Double-IRS-assisted downlink MISO system security communication optimization method based on graph neural network

Abstract

The invention relates to a double-IRS-assisted downlink MISO system security communication optimization method based on a graph neural network, and belongs to the field of wireless communication security. According to the method, the physical layer security of information transmission of the wireless communication system is guaranteed by adopting the double IRSs, the total information secrecy rate of the system is maximized by jointly optimizing reflected beam forming of the two IRSs and transmitted beam forming of the base station, meanwhile, the transmitted power constraint of the base station and the modulo constraint of IRS reflection coefficients are met, and through a GNN-based machine learning method, the information secrecy rate of the system is improved. Channel information is parameterized into GNN representation vectors, the representation vectors are updated layer by layer according to a GNN connection graph, and beam forming at a BS position and a reflection coefficient at an IRS position are optimized according to a system target. Compared with the existing reference scheme, the method provided by the invention can greatly improve the total secrecy rate of the system, and the consumed time is greatly reduced.

Description

Technical Field

[0001] The present invention belongs to the field of wireless communication security and relates to a dual IRS assisted downlink MISO system security communication optimization method based on graph neural network. Background Art

[0002] With the global commercialization of 5G, academia and industry have begun to conduct relevant research on 6G. In addition to the higher speed than 5G networks, 6G networks are also intelligent and open. As a key technology of 6G, intelligent reflection plane IRS technology has become a hot topic in industrial research in recent years. IRS uses a large number of low-cost passive components to adaptively and dynamically adjust the phase shift of the reflected signal, reconfigure the wireless propagation channel, and further optimize the communication performance.

[0003] The information transmission of wireless communication systems is vulnerable to eavesdropping, and information communication security has become one of the key issues that need to be solved urgently. For example, in order to eavesdrop on user information, eavesdroppers often place themselves in the same receiving position as the user and use antennas with greater receiving gain to eavesdrop on the user's private information. In recent years, in addition to using traditional encryption methods at the application layer, the concept of physical layer security (PLS) has been proposed, such as cooperative relaying and artificial noise. Due to the outstanding performance of IRS in the field of wireless communication security, the IRS-assisted wireless communication PLS problem has become a hot topic of research.

[0004] Although many works have studied the secure communication of IRS-assisted wireless communication systems, there is no relevant literature on the secure communication of dual IRS-assisted wireless communication systems that consider channel estimation and reflection links between IRSs. Since dual IRS-assisted wireless communication systems have a large number of channel parameters and the system structure is more complex, channel estimation poses a more difficult challenge. Channel estimation of dual IRS-assisted wireless communication systems is a time-consuming and arduous problem in itself. Considering the non-convexity of the optimization problem and the coupling of the optimization variables, the traditional solution is to introduce slack variables to decouple the optimization variables, and then transform the non-convex optimization problem into an approximate convex optimization problem, and use alternating optimization to obtain an approximate solution to the problem. This method has a large number of variables and iterations, and has the disadvantages of slow convergence and the results may not be close to the optimal solution. Summary of the invention

[0005] In view of this, the object of the present invention is to provide a dual IRS assisted downlink MISO system security communication optimization method based on graph neural network.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A method for optimizing secure communication of a dual IRS-assisted downlink MISO system based on a graph neural network, the method comprising the following steps:

[0008] S1. Establish a dual IRS assisted downlink MISO wireless communication system model, define the corresponding communication channel, the corresponding reflection phase shift matrix, the corresponding received signal representation and the corresponding receiving rate;

[0009] S2. Under the dual IRS assisted downlink MISO wireless communication system model, a secure communication optimization problem P1 is established with the goal of maximizing the sum of the total confidentiality rates of all legitimate users and satisfying the corresponding constraints;

[0010] S3, obtaining all channel state information of the dual IRS assisted downlink MISO wireless communication system model through large-scale time estimation, small-scale time estimation and pilot estimation methods respectively;

[0011] S4, using graph neural network GNN to simulate the optimal mapping of pilot information vector to base station beamforming and IRS reflection phase shift, transforming the secure communication optimization problem P1 into P2;

[0012] S5. Establish a graph neural network GNN model under the dual IRS assisted wireless energy communication system model, which includes an input layer, a D update layer and an output layer;

[0013] S6. Train the graph neural network GNN model. After training, the GNN model uses the secure communication optimization problem P2 as the objective function to solve the base station beamforming and IRS reflection phase shift.

[0014] Further, in step S1, the dual IRS-assisted downlink MISO wireless communication system model includes a base station BS, two intelligent reflection planes IRS1 and IRS2, K legal users U1, ..., U k and N active eavesdroppers E1, ..., E n , where the base station BS has M transmitting antennas, all legitimate users and eavesdroppers have single antennas, IRS1 is deployed near the BS and has L1 reflection units; IRS2 is deployed near the legitimate users and has L2 reflection units;

[0015] The BS simultaneously sends K independent confidential data streams to K legitimate users on the same frequency band. Unauthorized eavesdroppers attempt to eavesdrop on any data stream. IRS1 reflects the signal transmitted by the base station to the legitimate users and also reflects the signal to IRS2. IRS2 reflects the signal received from the base station and IRS1 to the legitimate users.

[0016] The channels from BS to IRS1 and IRS2 are represented as and The channel from IRS1 to IRS2 is represented as The channels from IRS1 and IRS2 to legitimate users are respectively expressed as and The channels from IRS1 and IRS2 to the eavesdropper are expressed as and Among them, 1≤k≤K, 1≤n≤N; C x×y Represents a collection of complex-valued matrices of dimension x-by-y.

[0017] Furthermore, in the dual IRS-assisted downlink MISO wireless communication system model, the reflection phase shift matrix of IRS1 is expressed as:

[0018]

[0019] [·] H represents the conjugate transpose of the matrix), represents the reflection coefficient of the l1th reflection unit, where is the reflection amplitude, is its reflected phase shift:

[0020]

[0021] Where Q is the phase shift interval of a single element on the IRS;

[0022] The reflection phase shift matrix of IRS2 is expressed as:

[0023]

[0024] in, represents the reflection coefficient of the l2th reflection unit, and the reflection amplitude is The reflected phase shift is:

[0025]

[0026] The base station's transmission signal is expressed as where w k ∈C M×1 is the beamforming matrix, s k Dedicated to legitimate users k The confidential information is subject to a complex Gaussian distribution with a mean of 0 and a variance of 1;

[0027] Legitimate user U k and Eavesdropper E n The received signal is expressed as:

[0028] y k =[G1θ1h 1,k +G2θ2h 2,k +G1θ1DH θ2h 2,k ] T x+u k ,1≤k≤K

[0029] y n =[G1θ1g 1,n +G2θ2g 2,n +G1θ1D H θ2g 2,n ] T x+u n ,1≤n≤N

[0030] where u k and u n are the receiving noises at the legitimate user and the eavesdropper respectively, and they obey the complex Gaussian distribution with a mean of 0, that is, δ represents the variance of the complex Gaussian distribution;

[0031] Then U k The achievable rate at which the kth confidential information is received is:

[0032]

[0033] In E n The achievable eavesdropping rate of the kth confidential information received at is:

[0034]

[0035] Will s k Transmit to U k The achievable confidentiality rate for N eavesdroppers is U k and E n Minimum confidentiality rate between:

[0036]

[0037] All channels are uncorrelated Rayleigh fading channels, that is:

[0038]

[0039] in, ρ D , They represent the large-scale fading factors of the channel respectively, and vec(·) represents matrix vectorization.

[0040] Further, in step S2, the established secure communication optimization problem P1 is expressed as:

[0041]

[0042] st:

[0043]

[0044] Among them, P BS is the transmit power constraint at the BS; by jointly optimizing the reflection phase shift matrix θ1 of IRS1, the reflection phase shift matrix θ2 of IRS2 and the beamforming matrix {w K}, ensuring that the reflection coefficient of the IRS satisfies the modulo-1 constraint and the base station does not exceed the maximum transmission power constraint to maximize the total confidentiality rate C of all legitimate users k sum.

