Secure communication optimization method for dual IRS-assisted wireless energy-carrying communication system based on graph neural network

Abstract

The present invention relates to a secure communication optimization method for a dual-IRS-assisted wireless energy-carrying communication system based on a graph neural network, and belongs to the field of wireless communication security. The method jointly optimizes the reflection beamforming of two IRSs and the transmit beamforming of the base station to maximize the total information transmission rate of the system, while satisfying the base station's transmit power constraint, maximum eavesdropping rate constraint, energy collection constraint, and modulo-one constraint of the IRS reflection coefficient. A machine learning method combining the Lagrange multiplier method and GNN is used to parameterize the pilot information used to estimate the channel into a representation vector of the GNN. The representation vector is updated layer by layer according to the GNN connection graph, and the beamforming at the BS and the reflection coefficient at the IRS are optimized according to the system goal. Compared with traditional methods using channel estimation and non-convex optimization, the present invention achieves a higher information transmission rate under the premise of meeting the needs of energy collection users and information collection users.

Description

Technical Field

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

[0002] Intelligent reflecting surfaces (IRS) are two-dimensional electromagnetic metasurfaces composed of a large number of low-cost passive components. They can modify the wireless propagation environment and improve the performance of wireless communication systems. Physical layer security (PLS) is an information security technology that leverages the randomness of wireless channels to achieve secure communications. Because IRS can improve the quality of channels for information collection users while simultaneously reducing the quality of channels for eavesdropping users, the two technologies have complementary advantages.

[0003] On the other hand, simultaneous wireless information and power transfer (SWIPT) technology has been widely studied since its proposal. Because it can power a large number of low-power devices in wireless sensor networks and the Industrial Internet, it is considered to be one of the key technologies for the future Internet of Things.

[0004] Combining IRS with SWIPT can leverage the advantages of both. On the one hand, IRS can improve information transmission capabilities. On the other hand, IRS can effectively compensate for RF signal path loss, thereby establishing an energy collection area near the IRS and improving energy transmission efficiency within this area.

[0005] Information transmission in the SWIPT system is vulnerable to eavesdropping, and information communication security has become a key issue that needs to be addressed urgently. For example, to meet charging needs, energy harvesters are typically closer to the base station (BS) than information harvesters, resulting in better signal quality. However, this creates information security risks: because data and energy signals are transmitted simultaneously, energy harvesters can receive stronger data signals than information harvesters, making it possible to eavesdrop on the private information of information harvesters. 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 problem of IRS-assisted PLS in wireless communications has become a hot research topic.

[0006] While many studies have investigated secure communications in IRS-assisted wireless communication systems, no technology exists for secure communications in dual-IRS-assisted SWIPT systems that consider channel estimation and the reflection link between the IRSs. Prior art publication CN113556164A discloses an energy-efficiency-prioritized beamforming optimization method for a single-IRS-assisted SWIPT system, but fails to consider communication security. Prior art publication CN116192220A discloses a secure rate optimization method for an IRS-assisted cognitive SWIPT system. However, due to the large number of variables and iterations involved, convergence is slow, and the resulting results may not necessarily approach the optimal solution. Designing the beamforming of the base station and the reflection vectors of the two IRSs to meet the needs of both energy-harvesting and information-collecting users remains a challenge. Compared to single-IRS system optimization, dual-IRS optimization requires considering not only the reflection channels from each IRS to the user but also how to better utilize the channel between the two IRSs for collaboration. Due to the large number of channel parameters and the more complex system structure, dual-IRS-assisted wireless communication systems present a more challenging challenge for channel estimation. Channel estimation for dual-IRS-assisted wireless communication systems is inherently time-consuming and arduous. Considering the non-convexity of the optimization problem and the coupled nature of the system variables, the traditional solution involves introducing slack variables to decouple the system variables. This then transforms the non-convex optimization problem into an approximate convex one, using alternating optimization to find an approximate solution. This approach involves a large number of variables and iterations, resulting in slow convergence and a solution that may not necessarily approach the optimal solution. Summary of the Invention

[0007] In view of this, the object of the present invention is to provide a secure communication optimization method for a dual IRS-assisted wireless energy-carrying communication system based on a graph neural network (GNN).

[0008] In order to achieve the above object, the present invention provides the following technical solutions:

[0009] A secure communication optimization method for a dual IRS-assisted wireless energy-carrying communication system based on a graph neural network, the method comprising the following steps:

[0010] S1. Establish a dual IRS-assisted wireless energy-carrying communication system model, define the corresponding communication channel, the corresponding reflection phase shift matrix, the corresponding received signal representation, and the corresponding receiving rate;

[0011] S2. Establish a secure communication optimization problem P0 under the dual IRS-assisted wireless energy communication system model with the goal of maximizing the average information collection user and information rate and satisfying the corresponding constraints;

[0012] S3, using a pilot estimation method to obtain all channel state information of the dual IRS assisted wireless energy communication system model and construct a corresponding pilot information vector;

[0013] 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 P0 into P1;

[0014] S5, introduce the Lagrange multiplier vector to further transform the secure communication optimization problem P1 into P2;

[0015] S6. 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;

[0016] S7. Train the graph neural network (GNN) model. After training, solve the base station beamforming and IRS reflection phase shift using the secure communication optimization problem P2 as the objective function under the premise of given Lagrange multipliers.

[0017] Furthermore, in step S1, the dual IRS-assisted wireless energy-carrying communication system model includes a base station BS, intelligent reflective surfaces IRS1 and IRS2, K information collection users U1, U2, ..., U K And N energy harvesting users E1, E2, ..., E N The base station BS has M transmitting antennas, and all users use single antennas. IRS1 is deployed near the BS and the energy collection user and has L1 reflection units. IRS2 is deployed near the energy collection user and has L2 reflection units. The BS simultaneously sends information to K information collection users and energy to N energy collection users. IRS1 reflects the signal transmitted by the base station to all users and reflects the signal to IRS2. IRS2 reflects the signal received from the base station and IRS1 to all users.

[0018] The channels from BS to IRS1 and IRS2 are represented as and The channel from IRS1 to IRS2 is represented as The channels from BS, IRS1 and IRS2 to the information collection user are expressed as and The channels from BS, IRS1 and IRS2 to energy harvesting users are represented as and Among them, 1≤k≤K, 1≤n≤N, C x×y represents a set of complex-valued matrices of x×y dimensions;

[0019] The reflection phase shift matrix of IRS1 is expressed as:

[0020]

[0021] represents the reflection coefficient of the l1th reflection unit, represents the reflection amplitude, Represents the reflection phase shift of the l1th reflection unit Where Q is the phase shift interval of a single element of 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, the reflection amplitude Reflection phase shift

[0025] The base station's transmitted signal is expressed as:

[0026]

[0027] in, For information collection user U k Confidential information of k ∈C M×1 is the corresponding beamforming matrix; For energy harvesting users E n Information, where z n ∈C M×1 is the beamforming matrix, and Obeys a complex Gaussian distribution with mean 0 and variance 1;

[0028] Then the information collection user U k and energy harvesting users E n The received signals are expressed as:

[0029] y k =[h d,k +G1θ1h 1,k +G2θ2h 2,k +G1θ1D H θ2h 2,k ] T x+u k ,1≤k≤K

[0030] y n =[g d,n +G1θ1g 1,n +G2θ2g 2,n +G1θ1D H θ2g2,n ] T x+u n ,1≤n≤N

[0031] where u k and u n are the receiving noise at the information collection user and the energy collection user, respectively, and δ represents the variance of the complex Gaussian distribution;

[0032] Then U k The achievable rate at which the kth confidential information is received is:

[0033]

[0034] E n The achievable eavesdropping rate of the kth confidential information received at is:

[0035]

[0036] Energy harvesting users E n The energy that can be collected is:

[0037]

[0038] Where η∈(0,1] is the energy harvesting efficiency.

