CN117560043B - Non-cellular network power control method based on graph neural network - Google Patents

Abstract

A cellular network-free power control method based on a graph neural network includes the following steps: adopting a time division duplex operation mode, utilizing the cellular network channel reciprocity, and performing cellular network channel estimation through pilot information sent in the uplink; Through the maximum ratio precoding scheme based on channel estimation values, the transmission symbols in the downlink data transmission stage are precoded, and then conjugate beamforming technology is used to send signals to users; the minimum user communication rate of the downlink is maximized. module, and then convert the problem of maximizing the minimum user communication rate of the downlink into a graph optimization problem, and use a power control algorithm based on a graph neural network to solve it to achieve an increase in the downlink communication rate.

Description

A cellular network power control method based on graph neural network

Technical Field

The present invention relates to the field of wireless communication technology, and in particular to a non-cellular network power control method based on graph neural network.

Background Art

In the traditional Multiple-Input Multiple-Output (MIMO) system, a large number of antennas are concentrated in the base station, and the user terminals are distributed around the base station, which has the advantages of low data sharing overhead and front-end transmission requirements. However, the distributed MIMO system can provide uniform and good service to all user terminals by taking advantage of the independent fading of the signal, thereby achieving the purpose of obtaining high diversity gain against shadow fading. The cellless network is a deconstruction of the traditional MIMO system. A large number of antennas are distributed in different locations over a wide area, and the users are also distributed over this wide area. These antennas are called access points. In theory, each user can communicate with each access point. By relying on time division duplex operation, with the help of the fronthaul network and central processing unit operating in the same time-frequency resources, a large number of geographically dispersed antennas serve a smaller number of user terminals together. The central processing unit sends downlink data and power control coefficients to the access point, and the access point feeds back the data received from the user terminal in the uplink to the central processing unit through the fronthaul link. All access points are connected to the central processor through the backhaul link for phase-coherent collaboration, serving all users simultaneously on the same time-frequency resources.

Methods based on deep learning are widely used to solve problems in the field of wireless communications and always achieve the desired results. Existing non-cellular network power control technologies usually use optimization methods, which will increase the demand for computing resources when processing large-scale data. Deep learning models may be more suitable for processing large-scale data due to their automatic feature learning and end-to-end learning characteristics, but some conventional neural network architectures, such as multi-layer perceptrons, usually produce poor performance in large-scale networks. Graph neural networks can utilize the topological structure of wireless communications to effectively solve resource allocation problems.

In summary, optimizing power control without cells using graph neural networks will produce the desired results.

Summary of the invention

According to the technical problems raised above, the technical means adopted by the present invention are as follows: a non-cellular network power control method based on graph neural network, comprising the following steps:

S1. Using the time division duplex operation mode, utilizing the reciprocity of the non-cellular network channel, and estimating the non-cellular network channel through the pilot information sent in the uplink;

S2, precoding the transmission symbols in the downlink data transmission phase through a maximum ratio precoding scheme based on the channel estimation value, and then sending the signal to the user using the conjugate beamforming technology;

S3. Model the problem of maximizing the minimum user communication rate of the downlink, and then transform the problem of maximizing the minimum user communication rate of the downlink into a corresponding graph optimization problem, and use a power control algorithm based on a graph neural network to solve it, so as to achieve an improvement in the downlink communication rate.

Further: the process of adopting the time division duplex operation mode, utilizing the reciprocity of the non-cellular network channel, and performing non-cellular network channel estimation through the pilot information sent in the uplink is as follows:

S11. In the non-cellular network system under consideration, there are M single-antenna access points and K single-antenna users. Each access point is connected to the central processor via a backhaul link. The M access points serve K users under the same time and frequency resources.

In the non-cellular network system, the time division duplex operation mode is adopted, and the channel reciprocity is utilized. In the uplink training phase, all users send pilot sequences to the access point, and the channel estimation to all users is performed at each access point. The acquired channel state information is used for uplink data transmission decoding and downlink data transmission encoding.