[0045] Further, in step S3, the channels G1, G2 and D are estimated by a large-scale time estimation method, and h is estimated by a small-scale time estimation method. 1,k ,h 2,k , g 1,n , g 2,n , and finally get the estimated vector of all channels in, are the estimation results of the corresponding channels respectively; the estimation methods for G1, G2 and D include:

[0046] It is estimated that the pilot used by G1 consists of L1 subframes, each subframe contains M time slots, and the pilot overhead is

[0047] Turn on IRS1 and turn off IRS2. In the tth subframe, the reflection coefficient at IRS1 is The reflection coefficient is taken from the L1×L1 DFT matrix;

[0048] Based on the full-duplex architecture, in the time slot l of the tth subframe, the BS's antenna m1 transmits a non-zero pilot The remaining antennas do not transmit pilot signals, so the pilot signal received by BS antenna m2 in time slot l of subframe t is:

[0049]

[0050] in, in Represents the suppressed crosstalk, which satisfies

[0051] Assume that the power of the BS pilot signal is consistent, that is, the pilot signal sent by BS antenna m1 satisfies in, is the transmit power, for given antennas m1 and m2, we have:

[0052]

[0053] Among them, the IRS reflection matrix represents the Hadamard product of the two;

[0054] In the time slot l2 of the tth subframe, the BS's antenna m1 transmits a pilot signal The signal received by antenna m3 is BS antenna m2 sends a pilot signal The signal received by antenna m3 is The signal received in all subframes is:

[0055]

[0056] Using the least squares estimation, let Get an estimate for:

[0057]

[0058] have:

[0059]

[0060] Where ÷ represents the matrix dot division operation, then we get the estimated

[0061] It is estimated that the pilot used by G2 consists of L2 subframes, each subframe contains M time slots, and the pilot overhead is

[0062] Turn on IRS2 and turn off IRS1. In the tth subframe, the reflection coefficient at IRS2 is The reflection coefficient is taken from the L2×L2 DFT matrix;

[0063] Based on the full-duplex architecture, in the time slot l of the tth subframe, the BS's antenna m1 transmits a non-zero pilot The remaining antennas do not transmit pilot signals, so the pilot signal received by BS antenna m2 in time slot l of subframe t is:

[0064]

[0065] in, in Represents the suppressed crosstalk, which satisfies

[0066] Assume that the power of the BS pilot signal is consistent, that is, the pilot signal sent by BS antenna m1 satisfies in, is the transmit power, for given antennas m1 and m2, we have:

[0067]

[0068] Among them, the IRS reflection matrix represents the Hadamard product of the two;

[0069] In the time slot l2 of the tth subframe, the BS's antenna m1 transmits a pilot signal The signal received by antenna m3 is BS antenna m2 sends a pilot signal The signal received by antenna m3 is The signal received in all subframes is:

[0070]

[0071] Using the least squares estimation, let Get an estimate for:

[0072]

[0073] have:

[0074]

[0075] Here ÷ represents the matrix dot division operation.

[0076] The estimation process of the channel D between IRSs includes:

[0077] IRS1 and IRS2 are turned on at the same time, and BS antenna m sends a non-zero pilot signal s at the tth pilot time. t , where t=1,2,···,τ D , τ D The number of pilots required for channel estimation at this stage;

[0078] The transmitted signal is reflected by the dual IRS and then received at the BS antenna m. The BS is assumed to be a full-duplex antenna, and the SI suppression method is used to suppress the self-interference generated by the same antenna transmission and reception. The signal received by the BS antenna m at the tth pilot time is:

[0079]

[0080] in, denote the channels from BS antenna m to IRS1 and IRS2, respectively, 1,t and θ 2,t represents the reflection coefficient vector of IRS1 and IRS2 at time t, i t and n t represents the self-interference and received noise after suppression at time t;

[0081] According to the estimated have:

[0082]

[0083] in, Denote the channel estimation vectors from BS antenna m to IRS1 and IRS2 respectively, then:

[0084]

[0085] according to And the result of multiplying two matrices is a scalar, so:

[0086] further:

[0087]

[0088] make get:

[0089]

[0090] Assume that for any t∈{1,2,...,τ D}, BS antenna m sends pilot signals that satisfy The received signal is D The time slots are superimposed as T v ×T h A matrix, where T v =L2,T h =L1, then:

[0091]

[0092] make Where I and N are the self-interference and receiving noise matrices of corresponding dimensions, and the estimated channel between IRS is finally obtained

[0093]

[0094] Furthermore, for estimating the channel h from two IRSs to K UEs 1,k and h 2,k , which comprises the following steps:

[0095] Turn on IRS1 and turn off IRS2. Assume that the pilot signal sent by user k is x k ∈C K×1 , the pilot length is the number of users K, and the pilot signals sent by different users are orthogonal to each other:

[0096]

[0097] Where P UE is the power of the user transmitting the pilot signal, then the signal received by the BS at time t is:

[0098]

[0099] Using the orthogonality of the pilot signal, we get:

[0100]

[0101] Where t=1,2,…,τ u , τ u is the number of pilots required for small time scale estimation, N t ∈C M×K represents the noise received by the BS,

[0102] Let C t =G1diag(v 1,t ),make In τ u The total received signal within the pilot time is expressed as:

[0103]

[0104] The estimated value is obtained based on the least squares estimation method:

[0105]

[0106] Turn on IRS2, turn off IRS1, and perform channel estimation in the same way to obtain

[0107] in C 2t =G2diag(v 2,t )

[0108] Turn on IRS1, turn off IRS2, and perform channel estimation in the same way to obtain

[0109] in C 3t =G1diag(v 1,t )

[0110] Turn on IRS2, turn off IRS1, and perform channel estimation in the same way to obtain

[0111] in C 4t=G2diag(v 2,t ).

[0112] Further, in step S4, the secure communication optimization problem P1 is transformed into P2:

[0113]

[0114] st:

[0115]

[0116] in, ({w k},θ1,θ2)=g(H) indicates that a graph neural network GNN is used to simulate the optimal mapping from channel information CSI to BS beamforming and IRS reflection phase shift.

[0117] Furthermore, in step S5, a graph neural network GNN model is designed to abstract the wireless communication environment into a graph G = (V, E), where V = [BS, IRS1, IRS2, U1, ..., U k ,E1,...,E n ] is the set of nodes in the graph, E = [e(BS,IRS1), e(BS,IRS2), e(IRS1,IRS2), e(IRS1,U1),..., e(IRS2,U k ),e(IRS1,E1),...,e(IRS2,E n )] is a set of edges, each node v∈V and each edge e(u,v)∈E has its corresponding representation vector x v and The representation vectors of nodes and edges are as follows:

[0118]

[0119] The feature vector of a node is combined with the node's own attributes, the feature vector of an edge is combined with the channel attributes, and the edge feature vectors of interference links and feedback links are ignored and do not participate in the graph representation vector update;

[0120] In GNN, the feature vector is converted into a graph representation vector, and all the representation vectors of the previous layer are used as input. The representation vector is updated layer by layer. After multiple layers, the representation vector of each node will contain enough information for designing beamforming vectors and reflection coefficients.

[0121] The entire GNN consists of three layers. The graph representation vector is learned through the input layer, where the edge representation vector is composed of channel parameters Get, and keep constant during the vector update process. The node representation vector IRS10 , IRS2 0 , B.S. 0 It is obtained by setting the initial value; D update layer is used to update the representation vector to obtain The output result is obtained through the output layer and through a fully connected linear layer. Then we will represent the vector The phase shift of the beamforming and IRS output to the BS is mapped by the normalization layer.