[0039] Furthermore, the direct channel h d,k and g d,n Obeying Rayleigh fading:

[0040]

[0041] in, They represent the large-scale fading factors of the channel, vec(·) represents matrix vectorization;

[0042] The reflection channels G1, G2, and D obey Rice fading. The Rice channel is expressed as:

[0043]

[0044] Where LOS is the line-of-sight portion of the channel, NLOS is the non-line-of-sight portion of the channel, ε is the Rice factor, and β is the path loss of the channel. Obey the standard complex Gaussian distribution The path loss coefficient β is related to the physical straight-line distance d between the two ends of the channel, is a function of azimuth and elevation; where, let Indicates that user U is collected from information kThe azimuth and elevation angles to IRS1, then the steering vector of the l1th reflection unit of IRS1 is Expressed as:

[0045]

[0046] Among them, d IRS1 is the distance between two adjacent reflection units in IRS1, λ c is the carrier wavelength, i1(l1)=mod(l1-1,L), Indicates rounding down, L and W are the length and width of IRS1, L×W=L1, then

[0047] Assume (x k ,y k ,z k ) is the information collection user U k The three-dimensional geographic coordinates, (x IRS1 ,y IRS2 ,z IRS3 ) is the three-dimensional geographic coordinate of IRS1, the azimuth and elevation are expressed as:

[0048]

[0049] in, For U k Straight-line distance to IRS1;

[0050] Similarly, IRS1 to energy harvesting user E n Channel g 1,n , IRS2 to information collection user U k Channel h 2,k , IRS2 to energy harvesting user E n Channel g 2,n The generation method of is consistent with this;

[0051] For the channel G1 from BS to IRS1, let is the azimuth and elevation angle of the reflection unit on IRS1 reaching the BS, and the steering vector at the BS is expressed as:

[0052]

[0053] Among them, d BS is the distance between two adjacent BS antennas, let are the azimuth and elevation angles from IRS1 to BS, then Expressed as:

[0054]

[0055] Assume (x BS ,y BS ,z BS ) is the three-dimensional geographic coordinate of the BS, and the azimuth and elevation angles are expressed as:

[0056]

[0057] Among them, d BS,IRS1 is the straight-line distance from BS to IRS1;

[0058] The generation method of the channel G2 from the BS to IRS2 and the reflection channel D from IRS1 to IRS2 is consistent with this.

[0059] Further, in step S2, 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},{z n}, maximize the total information rate R of all information collection users under the constraints of the maximum eavesdropping rate and minimum energy of the energy collection users, the modulus-one constraint of the reflection coefficient of the IRS, and the maximum transmission power of the base station. k The security communication optimization problem P0 is expressed as:

[0060]

[0061] st:

[0062]

[0063] Among them, P BS is the transmit power constraint at the BS, is the maximum eavesdropping rate limit of the energy harvesting user, and ζ is the minimum energy harvesting limit of the energy harvesting user.

[0064] Further, in step S3, for the information collection user U k , let user U k The pilot signal sent is x k ∈C K×1 , where the pilot length is taken as the number of information collecting users K, and the pilot signals sent by different users are orthogonal to each other, that is:

[0065]

[0066] Among them, P U is the power of the pilot transmitted by the information collection user;

[0067] Then the signal received by BS at time t is:

[0068]

[0069] Where t=1,2,...,τ u , τ u To estimate the number of pilots required, N t is the BS receiving noise, H k,t =h d,k +G1θ 1,t h 1,k +G2θ 2,t h 2,k +G1θ 1,t D H θ 2,t h 2,k ,1≤k≤K;

[0070] Utilize the orthogonality of the pilot signal and multiply x at the BS. k ,get:

[0071]

[0072] in,

[0073] The number of uses is τ u The pilot information is used as the input of GNN:

[0074]

[0075] Similarly, energy harvesting user E n The same pilot estimation method is used to obtain E at the BS. n The number of u Pilot information:

[0076]

[0077] Then we get the information collection user pilot Y U and energy harvesting user pilot Y E , which are respectively expressed as:

[0078] Y U =[y1,y2,..,y k ],1≤k≤K

[0079] Y E =[y1,y2,..,y n ],1≤n≤N

[0080] Information collection user pilot Y U and energy harvesting user pilot Y E As the input feature vector of the graph neural network GNN.

[0081] Furthermore, in step S4, the secure communication optimization problem P0 is transformed into P1:

[0082]

[0083] st:

[0084]

[0085] Among them, ({w k},{z n},θ1,θ2)=g(Y U ,Y E ) represents the use of graph neural network GNN to simulate the reception of pilot Y from BS U and Y E Optimal mapping to BS beamforming and IRS reflection phase shift.

[0086] Furthermore, in step S5, the Lagrange multiplier vector is first introduced:

[0087]

[0088] By transferring the constraints C2 and C3 into the objective function, we obtain a partial primal-dual optimization problem, thereby transforming the secure communication optimization problem P1 into P2:

[0089]

[0090] st:

[0091]

[0092] It is solved using alternating optimization: first, fix the dual variables to optimize the system variables to minimize the objective P2; then fix the system variables and optimize the dual variables to maximize P2;

[0093] For P2, given the system variables, the Lagrange multiplier and Update along the direction of gradient ascent based on the subgradient:

[0094]

[0095] Where l is the number of iterations and κ ≥ 0 is the update step size.

[0096] Furthermore, in step S6, a GNN model is designed to abstract the wireless communication environment into a graph G = (V, E), V = [IRS1, IRS2, U1, ..., U k ,E1,...,E n ] is the set of nodes in the graph, and each node v∈V corresponds to a representation vector xv , v∈V, where the node representation vector is:

[0097]

[0098] The node’s representation vector is received by the BS with pilot information Y U and Y E get;

[0099] In GNN, the feature vector Y U and Y E After normalization and standardization, it is converted into a graph node representation vector. All representation vectors of the previous layer are used as input and the representation vector is updated layer by layer. After multiple layers, the representation vector of each node is used to design the beamforming vector and reflection coefficient.

[0100] In GNN, the graph representation vector is learned through the input layer, where U k The input feature of the node is the received pilot y k , E n The input feature of the node is the received pilot y n , the input features of the IRS1 node By Y U and Y E Perform weighted averaging to obtain the input features of IRS2 node By Y U and Y E Perform weighted average to obtain;

[0101] D updates the layer to update the representation vector, and gets

[0102] The output result is obtained by passing it 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.

