Channel beamforming optimization method and system based on graph neural network

Abstract

The application provides a channel beamforming optimization method and system based on a graph neural network, and belongs to the field of wireless communication channel optimization. The method comprises the following steps: collecting a data set, unifying and enhancing expected link features and interference link features of CSI to obtain enhanced link features; based on energy efficiency EE maximization, a beamforming optimization model is constructed, and a beamforming vector composed of a power part and a direction part is defined based on the enhanced link features; a graph representation of a communication topology structure is constructed, features of nodes and directed edges are given, and the direction and power of the beamforming vector are learned, and then the beamforming vector is restored; a loss function is constructed, a deployment scheme is determined, the beamforming optimization model is trained, and after the training is completed, the beam of the channel is subjected to beamforming optimization. The application improves the generalization of the beamforming optimization process, while maintaining a small expansion performance loss, and improves the efficiency and practicality of the beamforming optimization.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of wireless communication channel optimization, and particularly relates to a channel beamforming optimization method and system based on a graph neural network. BACKGROUND

[0002] Various mobile intelligent terminals are everywhere in life and work, and the mobile intelligent terminals can realize remote control through networking. With the increase in the number of mobile intelligent terminals accessing the network and the increase in the amount of transmission data, the requirement for the transmission rate of data is higher and higher in order to provide better services. The spectrum resource in the wireless communication system is limited, and its scarcity is a key factor limiting the service capability of the wireless communication system. Therefore, interference management needs to be performed on the channel in the wireless communication system, so as to expand the spectrum utilization efficiency. In the interference channel system, multiple transmitting and receiving pairs share the same spectrum bandwidth, and the concentrated radio frequency signals are generally effectively managed by interference through beamforming design. Although some heuristic algorithms or convex optimization algorithms have been used to derive the (near) optimal beamforming design of various interference channel systems, the iterative framework in these algorithms leads to high computational complexity, and it is difficult to realize real-time signal processing for the time-varying wireless environment and dynamic network topology.

[0003] With the development of deep learning networks, researchers have found that neural networks can effectively simulate and "remember" the problem solving process of traditional algorithms by learning complex mapping relationships, such as from channel state information (CSI) to the optimal power allocation scheme. However, when facing the inherent topology structure of wireless networks, common fully connected multilayer perceptron and convolutional neural network often cannot meet the requirements, and it is difficult to fully grasp the structural features and relevance therein.

[0004] In the prior art, a graph neural network (GNN) is introduced to process complex network topology problems. The GNN improves data utilization efficiency through permutation invariance and equivariance characteristics, significantly reduces the dependence on large-scale labeled samples, can fully utilize the topological information contained in the topology structure, enhances the expression ability and generalization performance of the model, and at the same time, the parameter sharing and message passing mechanism of the GNN can flexibly cope with network structures of different scales and process graph data with varying numbers of nodes and edges. By abstracting a wireless network as a graph structure, taking a user or a base station as a node, and taking a channel connection as an edge, the GNN can naturally capture the topological characteristics and interaction patterns of the network, thereby reducing the energy consumption problem caused by a large amount of labeled data for a terminal. For example, a holographic beamforming method for a millimeter wave MIMO system assisted by a graph neural network is disclosed in Chinese Patent No. 202110462140.4. The method uses unsupervised learning, first collects uplink received signals of multiple users as a training data set, uses the training data set to perform unsupervised training on the graph neural network, obtains a trained graph neural network, and finally deploys the trained graph neural network in a base station. After the base station obtains uplink multi-user pilot signals, the downlink beamforming matrix is directly calculated by inputting the graph neural network. However, the above method does not consider the interference channel scenario and does not consider the channel quality of service, and has certain limitations for deployment and optimization of an actual communication system. When multiple base stations interfere with users, the channel performance is affected. In addition, in the case of dynamic changes in the number of users, the above method may not be suitable for different numbers of users, and the universality is poor. SUMMARY

[0005] In view of the above defects or deficiencies in the prior art, the present application aims to provide a channel beamforming optimization method and system based on a graph neural network (GNN), which outputs an approximately optimal beamforming matrix within a millisecond level of time through channel state information (CSI) of a multiple-input single-output (MISO) interference channel, thereby maximizing beam energy efficiency (EE) and improving spectrum resource utilization efficiency.

[0006] To achieve the above object, the embodiments of the present application adopt the following technical solutions:

[0007] In a first aspect, the embodiments of the present application provide a channel beamforming optimization method based on a graph neural network (GNN), which comprises the following steps:

[0008] Step S1, collecting a data set of a plurality of transmitter-receiver pairs;

[0009] Step S2, unify and enhance the expected link features and interference link features of the channel state information (CSI) of each signal transmitter to obtain enhanced link features, and construct a data set including a training set, a validation set and a test set based on the enhanced link features;

[0010] Step S3, construct a beamforming optimization model based on energy efficiency (EE) maximization under channel quality of service (QoS) constraints, and define a beamforming vector based on the enhanced link features, wherein the beamforming vector is composed of a power part and a direction part;

[0011] Step S4, model a multiple-input single-output (MISO) interference channel topology into a graph representation based on GNN, assign features to nodes and directed edges, and construct a direction part sub-model of the beamforming vector based on the graph representation and the GNN architecture;

[0012] Step S5, construct a power part sub-model of the beamforming vector based on a real graph attention network (GAT) architecture;

[0013] Step S6, recover the beamforming vector based on the output results of the direction part sub-model and the power part sub-model of the beamforming vector;

[0014] Step S7, construct a loss function of the beamforming optimization model, and train, validate and test the beamforming optimization model based on the training set, the validation set and the test set using an unsupervised method;

[0015] Step S8, determine a deployment scheme of the beamforming optimization model, and deploy the beamforming optimization model based on the determined deployment scheme;

[0016] Step S9, based on the trained channel beamforming optimization model, perform beamforming optimization on the channel beam based on a graph neural network.

[0017] As a preferred embodiment of the present application, in step S2, the enhanced link features are obtained by taking CSI as input, and the following formula is used when unifying and enhancing the expected link features and the interference link features:

[0018] (1)

[0019] In formula (1), h(j=k) represents the expected link features of the jth transmitter, and h(j≠k) represents the interference link features of the jth transmitter. jk (j=k) represents the expected link features of the jth transmitter, and h(j≠k) represents the interference link features of the jth transmitter. jk (j≠k) represents the interference link features of the jth transmitter. represents the enhanced link features. represents only adjusting The result of the direction part, so ; represents a connection operator, and for the transmitter , the transmitter and receiver k have:

[0020]

[0021] wherein .