[0122] Furthermore, in the input layer of GNN, the real and imaginary components of the channel state information H are first separated and then converted into a column vector to obtain:

[0123]

[0124] Then Through a deep neural network layer As the initial representation vector of the edge

[0125]

[0126] Set to a random matrix W = [w1,w2,..,w k ], the matrix requires constraint C1, and the representation vector of the BS node is obtained by W:

[0127]

[0128] Then the input feature vector Through a layer of deep neural network Used to generate BS nodes:

[0129]

[0130] Set up a randomization matrix The element q in this matrix 1l ,1≤l≤L1 satisfies the constraint C2, and the representation vector of the IRS1 node is obtained from V1:

[0131]

[0132] Then the input feature vector Through a layer of deep neural network Used to generate the IRS1 node:

[0133]

[0134] IRS2 constructs the representation vector in the same way as IRS1, with the following formula:

[0135]

[0136] The initial representation vectors of both the legitimate user node and the eavesdropping user node are set to zero vectors:

[0137]

[0138] Representation vector Contains the feature vectors of all nodes and edges, which are then passed to the D update layer;

[0139] The update of all node representation vectors in the D update layer is based on the aggregation of the previous representation vector of itself and the representation vectors of its adjacent nodes and directed edges. The mathematical expression is:

[0140]

[0141] Among them, E(v) represents the set of incoming edges with node v as the destination, V(v) represents the set of nodes adjacent to node v, is the aggregation function of the dth update layer, is a combination function;

[0142] The selection of aggregation function for GNN is as follows:

[0143]

[0144] where ψ(·) is a function that is invariant to the input permutation; and Both use deep neural networks;

[0145] For BS nodes, the representation vector is derived from:

[0146]

[0147] It is an MLP multi-layer perceptron, which is used to integrate node representation vectors; the introduction of nonlinear activation function enables GNN to learn more complex nonlinear feature mapping relationships; ψ1(·) uses element pooling averaging function:

[0148] ψ1(x1,x2,..,x k )=mean(x1,x2,..,x k )

[0149] The representation vector of the IRS1 node is updated from the neighboring nodes and adjacent edges, which contains the node and channel link representation vectors from the BS and the representation vectors from the legitimate user and eavesdropping user nodes:

[0150]

[0151] The representation vector of IRS2 is updated by adding the node and channel link representation vectors from IRS1:

[0152]

[0153] in, is the MLP connection layer, and selects the element-wise average function ψ1(·) as the aggregation function;

[0154] For a legitimate user node, its representation vector is updated as follows:

[0155]

[0156] in is an MLP connection layer, and selects the element pooling maximization function ψ2(·) as the aggregation function:

[0157] ψ2(x1,x2,..,x k )=max(x1,x2,..,x k )

[0158] For the eavesdropper node, the update of the representation vector is as follows:

[0159]

[0160] in is the MLP connection layer, and selects the element pooling maximization function ψ2(·) as the aggregation function;

[0161] After the update layer, the node representation vector of GNN update Passed to the output layer, the IRS reflection coefficient matrix is ​​finally obtained and the beamforming matrix W at the BS = [w1,w2,..,w K ]∈C M×K , while satisfying the unit mode constraint of θ and the total power constraint of W;

[0162] Will represent the vector Through a linear layer with 2M×K units get:

[0163]

[0164] The beamforming matrix is ​​then output through a normalization layer as follows:

[0165]

[0166] W=W * (1:M,:)+jW * (M+1:2M,:)

[0167] Where W(i:j,:) represents the submatrix of W, which is constructed by the indexes from the i-th row to the j-th row of W;

[0168] Pass a linear layer with 2L1 units Output As shown below:

[0169]

[0170] Then, the reflection phase shift of each reflection unit in IRS1 is obtained through the normalization layer, as follows:

[0171]

[0172] Where [V1] ij represents the element in the i-th row and j-th column of the matrix, symbol represents the index subvector from i to j;

[0173] Following the same principle, Pass a linear layer with 2L2 units Output As shown below:

[0174]

[0175] Then, the reflection phase shift of each reflection unit in IRS2 is obtained through the normalization layer, as follows:

[0176]

[0177] Through the output layer, beamforming at the BS and reflection phase shift at the IRS are obtained.

[0178] Furthermore, in step S6, the GNN graph neural network model is trained, and two hypotheses are proposed to obtain the eavesdropper's channel parameters:

[0179] The first one: During the GNN training phase, the legitimate receiver imitates the eavesdropper to send a pilot sequence to obtain more accurate information about the eavesdropper's channel parameters, that is, and

[0180] The second type: Information exchange between the eavesdropper and the BS does not occur, and the eavesdropper channel is modeled as:

[0181]

[0182] Randomly select N legitimate user channels from the estimated channels, and then add the CSI estimation error Ω n As an eavesdropper, the estimated channel is:

[0183]

[0184] g(·) is the mapping function that maps the estimated CSI to the BS beamforming matrix and the IRS reflection phase shift. E(·) is the mean function. GNN is used to implement the mapping function and obtain the representation vector of GNN.

[0185] The GNN loss function is defined as:

[0186]

[0187] GNN is used to extract the feature vectors of each node and edge from the network topology information, communication channel CSI and interference, and the beamforming at the BS and the IRS reflection beam vector are learned through training to maximize the average total information confidentiality rate of legitimate users under the constraints.

[0188] The beneficial effects of the present invention are:

[0189] The present invention proposes a method for optimizing secure communication of a dual IRS-assisted downlink MISO system based on a GNN graph neural network. First, the IRS, multiple users, and eavesdroppers are modeled, a GNN connection graph is constructed, and the system objective is converted into a GNN loss function. Then, a pilot transmission is performed to obtain the training input of the GNN. The GNN completes the mapping from the pilot to the BS beamforming and the IRS reflection phase shift through training to maximize the system objective, such as the total information transmission rate of legitimate users. The trained GNN has good generalization ability and can adapt to communication scenarios with different numbers of users. Compared with the traditional method of using channel estimation and non-convex optimization, a higher information transmission rate is obtained under the premise of ensuring the security of information transmission.

[0190] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0191] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0192] Figure 1 A dual IRS assisted downlink MISO communication system model provided by the present invention;

[0193] Figure 2 The signal transmission frame structure of the dual IRS assisted downlink MISO communication system provided by the present invention;

[0194] Figure 3 A GNN connection diagram for maximizing the total user safety rate of the dual IRS-assisted downlink MISO communication system provided by the present invention;

[0195] Figure 4 A GNN architecture diagram for maximizing the total user safety rate in a dual IRS-assisted downlink MISO communication system provided by the present invention;

[0196] Figure 5 It is a schematic diagram of the overall process of the method for optimizing secure communication of a dual IRS-assisted downlink MISO system based on a graph neural network of the present invention. DETAILED DESCRIPTION

[0197] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0198] Among them, the drawings are only used for illustrative explanations, and they only represent schematic diagrams rather than actual pictures, and should not be understood as limitations on the present invention. In order to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0199] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if the terms "upper", "lower", "left", "right", "front", "rear", etc. indicate the orientation or position relationship, they are based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, the terms describing the position relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0200] See also Figure 1 to Figure 5 , which is a secure communication optimization method for dual IRS-assisted downlink MISO system based on graph neural network.

[0201] Example

[0202] This embodiment provides a specific implementation of a method for optimizing secure communication of a dual IRS-assisted downlink MISO system based on a graph neural network, which includes the following steps:

[0203] The first step is to establish a dual IRS assisted downlink MISO communication system model and set the initial parameters, including the number of training samples, system parameters (number of BS antennas, number of IRS reflection units, number of legitimate users and number of eavesdropping users), input flag input_flag, Rayleigh channel factor, noise power, etc.

[0204] This embodiment considers a downlink MISO wireless communication system model assisted by dual IRSs, which consists of a base station BS, two IRSs, K legal users (denoted as U1, ..., U k ) and N active eavesdroppers (denoted as E1, ..., E n ), where the base station BS has M transmitting antennas, all legitimate users and eavesdroppers have single antennas, IRS1 is deployed on a high building close to the BS and has L1 reflection units, and IRS2 is deployed on a high building close to the user and has L2 reflection units. The BS simultaneously sends K independent confidential data streams to K legitimate users on the same frequency band. At the same time, unauthorized eavesdroppers attempt to independently eavesdrop on any data stream.

[0205] In order to improve the security of wireless information transmission, two IRSs can be used to assist in communication. Specifically, IRS1 reflects the signal transmitted by the base station to the legitimate user, and at the same time reflects the signal to IRS2; IRS2 reflects the signal received from the base station and IRS1 to the legitimate user. Compared with the traditional single IRS auxiliary system communication, the dual IRS cooperative auxiliary system communication can not only create a new communication link for users and improve the information transmission rate, but also the eavesdropper receives the signal reflected by the dual IRS, and the signal energy plays the role of artificial noise, thereby ensuring the security of information transmission.