[0103] Furthermore, in the input layer of GNN, the pilot information y k The real and imaginary components of are separated and then converted into column vectors to obtain:

[0104]

[0105] Among them, the information related to the node can be embedded in the column vector:

[0106]

[0107] Among them, loc k Collect the user's three-dimensional coordinate parameters for information;

[0108] Then Through a deep neural network layer As U k Initial representation vector of the node

[0109]

[0110] For energy harvesting users, the node representation vector is obtained in the same way:

[0111]

[0112] For an IRS node, its representation vector is formed by aggregating the representation vectors of the information collection user and the energy collection user:

[0113]

[0114] where ψ0(·) is an element-wise average function is a deep neural network layer;

[0115] The representation vector of IRS2 node is obtained in the same way as IRS1:

[0116]

[0117] The representation vector obtained by the input layer Contains the feature vectors of all nodes and edges and passes them to the D update layer;

[0118] The update of the representation vectors of all nodes in the update layer is based on the aggregation of the previous representation vector of the node and the representation vectors of its adjacent nodes. The specific mathematical expression is:

[0119]

[0120] Among them, V(v) represents the set of nodes adjacent to node v, is the aggregation function of the dth update layer, is a combination function;

[0121] The aggregation function of GNN is expressed as:

[0122]

[0123] Among them, ψ(·) is a function that is invariant to the input permutation, and Using deep neural networks;

[0124] For the IRS1 node, the representation vector comes from:

[0125]

[0126] in, It is a multi-layer perceptron, which is used to integrate node representation vectors and introduce the nonlinear activation function relu; ψ1(·) is implemented using the element pooling averaging function:

[0127] ψ1(x1,x2,..,x k )=mean(x1,x2,..,x k )

[0128] The representation vector of the IRS2 node is updated from the neighboring nodes, including the representation vectors from the IRS1 node and from the information collecting user and eavesdropping user nodes:

[0129]

[0130] in, It is an MLP connection layer, and the element-wise average function ψ1(·) is selected as the aggregation function;

[0131] For the information collection user node, its representation vector is updated as follows:

[0132]

[0133] in, is an MLP connection layer, and the element pooling maximization function ψ2(·) is selected as the aggregation function:

[0134] ψ2(x1,x2,..,x k )=max(x1,x2,..,x k )

[0135] For energy harvesting user nodes, the update of the representation vector is as follows:

[0136]

[0137] in, It is an MLP connection layer, and the element pool maximization function ψ2(·) is selected as the aggregation function;

[0138] Updated node representation vector Passed to the output layer, the IRS1 reflection coefficient matrix is ​​finally obtained IRS2 reflection coefficient matrix and the beamforming matrix W at the BS = [w1,w2,..,w K ]∈C M×K and Z=[z1,z2,..,z N ]∈C M×N, while satisfying the unit mode constraints of v1 and v2 and the total transmission power constraint of the BS;

[0139] Will represent the vector and Pass through a linear layer with 2M units respectively get:

[0140]

[0141] The beamforming matrix is ​​then output through a normalization layer as follows:

[0142]

[0143]

[0144] Where W(i:j,u:v:) represents the submatrix of W, which is constructed by the indices from the i-th row to the j-th row and the u-th column to the v-th column of W;

[0145] Pass a linear layer with 2L1 units Output As shown below:

[0146]

[0147] Then, the reflection phase shift of each reflection unit in IRS1 is obtained through the normalization layer as follows:

[0148]

[0149] Where, [V1] ij represents the element in the i-th row and j-th column of the matrix, and the symbol represents the index subvector from i to j;

[0150] Following the same principle, Pass a linear layer with 2L2 units Output As shown below:

[0151]

[0152] Then, the reflection phase shift of each reflection unit in IRS2 is obtained through the normalization layer as follows:

[0153]

[0154] Through the output layer, beamforming at the BS and reflection phase shift at the IRS are obtained.

[0155] Furthermore, in step S6, the GNN model is trained with the goal of minimizing the Lagrangian relaxation function P2 under the premise of a given Lagrangian multiplier, and its loss function is:

[0156]

[0157] Among them, L is the loss function of the GNN model during the l-th iteration.

[0158] The beneficial effects of the present invention are:

[0159] The present invention proposes a secure communication optimization method for a dual IRS-assisted wireless energy-carrying communication system based on a GNN graph neural network. First, the constraints are introduced into the objective function by introducing the Lagrange multiplier vector using the Lagrange multiplier method. A partial primal dual optimization problem is obtained. Then, the IRS and multiple users are modeled, a GNN connection graph is constructed, and the objective function with Lagrange multipliers is converted into a GNN loss function. Next, 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 objectives, such as the total information transmission rate of the information collection user. The trained GNN has good generalization ability and can adapt to communication scenarios with different numbers of users. Compared with the traditional method using channel estimation and non-convex optimization, it can obtain a higher information transmission rate under the premise of meeting the needs of energy collection users and information collection users.

[0160] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0161] 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 with reference to the accompanying drawings, in which:

[0162] Figure 1 A schematic structural diagram of a dual IRS-assisted wireless energy-carrying communication system model provided by the present invention;

[0163] Figure 2 A GNN connection diagram of the dual IRS-assisted wireless energy-carrying communication system security communication optimization method provided by the present invention;

[0164] Figure 3 A schematic diagram of the GNN structure of the dual IRS-assisted wireless energy-carrying communication system security communication optimization method provided by the present invention;

[0165] Figure 4 This is a schematic diagram of the overall process of the dual IRS-assisted wireless energy-carrying communication system security communication optimization method provided by the present invention. DETAILED DESCRIPTION

[0166] The following describes the embodiments of the present invention by means of 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 are only schematic illustrations of the basic concept of the present invention, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0167] Among them, the accompanying drawings are only for illustrative purposes and represent only schematic diagrams rather than actual pictures, and should not be understood as limiting the present invention. In order to better illustrate the embodiments of the present invention, some parts of the accompanying drawings may be omitted, enlarged or reduced, and do not represent the dimensions of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions may be omitted in the accompanying drawings.

[0168] 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 there are terms such as "upper", "lower", "left", "right", "front", "back", etc. indicating directions or positional relationships, they are based on the directions or positional relationships shown in the drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operate in a specific direction. Therefore, the terms describing the positional 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.

[0169] See also Figures 1 to 4 , which is a secure communication optimization method for dual IRS-assisted wireless energy-carrying communication system based on graph neural network.

[0170] Example

[0171] This embodiment provides a specific implementation of a method for optimizing secure communication in a dual IRS-assisted wireless energy-carrying communication system based on a graph neural network, specifically including the following contents:

[0172] Step 1: Establish a dual IRS-assisted wireless energy 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 information collection users and number of eavesdropping users), input flag input_flag, Rayleigh channel factor, Ricean channel factor, noise power, channel transmission power, etc. Figure 1 As shown, the dual IRS assisted wireless energy communication system model includes a base station BS, two IRSs, K information collection users (denoted as U1, ..., U k ) and N energy harvesting users (denoted as E1, ..., E n ). The base station (BS) has M transmitting antennas, and all users use a single antenna. IRS1 is deployed on a high-rise building near the BS and energy-harvesting users and has L1 reflectors. IRS2 is deployed on a high-rise building near the information-harvesting users and has L2 reflectors. The BS simultaneously transmits information to K information-harvesting users and energy to N energy-harvesting users. To meet energy charging requirements, energy-harvesting users are typically closer to the base station (BS) than information-harvesting users, making them potential information eavesdroppers.