[0022] As a preferred embodiment of the present application, the channel beamforming optimization model constructed in step S3 is:

[0023]

[0024] (2)

[0025] In formula (2), R k ({w i}) represents the information rate received by the kth receiver in the cell, K represents the number of transmitter-receiver pairs, represents the index set of the transmitter-receiver pair; the information symbol of the kth receiver is , is the beamforming vector carrying the information symbol, { } represents the beamforming vector of all K receivers, represents the circuit power, represents the information rate requirement of each receiver, represents the power budget of each transmitter, N T represents the number of antennas of each transmitter.

[0026] The beamforming vector is composed of a power part and a direction part , and is represented as:

[0027] (5).

[0028] As a preferred embodiment of the present application, when constructing the direction part sub-model of the beamforming vector based on the graph representation and GNN architecture in step S4, the constructed direction part sub-model includes three levels, in turn, sub-graph representation, complex graph attention layer CGAL and complex fully connected layer CFL; wherein,

[0029] The process of constructing the sub-graph representation is as follows, the MISO interference channel is represented as a graph , the graph comprises K independent subgraphs related to K transmitters; the jth subgraph is denoted as , wherein denotes a node set, denotes a directed edge set; and each node in represents a desired link and has node features , or represents an interference link and has node features ; each edge in represents an existing relationship between two endpoints without edge features; the adjacency matrix is used to specifically show the connection relationship between the nodes of each subgraph, and the adjacency matrix in

[0030] is given by the following formula:

[0031] In formula (10), is used to represent the features of the th node in , which is true for all

[0032] The process of constructing the complex graph attention layer CGAL uses CGALs; for the th ( ) CGAL, let denote the output node feature matrix, where denotes the feature dimension of each node in the th CGAL, and the input of the th CGAL is , the input of the first CGAL is , which is given by the following formula:

[0033] (11)

[0034] The number of attention heads of each CGAL is ; the coefficient of the th ( ) attention head in the th CGAL is denoted by , which is calculated by the following formula:

[0035] (12)

[0036] In formula (12), denotes a complex LeakyReLU activation function, and denote the complex learning weights related to the input node features and attention in the th CGAL, denote the set of all neighbor nodes of node .

[0037] are calculated by the following equation:

[0038] (13)

[0039] In equation (13), denotes the complex ReLu activation function, denotes the complex residual weight matrix.

[0040] The process of constructing the complex fully connected layer adopts CFLs; for the th CFL ( ), let denote the output node feature, where denotes the feature dimension of each node in the th CFL; the input of the first CFL is given by the following equation:

[0041] (14)

[0042] In equation (14), for the th CFL ( ), the node feature matrix is updated by the following way:

[0043] (15)

[0044] In equation (15), and denote the complex weight matrix and the complex bias, respectively; and the row vectors in are the same to ensure the scalability of the model to the number of transmitter-receiver pairs;

[0045] For the th CFL, the update process is given by the following equation:

[0046] (16)

[0047] In equation (16), and ; the real part of is applied to the Sigmoid activation function to obtain the output based on the complex graph attention network GAT, i.e.,

[0048] (17)

[0049] In equation (17), It is a calculation The mixing coefficient at that time.

[0050] In a preferred embodiment of the present invention, step S5 involves constructing a power sub-model of the beamforming vector based on a real-valued GAT architecture, aiming to... Mapped to It consists of three layers: a graph representation layer, a real-valued graph attention layer (RGAL), and a real-valued fully connected layer (RFL); among them,

[0051] The process of constructing the graph representation layer involves representing the MISO interference channel as a fully connected graph, denoted as . ,in Represents a set of nodes. Represents the set of directed edges; the graph contains Each node represents One expected link, and A stripe represents The first interference link; the first The characteristics of each node are determined by It indicates that, and the first The features of the strip are determined by express; The definition is as follows:

[0052] (18)

[0053] The real-valued graph attention layer RGAL is used in... Feature extraction is performed on the above to update its node features, and RGAL uses edge-assisted message passing, specifically including: assuming the use of The RGAL, for the first RGAL ( ),use and These represent the output node feature matrix and edge feature matrix, respectively. Indicates the first The feature dimension of each node in the RGAL, i.e., the th The input of each RGAL is The input to the first RGAL is given by the following formula:

[0054]

[0055] (19)

[0056] The number of attention heads per RGAL is ;No. The first RGAL The coefficient of each attention head is determined by It means, and It can be calculated using the following formula:

[0057] (20)

[0058] In equation (20), This represents the LeakyReLU activation function for real numbers. , and They respectively represent the first The input node features, edge features, and real-number learned weights related to the attention mechanism of each RGAL;

[0059] Calculated using the following formula:

[0060] (twenty one)

[0061] In equation (21), Represents the ReLU activation function for real numbers. Represents the residual weight matrix;

[0062] The process of constructing a real-number fully connected layer RFL is as follows, assuming that using The first RFL; for the first RFLs ( ),use Represents the output node features, where Indicates the first The feature dimensions of each node in each RFL; the input to the first RFL is It is given by the following formula:

[0063]

[0064] For the RFLs ( The node feature matrix is ​​updated in the following way:

[0065] (twenty two)

[0066] In equation (22), and Let these represent the real weight matrix and the real bias, respectively; and In All row vectors are set to be the same;

[0067] For the The update process for each RFL is given below:

[0068] (23)

[0069] In formula (23), and , apply the Sigmoid activation function to obtain the power output based on the real number GAT, that is:

[0070] (24)

[0071] In formula (24), is the power part of the beamforming vector, and for all , there is .

[0072] As a preferred embodiment of the present application, step S6 recovers the beamforming vector based on the output results of the beamforming vector direction part submodel and the power part submodel, including:

[0073] First, calculate ;

[0074] Then, calculate , and ;

[0075] Finally, recover and . As a preferred embodiment of the present application, step S7 updates the learnable parameters

[0076] using the following loss function:

[0077] (25) In formula (25), N represents the number of samples in the current batch, n represents the index of the nth sample in the batch,

[0078] and represents the penalty term.

[0079] As a preferred embodiment of the present application, the deployment scheme in step S8 adopts a distributed manner, and the specific steps of the distributed deployment scheme are as follows:

[0080] Step S811, the transmitter and receiver register themselves to the server of the system to build the proposed model, and report the existence of other transmitters and receivers to them and synchronize with them;

[0081] ​​​​Step S812, the transmitter processes the channel estimation to obtain the local CSI, and executes the proposed model. In particular, it exchanges OTA messages with other transmitters and receivers during power learning;

[0082] Step S813, the transmitter obtains the required beamforming vector for its receiver through the proposed model.