[0206] The baseband equivalent channel response is expressed as:

[0207] The channels from BS to IRS1 and IRS2 are represented as and The channel from IRS1 to IRS2 is represented as The channels from IRS1 and IRS2 to legitimate users are respectively expressed as and The channels from IRS1 and IRS2 to the eavesdropper are expressed as and Here 1≤k≤K, 1≤n≤N. x×y Represents a collection of complex-valued matrices of dimension x-by-y.

[0208] The reflection phase shift matrix of IRS1 is expressed as θ1=diag(v1), represents the reflection coefficient of the l1th reflection unit, where is the reflection amplitude, It is its reflected phase shift, which has two main forms, one is continuous phase shift The other is discrete phase shift:

[0209]

[0210] Where Q is the phase shift interval of a single element on the IRS. In practical applications, it is very expensive to implement continuous phase shift in hardware, so discrete phase shift is more widely used. However, it is also important to study continuous phase shift because it is the upper limit of discrete phase shift.

[0211] Similarly, the reflection phase shift matrix of IRS2 is expressed as θ2=diag(v2), represents the reflection coefficient of the l2th reflection unit, and the reflection amplitude is The reflected phase shift is:

[0212]

[0213] This paper only considers the reflection phase shift, so let and

[0214] The base station's transmission signal is expressed as where w k ∈C M×1 is the beamforming matrix, s k Dedicated to legitimate users k confidential information, and obeys a complex Gaussian distribution with a mean of 0 and a variance of 1.

[0215] Then the legitimate user U k and Eavesdropper E n The received signal can be expressed as:

[0216] y k =[G1θ1h 1,k +G2θ2h 2,k +G1θ1D H θ2h 2,k ] T x+u k ,1≤k≤K

[0217] y n =[G1θ1g 1,n +G2θ2g 2,n +G1θ1D H θ2g2,n ] T x+u n ,1≤n≤N

[0218] where u k and u n are the receiving noises at the legitimate user and the eavesdropper respectively, and they obey the complex Gaussian distribution with a mean of 0, that is, δ represents the variance of the complex Gaussian distribution.

[0219] From this we can get U k The achievable rate at which the kth confidential information is received is:

[0220]

[0221] In E n The achievable eavesdropping rate of the kth confidential information received at is:

[0222]

[0223] Each eavesdropper can eavesdrop on any of the K confidential messages, so k Transmit to U k The achievable confidentiality rate for N eavesdroppers is U k and E n The minimum confidentiality rate between

[0224]

[0225] In the second step, the present invention jointly optimizes the reflection phase shift matrix θ1 of IRS1, the reflection phase shift matrix θ2 of IRS2 and the beamforming matrix {w K}, ensuring that the reflection coefficient of the IRS satisfies the modulo-1 constraint and the base station does not exceed the maximum transmission power constraint to maximize the total confidentiality rate C of all legitimate users k Therefore, the security communication optimization problem P1 considered is specifically described as follows:

[0226]

[0227] st:

[0228]

[0229] Among them, P BS is the transmit power constraint at the BS.

[0230] In the third step, in order to optimize the objective function P1, it is necessary to know the channel parameters of the legitimate user and the eavesdropper. Therefore, channel estimation is first performed and the CSI is obtained using the pilot method.

[0231] Since the dual IRS communication scenario has a very large number of channels, the estimation difficulty increases exponentially, especially when the number of IRS elements is too large. In order to reduce the difficulty of channel estimation, an element grouping strategy is adopted. Each IRS surface is divided into several sub-surfaces. Each sub-surface consists of an arbitrary number of adjacent reflective elements. These reflective units share a common phase shift, thereby reducing the complexity of channel estimation.

[0232] Since the scenario is set in the center of a densely built town, the direct path is blocked by buildings, so it is assumed that the channel is an uncorrelated Rayleigh fading channel, that is:

[0233]

[0234] in, ρ D , They represent the large-scale fading factors of the channel respectively, and vec(·) represents matrix vectorization.

[0235] Since the positions between the BS and the IRS and between the two IRSs are relatively fixed, forming a quasi-static channel, G1, G2 and D can be estimated on a large time scale, that is, the channel is estimated once at a relatively long time interval. 1,k ,h 2,k , g 1,n , g 2,n is time-varying and needs to be estimated on a smaller time scale. Therefore, the frame structure design of signal transmission is as follows Figure 2 shown.

[0236] First, large-scale time estimation is performed. The BS antenna works in full-duplex mode. The BS transmits the pilot to the IRS through a single antenna. Then the IRS reflects the pilot back to the BS through a set of preset reflection coefficients. The BS performs large-scale time estimation based on the received signal. Since the channels from the BS to IRS1 and IRS2 can be estimated in the same way, the channel from the BS to IRS1 is used as an example. The pilot used for estimating G1 consists of L1 subframes, each of which contains M time slots. The pilot overhead is

[0237] Turn on IRS1 and turn off IRS2. In the tth subframe, the reflection coefficient at IRS1 is The reflection coefficient is taken from the L1×L1 DFT matrix. Based on the full-duplex architecture, in the time slot l of the tth subframe, the non-zero pilot is transmitted by the antenna m1 of the BS. The remaining antennas do not transmit pilot signals, so the pilot signal received by BS antenna m2 in time slot l of subframe t is:

[0238]

[0239] in, in represents the suppressed cross-talk induced interference (CI). The crosstalk is caused by the BS working in full-duplex mode, and the signal sent by antenna m1 is directly received by antenna m2. CI suppression methods have been widely studied. A standard suppression method can reduce the interference to a level about 3dB higher than the receiver noise. Therefore, it is assumed that the suppressed CI satisfies

[0240] Assume that the power of the BS pilot signal is consistent, that is, the pilot signal sent by BS antenna m1 satisfies in, is the transmit power, for given antennas m1 and m2, we have:

[0241]

[0242] Among them, the IRS reflection matrix represents the Hadamard product of the two.

[0243] In the time slot l2 of the tth subframe, the BS's antenna m1 transmits a pilot signal The signal received by antenna m3 is BS antenna m2 sends a pilot signal The signal received by antenna m3 is The signal received in all subframes is:

[0244]

[0245] Using the least squares estimation, let Get an estimate for:

[0246]

[0247] Using the formula:

[0248]

[0249] where ÷ represents the matrix dot division operation. Thus, we get the estimate The estimation method of G2 is the same and therefore omitted.

[0250] Next, the channel D between the IRSs is estimated. IRS1 and IRS2 are turned on at the same time, and BS antenna m sends a non-zero pilot signal s at the tth pilot time. t, where t=1,2,···,τ D . Where τ D The number of pilots required for channel estimation at this stage. The transmitted signal is received at the BS antenna m after being reflected by the dual IRS. The BS is set to a full-duplex antenna. The SI suppression method can suppress the self-interference problem generated when the same antenna is transmitting and receiving to a lower level.

[0251] The signal received by BS antenna m at the tth pilot time is:

[0252]

[0253] Among them denote the channels from BS antenna m to IRS1 and IRS2, respectively, 1,t and θ 2,t represents the reflection coefficient vector of IRS1 and IRS2 at time t, i t and n t represents the self-interference and received noise after suppression at time t.

[0254] Using the previously estimated And assuming that the estimation accuracy is high, that is:

[0255]

[0256] Among them denote the channel estimation vectors from BS antenna m to IRS1 and IRS2 respectively. Therefore, we get:

[0257]

[0258] because And the result of multiplying two matrices is a scalar, so we have

[0259] So we get:

[0260]

[0261] make get:

[0262]

[0263] Assume that for any t∈{1,2,...,τ D}, BS antenna m sends pilot signals that satisfy The received signal is D The time slots are superimposed as T v ×T h The matrix of T v =L2,Th =L1, so we get the following results:

[0264]

[0265] make Where I and N are the self-interference and receive noise matrices of corresponding dimensions.

[0266] Get the estimated channel between IRS

[0267]

[0268] So far, the large-time-scale channel estimation has been completed. Now we will carry out the small-time-scale channel estimation. Estimate the channel h from two IRSs to K UEs 1,k and h 2,k Since it is estimated that h 1,k and h 2,k The method is the same as h 1,k Take this as an example.