The channel coefficient between the kth user and the mth access point is expressed as express:

Where, m = 1,…,M, k = 1,..,K, is the large-scale fading coefficient between access point m and user k , which mainly reflects the impact of path loss and shadow fading on the channel. is the small-scale fading coefficient, each small-scale fading coefficient are all independent and identically distributed, represents a complex Gaussian random variable with mean 0 and variance 1;

Large-scale fading coefficients via path loss and uncorrelated log-normal shadowing To model:

in: represents the path loss, With standard deviation and The shadow fading of It can be expressed as follows:

in: , is the carrier frequency, is the antenna height of the access point, is the user's antenna height, is the distance from the mth access point to the kth user, and is the reference distance;

Shadow fading is interrelated and a two-component model is used to calculate the shadow fading coefficients: :

in, , , are two independent random variables, represents a Gaussian random variable with mean 0 and variance 1, , is a parameter;

and The covariance function of is:

in, It is access point and The distance between access points, It is Users and The distance between users, is the correlation distance;

By channel conditions , we get the pilot information sent by user k received by the mth access point in the uplink for:

in, is the uplink pilot transmission duration, is the pilot sequence used by the kth user, where is a random variable, , Representation in the complex domain dimensional vector, . is the Euclidean norm, is the normalized signal-to-noise ratio of each pilot, is the additional noise at the mth access point;

Based on the received pilot sequence, the mth access point performs channel estimation. exist Projection on for:

in for The conjugate transpose of represents the conjugate transpose, Indicates users, where k and are all included in the user set K, For users A random variable, .

S12, according to the minimum mean square error criterion, the channel coefficient Estimated to be:

in, Indicates the distance from the mth access point to the The large-scale fading coefficient between users, represents the mean, Indicates conjugation.

Further: the process of precoding the transmission symbols in the downlink data transmission phase by using the maximum ratio precoding scheme based on the channel estimation value and then sending the signal to the user by using the conjugate beamforming technology is as follows:

S21. In the downlink data transmission phase, the access point m uses beamforming to precode the data to be transmitted to the user k according to the channel estimation result:

in, is the symbol sent to the kth user, and , is the normalized downlink signal-to-noise ratio, is the power control coefficient of the downlink from the mth access point to the kth user; The conjugate beam technology is used. In the signal transmission part, represents the conjugate form of the channel estimate;

The selection of the power control coefficient needs to satisfy the power constraint of each access point:

Also expressed as: , , expressed as the channel coefficient estimate The mean square of

During the downlink data transmission phase in a non-cellular system, all access points send data signals to users simultaneously on the same time-frequency resources;

S22, the signal received by the kth user is:

in, is the additive noise of the kth user, is the symbol sent to the k'th user, is the power control coefficient of the downlink from the mth access point to the k'th user, is the channel estimation coefficient between the mth access point and the k'th user;

Assuming that each user knows the channel statistics, the received signal Written as:

here,

in, represents the strength of the desired signal of the kth user, represents the uncertainty in the beamforming gain, Indicates from Interference of individual users;

The expression of downlink communication rate to the kth user is:

Expand the formula, Refers to the achievable rate of the kth user in the downlink. The expression is as follows.

in, Expressed as the channel coefficient estimate The mean square of .

Furthermore, the problem of maximizing the minimum downlink user communication rate is modeled, and then the problem of maximizing the minimum downlink user communication rate is converted into a corresponding graph optimization problem, and a power control algorithm based on a graph neural network is used to solve it. The process of improving the downlink communication rate is as follows:

S31, optimize the access point transmission power control to maximize the minimum user communication rate as follows:

The constrained optimization problem of maximizing the communication rate is modeled as follows:

Among them, C1 is the transmit power constraint;

The graph of a graph optimization model is usually composed of Indicates that Represents a collection of nodes. represents the set of adjacent nodes that form the edge, x and y represent the set The nodes and edges have different characteristics, so the graph can be represented by Represents, mapping nodes to their features, node features , mapping edges to their features, edge features , and Represented as the dimension size of node features and edge features;

Define node feature matrix ,in , represented as the i-th row of the node feature matrix Z, that is, the node feature of the i-th node, Represented as the i-th node. Adjacent feature tensor ,in , represented as the feature of the edge between node i and node j, where , Represented as the edge between node i and node j;

S32, solving the established downlink minimum user communication rate maximization problem model to obtain an access point transmission power control scheme that maximizes the minimum user communication rate:

Let M access points and K users be nodes, and construct the non-cellular system model as a bipartite graph; use the large-scale fading coefficient As input to the neural network, optimize the variables It is expressed as:

represents a real number;

The large-scale fading matrix is defined as ,in , the adjacency feature tensor of the bipartite graph is ,in ;

By replacing the communication rate expression Replace with , and the large-scale fading coefficient Replace with , the optimization problem of maximizing the minimum downlink user communication rate can be transformed into the following graph optimization problem:

S33. Define the loss function as the negative value of the objective function:

Graph neural networks extend convolutional neural networks to graphs. In a graph neural network layer, each node updates its hidden state based on aggregated information from neighboring nodes.