[0083] As a preferred embodiment of the present application, in step S812, OTA calculation is used to facilitate the implementation of the distributed deployment scheme, and the process of executing the proposed beamforming optimization model and message passing is as follows:

[0084] After local feature enhancement and direction learning, the jth node obtains ; define as the message of the jth node in the ith round of OTA message, that is:

[0085] (26)

[0086] In formula (26), in the first round of message passing, the jth node needs to broadcast its to other nodes and send to the ith node; in the ith round of message passing, the jth node needs to broadcast its to other nodes.

[0087] The total signaling overhead of OTA implementation is given by:

[0088] (27)

[0089] In formula (27), is the number of symbols of OTA messages in the ith round of message passing, which is related to .

[0090] In a second aspect, the embodiments of the present application also provide a channel beamforming optimization system based on a graph neural network, which comprises a data acquisition module, a link feature enhancement module, a model construction module, a direction sub-model construction module, a power sub-model construction module, a loss function definition module, a training and evaluation module, a deployment scheme determination module and an output module; wherein,

[0091] ​​​​​​​The data collection module is configured to collect data sets of a plurality of transmitter-receiver pairs, and to construct data sets including training sets, validation sets and test sets based on enhanced link features, and send the constructed data sets to the training and evaluation module.

[0092] The link feature enhancement module is configured to unify and enhance the expected link features and interference link features of the channel state information (CSI) of each signal transmitter to obtain enhanced link features.

[0093] The model construction module is configured to construct a beamforming optimization model based on energy efficiency (EE) maximization under channel quality of service (QoS) constraints, and define a beamforming vector based on the enhanced link features, wherein the beamforming vector is composed of a power part and a direction part, and to recover the beamforming vector based on the output results of the direction part sub-model and the power part sub-model of the beamforming vector.

[0094] The direction sub-model construction module is configured to model the MISO interference channel topology into a graph representation based on a graph neural network (GNN), assign features to nodes and directed edges, and construct a direction part sub-model of the beamforming vector based on the graph representation and the GNN architecture.

[0095] The power sub-model construction module is configured to construct a power part sub-model of the beamforming vector based on a real GAT architecture.

[0096] The loss function definition module is configured to construct a loss function of the beamforming optimization model.

[0097] The training and evaluation module is configured to train, validate and test the beamforming optimization model based on the loss function using an unsupervised method.

[0098] The deployment scheme determination module is configured to determine a deployment scheme of the beamforming optimization model, and deploy the beamforming optimization model based on the determined deployment scheme.

[0099] The output module is configured to perform beamforming optimization on the channel based on the trained channel beamforming optimization model based on the graph neural network.

[0100] The technical scheme provided by the embodiments of the present application has the following beneficial effects:

[0101] The channel beamforming optimization method and system based on the graph neural network use a hybrid maximum ratio transmission and zero forcing scheme, reconstruct the problem considered, greatly reduce the output ports of the expected mapping from the CSI vector to the beamforming vector, and improve the model performance; the scheme adopts a two-stage learning strategy, effectively separates the direction learning and power learning, so that the system can more accurately capture the complex relationship between links; by introducing a multi-head attention mechanism and a residual connection, the problem of over-smoothing in the deep network is effectively alleviated, and the accuracy of feature extraction is improved; the proposed model has good generalization in the beamforming optimization process, while maintaining a small expansion performance loss. In practical applications, the system inference time is only less than 0.1 millisecond, greatly reducing the computational overhead. In addition, the present application supports centralized and distributed deployment methods, fully proving the efficiency and practicality of the method in MISO interference channel beamforming.

[0102] Of course, implementing any product or method of the present application does not necessarily require achieving all the advantages described above at the same time. BRIEF DESCRIPTION OF DRAWINGS

[0103] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0104] Figure 1 The figure is a flowchart of the channel beamforming optimization method based on the graph neural network described in the embodiments of the present application. DETAILED DESCRIPTION

[0105] The technical solutions in the embodiments of the present application will be described clearly and completely in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all embodiments. The components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations. It should be noted that the embodiments and features in the embodiments of the present application can be combined with each other without conflict.

[0106] It should be noted that: similar reference numerals and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. In the description of the present application, the terms "first", "second", "third", "fourth" and the like are only used to distinguish the description, and cannot be understood as indicating or implying relative importance.

[0107] For the beamforming design problem of the wireless communication channel in the prior art, the embodiment of the present application provides a channel beamforming optimization method and system based on a graph neural network (GNN), which outputs an approximately optimal beamforming matrix in a millisecond level of time through the channel state information (CSI) of a multiple-input single-output (MISO) interference channel of the GNN, so as to maximize the beam energy efficiency (EE) and improve the spectrum resource utilization efficiency. The embodiment of the present application introduces a hybrid maximum ratio transmission and zero forcing scheme, a feature enhancement module, a subgraph representation, a multi-head attention mechanism and a residual connection, which not only can fully utilize the topological information in the MISO interference channel, but also exhibits adaptability to network size changes, improves message passing efficiency, enhances feature extraction capability and realizes scalability of the number of transmitting and receiving pairs. Specifically, the embodiment first models the MISO interference channel by graph representation and generates a corresponding graph representation dataset accordingly; then, the GNN is unsupervisedly learned by using a training sample and the weight obtained by the training is reserved; finally, the generalization performance, scalability and inference time of the GNN are comprehensively evaluated by using a test set, so as to ensure the efficiency and reliability of the GNN in practical applications. Numerical results verify the effectiveness of the GNN-based beamforming scheme, which has better generalization performance than traditional optimization algorithms and maintains a small extension performance loss; in terms of inference time, only less than 0.1 millisecond is required, which fully proves the efficiency and practicability of the GNN in the MISO interference channel beamforming.

[0108] As shown in Figure 1 the GNN-based channel beamforming optimization method provided by the embodiment of the present application comprises the following steps:

[0109] Step S1, collecting a dataset of a plurality of transmitter-receiver pairs.

[0110] In this step, the transmitter-receiver pairs form the transmitting and receiving pairs in the wireless communication link, and the link therebetween forms a channel. The dataset of the transmitter-receiver pairs includes channel state information (CSI) and the like.

[0111] Step S2, unifying and enhancing the expected link features and interference link features of the channel state information (CSI) of each signal transmitter to obtain enhanced link features, and constructing a dataset including a training set, a validation set and a test set based on the enhanced link features.

[0112] In this step, the channel beamforming problem involves two types of links: desired links and interfering links, corresponding to desired link features and interfering link features, respectively. These two link features result in heterogeneous graph structure data in the graph representation. However, this heterogeneity is difficult to capture during message passing. Therefore, this embodiment unifies these two types of links into a new type, namely, enhanced links, which makes the aggregation results of the subsequent direction learning module more effective. Specifically, using CSI as input, the following formula is used for feature unification and enhancement:

[0113] (1)

[0114] In equation (1), h represents the CSI from the j-th transmitter to the k-th receiver. jk (j=k) represents the desired link characteristics of the j-th transmitter, h jk (j≠k) represents the interference link characteristics of the j-th transmitter; Indicates enhanced link characteristics; Indicates only adjustment The result of the direction part, therefore ; This indicates a concatenation operator, and for the transmitter... ,transmitter And receiver k has:

[0115]

[0116] in .