[0269] Turn on IRS1 and turn off IRS2. Assume that the pilot signal sent by user k is x k ∈C K×1 , the pilot length is the number of users K, and the pilot signals sent by different users are orthogonal to each other. That is:

[0270]

[0271] Where P UE is the power of the pilot signal transmitted by the user. Then the signal received by the BS at time t is:

[0272]

[0273] Using the orthogonality of the pilot signal, we get:

[0274]

[0275] Where t=1,2,…,τ u , τ u is the number of pilots required for small time scale estimation, N t ∈C M×K Indicates the noise received by the BS. Let C t =G1diag(v 1,t ),make In τ u The total received signal within the pilot time is expressed as:

[0276]

[0277] The estimated value is obtained based on the least squares estimation method:

[0278]

[0279] h 2,k The same method can be used to obtain the eavesdropper channel Considering a more general situation, the eavesdropper channel cannot usually be estimated using the pilot method, because the eavesdropper generally does not interact with the BS for the purpose of hiding itself, so a bounded channel error model is used to characterize the uncertainty of the eavesdropper channel. That is, the eavesdropper channel is modeled as:

[0280]

[0281]

[0282] in is the channel estimate of the eavesdropper at the BS. 1,n , Δg 2,n represents the CSI estimation error of the eavesdropper. The continuous set Ω n Contains all possible CSI estimation errors, whose norm is ε n >0 is the boundary, the uncertainty radius ε n Represents the uncertainty level of CSI. This model is a flexible and general CSI uncertainty model that can explain the CSI uncertainty caused by different factors in the CSI estimation process of IRS-assisted wireless communication systems, such as quantization error caused by IRS phase shift, noise impact and outdated feedback.

[0283] In the fourth step, the graph neural network GNN is used to simulate the optimal mapping from channel information CSI to BS beamforming and IRS reflection phase shift, transforming the secure communication optimization problem P1 into P2:

[0284]

[0285] st:

[0286]

[0287] in,

[0288] The fifth step is to design the GNN graph model. The neural network architecture diagram of GNN is shown as follows: Figure 3 shown.

[0289] The wireless communication environment is abstracted as a graph. G = (V, E), V = [BS, IRS1, IRS2, U1, ..., U k ,E1,...,E n] is a set of nodes in the graph, for example, BS, IRS and mobile users and eavesdroppers are regarded as a node in the graph. E = [e(BS, IRS1), e(BS, IRS2), e(IRS1, IRS2), e(IRS1, U1), ..., e(IRS2, U k ),e(IRS1,E1),...,e(IRS2,E n )] is a set of edges. If there is a direct communication link with node i as the sender and node j as the receiver, an edge is drawn from node i to j, such as Figure 3 If there is an interference link between nodes, such as node i interfering with node j, a red edge is drawn from node i to node j, as shown in Figure 3 If there is a feedback relationship between nodes, such as the representation vector of node i is used to design the representation vector of node j, a blue edge is drawn from node i to node j, as shown in Figure 3 As shown by the blue arrow in the middle. Each node v∈V and each edge e(u,v)∈E has its corresponding representation vector x v and For example, the representation vectors of nodes and edges are as follows:

[0290]

[0291] The feature vector of a node combines the node's own attributes, such as the power constraint of the BS node and the phase modulus constraint of the IRS node. The feature vector of an edge combines the channel attributes. For example, the feature vector of the edge from BS to IRS1 is Obtained. The edge feature vectors of the interference link and the feedback link are ignored and do not participate in the update of the graph representation vector, because the interference channel between the two users does not participate in the objective function calculation in this article, and the feedback link belongs to an abstract representation vector update method. In GNN, the feature vector is converted into a graph representation vector, and all the representation vectors of the previous layer are used as input to update the representation vector layer by layer. After multiple layers, the representation vector of each node will contain enough information for designing beamforming vectors and reflection coefficients. Specifically, GNN is trained in such a way that the phase shift of IRS1 can be obtained by node IRS1, the phase shift of IRS2 can be obtained by node IRS2, and the BS beamforming row matrix can be obtained by nodes U1~U k get.

[0292] Compared with fully connected neural networks, GNNs capture the interactions between users, eavesdroppers, and IRSs more naturally. In particular, the update of each legitimate user node is a function of all its neighboring nodes and IRS nodes, which enables GNNs to learn to avoid interference. The update of each eavesdropper node is a function of all legitimate user nodes and IRS nodes, which enables GNNs to learn to increase the interference of eavesdroppers. The layer structure of the graph neural network is represented as follows Figure 4 shown.

[0293] The entire GNN consists of three layers. The graph representation vector is learned through the input layer, where the edge representation vector is composed of channel parameters Get, and keep constant during the vector update process. The node representation vector IRS1 0 , IRS2 0 , B.S. 0 It is obtained by setting the initial value. For example, using TensorFlow, you can create a trainable variable with a shape satisfying (1, L1), and each element of the variable satisfies the modulo-1 constraint. This variable can be used as the graph representation vector of IRS1, denoted as D updates the layer to update the representation vector, and gets The output result is obtained through the output layer. Specifically, it is first obtained through a fully connected linear layer Then we will represent the vector The phase shift of the beamforming and IRS output to the BS is mapped by the normalization layer.

[0294] 1) Input layer: Since TensorFlow does not support complex-valued operations, the real and imaginary components of the channel state information H are first separated and then converted into column vectors to obtain:

[0295]

[0296] Then Through a deep neural network layer As the initial representation vector of the edge

[0297]

[0298] Set to a random matrix W = [w1,w2,..,w k ], the matrix needs to satisfy constraint 31a, and the representation vector of the BS node can be obtained by W.

[0299]

[0300] Then the input feature vector Through a layer of deep neural network Used to generate BS nodes, for example:

[0301]

[0302] Set up a randomization matrix The element q in this matrix 1l ,1≤l≤L1 needs to satisfy constraint 32b, and the representation vector of IRS1 node can be obtained from V1.

[0303]

[0304] Then the input feature vector Through a layer of deep neural network Used to generate an IRS1 node, for example:

[0305]

[0306] IRS2 constructs the representation vector in the same way as IRS1, with the following formula:

[0307]

[0308] The initial representation vectors of both the legitimate user node and the eavesdropping user node are set to zero vectors, that is:

[0309]

[0310] Representation vector Contains the feature vectors of all nodes and edges, and is then passed to the D update layer.

[0311] D Update layer:

[0312] The update of the representation vectors of all nodes in the update layer is based on the aggregation of their previous representation vectors and the representation vectors of their adjacent nodes and directed edges. The specific mathematical expression is:

[0313]

[0314] Here E(v) represents the set of incoming edges with node v as the destination, and V(v) represents the set of nodes adjacent to node v. is the aggregation function of the dth update layer, is a combination function.

[0315] The key to designing GNN is to choose appropriate aggregation functions and combination functions so that it has good scalability. The selection of aggregation functions is as follows:

[0316]

[0317] where ψ(·) is a function that is invariant to the input permutation, such as element pool maximization or element pool averaging function. and Both can be implemented using deep neural networks.

[0318] For BS nodes, the representation vector is derived from:

[0319]

[0320] It is a layer of MLP. The MLP multi-layer perceptron is used to integrate node representation vectors and introduce nonlinear activation functions, so that GNN can learn more complex nonlinear feature mapping relationships. ψ1(·) is implemented using the element pooling averaging function, as shown below:

[0321] ψ1(x1,x2,..,x k )=mean(x1,x2,..,x k )

[0322] The representation vector of the IRS1 node is updated from the adjacent nodes and adjacent edges, which includes the node and channel link representation vectors from the BS and the representation vectors from the legitimate user and eavesdropping user nodes:

[0323]

[0324] Similar to IRS1, the representation vector update of IRS2 adds the node and channel link representation vectors from IRS1:

[0325]

[0326] in, It is an MLP connection layer, and the element-wise average function ψ1(·) is selected as the aggregation function, which is consistent with the fact that IRS needs to adjust its reflection vector so that all legitimate users can obtain the largest possible information rate while suppressing eavesdroppers and minimizing the information rate obtained by eavesdroppers.

[0327] For a legitimate user node, its representation vector is updated as follows:

[0328]

[0329] in is an MLP connection layer, and the element-wise pooling maximization function ψ2(·) is selected as the aggregation function, which is consistent with the fact that multi-user interference is usually dominated by the user with the strongest signal.