Assume that the node feature on node v is , the node feature on node u is , the feature of the edge e formed by nodes v and u is , Representing complex numbers, the message passing paradigm defines the following node-by-node and edge-by-edge computations:

in, is the message aggregated on the edge in the t+1th layer of the neural network, It is the feature of the neural network at the node v in the t+1 layer, t is the number of layers of the neural network, and t+1 represents the neural network in the t+1 layer. is the set of edges, It is a message function defined on each edge, which generates messages by combining the features on the edge with the features of the nodes at both ends. The aggregation function Aggregate the messages received by the node and update the function The node’s features are updated by combining the aggregated messages with the node’s own features;

S34. Heterogeneous neural networks are used in non-cellular network systems. Each layer of the neural network contains two types of message transmission, namely, messages transmitted from the access point to the user and messages transmitted from the user to the access point. Therefore, different weight matrices are used to parameterize different message transmission processes; the feature of node m is initialized to an empty vector ,in is an empty vector in the real field;

For a T-layer graph neural network, the update of node m in the tth layer is:

That is, the node feature of node m in the t-th layer network is ;

in, are the learnable weights in the t-th layer of the neural network, , is the node feature of node m in the T-th layer network, is the activation function, is the node feature of node m in the t-1th layer of the graph neural network, is the node feature of node k in the t-1th layer of the graph neural network, is a multilayer perceptron that maps the final hidden state to the transmit power, and the aggregation function The choice is to sum;

S35. Improve the graph neural network architecture according to the graph neural network design guidelines and the characteristics of the downlink data transmission model without cellular network; run the message passing from user to access point only in the first iteration:

That is, the node feature of node m in the first layer of the neural network is .

For aggregate functions Select Average Aggregation, are the learnable weights in the first layer of the neural network, is the activation function. For the subsequent message passing process, only the message passing between users is considered:

That is, the node feature of node m in the t-th layer network is .

in, , is the learnable parameter in the t-th layer of the neural network, is a learnable multilayer perceptron that maps hidden layers to transmit powers.

The present invention provides a non-cellular network power control method based on graph neural network, which can precode downlink data transmission according to uplink channel estimation, optimize downlink transmission power through graph neural network, and effectively improve the communication of the system.

Based on the above reasons, the present invention can be widely promoted in fields such as wireless communication.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

FIG. 1 is a flow chart of the method of the present invention.

FIG. 2 is a scene diagram used in an embodiment of the present invention.

FIG3 is a diagram of a graph optimization model provided by an embodiment of the present invention.

FIG4 is a flowchart of a neural network provided by an embodiment of the present invention.

FIG5 is a graph showing the results of a test set of a trained neural network provided by an embodiment of the present invention;

FIG6 is a comparison chart between the non-cellular network power control method based on graph neural network and the multi-layer perceptron method.

DETAILED DESCRIPTION

In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

FIG. 1 is a flow chart of the method of the present invention.

As shown in FIG1 , an embodiment of the present invention provides a non-cellular network power control method based on a graph neural network, characterized in that it includes the following steps:

S1. Using the time division duplex operation mode, utilizing the reciprocity of the non-cellular network channel, and estimating the non-cellular network channel through the pilot information sent in the uplink;

S2, precoding the transmission symbols in the downlink data transmission phase through a maximum ratio precoding scheme based on the channel estimation value, and then sending the signal to the user using the conjugate beamforming technology;

S3. Model the problem of maximizing the minimum user communication rate of the downlink, and then transform the problem of maximizing the minimum user communication rate of the downlink into a corresponding graph optimization problem, and use a power control algorithm based on a graph neural network to solve it, so as to achieve an improvement in the downlink communication rate.

Steps S1/S2/S3 are executed sequentially;

FIG2 is a scene diagram used in an embodiment of the present invention;

Furthermore, the specific contents of adopting the time division duplex operation mode, utilizing the reciprocity of the non-cellular network channel, and performing non-cellular network channel estimation through the pilot information sent in the uplink are:

FIG2 is a scenario diagram used in an embodiment of the present invention; S11. In the non-cellular network system under consideration, there are M single-antenna access points and K single-antenna users, each access point is connected to the central processor via a backhaul link, and the M access points serve K users under the same time and frequency resources.

The process of signal transmission from access point to user is called downlink, and the reverse is uplink.

In this non-cellular network system, a time division duplex operation mode is adopted, and channel reciprocity is utilized. In the uplink training phase, all users send pilot sequences to the access point, and channel estimation to all users is performed at each access point. The acquired channel state information is used for uplink data transmission decoding and downlink data transmission encoding.