[0117] By unifying and enhancing the features of desired and interfering links as described above, a more unified and information-rich feature representation is obtained, namely, enhanced link features. This lays the foundation for subsequent GNN processing and improves the model's ability to understand and process heterogeneous network structures.

[0118] Step S3: Based on maximizing energy efficiency (EE) under the channel quality-of-service (QoS) constraint, construct a beamforming optimization model; and define a beamforming vector based on enhanced link characteristics, wherein the beamforming vector consists of a power part and a direction part.

[0119] In this step, the beamforming optimization model constructed, i.e., the EE maximization problem modeled, is as follows:

[0120]

[0121] (2)

[0122] In formula (2), R k ({w i}) represents the information rate received by the kth receiver in the cell, and K represents the number of transmitter-receiver pairs. It is assumed here that the K transmitter-receiver pairs operate on the same frequency spectrum and utilize to represent the index set of the transmitter-receiver pairs. The information symbol of the kth receiver is , , , , , , , T , ,

[0123] The received signal of the kth receiver can be represented as:

[0124] (3)

[0125] Let , , then the information rate received by the kth receiver in the cell is represented as:

[0126] (4)

[0127] In formulas (3) and (4), , , ,

[0128] , , , , ,

[0129] , (5)

[0130] For the directional part, a hybrid maximum ratio transmission (MRT) and zero forcing (ZF) scheme is adopted, aiming to set the directional part as a linear combination of the MRT direction and the ZF direction, and is given by the following formula:

[0131] (6)

[0132] In formula (6), is a mixing coefficient when calculating , is the first column of , where , is defined as follows:

[0133] (7)

[0134] In formula (7), , represents a matrix composed of the CSI related to the jth transmitter.

[0135] Based on formulas (2)-(7), can be expressed as:

[0136] (8)

[0137] Then, the EE maximization problem, i.e., the constructed beamforming optimization model, is re-expressed as:

[0138] (9)

[0139] Step S4, the MISO interference channel topology is modeled into a graph representation based on a graph neural network (GNN), features are given to nodes and directed edges, and based on the graph representation and the GNN architecture, a directional part submodel of the beamforming vector is constructed.

[0140] In this step, the GNN architecture used to construct the direction of the beamforming vector is a complex number architecture. The construction process includes three levels, in order: subgraph representation, complex graph attention layer (CGAL), and complex fully-connected layer (CFL). The directional learning module based on the complex GNN aims to map the enhanced link features to .

[0141] wherein the process of constructing the subgraph representation is as follows: the MISO interference channel is represented as a graph , the graph contains K independent subgraphs related to K transmitters. The jth subgraph is represented as , where represents a node set, represents a directed edge set. Specifically, each node in the node set or represents an interference link and has node features as ; Each edge in the existing relationship between the two end points without edge features. Adjacency matrix is used to specifically show the connection relationship between the nodes of each subgraph, and Adjacency matrix in is given by the following formula:

[0142] (10)

[0143] In formula (10), use to represent the features of the th node in , which is true for all .

[0144] The process of constructing the complex graph attention layer CGAL uses CGAL. For the th ( ) CGAL, use to represent the output node feature matrix, where represents the feature dimension of each node in the th CGAL. That is, the input of the th CGAL is . In particular, the input of the first CGAL is , which is given by the following formula:

[0145] (11)

[0146] The number of attention heads of each CGAL is . The coefficient of the th ( ) attention head in the th CGAL is denoted by , which is calculated by the following formula:

[0147] (12)

[0148] In formula (12), represents a complex LeakyReLU activation function, and respectively represent complex learning weights related to the input node features and attention in the th CGAL, represents the set of all neighbor nodes of node .

[0149] Then, is calculated by the following equation:

[0150] (13)

[0151] In equation (13), denotes the complex ReLu activation function, denotes the complex residual weight matrix. The residual weight is used to realize the residual connection to alleviate the over-smoothing problem, which is achieved by adding the linear mapping of the original node feature (i.e. ) to the extracted node feature.

[0152] The process of constructing the complex fully connected layer adopts complex fully connected layers (CFLs). For the -th CFL ( ), let denote the output node feature, where denotes the feature dimension of each node in the -th CFL. The input of the first CFL is given by the following equation:

[0153] (14)

[0154] In equation (14), for the -th CFL ( ), the node feature matrix is updated by the following way:

[0155] (15)

[0156] In equation (15), and denote the complex weight matrix and the complex bias, respectively. Note that the row vectors in are the same to guarantee the scalability of the model to the number of transmitter-receiver pairs. In addition, a complex batch normalization layer is added after each CFL to prevent overfitting and enhance the convergence behavior.

[0157] For the -th CFL, the update process is given by the following equation:

[0158] (16)

[0159] In equation (16), and . Then, the real part of is applied with a Sigmoid activation function to obtain the output based on the complex graph attention network (GAT), i.e.,

[0160] (17)

[0161] In formula (17), is a mixing coefficient when calculating .

[0162] Through the above three levels of learning, the construction of the beamforming vector direction part submodel is completed.

[0163] Step S5, constructing the power part submodel of the beamforming vector based on the real GAT architecture.

[0164] In this step, the construction of the power part submodel aims to map to , including three levels, which are in turn a graph representation layer, a real graph attention layer (RGAL) and a real fully-connected layer (RFL).

[0165] Among them, the process of constructing the graph representation layer represents the MISO interference channel as a fully connected graph, denoted as , where represents a node set, represents a directed edge set. There are nodes in the graph, representing expected links, and edges, representing interference links. The feature of the th node is represented by , and the feature of the th edge is represented by . The definition of

[0166] (18)

[0167] The real graph attention layer RGAL is used to perform feature extraction on to update its node features. Unlike CGAL, which only performs message passing based on node features, RGAL adopts edge-aided message passing.

[0168] Suppose RGALs are used. For the th RGAL ( ), the output node feature matrix and edge feature matrix are represented by and respectively, where represents the The feature dimension of each node in the RGAL. That is, the ... The input of each RGAL is Specifically, the input for the first RGAL is given as follows:

[0169]

[0170] (19)

[0171] The number of attention heads per RGAL is . No. The first RGAL One attention point ( The coefficient of ) is from It is indicated that the following formula is used for calculation:

[0172] (20)

[0173] In equation (20), This represents the LeakyReLU activation function for real numbers. , and Respectively represent the first The input node features, edge features, and real-valued learned weights related to the attention mechanism of each RGAL.