[0173] To meet energy transmission requirements and improve the security of wireless information transmission, two IRSs can be used to coordinate and assist communication. Specifically, IRS1 reflects the signal transmitted by the base station to all users and simultaneously reflects the signal to IRS2; IRS2 then reflects the signal received from the base station and IRS1 to all users. Compared with traditional single-IRS-assisted system communication, dual-IRS collaborative auxiliary system communication not only creates a new communication link for users, improving information transmission rate and energy transmission power, but also energy-harvesting users receive the signals reflected by the two IRSs, which act as artificial noise, thereby ensuring the security of information transmission.

[0174] More specifically, in the established dual-IRS-assisted wireless energy-carrying communication system model, the reflection channel obeys Ricean fading, the direct channel obeys Rayleigh fading, and the IRS phase shift adopts a discrete form.

[0175] The baseband equivalent channel response is expressed as:

[0176] The channels from BS to IRS1 and IRS2 are represented as and The channel from IRS1 to IRS2 is represented as The channels from BS, IRS1 and IRS2 to the information collection user are represented as and The channels from BS, IRS1 and IRS2 to the energy harvesting user are denoted as g d,n ∈C M×1 , and Among them, 1≤k≤K, 1≤n≤N, C x×y Represents a collection of complex-valued matrices of dimension x×y.

[0177] The reflection phase shift matrix of IRS1 is expressed as 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:

[0178]

[0179] Where Q is the phase shift interval of a single element in the IRS. In practical applications, continuous phase shifting is very expensive to implement in hardware, so discrete phase shifting is more widely used. However, studying continuous phase shift is also important because it is the upper limit of discrete phase shifting.

[0180] The reflection phase shift matrix of IRS2 is expressed as It represents the reflection coefficient of the l2th reflection unit, and the reflection amplitude is β 2l ∈[0,1], the reflection phase shift is:

[0181]

[0182] This embodiment only considers the reflection phase shift, so and

[0183] The base station's transmitted signal is expressed as in For information collection user U k Confidential information of k ∈C M×1 is the corresponding beamforming matrix; For energy harvesting users E n Information, where z n ∈C M×1 is the beamforming matrix, and They all obey a complex Gaussian distribution with mean 0 and variance 1.

[0184] Then the information collection user U k and energy harvesting users E n The received signal can be expressed as:

[0185] y k =[h d,k +G1θ1h 1,k+G2θ2h 2,k +G1θ1D H θ2h 2,k ] T x+u k ,1≤k≤K

[0186] y n =[g d,n +G1θ1g 1,n +G2θ2g 2,n +G1θ1D H θ2g 2,n ] T x+u n ,1≤n≤N

[0187] where u k and u n are the receiving noises at the information collection user and the energy collection user, respectively, and they obey the complex Gaussian distribution with a mean of 0, that is,

[0188] From this we can get the achievable rate of receiving the kth confidential information at Uk:

[0189]

[0190] The achievable eavesdropping rate of the kth confidential information received at En is:

[0191]

[0192] The energy that can be collected by energy harvesting user En is:

[0193]

[0194] Where η∈(0,1] is the energy harvesting efficiency.

[0195] Assume h d,k , g d,n is an uncorrelated Rayleigh fading channel, that is:

[0196]

[0197] in, Represent the large-scale fading factor of the channel, and vec(·) represents the matrix vectorization. The remaining channels are all Rice fading channels. The Rice channel is obtained by the following formula:

[0198]

[0199] Where LOS is the line-of-sight portion of the channel, NLOS is the non-line-of-sight portion of the channel, ε is the Ricean factor, and β is the path loss of the channel. Obeys the standard complex Gaussian distribution, that is, The path loss coefficient β is set to 30+22log(d), where d is the physical straight-line distance between the two ends of the channel. is a function of azimuth and elevation. Specifically, let Indicates that user U is collected from information k The azimuth and elevation angles to IRS1. Then the steering vector of the l1th reflection unit of IRS1 is It can be expressed as:

[0200]

[0201] Among them, d IRS1 is the distance between two adjacent reflection units in IRS1, λ c is the carrier wavelength, i1(l1)=mod(l1-1,L), ( To round down, L and W are the length and width of IRS1, L×W=L1). Therefore, Assume (x k ,y k ,z k ) is the information collection user U k The three-dimensional geographic coordinates, (x IRS1 ,y IRS2 ,z IRS3 ) is the three-dimensional geographic coordinate of IRS1. The azimuth and elevation can be expressed as:

[0202]

[0203] in, For U k Straight-line distance to IRS1. IRS1 to energy harvesting user E n Channel g 1,n , IRS2 to information collection user U k Channel h 2,k , IRS2 to energy harvesting user E n Channel g 2,n Can be generated in the same way.

[0204] For the channel G1 from BS to IRS1, let is the azimuth and elevation angle of the reflection unit on IRS1 reaching the BS, then the steering vector at the BS can be expressed as:

[0205]

[0206] Among them, d BS is the distance between two adjacent BS antennas, let are the azimuth and elevation angles from IRS1 to BS, then It can be expressed as:

[0207]

[0208] Assume (x BS ,y BS ,z BS ) is the three-dimensional geographic coordinate of the BS, the azimuth and elevation angles can be expressed as:

[0209]

[0210] Among them, d BS,IRS1 is the straight-line distance from the BS to IRS1. The channel G2 from the BS to IRS2 and the reflection channel D from IRS1 to IRS2 can be generated in the same way.

[0211] The second step is to establish a secure communication optimization problem; 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},{z n}, ensuring that the eavesdropping rate of the energy collection user is less than or equal to the maximum eavesdropping rate, the received energy is not less than the minimum energy requirement, the reflection coefficient of the IRS satisfies the modulo-one constraint, and the base station does not exceed the maximum transmission power constraint to maximize the total information rate R of all information collection users k Therefore, the problem under consideration is described as follows:

[0212]

[0213] Among them, P BS is the transmit power constraint at the BS, is the maximum eavesdropping rate limit of the energy harvesting user, and ζ is the minimum energy harvesting limit of the energy harvesting user. Due to the high coupling between the objective function and the system variables in constraints C2 and C3, and the non-convexity of constraints C4 and C5, it is difficult to find a global optimal solution to the problem.

[0214] The third step is to perform channel estimation and use the pilot method to obtain the channel state information (CSI) to extract the channel parameters of the information collection user and the energy collection user, thereby optimizing the objective function P0.

[0215] Due to the large number of reflection units in massive antennas and dual IRSs, the complexity of channel estimation and the required pilot overhead increase exponentially. Many researchers are committed to designing efficient channel estimation schemes for different IRS architectures, aiming to achieve higher channel estimation accuracy with lower pilot overhead.

[0216] The present invention uses a GNN graph neural network to simulate the optimal mapping from BS received pilot to BS beamforming and IRS reflection phase shift. The GNN representation vector can be obtained from the result of channel estimation, that is, estimated CSI, or from the pilot information received by the BS. This is because the purpose of the pilot method for channel estimation is to design a reasonable estimation algorithm to recover a more accurate channel CSI from the pilot information. However, GNN has the characteristic of information integration. Since the pilot information already contains implicit CSI information, GNN can embed the pilot information as feature information into the graph representation vector. This not only reduces the time overhead caused by the channel estimation algorithm, but also minimizes the calculation error of the objective function caused by the error generated by the channel estimation algorithm.