[0330] ψ2(x1,x2,..,x k )=max(x1,x2,..,xk )

[0331] For the eavesdropper node, the update of the representation vector is as follows:

[0332]

[0333] in is an MLP connection layer, and the element-wise pooling maximization function ψ2(·) is selected as the aggregation function, which empirically performs well, consistent with the fact that multi-signal interference is usually dominated by the strongest signal.

[0334] Output layer:

[0335] After the update layer, the node representation vector of GNN update Passed to the output layer. Finally, the IRS reflection coefficient matrix is ​​obtained and the beamforming matrix W at the BS = [w1,w2,..,w K ]∈C M×K , while satisfying the unit mode constraint of θ and the total power constraint of W.

[0336] Will represent the vector Through a linear layer with 2M×K units get:

[0337]

[0338] The beamforming matrix is ​​then output through a normalization layer as follows:

[0339]

[0340] W=W * (1:M,:)+jW * (M+1:2M,:)

[0341] Where W(i:j,:) represents a submatrix of W, which is constructed by the indices from the i-th row to the j-th row of W.

[0342] Pass a linear layer with 2L1 units Output As shown below:

[0343]

[0344] Then, the reflection phase shift of each reflection unit in IRS1 is obtained through the normalization layer, as follows:

[0345]

[0346] Where [V1]ij represents the element in the i-th row and j-th column of the matrix, symbol Represents the subvector of indices from i to j.

[0347] Following the same principle, Pass a linear layer with 2L2 units Output As shown below:

[0348]

[0349] Then, the reflection phase shift of each reflection unit in IRS2 is obtained through the normalization layer, as follows:

[0350]

[0351] Through the output layer, beamforming at the BS and reflection phase shift at the IRS are obtained.

[0352] In summary, Table 1 summarizes the above machine learning algorithms.

[0353] Table 1

[0354]

[0355]

[0356] Step 6: Train the GNN graph neural network model. In order to train the GNN model, two assumptions for obtaining the eavesdropper’s channel parameters are proposed with reference to formulas 30 and 31.

[0357] The first one: During the GNN training phase, the legitimate receiver imitates the eavesdropper to send a pilot sequence to obtain more accurate information about the eavesdropper's channel parameters, that is, and

[0358] The second type: Generally speaking, information interaction between the eavesdropper and the BS does not occur. However, due to the high spatial correlation between the eavesdropper and the legitimate user, and considering that the number of eavesdroppers is often much smaller than that of legitimate users, N channels can be randomly selected from the estimated legitimate user channels, and then the CSI estimation error Ω is added. n As the estimated channel of the eavesdropper, that is:

[0359]

[0360] g(·) is a mapping function that maps the estimated CSI to the BS beamforming matrix and the IRS reflection phase shift. E(·) is a mean function. GNN is used to implement the mapping function, and the GNN representation vector is obtained using the estimated CSI.

[0361] The GNN loss function is defined as:

[0362]

[0363] The main idea is as follows: use GNN to extract the feature vectors of each node and edge from the network topology information, communication channel CSI and interference, and learn the beamforming at the BS and the IRS reflection beam vector through training to maximize the average total information confidentiality rate of legitimate users that meet the constraints.

[0364] Since the number of GNN nodes in this embodiment is small, each node can obtain the representation vector of other nodes after two layers of updates. Therefore, a GNN model with D=2 is adopted, the number of legitimate users is set to 4, the number of eavesdropping users is set to 2, and the structure of each sub-neural network in GNN is shown in Table 2 below:

[0365] Table 2

[0366]

[0367] TensorFlow is used to implement the proposed GNN. GNN is trained using the Adam optimizer with an initial learning rate of 10 -3 , after 200 iterations, the learning rate dropped by 0.98 times. In each iteration, the parameters of each sub-neural network were updated by training 100 times, and 1024 samples were used to calculate the gradient in each iteration. If the loss function did not decrease in 5 consecutive training cycles, the training was terminated.

[0368] This embodiment requires CSI to generate training samples, but CSI information is no longer needed after GNN training is completed, that is, GNN training is completed offline, so it does not affect the time complexity of the proposed method. We use the gradient-based backpropagation method to train the proposed GNN neural network, and learn to adjust the weights in an unsupervised manner to minimize the loss function. The training process is shown in Table 3 below:

[0369]

[0370] As shown in Table 3, it includes:

[0371] Step 1: Set the sample quantity, system parameters and other information;

[0372] Step 2: Perform channel estimation to obtain channel state information H;

[0373] Step 3: Create a GNN model, set the model's learning rate, maximum number of iterations and other parameters, perform a training run to obtain the training loss and set the optimal loss as the current loss value;

[0374] Step 4: Enter the i-th iteration. Each iteration needs to be trained J times. Each training will perform a channel estimation and use the estimated channel parameters to train the model. Finally, use the original channel parameters H to train the model again to get the training loss. Compare the current loss value with the optimal loss. If it is less than the optimal loss, it proves that the performance of the model has been optimized, and the optimal loss needs to be updated and enter the next iteration. If it is greater than the optimal loss, it proves that the performance of the model has not been improved. Then determine whether the performance of the model has not improved in 5 consecutive iterations. If so, it proves that the performance of the model has reached the optimal level, the model training is completed, and the loop is exited. If the maximum number of iterations is reached, the model training is completed.

[0375] This embodiment also tests the trained GNN model to try the output effect of GNN when the number of users and the number of eavesdroppers are different. Compared with the alternating optimization scheme of estimating channel parameters, the GNN-based machine learning method proposed in the present invention can achieve a higher system total information confidentiality rate in a shorter time, has better generalization ability, and can adapt to scenarios with different numbers of users.

[0376] In this embodiment, Figure 1 The present invention provides a dual IRS assisted downlink MISO communication system model, the scene is set in a city with tall buildings. In the figure, the direct channel between the base station and the user is blocked by the building, and the signal can only be transmitted to the IRS through wireless transmission, and the IRS then reflects the signal to the legitimate user. At the same time, the N single-antenna eavesdroppers in the system will eavesdrop on the legitimate user information. Figure 2 The signal transmission frame structure of the dual IRS-assisted downlink MISO communication system is divided into two parts: channel estimation and data transmission. It combines the characteristics of BS and IRS that they are generally not mobile, while legitimate users and eavesdropping users may move at any time. The channel estimation process is further divided into large-time-scale channel estimation and small-time-scale channel estimation. Figure 3The connection between each node of the GNN model is given. The GNN connection graph is based on the signal transmission process in the actual communication environment. BS, IRS1 and IRS2, as well as legal users and eavesdropping users are abstracted as nodes, and physical communication links are abstracted as edges associated between nodes. Interference links and feedback links are innovatively added. The graph is a directed graph, in which the BS node sends data to the IRS node and receives feedback from all legal users. The IRS node connects all legal users and eavesdroppers, which means that although the IRS serves legal users, the eavesdropper, who is highly correlated with the channel, can also obtain the IRS reflection signal. Therefore, the IRS is actually serving the eavesdropper; all legal users are connected to each other, which represents the interference between different signals; the eavesdropper is associated with all legal users, which means that they can choose any legal user to monitor, but at the same time, the interference of other legal users will also affect the eavesdropper. The eavesdroppers do not contact each other because, generally speaking, the number of eavesdroppers is small and the interference between them can be ignored; Figure 4 The structure diagram of the GNN model includes an input layer, an update layer, and an output layer. The input layer converts the channel information into a node representation vector and then passes it to the update layer; the update layer updates the representation vectors of all nodes from the aggregation of itself and adjacent nodes. The update layer can have multiple layers. Generally speaking, the GNN model will adopt a two-layer structure, especially when the number of nodes is small, the effect of multiple layers is not improved much; after the update is completed, in order to obtain the base station beamforming vector and IRS phase shift, the representation vector of the relevant node needs to be passed to the output layer, and the BS beamforming vector and the reflected phase shift of the two IRSs are output under the conditions of satisfying the phase shift modulus constraint and the total power constraint at the BS.