[0174] Then, Calculated using the following formula:

[0175] (twenty one)

[0176] In equation (21), Represents the ReLU activation function for real numbers. This represents the residual weight matrix.

[0177] The process of constructing a real-number fully connected layer RFL is as follows, assuming that using The first RFL. For the first RFL ( ),use Represents the output node features, where Indicates the first The feature dimensions of each node in each RFL. The input to the first RFL is... The following is given:

[0178]

[0179] For the RFLs ( The node feature matrix is ​​updated in the following way:

[0180] (twenty two)

[0181] In equation (22), and These represent the real weight matrix and the real bias, respectively. Note that... In All row vectors were set to be identical. Additionally, a real-number batch normalization layer was added after each RFL.

[0182] For the The update process for each RFL is given below:

[0183] (twenty three)

[0184] In equation (23), and Then, regarding Applying the sigmoid activation function, we obtain the power output based on the real number GAT, i.e.:

[0185] (twenty four)

[0186] In equation (24), It is the power component of the beamforming vector, and for all They all .

[0187] Through the above three levels of learning, the sub-model of beamforming vector power is constructed.

[0188] Step S6: Based on the output results of the beamforming vector direction sub-model and the power sub-model, recover the beamforming vector.

[0189] In this step, the goal of solving the EE maximization problem is to find the beamforming vector. Therefore, the results after learning the direction and power are then reconstructed into a beamform vector. Specifically, this embodiment first uses... Calculate Then use , and Calculate Ultimately, using and Recover .

[0190] Step S7: Construct the loss function of the beamforming optimization model. The beamforming optimization model is trained, validated, and tested using an unsupervised method based on the training set, validation set, and test set.

[0191] In this step, when training, first design parameters such as total number of rounds E and batch size N, initialize model parameters and optimizers based on the designed parameters, and load the training set; start training, set the current round e = 1 when training for the first time; when e ≤ E, randomly extract N samples into the beamforming optimization model, calculate the loss according to the loss function and perform gradient backpropagation, update the model weight and other parameters, after traversing all samples, e = e + 1, and then judge the size of e and E; when e ≥ E, the training is completed, the model is evaluated on the test set, and the training is ended.

[0192] Unsupervised method is used for training, which does not require a large amount of labeled data, reducing the cost of data labeling. For a batch containing samples, for example , where represents the index of the i-th sample in the batch, so the following loss function is used to update the learnable parameters : : (25)

[0193] In formula (25), a penalty term is added to improve the constraint satisfaction rate.

[0194] In this step, in a specific embodiment, the number of transmitter-receiver pairs is set to seven groups. The number of transmitter-receiver pairs is set to . The number of antennas for each transmitter is set to . The power budget and constant circuit power are set to W and W, respectively. The rate requirement of each receiver is set to 1 bit / s / Hz. Small-scale fading uses the Rayleigh fading model. The average signal-to-noise ratio is set to 10 dB. Each training sample includes channel vectors, i.e. , and each validation or test sample includes channel vectors and a label indicating the corresponding maximum EE.

[0195] The dataset of the transmitter-receiver pair is divided into two types:

[0196] Type A: This type of dataset contains 100,000 samples, which are divided into training set, validation set and test set in the ratio of 0.96:0.02:0.02; including the following 4 groups:

[0197] Group 1: 4 antennas, 2 transceiver pairs, 100,000 samples;

[0198] Group 2, 4 antennas, 4 transceiver pairs, 100000 samples;

[0199] Group 3, 4 antennas, 6 transceiver pairs, 100000 samples;

[0200] Group 4, 4 antennas, 8 transceiver pairs, 100000 samples.

[0201] Type B: This type of dataset contains only 2,000 test samples, which is used to test the performance of the model on unseen problem scales. It includes the following 3 groups:

[0202] Group 5, 4 antennas, 3 transceiver pairs, 2000 samples;

[0203] Group 6, 4 antennas, 5 transceiver pairs, 2000 samples;

[0204] Group 7, 4 antennas, 7 transceiver pairs, 2000 samples.

[0205] The learning rate is initialized to Adam is used as the optimizer during the training phase. The batch size is set to 64, and the model is trained for 500 epochs. The learnable weights with the best performance are used as the training results.

[0206] The following indicators are used to evaluate the model from the perspectives of model effectiveness and task requirements, including:

[0207] Optimal performance: The average ratio of the EE of the feasible solution obtained by the deep learning model to the maximum EE on the test set, where the test set has the same parameter settings as the training set;

[0208] Scalable performance: The average ratio of the EE of the feasible solution obtained by the deep learning model to the maximum EE on the test set, where the test set has different parameter settings from the training set;

[0209] Feasibility rate: The percentage of problems for which the deep learning model obtains a feasible solution;

[0210] Inference time: The average running time required by the deep learning model to calculate a feasible solution given a channel vector.

[0211] The following table shows the performance of the deep learning model on the test set: Results of ablation experiments on message passing, residual connection, subgraph representation, and feature enhancement in the proposed model under the scenario (Dataset No. 3). All five mechanisms can improve the optimal performance and feasibility rate of the deep learning model with only a limited increase in inference time. In addition, in this example, the proposed model can achieve an optimal performance of over 94% in less than 1 / 10 of a millisecond under the computer configuration of the present patent, which is much more efficient than traditional convex optimization-based algorithms.

[0212] First: message passing is ×; residual connection is ×; subgraph representation is ×; feature enhancement is ×; optimal performance is 84.93%; feasibility rate is 89.35%; inference time is 0.0501 ms;

[0213] Second: message passing is √; residual connection is ×; subgraph representation is ×; feature enhancement is ×; optimal performance is 85.75%; feasibility rate is 95.10%; inference time is 0.0674 ms;

[0214] Third: message passing is √; residual connection is √; subgraph representation is ×; feature enhancement is ×; optimal performance is 86.70%; feasibility rate is 95.85%; inference time is 0.0684 ms;

[0215] Fourth: message passing is √; residual connection is √; subgraph representation is √; feature enhancement is ×; optimal performance is 93.25%; feasibility rate is 100%; inference time is 0.0804 ms;

[0216] Fifth: message passing is √; residual connection is √; subgraph representation is √; feature enhancement is √; optimal performance is 94.10%; feasibility rate is 100%; inference time is 0.0804 ms.

