the cooperative interference node on the legal target node; Step 3: Use the "3σ principle" of Gaussian distribution and the triangle inequality to relax the optimization problem; Step 4: Use orthogonal transformation to transform the optimization problem into an optimization problem in the real number domain; Step 5: Solve the optimization problem using a two-layer optimization method; The wireless cooperative relay eavesdropping channel model described in step 1 is established, the signals obtained by the legitimate target node and the eavesdropping node are calculated, and then artificial noise is sent through the relay node to interfere with the eavesdropping of the eavesdropping node, and the estimated signals obtained by the legitimate target node and the eavesdropping node after interference are calculated. Finally, when the artificial noise generated by the relay node is located in the null space of the legitimate channel, the mean square error of the legitimate target node and the minimum mean square error of the eavesdropping node are calculated, as follows: Step 1.1, establish a wireless cooperative relay eavesdropping channel model; Step 1.2, calculate the signals obtained by the legitimate target node and the eavesdropping node; Step 1.3, the relay node sends artificial noise to interfere with the eavesdropping node's eavesdropping, and calculates the estimated signal obtained by the legitimate target node and the eavesdropping node after interference; Step 1.4, calculate the minimum mean square error of the legitimate target node and the eavesdropping node when the artificial noise generated by the relay node is located in the null space of the legitimate channel; The establishment of the wireless cooperative relay eavesdropping channel model described in step 1.1 is as follows: A wireless cooperative relay eavesdropping channel model is established, which consists of a sending node S, n relay nodes {R1,…,R n }, a legitimate target node D, a friendly cooperative interference node J and an eavesdropping node E, where the number of relay nodes n>1, the source node, relay node and legitimate target node are all equipped with a single antenna, and the relay node adopts the amplification and forwarding protocol; At a certain moment, the source node communicates with the relay node, and the friendly cooperative interference node J of the source node performs cooperative interference to enhance the security performance of the system. All nodes are set to use half-duplex mode. Since the distance between the source node and the legitimate target node is very far, there is no direct link between the source node and the legitimate target node, and the signal must be forwarded through the relay node, that is, the signal reaches the target node after two stages of transmission; the eavesdropping node is set near the relay node, and can intercept the signals sent by the source node and the relay node; in the process of signal transmission, the relay node cooperates to forward the signal sent by the source node, and the friendly cooperative interference node sends interference signals to interfere with the signal reception of the eavesdropping node; use represents the complex channel gain from the source node to all relay nodes, represents the complex channel gain from all relay nodes to the legitimate target node, represents the complex channel gain from the cooperative interference node to all relay nodes, represents the channel gain from all relay nodes to the eavesdropping node, represents the channel gain from the cooperative interference node to the eavesdropping node, represents the channel gain from the source node to the eavesdropping node; h sr 、h rd 、h e 、h se and h je Each element in is an independent and identically distributed complex Gaussian random variable.

2. The method for robust secure transmission of wireless relay communication under coordinated interference according to claim 1, characterized in that: The calculation of the signals obtained by the legitimate target node and the eavesdropping node described in step 1.2 is as follows: Suppose the source node sends a secret signal s to the legitimate target node through the relay node, and the signal is satisfied The signal sent by the source node must go through two stages of transmission to reach the legitimate target node. In the first transmission stage, the source node sends a signal to the relay node in the form of broadcast. Since there is no direct link between the source node and the legitimate target node, the legitimate target node cannot receive the signal sent by the source node; since the eavesdropping node is near the relay node, the eavesdropping node can intercept the signal sent by the source node; at the same time, in this stage, the cooperative interference node J sends an interference signal z to deteriorate the receiving performance of the eavesdropping node; therefore, in the first stage of transmission, the signal x received by the relay node r =(x r,1 ,…,x r,n ) T for: Among them, P s is the signal transmission power, P j is the transmission power of the cooperative interference signal, z is the interference signal sent by the cooperative interference node J at this stage, and after normalization, it satisfies The covariance matrix is Zero-mean Gaussian additive white noise vector, I n is the n×n identity matrix; At the same time, the eavesdropping node receives the signal x e for: in, Variance Zero-mean additive white Gaussian noise; In the second stage of transmission, n relay nodes amplify the received signal and forward it to the legitimate target node. In this stage, the eavesdropping node can also intercept the signal forwarded by the relay node. The relay node uses distributed beamforming technology, that is, multiplying the signal by the transmit beamforming matrix before sending it. For the received signal vector x r weighting; Set the maximum transmission power of each relay node to P i ,i=1,…,n, the power consumption P of the relay node sending useful signals t for: Where w=(w1,…,w n ) T , R sr =diag(|h sr,1 | 2 ,···,|h sr,n | 2 ), R jr =diag(|h jr,1 | 2 ,···,|h jr,n | 2 ); The legitimate target node receives the signal y d for: in, The variance is Zero-mean additive white Gaussian noise; At the same time, the eavesdropping node can also eavesdrop on the signal of the second phase, and the signal y e for: in, The variance is Zero-mean additive white Gaussian noise.