[0377] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A method for optimizing secure communication of a dual IRS-assisted downlink MISO system based on graph neural network, characterized in that: The method comprises the following steps: S1. Establish a dual IRS assisted downlink MISO wireless communication system model, define the corresponding communication channel, the corresponding reflection phase shift matrix, the corresponding received signal representation and the corresponding receiving rate; S2. Under the dual IRS assisted downlink MISO wireless communication system model, a secure communication optimization problem P1 is established with the goal of maximizing the sum of the total confidentiality rates of all legitimate users and satisfying the corresponding constraints; S3, obtaining all channel state information of the dual IRS assisted downlink MISO wireless communication system model through large-scale time estimation, small-scale time estimation and pilot estimation methods respectively; S4, using graph neural network GNN to simulate the optimal mapping of pilot information vector to base station beamforming and IRS reflection phase shift, transforming the secure communication optimization problem P1 into P2; S5. Establish a graph neural network GNN model under the dual IRS assisted wireless energy communication system model, which includes an input layer, a D update layer and an output layer; S6. Train the graph neural network GNN model. After training, the GNN model uses the secure communication optimization problem P2 as the objective function to solve the base station beamforming and IRS reflection phase shift.

2. According to claim 1, a dual IRS assisted downlink MISO system security communication optimization method based on graph neural network is characterized in that: In step S1, the dual IRS-assisted downlink MISO wireless communication system model includes a base station BS, two intelligent reflection planes IRS1 and IRS2, K legal users U1, ..., U k and N active eavesdroppers E1, ..., E n , where the base station BS has M transmitting antennas, all legitimate users and eavesdroppers have single antennas, IRS1 is deployed near the BS and has L1 reflection units; IRS2 is deployed near the legitimate users and has L2 reflection units; The BS simultaneously sends K independent confidential data streams to K legitimate users on the same frequency band. Unauthorized eavesdroppers attempt to eavesdrop on any data stream. IRS1 reflects the signal transmitted by the base station to the legitimate users and also reflects the signal to IRS2. IRS2 reflects the signal received from the base station and IRS1 to the legitimate users. The channels from BS to IRS1 and IRS2 are represented as and The channel from IRS1 to IRS2 is represented as The channels from IRS1 and IRS2 to the legitimate users are respectively expressed as and The channels from IRS1 and IRS2 to the eavesdropper are respectively expressed as and Among them, 1≤k≤K, 1≤n≤N; C x×y Represents a collection of complex-valued matrices of dimension x-by-y.

3. According to claim 2, a dual IRS assisted downlink MISO system security communication optimization method based on graph neural network is characterized in that: In the dual IRS-assisted downlink MISO wireless communication system model, the reflection phase shift matrix of IRS1 is expressed as: represents the reflection coefficient of the l1th reflection unit, where is the reflection amplitude, is its reflected phase shift: Where Q is the phase shift interval of a single element on the IRS; The reflection phase shift matrix of IRS2 is expressed as: in, represents the reflection coefficient of the l2th reflection unit, and the reflection amplitude is The reflected phase shift is: The base station's transmission signal is expressed as where w k ∈C M+1 is the beamforming matrix, s k Dedicated to legitimate users k The confidential information is subject to a complex Gaussian distribution with a mean of 0 and a variance of 1; Legitimate user U k and Eavesdropper E n The received signal is expressed as: y k =[G1θ1h 1,k +G2θ2h 2,k +G1θ1D H θ2h 2,k ] T x+u k ,1≤k≤K y n =[G1θ1g 1,n +G2θ2g 2,n +G1θ1D H θ2g 2,n ] T x+u n ,1≤n≤N where u k and u n are the receiving noises at the legitimate user and the eavesdropper respectively, and they obey the complex Gaussian distribution with a mean of 0, that is, δ represents the variance of the complex Gaussian distribution; Then U k The achievable rate at which the kth confidential information is received is: In E n The achievable eavesdropping rate of the kth confidential information received at is: Will s k Transmit to U k The achievable confidentiality rate for N eavesdroppers is U k and E n Minimum confidentiality rate between: All channels are uncorrelated Rayleigh fading channels, that is: in, They represent the large-scale fading factors of the channel respectively, and vec(·) represents matrix vectorization.

4. According to claim 3, a dual IRS assisted downlink MISO system security communication optimization method based on graph neural network is characterized in that: In step S2, the established secure communication optimization problem P1 is expressed as: st: Among them, P BS is the transmit power constraint at the BS; by jointly optimizing the reflection phase shift matrix θ1 of IRS1, the reflection phase shift matrix θ2 of IRS2 and the beamforming matrix {w K }, ensuring that the reflection coefficient of the IRS satisfies the modulo-1 constraint and the base station does not exceed the maximum transmission power constraint to maximize the total confidentiality rate C of all legitimate users k sum.

5. According to claim 4, a dual IRS assisted downlink MISO system security communication optimization method based on graph neural network is characterized in that: In step S3, the channels G1, G2 and D are estimated by a large-scale time estimation method, and h is estimated by a small-scale time estimation method. 1,k ,h 2,k , g 1,n , g 2,n , and finally get the estimated vector of all channels in, are the estimation results of the corresponding channels respectively; the estimation methods for G1, G2 and D include: It is estimated that the pilot used by G1 consists of L1 subframes, each subframe contains M time slots, and the pilot overhead is Turn on IRS1 and turn off IRS2. In the tth subframe, the reflection coefficient at IRS1 is The reflection coefficient is taken from the L1×L1 DFT matrix; Based on the full-duplex architecture, in the time slot l of the tth subframe, the BS's antenna m1 transmits a non-zero pilot The remaining antennas do not transmit pilot signals, so the pilot signal received by BS antenna m2 in time slot 1 of subframe t is: in, in Represents the suppressed crosstalk, which satisfies Assume that the power of the BS pilot signal is consistent, that is, the pilot signal sent by BS antenna m1 satisfies in, is the transmit power. For given antennas m1 and m2, we have: Among them, the IRS reflection matrix represents the Hadamard product of the two; In the time slot l2 of the tth subframe, the BS's antenna m1 transmits a pilot signal The signal received by antenna m3 is BS antenna m2 sends a pilot signal The signal received by antenna m3 is The signal received in all subframes is: Using the least squares estimation, let Get an estimate for: have: Where ÷ represents the matrix dot division operation, then we get the estimated It is estimated that the pilot used by G2 consists of L2 subframes, each subframe contains M time slots, and the pilot overhead is Turn on IRS2 and turn off IRS1. In the tth subframe, the reflection coefficient at IRS2 is The reflection coefficient is taken from the L2×L2 DFT matrix; Based on the full-duplex architecture, in the time slot l of the tth subframe, the BS's antenna m1 transmits a non-zero pilot The remaining antennas do not transmit pilot signals, so the pilot signal received by BS antenna m2 in time slot l of subframe t is: in, in Represents the suppressed crosstalk, which satisfies Assume that the power of the BS pilot signal is consistent, that is, the pilot signal sent by BS antenna m1 satisfies in, is the transmit power. For given antennas m1 and m2, we have: Among them, the IRS reflection matrix represents the Hadamard product of the two; In the time slot l2 of the tth subframe, the BS's antenna m1 transmits a pilot signal The signal received by antenna m3 is BS antenna m2 sends a pilot signal The signal received by antenna m3 is The signal received in all subframes is: Using the least squares estimation, let Get an estimate for: have: Where ÷ represents the matrix dot division operation, we get The estimation process of the channel D between IRSs includes: IRS1 and IRS2 are turned on at the same time, and BS antenna m sends a non-zero pilot signal s at the tth pilot time. t , where t=1,2,···,τ D , τ D The number of pilots required for channel estimation at this stage; The transmitted signal is reflected by the dual IRS and then received at the BS antenna m. The BS is assumed to be a full-duplex antenna, and the SI suppression method is used to suppress the self-interference generated by the same antenna transmission and reception. The signal received by the BS antenna m at the tth pilot time is: in, denote the channels from BS antenna m to IRS1 and IRS2, respectively, 1,t and θ 2,t represents the reflection coefficient vector of IRS1 and IRS2 at time t, i t and n t represents the self-interference and received noise after suppression at time t; According to the estimated have: in, Denote the channel estimation vectors from BS antenna m to IRS1 and IRS2 respectively, then: according to And the result of multiplying two matrices is a scalar, so: further: make get: Assume that for any t∈{1,2,...,τ D }, BS antenna m sends pilot signals that satisfy The received signal is D The time slots are superimposed as T v ×T h A matrix, where T v =L2,T h =L1, then: make Where I and N are the self-interference and receiving noise matrices of corresponding dimensions, and the estimated channel between IRS is finally obtained 6. According to claim 5, a dual IRS assisted downlink MISO system security communication optimization method based on graph neural network is characterized in that: For estimating the channel h from two IRSs to K UEs 1,k and h 2,k , which comprises the following steps: Turn on IRS1 and turn off IRS2. Assume that the pilot signal sent by user k is x k ∈C K×1 , the pilot length is the number of users K, and the pilot signals sent by different users are orthogonal to each other: Where P UE is the power of the user transmitting the pilot signal, then the signal received by the BS at time t is: Using the orthogonality of the pilot signal, we get: Where t=1,2,…,τ u , τ u is the number of pilots required for small time scale estimation, N t ∈C M×K represents the noise received by the BS, Let C t =G1diag(v 1,t ),make In τ u The total received signal within the pilot time is expressed as: The estimated value is obtained based on the least squares estimation method: Turn on IRS2, turn off IRS1, and perform channel estimation in the same way to obtain in C 2t =G2diag(v 2,t ) Turn on IRS1, turn off IRS2, and perform channel estimation in the same way to obtain in C 3t =G1diag(v 1,t ) Turn on IRS2, turn off IRS1, and perform channel estimation in the same way to obtain in C 4t =G2diag(v 2,t ).