The channel coefficient between the kth user and the mth access point is expressed as express:

Where, m = 1,…,M, k = 1,..,K, is the large-scale fading coefficient between access point m and user k, which mainly reflects the impact of path loss and shadow fading on the channel. is the small-scale fading coefficient, each small-scale fading coefficient are all independent and identically distributed, represents a complex Gaussian random variable with mean 0 and variance 1.

Large-scale fading coefficients via path loss and uncorrelated log-normal shadowing To model:

in: represents the path loss, With standard deviation and The shadow fading of It can be expressed as follows:

in: , is the carrier frequency, is the antenna height of the access point, is the user's antenna height, is the distance from the mth access point to the kth user, and is the reference distance.

In the real world, adjacent transmitters and receivers may be surrounded by common obstacles. Therefore, shadow fading is correlated. A two-component model is used to calculate the shadow fading coefficient. :

in, , , are two independent random variables, represents a complex Gaussian random variable with mean 0 and variance 1, , is a parameter.

and The covariance function of is:

in, It is access point and The distance between access points, It is Users and The distance between users, It is the relevant distance, which depends on the environment and is generally between 20m and 200m.

By channel condition , we can get the pilot information sent by user k received by the mth access point in the uplink for:

in, is the uplink pilot transmission duration, is the pilot sequence used by the kth user, where is a random variable, , Representation in the complex domain dimensional vector, . is the Euclidean norm, is the normalized signal-to-noise ratio of each pilot, is the additional noise at the mth access point.

Based on the received pilot sequence, the mth access point performs channel estimation. exist Projection on for:

in for The conjugate transpose of represents the conjugate transpose, Indicates users, where k and are all included in the user set K, For users A random variable, .

S12, according to the minimum mean square error criterion, the channel coefficient Estimated to be:

in, Indicates the distance from the mth access point to the The large-scale fading coefficient between users, represents the mean, Indicates conjugation.

The process of precoding the transmission symbols in the downlink data transmission phase by using the maximum ratio precoding scheme based on the channel estimation value and then sending the signal to the user by using the conjugate beamforming technology is as follows:

S21. In the downlink data transmission phase, the access point m uses beamforming to precode the data to be transmitted to the user k according to the channel estimation result:

in, is the symbol sent to the kth user, and , is the normalized downlink signal-to-noise ratio, is the power control coefficient for the downlink from the mth access point to the kth user. The power control coefficient must satisfy the power constraint of each access point:

It can also be expressed as: , , expressed as the channel coefficient estimate The mean square of .

During the downlink data transmission phase in a non-cellular system, all access points send their data signals to users simultaneously on the same time-frequency resources;

S22, the signal received by the kth user is:

in, is the additive noise of the kth user, is the symbol sent to the k'th user, is the power control coefficient of the downlink from the mth access point to the k'th user, is the channel estimation coefficient between the mth access point and the kth user. Assume that each user knows the channel statistics and receives the signal can be written as:

here,

in, represents the strength of the desired signal of the kth user, represents the uncertainty in the beamforming gain, Indicates from The interference of the kth user can be obtained as follows:

Expanding the formula, we can get the complete communication rate of user k expression:

in, Expressed as the channel coefficient estimate The mean square of .

According to the non-cellular network power control method based on graph neural network described in requirement 1, the problem of maximizing the minimum user communication rate of the downlink is modeled, and then the problem of maximizing the minimum user communication rate of the downlink is converted into a corresponding graph optimization problem, and a power control algorithm based on graph neural network is used to solve it. The process of improving the downlink communication rate is as follows:

S31. Optimize access point transmission power control to maximize the minimum user communication rate:

The constrained optimization problem of maximizing the communication rate is modeled as follows:

Among them, C1 is the transmission power constraint.

FIG3 is a graph optimization model diagram provided by an embodiment of the present invention;

The graph of a graph optimization model is usually composed of Indicates that Represents a collection of nodes. represents the set of adjacent nodes that form the edge, x and y represent the set The nodes and edges have different characteristics, so the graph can be represented by Represents, mapping nodes to their features, node features , mapping edges to their features, edge features , and Represented as the dimension size of node features and edge features.

Define node feature matrix ,in , represented as the i-th row of the node feature matrix Z, that is, the node feature of the i-th node, Represented as the i-th node. Adjacent feature tensor ,in , represented as the feature of the edge between node i and node j, where , Represented as the edge between node i and node j.

S32. Solve the established model of maximizing the downlink minimum user communication rate problem to obtain an access point transmission power control scheme that maximizes the minimum user communication rate.

In order to transform the optimization problem of maximizing the downlink minimum user communication rate into a graph optimization problem, M access points and K users are used as nodes, and the cellular-free system model is constructed as a bipartite graph. As input to the neural network, the optimization variable It is expressed as:

represents a real number;

The large-scale fading matrix is defined as ,in , the adjacency feature tensor of the bipartite graph is ,in .