[0217] The following paragraphs evaluate the optimality, scalability, and feasibility rate of the proposed model. As shown in the following paragraphs, the models trained using (Dataset No. 1), (Dataset No. 2), and (Dataset No. 3) are tested under (Dataset Nos. 1 to 7). That is, the proposed model is tested under the transmitter-receiver pair scenario that is not seen in some training sets. It is observed that when , the model can achieve good optimality and feasibility rate. In terms of scalability, the model performs well when is close to . Such results are attractive because they allow the operator to directly activate / deactivate a few transmitter-receiver pairs in the interference channel system without retraining the model, which greatly improves flexibility.

[0218] and Optimal performance / Scalable performance is 99.92%, Feasibility rate is 100%. and Optimal performance / Scalable performance is 83.28%, Feasibility rate is 100%.

[0219] and Optimal performance / Scalable performance is 94.91%, Feasibility rate is 99.70%.

[0220] and Optimal performance / Scalable performance is 93.25%, Feasibility rate is 99.95%.

[0221] and Optimal performance / Scalable performance is 86.99%, Feasibility rate is 100%.

[0222] and Optimal performance / Scalable performance is 80.33%, Feasibility rate is 81.80%.

[0223] and Optimal performance / Scalable performance is 89.02%, Feasibility rate is 99.51%.

[0224] and Optimal performance / Scalable performance is 80.02%, Feasibility rate is 99.75%.

[0225] and Optimal performance / Scalable performance is 79.83%, Feasibility rate is 82.00%.

[0226] and Optimal performance / Scalable performance is 91.61%, Feasibility rate is 58.90%.

[0227] and Optimal performance / Scalable performance is 90.45%, Feasibility rate is 100%.

[0228] and​​ When the optimal performance / scalable performance is 73.02%, the feasibility rate is 75.55%.

[0229] And When the optimal performance / scalable performance is 89.66%, the feasibility rate is 36.70%.

[0230] And When the optimal performance / scalable performance is 94.10%, the feasibility rate is 100%.

[0231] And When the optimal performance / scalable performance is 66.48%, the feasibility rate is 65.30%.

[0232] And When the optimal performance / scalable performance is 86.84%, the feasibility rate is 23.95%.

[0233] And When the optimal performance / scalable performance is 93.14%, the feasibility rate is 98.90%.

[0234] And When the optimal performance / scalable performance is 61.24%, the feasibility rate is 48.75%.

[0235] And When the optimal performance / scalable performance is 83.32%, the feasibility rate is 12.50%.

[0236] And When the optimal performance / scalable performance is 92.42%, the feasibility rate is 51.00%.

[0237] Step S8, determine the deployment scheme of the beamforming optimization model, and deploy the beamforming optimization model based on the determined deployment scheme.

[0238] In this step, the deployment scheme can be implemented in a centralized or distributed manner.

[0239] When the centralized deployment scheme is adopted, all the transmitters will feed back the collected CSI to a computing center, and share the parameters of the model in the training stage.

[0240] When using a distributed deployment scheme, each transmitter only collects its own relevant CSI. Transmitters exchange messages to train their respective models locally. Distributed deployment can be achieved through over-the-air (OTA) computing. With a distributed implementation, a pair of transmitters and receivers can join a jamming channel system via a "plug-and-play" protocol. The scalability of the number of transmitters and receivers is crucial for achieving "plug-and-play" implementation, as the proposed model does not need to be rebuilt or retrained. The specific steps of the distributed deployment scheme are as follows:

[0241] In step S811, the transmitter and receiver register themselves with the server of the system to build the proposed model and report their existence to other transmitter and receiver pairs and synchronize with them.

[0242] In step S812, the transmitter processes channel estimation to obtain its local CSI and executes the proposed model. Specifically, it exchanges OTA messages with other transmitters and receivers during power learning.

[0243] In step S813, the transmitter obtains the required beamforming vector for its receiver using the proposed model.

[0244] In step S812, OTA computation is used to facilitate the implementation of the distributed deployment scheme. The process of executing the proposed beamforming optimization model and message passing is as follows:

[0245] After performing feature enhancement and orientation learning locally, the first Each node obtains .definition For the j-th node in the th... The messages in the OTA message round, namely:

[0246] (26)

[0247] In equation (26), specifically, in the first round of message passing, the first... Each node needs to send to other nodes. Each node broadcasts its and will Send to the The node. At the... wheel( In message passing, the first Each node needs to send to other nodes. Each node broadcasts its This is because edge features are not updated in the power learning module based on real GAT.

[0248] This message passing can be realized over wired or wireless channels. The difference lies in the signal processing to recover the OTA messages. However, the signaling overhead due to exchanging the OTA messages is similar, including two parts, i.e., the node features in the first round and the edge features in the second round. Therefore, the total signaling overhead of the OTA implementation is given by

[0249] (27)

[0250] In equation (27), is the number of symbols of the OTA messages in the i-th round, and Note that to reduce the signaling overhead, one can set which will lead to single-valued OTA message passing. Intuitively, single-valued distributed learning can degrade the learning performance.

[0251] In step S9, the channel beamforming optimization model trained is used to perform beamforming optimization on the channel based on the graph neural network.

[0252] Based on the same idea, the embodiment of the present application also provides a channel beamforming optimization system based on a graph neural network, which comprises a data acquisition module, a link feature enhancement module, a model construction module, a direction sub-model construction module, a power sub-model construction module, a loss function definition module, a training and evaluation module, a deployment scheme determination module and an output module; wherein,

[0253] The data acquisition module is used to acquire a data set of a plurality of transmitter-receiver pairs; and is also used to construct a data set comprising a training set, a validation set and a test set based on enhanced link features, and send the constructed data set to the training and evaluation module;

[0254] The link feature enhancement module is used to unify and enhance the expected link features and interference link features of the channel state information (CSI) of each signal transmitter to obtain enhanced link features;

[0255] The model construction module is used to construct a beamforming optimization model based on energy efficiency (EE) maximization under channel quality of service (QoS) constraints, and define a beamforming vector based on the enhanced link features, wherein the beamforming vector is composed of a power part and a direction part; and is also used to recover the beamforming vector based on the output results of the direction part sub-model and the power part sub-model of the beamforming vector;

[0256] The direction sub-model construction module is used to model the MISO interference channel topology into a graph representation based on a graph neural network (GNN), give node and directed edge features, and construct a direction part sub-model of the beamforming vector based on the graph representation and the GNN architecture.​​

[0257] The power sub-model construction module is configured to construct a power part sub-model of the beamforming vector based on a real GAT architecture;

[0258] The loss function definition module is configured to construct a loss function of the beamforming optimization model;

[0259] The training and evaluation module is configured to train, verify and test the beamforming optimization model based on the loss function by using an unsupervised method;

[0260] The deployment scheme determination module is configured to determine a deployment scheme of the beamforming optimization model, and deploy the beamforming optimization model based on the determined deployment scheme;

[0261] The output module is configured to perform beamforming optimization on the channel based on the trained channel beamforming optimization model and the graph neural network.