[0217] Many documents have proposed channel estimation schemes for large-scale MIMO communication systems assisted by dual IRS collaboration. Since the BS and IRS are generally fixed in position, the channel is generally high-dimensional and quasi-static, while the channels of information collection users and energy collection users are low-dimensional and time-varying because they need to move frequently. Frequent estimation is not required for quasi-static channels, but frequent estimation is required for time-varying channels. However, combined with the objective function, the present invention does not need to obtain the estimated value of each channel, but only needs to obtain the total channel information from the BS to the energy collection user and the information collection user. For the information collection user U k In terms of BS and U k The total channel between k =h d,k +G1θ1h 1,k +G2θ2h 2,k +G1θ1D H θ2h 2,k ,1≤k≤K. Therefore, the present invention adopts the simplest pilot estimation method.

[0218] Since information is collected from user U k and energy harvesting users E n The pilot transmission method is the same as that of k Assume that user U k The pilot signal sent is x k ∈C K×1 , where the pilot length is taken as the number of information collecting users K, and the pilot signals sent by different users are orthogonal to each other. That is:

[0219]

[0220] Among them, P U is the power of the pilot signal transmitted by the information collection user. The signal received by the BS at time t is:

[0221]

[0222] Where t=1,2,...,τ u , τ u To estimate the number of pilots required, N t is the BS receiving noise, H k,t =h d,k +G1θ 1,t h 1,k +G2θ 2,t h 2,k +G1θ 1,t D H θ 2,t h 2,k ,1≤k≤K. Using the orthogonality of the pilot signal, multiply x on the right at the BS. k ,get:

[0223]

[0224] in, Note that due to H k,t It is a complex combination channel. It is a difficult problem to obtain the CSI of each channel. The traditional method requires step-by-step quasi-static channel estimation from BS to IRS, and then use the estimated results to perform cascade channel estimation between IRSs, and finally perform user channel estimation. The present invention uses GNN to realize the mapping from channel CSI to BS beamforming and IRS reflection phase shift, and converts the target optimization function P0 into P1. The present invention uses GNN to realize the mapping from channel CSI to BS beamforming and IRS reflection phase shift, and does not need to obtain accurate channel estimation results. Since the pilot information already contains the complete channel state information CSI, the pilot is embedded in the GNN as a feature vector. Specifically, the number of τ is used u The pilot information is used as the input of GNN.

[0225]

[0226] Energy harvesting users E n The same pilot estimation method is used to obtain E at the BS. n The channel CSI is expressed as follows:

[0227]

[0228] After the above steps, the input feature vector of GNN is obtained, which is the information collection user pilot Y U and energy harvesting user pilot Y E , and the two are expressed as follows:

[0229] Y U =[y1,y2,..,yk ],1≤k≤K

[0230] Y E =[y1,y2,..,y n ],1≤n≤N

[0231] The fourth step is to use the graph neural network GNN to simulate the reception of the pilot Y from the BS U and Y E The optimal mapping to BS beamforming and IRS reflection phase shift transforms the target optimization problem P0 into P1:

[0232]

[0233] st:

[0234]

[0235] In the fifth step, since the system variables in the constraints C2 and C3 in this problem are highly coupled and the constraints are non-convex, the constraints are difficult to handle directly. Therefore, the Lagrange multiplier method is used to introduce the constraints into the target P1.

[0236] First, introduce the Lagrange multiplier vector:

[0237]

[0238] By transferring the constraints C2 and C3 into the objective function, we obtain a partial primal-dual optimization problem as follows:

[0239]

[0240] st:

[0241]

[0242] Generally speaking, alternating optimization is the preferred method for solving the maximum-minimum problem. First, the dual variables are fixed to optimize the system variables to minimize the target P2. Then the system variables are fixed and the dual variables are optimized to maximize P2. For P2, given the system variables, the Lagrange multiplier and Updates can be made based on the subgradient along the direction of gradient ascent.

[0243]

[0244] Where; is the number of iterations, κ≥0 is the update step size.

[0245] The sixth step is to design the GNN model, such as Figure 2The neural network architecture diagram of GNN shown in the figure abstracts the wireless communication environment into a graph G = (V, E), V = [IRS1, IRS2, U1, ..., U k ,E1,...,E n ] is a set of nodes in the graph, such as IRS and information collection users and energy collection users are regarded as a node in the graph. Each node v∈V has its corresponding representation vector x v , v∈V. For example, the representation vector of a node is as follows:

[0246]

[0247] The node’s representation vector is received by the BS with pilot information Y U and Y E In GNN, the feature vector Y U and Y E After normalization and standardization, it is converted into a graph node representation vector. All the representation vectors of the previous layer are used as input and the representation vector is updated layer by layer. After multiple layers, the representation vector of each node will contain enough information to design the beamforming vector and reflection coefficient. 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 matrix can be obtained by node U k and E n If there is a relationship between nodes that represent vector updates, a directed edge is used to connect them. The edges from the IRS to the information collection user and the energy collection user represent the existence of data transmission and energy transmission relationships, the edges between information collection users represent the existence of link interference, the edges from energy collection users to information collection users represent the existence of interference, the edges between energy collection users represent the existence of energy interference, and the edges from information collection users to energy collection users represent the existence of interference.

[0248] Compared with fully connected neural networks, GNNs more naturally capture the interactions between information collection users, energy collection users, and IRSs. In particular, the update of each information collection user node is a function of all its neighboring nodes, energy collection user nodes, and IRS nodes, which enables GNNs to learn to avoid interference and increase the information rate of information collection users. The update of each energy collection user node is a function of all information collection user nodes, all its neighboring energy collection user nodes, and IRS nodes, which enables GNNs to learn to avoid energy collection users eavesdropping on information collection users while meeting energy collection requirements. The representation vector update of the IRS1 node comes from all energy collection users and information collection users, thereby better meeting the needs of all users. The representation vector update of the IRS2 node comes from all energy collection users and information collection users and the IRS1 node, which means that IRS2 needs to receive the reflected information of the IRS1 node to collaboratively complete the service. The layer structure of the graph neural network is represented as follows Figure 3 shown.

[0249] The entire GNN consists of three layers, which are used to learn the graph representation vector through the input layer, where U k The input feature of the node is the received pilot y k , where E n The input feature of the node is the received pilot y n , the input features of IRS1 node are Y U and Y E The weighted average is obtained, which is recorded as Similarly, the input features of IRS2 node are composed of Y U and Y E The weighted average is obtained, which is recorded 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.

[0250] 1) Input layer: Since TensorFlow does not support complex-valued operations, the pilot information y k The real and imaginary components of are separated and then converted into column vectors to obtain:

[0251]

[0252] The representation vector of each node in a GNN can be obtained by embedding the useful information of the node. Therefore, any useful information related to the node can be embedded into the representation vector to obtain sufficiently detailed and complete effective information. For example, the three-dimensional geographic coordinates of the user are added to the information collection:

[0253]

[0254] where loc k Collect the user's three-dimensional coordinate parameters for information.

[0255] Then Through a deep neural network layer As U k Initial representation vector of the node

[0256]

[0257] For energy harvesting users, the node representation vector is obtained in the same way:

[0258]

[0259] For an IRS node, its representation vector is formed by the aggregation of the representation vectors of the information collection user and the energy collection user. That is:

[0260]

[0261] where ψ0(·) is an element-wise average function:

[0262]

[0263] The reason for this design is that the pilot signals sent by the information collection user and the energy collection user already contain the information of the IRS reflection vector, and the IRS information contained in the pilot signals sent by each user is equivalent. is a deep neural network layer.