3. The method for robust secure transmission of wireless relay communication under coordinated interference according to claim 2, characterized in that: The relay node described in step 1.3 sends artificial noise to interfere with the eavesdropping node's eavesdropping, and calculates the estimated signal obtained by the legitimate target node and the eavesdropping node after interference, as follows: In the second stage of transmission, the relay node sends artificial noise To interfere with the eavesdropping node's eavesdropping, so the signal y sent by the relay node r =(y r,1 ,…,y r,n ) T for: y r =W b x r +n an (6) Among them, the power of each relay node satisfies represents the artificial noise power; Considering artificial noise, the received signal y of the legitimate target node d becomes: Set the legal target node to use a linear receiving filter To process the received signal y d , thus obtaining an estimate of its expected sign, where β is a positive scalar; Then the estimated signal obtained by the legal target node is for: The signal y received by the eavesdropping node e becomes:

4. The method for robust secure transmission of wireless relay communication under coordinated interference according to claim 3, characterized in that: When the artificial noise generated by the calculation relay node described in step 1.4 is located in the null space of the legal channel, the mean square error of the legal target node and the minimum mean square error of the eavesdropping node are as follows: In the second stage of transmission, since artificial noise interferes with the reception of the legitimate target node, it must be processed accordingly; in order to prevent artificial noise from interfering with the reception performance of the legitimate target node, the artificial noise n generated by the relay node an Must be on a legal channel rd The null space of So, we can get: n an =Pv a (10) Where Π is h rd A set of orthogonal bases of the null space that satisfies ΠΠ H =I n , v a is zero mean and has a variance of iid Gaussian random vector; According to formula (10), the mean square errors of the legal target nodes are obtained as follows: Among them, r h1 =(h sr,1 h rd,1 ,…,h sr,n h rd,n ) T , r h2 =(h jr,1 h rd,1 ,…,h jr,n h rd,n ) T , Re(·) represents the real part of the complex number, R rd =diag(|h rd,1 | 2 ,···,|h rd,n | 2 ); Combining formula (2) and formula (9), the signal model of the eavesdropping node in the two-stage transmission process is: y e =H e x+n e (12) where y e =(x e , y e ), T x = (s, z) T , Assuming that the eavesdropping node knows the transmit beamforming matrix and artificial noise covariance matrix of the relay node, the minimum mean square error of the eavesdropping node is: in, G e,1 Represents G e The first row of elements in .

5. The method for robust secure transmission of wireless relay communication under coordinated interference according to claim 4, characterized in that: In step 2, when a channel state information error occurs, the optimization problem is to satisfy the mean mean square error (MSE) constraint of the legal target node and the power constraint of each relay node within the given legal link channel state information error that obeys the Gaussian distribution, while considering eliminating the influence of the interference signal sent by the cooperative interference node on the legal target node, as follows: The total power consumed by the relay node is divided into the transmission power of the useful signal and the transmission power of the artificial noise. In order to maximize the deterioration of the reception quality of the potential eavesdropper when the channel state information of the eavesdropper is unknown, the mean square error constraint c of the legitimate target node and the i-th relay power constraint P are satisfied. i Under the condition of , the transmission power of artificial noise is maximized to interfere with potential eavesdropping nodes, thereby enhancing the physical layer security performance of the system. This problem is equivalent to minimizing the power of useful signals transmitted by relay nodes under the same constraints. This optimization problem is: in, [·] i,i Represents the element in the i-th row and i-th column of the matrix; The following Gaussian error model is used to represent the real channel state information in actual communication: Among them, h sr ,h rd and h jr Indicates the real channel state information in actual communication. and represents the estimated channel state information from the source node to the relay node, from the relay node to the legitimate target node, and from the cooperative interference node to the relay node, e sr =(e sr,1 ,…,e sr,n ) T , e rd =(e rd,1 ,…,e rd,n ) T and e jr =(e jr,1 ,…,e jr,n ) T The variances are and The zero-mean additive Gaussian error is assumed; the estimation error and channel gain are assumed to be statistically independent; In the case of non-ideal CSI of the legal link, the average MSE of the legal target node is: in, Non-ideal channel state information will lead to a reduction in the artificial noise power received by the interfering eavesdropping node. Then, within a given channel state information error, the minimum artificial noise transmission power satisfies the following inequality constraints: in, Substituting formula (17) into formula (16), we obtain the following inequality: The relay weight w is designed to maximize the power of artificial noise. Considering the error in the channel state information from the source node to all relay nodes and the channel state information from all relay nodes to the legitimate target node, the optimization problem of the relay node sending artificial noise power is a maximum minimization problem in mathematics, which is equivalent to the minimum maximization problem of the relay node sending useful signal power. Therefore, within the given channel state information error of the legitimate link, the average MSE constraint c of the legitimate target node and the power constraint P of each relay node are satisfied. i Under the condition of eliminating the interference signal sent by the cooperative interference node on the legitimate target node, the secure transmission scheme of non-ideal CSI under cooperative interference is designed as the following optimization problem:

6. The method for robust secure transmission of wireless relay communication under coordinated interference according to claim 5, characterized in that: In step 3, the optimization problem is relaxed by using the "3σ principle" of Gaussian distribution and the triangle inequality, as follows: definition as well as Substituting them into the optimization problem (19), the optimization problem (19) is converted into: Using the "3σ principle" of Gaussian distribution and the triangle inequality, we get the following formula: in, Then, using the "3σ principle" of Gaussian distribution and the triangle inequality, we get the following formula: in, Using inequalities (21) and (22), we obtain: Using inequalities (21), (22) and (23), the optimization problem (20) is transformed into the following optimization problem: where y1 = (y 1,1 , ···, y 1,n ), T , y2 = (y 2,1 , ···, y 2,n ), T , Substituting formula (18) into the optimization problem (24), we get the following optimization problem: Using the triangle inequality and variable substitution, the optimization problem (25) is transformed into the following optimization problem: Among them, u1=(u 1,1 ,···,u 1,n ) T , u2=(u 2,1 ,···,u 2,n ) T , u3=(u 3,1 ,···,u 3,n ) T , 7. The method for robust secure transmission of wireless relay communication under coordinated interference according to claim 6, characterized in that: In step 4, the optimization problem is converted into an optimization problem in the real number domain by using orthogonal transformation, as follows: The first constraint of the optimization problem (26) is a complex conjugate matrix, so there exists an orthogonal matrix Γ such that Γ H AΓ=Λ,where Γ H Γ=I n , Λ=diag(λ1,···,λ n ) is a diagonal matrix; make Then the optimization problem (26) is equivalently transformed into the following optimization problem over the real number field: in, I w,i =diag(0,···,1,1,···,0), the 2i-1th and 2ith elements are 1; The following equivalent problem is obtained: Using (28), the optimization problem (27) is transformed into: in, f 1,i =(0,-1,···,1,···,ξ 1,i ···,0) the 2n+ith element is -1, the 4n+ith element is 1, and the 5n+ith element is ξ 1,i , f 2,i =(0,-1,···,1,···,ξ 2,i ···,0) the 3n+ith element is -1, the 5n+ith element is 1, and the 6n+ith element is ξ 2,i , The 4n+ith element in is 1, The 5n+ith element in is 1, The 5n+ith element in is 1; When the following two conditions are met, A in the first constraint of the optimization problem (26) is a Hermitian positive definite matrix: Condition 1: Condition 2: The actual communication scenario that meets condition 1 is: the signal transmission power is greater than the noise power; the actual communication scenario that meets condition 2 is: the channel quality from the relay node to the legitimate target node is better than the channel quality from the source node to the relay node; When A in the optimization problem (26) is a Hermitian positive definite matrix, the first constraint in the optimization problem (29) is The diagonal elements of are positive. In this case, the first constraint of problem (29) can be written as follows: Using (32), the optimization problem (29) is transformed into: in, υ is any variable.

8. The method for robust secure transmission of wireless relay communication under coordinated interference according to claim 7, characterized in that: The two-level optimization method described in step 5 is used to solve the optimization problem, as follows: The problem (33) is solved using the two-level optimization method. When β is fixed, the problem (33) is a SOCP problem, which is a convex optimization problem. The interior point method is used to solve the problem and obtain the optimal solution. When the relay weight w is fixed, β is obtained by solving the following average MSE minimization problem of legal target nodes: in, The optimization problem (34) is convex, and β can be directly solved as: After obtaining w and β, the power consumed by the relay node to send useful signals is P t,i =[ww H ] i,i [T] i,i , the remaining power is used to send artificial noise; Obtained by solving the following problem: in, The optimization problem (36) is a linear programming problem, and the interior point method is used to solve it to obtain the optimal value.

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