7. The method for optimizing secure communication of a dual IRS-assisted downlink MISO system based on graph neural network according to claim 6 is characterized in that: In step S4, the secure communication optimization problem P1 is transformed into P2: st: in, ({w k },θ1,θ2)=g(H) indicates that a graph neural network GNN is used to simulate the optimal mapping from channel information CSI to BS beamforming and IRS reflection phase shift.

8. The method for optimizing secure communication of a dual IRS-assisted downlink MISO system based on graph neural network according to claim 7 is characterized in that: In step S5, a graph neural network GNN model is designed to abstract the wireless communication environment into a graph G = (V, E), where V = [BS, IRS1, IRS2, U1, ..., U k ,E1,...,E n ] is the set of nodes in the graph, E = [e(BS,IRS1),e(BS,IRS2),e(IRS1,IRS2),e(IRS1,U1),...,e(IRS2,U k ),e(IRS1,E1),...,e(IRS2,E n )] is a set of edges, each node v∈V and each edge e(u,v)∈E has its corresponding representation vector x v and The representation vectors of nodes and edges are as follows: The feature vector of a node is combined with the node's own attributes, the feature vector of an edge is combined with the channel attributes, and the edge feature vectors of interference links and feedback links are ignored and do not participate in the graph representation vector update; In GNN, the feature vector is converted into a graph representation vector, and all the representation vectors of the previous layer are used as input. The representation vector is updated layer by layer. After multiple layers, the representation vector of each node will contain enough information for designing beamforming vectors and reflection coefficients. The entire GNN consists of three layers. The graph representation vector is learned through the input layer, where the edge representation vector is composed of channel parameters Get, and keep constant during the vector update process; the node representation vector IRS1 0 , IRS2 0 , B.S. 0 It is obtained by setting the initial value; D update layer is used to update the representation vector to obtain The output result is obtained through the output layer and through a fully connected linear layer. Then we will represent the vector The phase shift of the beamforming and IRS output to the BS is mapped by the normalization layer.

9. The method for optimizing secure communication of a dual IRS-assisted downlink MISO system based on graph neural network according to claim 8, characterized in that: In the input layer of GNN, the real and imaginary components of the channel state information H are first separated and then converted into a column vector to obtain: Then Through a deep neural network layer As the initial representation vector of the edge Set to a random matrix W = [w1,w2,..,w k ], the matrix requires constraint C1, and the representation vector of the BS node is obtained by W: Then the input feature vector Through a layer of deep neural network Used to generate BS nodes: Set up a randomization matrix The element q in this matrix 1l ,1≤l≤L1 satisfies the constraint C2, and the representation vector of the IRS1 node is obtained from V1: Then the input feature vector Through a layer of deep neural network Used to generate the IRS1 node: IRS2 constructs the representation vector in the same way as IRS1, with the following formula: The initial representation vectors of both the legitimate user node and the eavesdropping user node are set to zero vectors: Representation vector Contains the feature vectors of all nodes and edges, which are then passed to the D update layer; The update of all node representation vectors in the D update layer is based on the aggregation of the previous representation vector of itself and the representation vectors of its adjacent nodes and directed edges. The mathematical expression is: Among them, E(v) represents the set of incoming edges with node v as the destination, V(v) represents the set of nodes adjacent to node v, is the aggregation function of the dth update layer, is a combination function; The selection of aggregation function for GNN is as follows: where ψ(·) is a function that is invariant to the input permutation; and Both use deep neural networks; For BS nodes, the representation vector is derived from: It is an MLP multi-layer perceptron, which is used to integrate node representation vectors; the introduction of nonlinear activation function enables GNN to learn more complex nonlinear feature mapping relationships; ψ1(·) uses element pooling averaging function: ψ1(x1,x2,..,x k )=mean(x1,x2,..,x k ) The representation vector of the IRS1 node is updated from the neighboring nodes and adjacent edges, which contains the node and channel link representation vectors from the BS and the representation vectors from the legitimate user and eavesdropping user nodes: The representation vector of IRS2 is updated by adding the node and channel link representation vectors from IRS1: in, is the MLP connection layer, and selects the element-wise average function ψ1(·) as the aggregation function; For a legitimate user node, its representation vector is updated as follows: in is an MLP connection layer, and selects the element pooling maximization function ψ2(·) as the aggregation function: ψ2(x1,x2,..,x k )=max(x1,x2,..,x k ) For the eavesdropper node, the update of the representation vector is as follows: in is the MLP connection layer, and selects the element pooling maximization function ψ2(·) as the aggregation function; After the update layer, the node representation vector of GNN update Passed to the output layer, the IRS reflection coefficient matrix is ​​finally obtained and the beamforming matrix W at the BS = [w1,w2,..,w K ]∈C M×K , while satisfying the unit mode constraint of θ and the total power constraint of W; Will represent the vector Through a linear layer with 2M×K units get: The beamforming matrix is ​​then output through a normalization layer as follows: W=W * (1:M,:)+j W * (M+1:2M,:) Where W(i:j,:) represents the submatrix of W, which is constructed by the indexes from the i-th row to the j-th row of W; Pass a linear layer with 2L1 units Output As shown below: Then, the reflection phase shift of each reflection unit in IRS1 is obtained through the normalization layer, as follows: Where [V1] ij represents the element in the i-th row and j-th column of the matrix, symbol represents the index subvector from i to j; Following the same principle, Pass a linear layer with 2L2 units Output As shown below: Then, the reflection phase shift of each reflection unit in IRS2 is obtained through the normalization layer, as follows: Through the output layer, beamforming at the BS and reflection phase shift at the IRS are obtained.

10. The method for optimizing secure communication of a dual IRS-assisted downlink MISO system based on graph neural network according to claim 9, characterized in that: In step S6, the GNN graph neural network model is trained and two hypotheses are proposed to obtain the eavesdropper’s channel parameters: The first one: During the GNN training phase, the legitimate receiver imitates the eavesdropper to send a pilot sequence to obtain more accurate information about the eavesdropper's channel parameters, that is, and The second type: Information exchange between the eavesdropper and the BS does not occur, and the eavesdropper channel is modeled as: Randomly select N legitimate user channels from the estimated channels, and then add the CSI estimation error Ω n As an eavesdropper, the estimated channel is: g(·) is the mapping function that maps the estimated CSI to the BS beamforming matrix and the IRS reflection phase shift. E(·) is the mean function. GNN is used to implement the mapping function and obtain the representation vector of GNN. The GNN loss function is defined as: GNN is used to extract the feature vectors of each node and edge from the network topology information, communication channel CSI and interference, and the beamforming at the BS and the IRS reflection beam vector are learned through training to maximize the average total information confidentiality rate of legitimate users under the constraints.

Images