[0264] The representation vector of IRS2 node is obtained in the same way as IRS1:

[0265]

[0266] Represents a vector Contains the feature vectors of all nodes and edges, which are then passed to the D update layer.

[0267] D update layer:

[0268] The update of the representation vectors of all nodes in the update layer is based on the aggregation of the previous representation vector of the node itself and the representation vectors of its adjacent nodes. The specific mathematical expression is:

[0269]

[0270] Here V(v) represents the set of nodes adjacent to node v. is the aggregation function of the dth update layer, is a combination function.

[0271] The key to designing GNN is to choose appropriate aggregation functions and combination functions to make it scalable. The selection of aggregation functions is as follows:

[0272]

[0273] where ψ(·) is a function that is invariant to the input permutation, such as element pooling maximization or element pooling averaging function. and Both can be implemented using deep neural networks.

[0274] For the IRS1 node, the representation vector comes from:

[0275]

[0276] It is a layer of MLP. The MLP (Multi-Layer-Perceptron, MLP) multi-layer perceptron is used to integrate node representation vectors. The introduction of the nonlinear activation function relu enables GNN to learn more complex nonlinear feature mapping relationships. ψ1(·) is implemented using the element pooling averaging function as shown below:

[0277] ψ1(x1,x2,..,x k )=mean(x1,x2,..,x k )

[0278] The representation vector of the IRS2 node is updated from the neighboring nodes, including the representation vectors from the IRS1 node and from the information collecting user and eavesdropping user nodes:

[0279]

[0280] 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 the IRS needs to adjust its reflection vector to serve the information collection user and the energy collection user as much as possible and meet the information eavesdropping rate and energy collection constraints of the energy collection user.

[0281] For the information collection user node, its representation vector is updated as follows:

[0282]

[0283] in is an MLP connection layer, and the element pool 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.

[0284] ψ2(x1,x2,..,x k )=max(x1,x2,..,x k )

[0285] For energy harvesting user nodes, the update of the representation vector is as follows:

[0286]

[0287] 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-signal interference is usually dominated by the strongest signal.

[0288] Output layer:

[0289] After the update layer, the node representation vector of the GNN update Passed to the output layer. Finally, the IRS1 reflection coefficient matrix is ​​obtained IRS2 reflection coefficient matrix and the beamforming matrix W at the BS = [w1,w2,..,w K ]∈C M×K and Z=[z1,z2,..,z N ]∈C M×N , while satisfying the unit mode constraints of v1 and v2 and the total transmission power constraint of the BS.

[0290] Will represent the vector and Pass through a linear layer with 2M units respectively get:

[0291]

[0292] The beamforming matrix is ​​then output through a normalization layer as follows:

[0293]

[0294] where W(i:j,u:v:) represents a submatrix of W, which is constructed from the indices of rows i to j and columns u to v of W.

[0295] Pass a linear layer with 2L1 units Output As shown below:

[0296]

[0297] Then, the reflection phase shift of each reflection unit in IRS1 is obtained through the normalization layer as follows:

[0298]

[0299] 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.

[0300] Following the same principle, Pass a linear layer with 2L2 units Output As shown below:

[0301]

[0302] Then, the reflection phase shift of each reflection unit in IRS2 is obtained through the normalization layer as follows:

[0303]

[0304] Through the output layer, beamforming at the BS and reflection phase shift at the IRS are obtained.

[0305] The GNN-based machine learning algorithm in the above process is shown in Table 1 below:

[0306] Table 1

[0307]

[0308]

[0309] Step 7: Train the GNN model, output the training results, and use the obtained base station beamforming vector, IRS phase shift, and related channel parameters to calculate the objective function. The training process is as follows:

[0310] Input: Received pilot information at the BS as training data set and the learning step size of the Lagrange multiplier

[0311] Output: trained GNN model;

[0312] Step 1: Set the number of samples to 1024, the system parameters (number of BS antennas, number of IRS reflection units, number of information collection users and number of energy collection users), input flag input_flag, Rayleigh and Rice channel factors, noise power, etc.

[0313] Step 2: Estimate the channel according to the proposed channel estimation scheme and obtain the pilot information:

[0314]

[0315] Step 3: Initialize the Lagrange multiplier:

[0316] Step 4: Set the learning rate, maximum number of iterations I, and maximum number of training times per iteration J. Set the training loss unchanged flag No_change to 0. Perform a GNN training as training data, obtain the training loss train_loss[0], and set the best training loss best_loss = train_loss[0]; train a certain number of rounds of training data with a small batch of data of size b, and in the jth training round of the i-th iteration round, perform the following steps:

[0317] Perform multiple pilot transmissions to obtain pilot data as a training data set

[0318] Randomly select a mini-batch β from the training dataset b Training is performed using the base station beamforming and the IRS reflection phase shift as input, which is used to obtain the mini-batch-level Lagrangian relaxation loss function. The subgradient of the Lagrangian multiplier is calculated. After completing the mini-batch training, the Lagrangian multiplier is updated and the next round of training begins.

[0319] After J rounds of training, use the pilot After a training run, the training loss is calculated and compared to the optimal loss. If the current training loss is less than the optimal loss, model performance has improved, and the optimal loss needs to be updated and the next iteration should be entered. If the current training loss is greater than the optimal loss, model performance has not improved, and a determination is made as to whether there has been no improvement after five consecutive iterations. If so, training ends; otherwise, the next iteration continues. Finally, if the maximum number of iterations has been reached, training ends.

[0320] The specific training process is shown in Table 2:

[0321] Table 2

[0322]

[0323]

[0324] The input of the algorithm is the received pilot information at the BS as the training data set And the learning step size of the Lagrange multiplier. GNN is trained for a certain number of rounds on the training dataset with small batches of data of size b. The BS beamforming and IRS reflection phase shift strategies generated by the GNN model are obtained, and then the value of the Lagrange relaxation function is calculated using the current Lagrange multiplier. The GNN model then updates the model learning parameters according to the Lagrange relaxation function, which is the loss function. During each small batch training round, the subgradient of the Lagrange multiplier is calculated. Finally, after each training round, the Lagrange multiplier is updated based on the subgradient. Among them, σ c (·) is a mapping function that maps the data in the constraint set to the Lagrange multiplier space.

[0325] Once the GNN model is complete, its learned parameters and Lagrange multipliers are updated until problem P2 is stable and satisfies the constraints. Once the GNN model is trained, it can be directly applied to a similar scenario involving dual IRS-assisted wireless energy communication, without having to consider constraints or Lagrange multipliers.

[0326] Use the trained GNN model to optimize the given dual variable λ (1) and λ (2) System variables {w k},{z n}, θ1, θ2, GNN is used to extract the feature vector of each node from the BS received pilot signal and learn the beamforming at the BS and the IRS reflected beam vector through training to maximize the average information collection user and information rate under the constraints. The GNN model will be trained with the goal of minimizing the Lagrangian relaxation function P2 under the premise of given Lagrangian multipliers, that is, using P2 as the objective function.

[0327]

[0328] L is the loss function of the GNN model during the lth iteration.

[0329] In the eighth step, this embodiment tests the trained GNN model and attempts to evaluate the output effect of GNN when the number of users and the number of energy harvesting users are different. Compared with traditional non-convex optimization methods, the GNN-based machine learning method has better generalization ability and stronger scalability, can achieve better confidentiality and security effects, and takes less time.