[0262] The modules in the embodiment are implemented by a processor, and a memory is appropriately added when storage is needed. The processor can be, but is not limited to, a microprocessor (MPU), a central processing unit (CPU), a network processor (NP), a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. The memory can include a random access memory (RAM) and can also include a non-volatile memory (NVM), such as at least one disk memory. Optionally, the memory can also be at least one storage device located away from the aforementioned processor.

[0263] In the above embodiments, all or part can be realized by software, hardware, firmware or any combination thereof. When realized by software, all or part can be realized in the form of a computer program product. The computer program product includes one or more computer instructions. When loaded and executed by a computer, all or part generates the flow or function described in the embodiments of the present application. The computer can be a general-purpose computer, a special-purpose computer, a computer network or other programmable device. The computer instructions can be stored in a computer readable storage medium or transferred from one computer readable storage medium to another, for example, the computer instructions can be transferred from one website, computer, server or data center to another through wired (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (such as infrared, wireless, microwave, etc.) mode.

[0264] In addition, it should be noted that the channel beamforming optimization system based on the graph neural network and the channel beamforming optimization method based on the graph neural network described in the embodiments are corresponding. The description and limitation of the method also apply to the system, which will not be repeated here.

[0265] As can be seen from the above scheme, the channel beamforming optimization method and system based on the graph neural network provided by the embodiments of the present application use a hybrid maximum ratio transmission and zero forcing scheme, reconstruct the problem considered, greatly reduce the output ports of the expected mapping from the CSI vector to the beamforming vector, and improve the model performance; The two-stage learning strategy is adopted, which effectively separates the direction learning and power learning, so that the system can more accurately capture the complex relationship between links; By introducing the multi-head attention mechanism and residual connection, the over-smoothing problem in the deep network is effectively alleviated, and the accuracy of feature extraction is improved; The proposed model has good generalization in the beamforming optimization process, while maintaining a small expansion performance loss. In practical applications, the system inference time only needs less than 0.1 milliseconds, greatly reducing the computational overhead. In addition, the present application supports centralized and distributed deployment, fully proving the efficiency and practicality of the method in MISO interference channel beamforming.

[0266] The above description is only the preferred embodiment of the present application and the explanation of the technical principles applied, and is not intended to limit the scope of the application claimed, but only represents the preferred embodiment of the present application. Those skilled in the art should understand that the scope of the application involved in the present application is not limited to the technical solutions formed by the specific combinations of the above technical features, and should also cover other technical solutions formed by the combinations of the above technical features or their equivalent features without departing from the inventive concept. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of the present application.

Claims

1. A channel beamforming optimization method based on graph neural networks, characterized in that, The method includes the following steps: Step S1: Collect datasets of several transmitter-receiver pairs; Step S2: Unify and enhance the expected link features and interference link features of the Channel State Information (CSI) of each signal transmitter to obtain enhanced link features. Based on the enhanced link features, construct a dataset including a training set, a validation set, and a test set. The enhanced link features obtained in step S2, using CSI as input, are unified and enhanced using the following formula: （1） In equation (1), h represents the CSI from the j-th transmitter to the k-th receiver. jk (j=k) represents the desired link characteristics of the j-th transmitter, h jk (j≠k) represents the interference link characteristics of the j-th transmitter; Indicates enhanced link characteristics; Indicates only adjustment The result of the direction part, therefore ; This indicates a concatenation operator, and for the transmitter... ,transmitter And receiver k has: in, H denotes the conjugate transpose of the matrix; Step S3: Based on maximizing energy efficiency (EE) under channel service quality constraints, construct a beamforming optimization model and define a beamforming vector based on enhanced link characteristics. The beamforming vector consists of a power component and a direction component. Step S4: Model the multi-input single-output MISO interference channel topology as a graph representation based on graph neural network (GNN), assign node and directed edge features, and construct the direction sub-model of beamforming vector based on graph representation and GNN architecture. Step S5: Construct a power sub-model of beamforming vectors based on the real graph attention network GAT architecture; Step S6: Based on the output results of the beamforming vector direction sub-model and the power sub-model, recover the beamforming vector; Step S7: Construct the loss function of the beamforming optimization model. The beamforming optimization model is trained, validated, and tested using an unsupervised method based on the training set, validation set, and test set. Step S8: Determine the deployment scheme of the beamforming optimization model, and deploy the beamforming optimization model based on the determined deployment scheme. Step S9: Based on the trained and mature channel beamforming optimization model, the channel beam is optimized using a graph neural network.

2. The channel beamforming optimization method based on graph neural networks according to claim 1, characterized in that, The channel beamforming optimization model constructed in step S3 is as follows: （2） In equation (2), R k ({w i }) represents the information rate received by the k-th receiver in the cell, where K represents the number of transmitter-receiver pairs. This represents the set of indices for the transmitter-receiver pair; the information symbol for the k-th receiver is... , For carrying Beamforming vector of information symbols, { } represents the beamforming vectors for all K receivers. Indicates circuit power. This indicates the information rate requirement for each receiver. N represents the power budget for each transmitter. T Indicates the number of antennas for each transmitter; The beamforming vector From the power section and direction part Composition, represented as: （5）。 3. The channel beamforming optimization method based on graph neural networks according to claim 2, characterized in that, In step S4, when constructing the directional sub-model of the beamforming vector based on graph representation and GNN architecture, the constructed directional sub-model includes three layers: subgraph representation, complex graph attention layer CGAL, and complex fully connected layer CFL; among them, The process of constructing the subgraph representation is as follows: the MISO interference channel is represented as a graph. ,picture It contains K independent subgraphs associated with K transmitters; the j-th subgraph is represented as ,in Represents a set of nodes. Represents a directed edge set; and Each node in the diagram represents the desired link and has node characteristics. , or indicates an interfering link and has node characteristics as ; Each edge in the adjacency matrix represents the existing relationship between two endpoints, without edge features; Used to specifically illustrate the connection relationships between nodes in each subgraph, and Adjacency matrix in Given by the following formula: （10） In equation (10), the following is used express The Middle The characteristics of each node, for all Established; The process of constructing the complex graph attention layer CGAL uses The CGAL; for the CGAL... indivual( CGAL, using Represents the output node feature matrix, where Indicates the first The feature dimension of each node in a CGAL, the first The input of CGAL is The first CGAL input is It is given by the following formula: （11） The number of attention heads per CGAL is ;No. The first CGAL indivual( The coefficient of attention head is used It is expressed as being calculated using the following formula: （12） In equation (12), This represents the LeakyReLU activation function for complex numbers. and Respectively represent the first Complex learned weights related to input node features and attention in each CGAL. Represents a node The set of all neighboring nodes; Calculated using the following formula: （13） In equation (13), This represents the complex ReLU activation function. Represents the complex residual weight matrix; The process of constructing a complex fully connected layer adopts The first CFL; for the first CFLs ( ),use Represents the output node features, where Indicates the first The feature dimensions of each node in each CFL; the input of the first CFL Given by the following formula: （14） In equation (14), for the first... CFLs ( The node feature matrix is ​​updated in the following way: （15） In equation (15), and Let these represent the complex weight matrix and the complex bias, respectively; and In All row vectors are identical to ensure the scalability of the model for the number of transmitter-receiver pairs; For the The update process for each CFL is given by the following formula: （16） In equation (16), and ;right Applying the sigmoid activation function to the real part of the complex graph attention network (GAT) yields the output: （17） In equation (17), It is a calculation The mixing coefficient at that time.