[0330] In this embodiment, Figure 1This paper provides a dual-IRS-assisted SWIPT multi-user communication system model, set in a high-rise urban environment. The base station and users have direct and reflected channels. The base station transmits information and energy directly to information and energy collection users via wireless transmission, or reflects signals to the users via the IRS. Meanwhile, N single-antenna energy collection users in the system can eavesdrop and collect user information. Figure 2 This is the GNN connection diagram for a dual-IRS-assisted downlink SWIPT multi-user communication system, showing the connections between the model's nodes. Based on the signal transmission and interference in a real-world communication environment, the GNN connection diagram abstracts IRS1 and IRS2, as well as information-collecting users and energy-collecting users, as nodes, and abstracts communication links and interference links as edges between nodes. The diagram is a directed graph, in which IRS nodes send data to all user nodes and receive feedback from them. Information-collecting users receive information from IRS nodes and are subject to signal interference from other information-collecting users and energy-collecting users. Energy-collecting users receive energy from IRS nodes and, while eavesdropping on information-collecting users, are subject to signal interference from all energy-collecting users, as well as interference from information-collecting users other than the target information user. Figure 3 The following is a diagram of the GNN model architecture, consisting of an input layer, an update layer, and an output layer. The input layer converts pilot information into node representation vectors and then passes them to the update layer. The update layer updates all node representation vectors by aggregating the representation vectors of the node itself and its neighbors. The update layer can have multiple layers. Generally speaking, GNN models use a two-layer structure, especially when the number of nodes is small, as multiple layers provide minimal improvement. After the update is complete, to obtain the base station beamforming vector and IRS phase shift, the representation vectors of the relevant nodes are passed to the output layer. Subject to the phase shift modulus constraint and the total power constraint at the base station, the base station beamforming vector and the reflected phase shifts of the two IRSs are output. Figure 4 This is the training process of the GNN model.

[0331] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. 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 solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. A secure communication optimization method for a dual IRS-assisted wireless energy-carrying communication system based on a graph neural network, characterized by: The method comprises the following steps: S1. Establish a dual IRS-assisted wireless energy-carrying 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. Establish a secure communication optimization problem P0 under the dual IRS-assisted wireless energy communication system model with the goal of maximizing the average information collection user and information rate and satisfying the corresponding constraints; S3, using a pilot estimation method to obtain all channel state information of the dual IRS assisted wireless energy communication system model and construct a corresponding pilot information vector; 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 P0 into P1; S5, introduce the Lagrange multiplier vector to further transform the secure communication optimization problem P1 into P2; S6. 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; S7. Train the graph neural network (GNN) model. After training, solve the base station beamforming and IRS reflection phase shift using the secure communication optimization problem P2 as the objective function under the premise of given Lagrange multipliers.

2. The method for optimizing secure communication of a dual IRS-assisted wireless energy-carrying communication system based on a graph neural network according to claim 1, characterized in that: In step S1, the dual IRS-assisted wireless energy communication system model includes a base station BS, intelligent reflective surfaces IRS1 and IRS2, K information collection users U1, U2, ..., U K And N energy harvesting users E1, E2, ..., E N The base station BS has M transmitting antennas, and all users use single antennas. IRS1 is deployed near the BS and the energy collection user and has L1 reflection units. IRS2 is deployed near the energy collection user and has L2 reflection units. The BS simultaneously sends information to K information collection users and energy to N energy collection users. IRS1 reflects the signal transmitted by the base station to all users and reflects the signal to IRS2. IRS2 reflects the signal received from the base station and IRS1 to all 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 BS, IRS1 and IRS2 to the information collection user are denoted as h d,k ∈C M×1 , and The channels from BS, IRS1 and IRS2 to the energy harvesting user are denoted as g d,n ∈C M×1 , and Among them, 1≤k≤K, 1≤n≤N, C x×y represents a set of complex-valued matrices of x×y dimensions; The reflection phase shift matrix of IRS1 is expressed as: represents the reflection coefficient of the l1th reflection unit, represents the reflection amplitude, Represents the reflection phase shift of the l1th reflection unit l1 = {1, .., L1}, where Q is the phase shift interval of a single element of the IRS; The reflection phase shift matrix of IRS2 is expressed as: in, Represents the reflection coefficient of the l2th reflection unit, the reflection amplitude Reflection phase shift The base station's transmitted signal is expressed as: in, For information collection user U k Confidential information of k ∈C M×1 is the corresponding beamforming matrix; For energy harvesting users E n Information, where z n ∈C M×1 is the beamforming matrix, and Obeys a complex Gaussian distribution with mean 0 and variance 1; Then the information collection user U k and energy harvesting users E n The received signals are expressed as: y k =[h d,k +G1θ1h 1,k +G2θ2h 2,k +G1θ1D H θ2h 2,k ] T x+u k ,1≤k≤K y n =[g d,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 noise at the information collection user and the energy collection user, respectively, and δ represents the variance of the complex Gaussian distribution; Then U k The achievable rate at which the kth confidential information is received is: E n The achievable eavesdropping rate of the kth confidential information received at is: Energy harvesting users E n The energy that can be collected is: Where η∈(0,1] is the energy harvesting efficiency.

3. The method for optimizing secure communication of a dual IRS-assisted wireless energy-carrying communication system based on a graph neural network according to claim 2, characterized in that: Direct channel h d,k and g d,n Obeying Rayleigh fading: in, They represent the large-scale fading factors of the channel, vec(·) represents matrix vectorization; The reflection channels G1, G2, and D obey Rice fading. The Rice channel is expressed as: Where LOS is the line-of-sight portion of the channel, NLOS is the non-line-of-sight portion of the channel, ε is the Rice factor, and β is the path loss of the channel. Obey the standard complex Gaussian distribution The path loss coefficient β is related to the physical straight-line distance d between the two ends of the channel, is a function of azimuth and elevation; where, let Indicates that user U is collected from information k The azimuth and elevation angles to IRS1, then the steering vector of the l1th reflection unit of IRS1 is Expressed as: Among them, d IRS1 is the distance between two adjacent reflection units in IRS1, λ c is the carrier wavelength, i1(l1)=mod(l1-1,L), Indicates rounding down, L and W are the length and width of IRS1, L×W=L1, then Assume (x k ,y k ,z k ) is the information collection user U k The three-dimensional geographic coordinates, (x IRS1 ,y IRS2 ,z IRS3 ) is the three-dimensional geographic coordinate of IRS1, the azimuth and elevation are expressed as: Among them, d Uk,IRS1 For U k Straight-line distance to IRS1; Similarly, IRS1 to energy harvesting user E n Channel g 1,n , IRS2 to information collection user U k Channel h 2,k , IRS2 to energy harvesting user E n Channel g 2,n The generation method of is consistent with this; For the channel G1 from BS to IRS1, let is the azimuth and elevation angle of the reflection unit on IRS1 reaching the BS, and the steering vector at the BS is expressed as: Among them, d BS is the distance between two adjacent BS antennas, let are the azimuth and elevation angles from IRS1 to BS, then Expressed as: Assume (x BS ,y BS ,z BS ) is the three-dimensional geographic coordinate of the BS, and the azimuth and elevation angles are expressed as: Among them, d BS,IRS1 is the straight-line distance from BS to IRS1; The generation method of the channel G2 from the BS to IRS2 and the reflection channel D from IRS1 to IRS2 is consistent with this.

4. The method for optimizing secure communication of a dual IRS-assisted wireless energy-carrying communication system based on a graph neural network according to claim 2, wherein: In step S2, 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 },{z n }, maximize the total information rate R of all information collection users under the constraints of the maximum eavesdropping rate and minimum energy of the energy collection users, the modulus-one constraint of the reflection coefficient of the IRS, and the maximum transmission power of the base station. k The security communication optimization problem P0 is expressed as: st: Among them, P BS is the transmit power constraint at the BS, is the maximum eavesdropping rate limit of the energy harvesting user, and ζ is the minimum energy harvesting limit of the energy harvesting user.

5. The method for optimizing secure communication of a dual IRS-assisted wireless energy-carrying communication system based on a graph neural network according to claim 4, characterized in that: In step S3, for the information collection user U k , let user U k The pilot signal sent is x k ∈C K×1 , where the pilot length is taken as the number of information collecting users K, and the pilot signals sent by different users are orthogonal to each other, that is: Among them, P U is the power of the pilot transmitted by the information collection user; Then the signal received by BS at time t is: Where t=1,2,...,τ u , τ u To estimate the number of pilots required, N t is the BS receiving noise, H k,t =h d,k +G1θ 1,t h 1,k +G2θ 2,t h 2,k +G1θ 1,t D H θ 2,t h 2,k ,1≤k≤K; Utilize the orthogonality of the pilot signal and multiply x at the BS. k ,get: in, The number of uses is τ u The pilot information is used as the input of GNN: Similarly, energy harvesting user E n The same pilot estimation method is used to obtain E at the BS. n The number of u Pilot information: Then we get the information collection user pilot Y U and energy harvesting user pilot Y E , which are respectively expressed as: Y U =[y1,y2,..,y k ],1≤k≤K Y E =[y1,y2,..,y n ],1≤n≤N Information collection user pilot Y U and energy harvesting user pilot Y E As the input feature vector of the graph neural network GNN.

6. The method for optimizing secure communication of a dual IRS-assisted wireless energy-carrying communication system based on a graph neural network according to claim 5, characterized in that: In step S4, the secure communication optimization problem P0 is transformed into P1: st: Among them, ({w k },{z n },θ1,θ2)=g(Y U ,Y E ) represents the use of graph neural network GNN to simulate the reception of pilot Y from BS U and Y E Optimal mapping to BS beamforming and IRS reflection phase shift.

7. The method for optimizing secure communication of a dual IRS-assisted wireless energy-carrying communication system based on a graph neural network according to claim 6, characterized in that: In step S5, the Lagrange multiplier vector is first introduced: By transferring the constraints C2 and C3 into the objective function, we obtain a partial primal-dual optimization problem, thereby transforming the secure communication optimization problem P1 into P2: st: It is solved using alternating optimization: first, fix the dual variables to optimize the system variables to minimize the objective P2; then fix the system variables and optimize the dual variables to maximize P2; For P2, given the system variables, the Lagrange multiplier and Update along the direction of gradient ascent based on the subgradient: in is the number of iterations, and κ≥0 is the update step size.

8. The method for optimizing secure communication of a dual IRS-assisted wireless energy-carrying communication system based on a graph neural network according to claim 7, characterized in that: In step S6, a GNN model is designed to abstract the wireless communication environment into a graph G = (V, E), where V = [IRS1, IRS2, U1, ..., U k ,E1,...,E n ] is the set of nodes in the graph, and each node v∈V corresponds to a representation vector x v , v∈V, where the node representation vector is: The node’s representation vector is received by the BS with pilot information Y U and Y E get; In GNN, the feature vector Y U and Y E After normalization and standardization, it is converted into a graph node representation vector. All representation vectors of the previous layer are used as input and the representation vector is updated layer by layer. After multiple layers, the representation vector of each node is used to design the beamforming vector and reflection coefficient. In GNN, the graph representation vector is learned through the input layer, where U k The input feature of the node is the received pilot y k , E n The input feature of the node is the received pilot y n , the input features of the IRS1 node By Y U and Y E Perform weighted averaging to obtain the input features of IRS2 node By Y U and Y E Perform weighted average to obtain; D updates the layer to update the representation vector, and gets The output result is obtained by passing it 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 wireless energy-carrying communication system based on a graph neural network according to claim 8, characterized in that: In the input layer of GNN, the pilot information y k The real and imaginary components of are separated and then converted into column vectors to obtain: Among them, the information related to the node can be embedded in the column vector: Among them, loc k Collect the user's three-dimensional coordinate parameters for information; Then Through a deep neural network layer As U k Initial representation vector of the node For energy harvesting users, the node representation vector is obtained in the same way: For an IRS node, its representation vector is formed by aggregating the representation vectors of the information collection user and the energy collection user: where ψ0(·) is an element-wise average function is a deep neural network layer; The representation vector of IRS2 node is obtained in the same way as IRS1: The representation vector obtained by the input layer Contains the feature vectors of all nodes and edges and passes them to the D update layer; The update of the representation vectors of all nodes in the update layer is based on the aggregation of the previous representation vector of the node and the representation vectors of its adjacent nodes. The specific mathematical expression is: Among them, 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 aggregation function of GNN is expressed as: Among them, ψ(·) is a function that is invariant to the input permutation, and Using deep neural networks; For the IRS1 node, the representation vector comes from: in, It is a multi-layer perceptron, which is used to integrate node representation vectors and introduce the nonlinear activation function relu; ψ1(·) is implemented using the element pooling averaging function: ψ1(x1,x2,..,x k )=mean(x1,x2,..,x k ) The representation vector of the IRS2 node is updated from the neighboring nodes, including the representation vectors from the IRS1 node and from the information collecting user and eavesdropping user nodes: in, It is an MLP connection layer, and the element-wise average function ψ1(·) is selected as the aggregation function; For the information collection user node, its representation vector is updated as follows: in, is an MLP connection layer, and the element pooling maximization function ψ2(·) is selected as the aggregation function: ψ2(x1,x2,..,x k )=max(x1,x2,..,x k ) For energy harvesting user nodes, the update of the representation vector is as follows: in, It is an MLP connection layer, and the element pool maximization function ψ2(·) is selected as the aggregation function; Updated node representation vector Passed to the output layer, the IRS1 reflection coefficient matrix is ​​finally obtained IRS2 reflection coefficient matrix and the beamforming matrix W at the BS = [w1,w2,..,w K ]∈C M×K and Z=[z1,z2,..,z N ]∈C M×N , while satisfying the unit mode constraints of v1 and v2 and the total transmission power constraint of the BS; Will represent the vector and Pass through a linear layer with 2M units respectively get: The beamforming matrix is ​​then output through a normalization layer as follows: Where W(i:j,u:v:) represents the submatrix of W, which is constructed by the indices from the i-th row to the j-th row and the u-th column to the v-th column 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 wireless energy-carrying communication system based on a graph neural network according to claim 8, characterized in that: In step S6, the GNN model is trained with the goal of minimizing the Lagrangian relaxation function P2 under the premise of a given Lagrangian multiplier, and its loss function is: Among them, L is the The loss function of the GNN model during the iteration.

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