4. The channel beamforming optimization method based on graph neural networks according to claim 3, characterized in that, Step S5 involves constructing a power sub-model of the beamforming vector based on the real-valued GAT architecture, aiming to... Mapped to It consists of three layers: a graph representation layer, a real-valued graph attention layer (RGAL), and a real-valued fully connected layer (RFL); among them, The process of constructing the graph representation layer involves representing the MISO interference channel as a fully connected graph, denoted as . ,in Represents a set of nodes. Represents the set of directed edges; the graph contains Each node represents One expected link, and A stripe represents The first interference link; the first The characteristics of each node are determined by It indicates that, and the first The characteristics of the strip are determined by express; The definition is as follows: （18） The real-valued graph attention layer RGAL is used in... Feature extraction is performed on the above to update its node features, and RGAL uses edge-assisted message passing, specifically including: assuming the use of The RGAL, for the first RGAL ( ),use and These represent the output node feature matrix and edge feature matrix, respectively. Indicates the first The feature dimension of each node in the RGAL, i.e., the th The input of each RGAL is The input to the first RGAL is given by the following formula: （19） The number of attention heads per RGAL is ;No. The first RGAL The coefficient of each attention head is determined by It means, and It can be calculated using the following formula: （20） In equation (20), This represents the LeakyReLU activation function for real numbers. , and Respectively represent the first The input node features, edge features, and real-number learned weights related to the attention mechanism of each RGAL; Calculated using the following formula: （21） In equation (21), Represents the ReLU activation function for real numbers. Represents the residual weight matrix; The process of constructing a real-number fully connected layer RFL is as follows, assuming that using The first RFL; for the first RFLs ( ),use Represents the output node features, where Indicates the first The feature dimensions of each node in each RFL; the input to the first RFL is It is given by the following formula: For the RFLs ( The node feature matrix is ​​updated in the following way: （22） In equation (22), and Let these represent the real weight matrix and the real bias, respectively; and In All row vectors are set to be the same; For the The update process for each RFL is given below: （23） In equation (23), and ,right Applying the sigmoid activation function, we obtain the power output based on the real number GAT, i.e.: （24） In equation (24), It is the power component of the beamforming vector, and for all They all .

5. The channel beamforming optimization method based on graph neural networks according to claim 4, characterized in that, Step S6, based on the output results of the beamforming vector direction sub-model and the power sub-model, recovers the beamforming vector, including: First use Calculate ; Then use , and Calculate ; Ultimately, using and Recover .

6. The channel beamforming optimization method based on graph neural network (GNN) according to claim 5, characterized in that, Step S7 uses the following loss function to update the learnable parameters. : （25） In equation (25), N represents the number of samples in the current batch, and n represents the index of the nth sample in the batch. This indicates a penalty.

7. The channel beamforming optimization method based on graph neural networks according to claim 1, characterized in that, The deployment scheme in step S8 adopts a distributed approach. The specific steps of the distributed deployment scheme are as follows: In step S811, the transmitter and receiver register themselves with the server of the system to build the proposed model and report their existence to other transmitter and receiver pairs and synchronize with them. In step S812, the transmitter processes channel estimation to obtain local CSI and executes the proposed model; the transmitter's model exchanges OTA messages with other transmitters and receivers during power learning. In step S813, the transmitter obtains the required beamforming vector for its receiver using the proposed model.

8. The channel beamforming optimization method based on graph neural networks according to claim 7, characterized in that, In step S812, OTA computation is used to facilitate the implementation of the distributed deployment scheme. The proposed beamforming optimization model and message passing process are as follows: After performing feature enhancement and orientation learning locally, the first Each node obtains ;definition For the j-th node in the th order The messages in the OTA message round, namely: （26） In equation (26), in the first round of message passing, the first... Each node needs to send to other nodes. Each node broadcasts its and will Send to the The node; at the node; wheel( In message passing, the first Each node needs to send to other nodes. Each node broadcasts its ; The total signaling overhead of OTA implementation is given below: （27） In equation (27), It is the first The number of symbols in an OTA message during round-robin messaging, and Related.

9. A channel beamforming optimization system based on graph neural networks, characterized in that, The system for performing the method according to any one of claims 1 to 8, comprising: a data acquisition module, a link feature enhancement module, a model building module, a direction sub-model building module, a power sub-model building module, a loss function definition module, a training and evaluation module, a deployment scheme determination module, and an output module; wherein... The data acquisition module is used to acquire datasets of several transmitter-receiver pairs; it is also used to construct a dataset including a training set, a validation set, and a test set based on enhanced link features, and send the constructed dataset to the training and evaluation module. The link feature enhancement module is used to unify and enhance the expected link features and interference link features of the Channel State Information (CSI) of each signal transmitter to obtain enhanced link features. The model building module is used to construct a beamforming optimization model based on maximizing energy efficiency (EE) under channel service quality constraints, and to define a beamforming vector based on enhanced link characteristics, wherein the beamforming vector consists of a power component and a directional component; it is also used to recover the beamforming vector based on the output results of the directional component sub-model and the power component sub-model of the beamforming vector. The directional sub-model building module is used to model the topology of the MISO interference channel into a graph representation based on a graph neural network (GNN), assign node and directed edge features, and construct a directional sub-model of the beamforming vector based on the graph representation and GNN architecture. The power sub-model construction module is used to construct a power part sub-model of the beamforming vector based on the real GAT architecture; The loss function definition module is used to construct the loss function of the beamforming optimization model; The training and evaluation module is used to train, validate, and test the beamforming optimization model using an unsupervised method based on a loss function. The deployment scheme determination module is used to determine the deployment scheme of the beamforming optimization model and to deploy the beamforming optimization model based on the determined deployment scheme. The output module is used to optimize the beamforming of the channel based on a trained and mature channel beamforming optimization model and a graph neural network.

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