By replacing the communication rate expression Replace with , and the large-scale fading coefficient Replace with , the optimization problem of maximizing the minimum downlink user communication rate can be transformed into a graph optimization problem:

S33. Define the loss function as the negative value of the objective function:

Graph neural networks extend convolutional neural networks to graphs. In a graph neural network layer, each node updates its hidden state based on the aggregated information from neighboring nodes.

Graph neural network is a message passing process with learnable parameters. Message passing is a general framework and programming paradigm for implementing graph neural networks. Assume that the node feature on node v is , the node feature on node u is , the feature of the edge e formed by nodes v and u is , Representing complex numbers, the message passing paradigm defines the following node-by-node and edge-by-edge computations:

in, is the message aggregated on the edge in the t+1th layer of the neural network, It is the feature of the node in the t+1th layer of the neural network, t is the number of layers of the neural network, and t+1 means the node is in the t+1th layer of the neural network. is the set of edges, is a message function defined on each edge, which generates a message by combining the features of the edge with the features of the nodes at both ends. Aggregate the messages received by the node and update the function The node’s features are updated by combining the aggregated messages with the node’s own features;

S34. In the non-cellular network system of the present application, a heterogeneous neural network is used. Each layer of the neural network contains two types of message transmission, namely, messages transmitted from the access point to the user and messages transmitted from the user to the access point. Therefore, different weight matrices are used to parameterize different message transmission processes. Since there is no node feature, the feature of node m is initialized to an empty vector ,in is the empty vector in the field of real numbers.

For a T-layer graph neural network, the update of node m in the tth layer is:

That is, the node feature of node m in the t-th layer network is .

.

in, are the learnable weights in the t-th layer of the neural network, , is the node feature of node m in the T-th layer network, is the activation function, is the node feature of node m in the t-1th layer of the graph neural network, is the node feature of node k in the t-1th layer of the graph neural network, is a multilayer perceptron that maps the final hidden state to the transmit power, and the aggregation function The choice is to sum;

S35, however, the current message passing process is not optimal, so the graph neural network architecture can be improved according to the graph neural network design guide and the characteristics of the non-cellular network downlink data transmission model. Since there are neither node features nor optimization variables on the user node, we only run the message passing from the user to the access point in the first iteration: Figure 4 is a neural network flow chart provided by an embodiment of the present invention;

That is, the node feature of node m in the first layer of the neural network is .

To simplify message passing, the initial neural network input is the large-scale fading coefficient , after passing through the neural network, it is mapped to the variable to be optimized in this paper: power control coefficient ;

For aggregate functions Select Average Aggregation, are the learnable weights in the first layer of the neural network, is the activation function. For the subsequent message passing process, only the message passing between users is considered:

That is, the node feature of node m in the t-th layer network is .

in, , is the learnable parameter in the t-th layer of the neural network, is a learnable multilayer perceptron that maps hidden layers to transmit powers.

Simulation conditions

In the simulation scenario, access points and users are randomly distributed in a rectangular area of 1km*1km, and the carrier frequency , access point antenna height , user's antenna height , , , the standard deviation of shadow fading , the normalized signal-to-noise ratio of each pilot , normalized downlink signal-to-noise ratio .

Simulation content and result analysis

Simulation 1: Train the graph neural network with the training set and verify it with the test set data.

As shown in Figure 5, the graph model constructed by the scenario system model shown in Figure 2 is input into the neural network for training. The network trained by the training set is verified by the test set. The number of training sets and test sets is 4000, the number of access points is 100, and the number of users is 40. After 50 periods, the data of the test set has good convergence.

Simulation 2: The method proposed in this application is compared with the multi-layer perceptron method. As can be seen from Figure 6, the performance of the proposed non-cellular network power control method based on graph neural network is better than that of the multi-layer perceptron. In the trained network, the performance of the proposed method is 20% higher than that of the multi-layer perceptron, which verifies the effectiveness of the method of the present invention.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. However, these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims (1)

1. A non-cellular network power control method based on graph neural network, characterized in that it includes the following steps: S1. Using the time division duplex operation mode, utilizing the reciprocity of the non-cellular network channel, and estimating the non-cellular network channel through the pilot information sent in the uplink; S2, precoding the transmission symbols in the downlink data transmission phase through a maximum ratio precoding scheme based on the channel estimation value, and then sending the signal to the user using the conjugate beamforming technology; S3. Modeling the problem of maximizing the minimum user communication rate of the downlink, and then converting the problem of maximizing the minimum user communication rate of the downlink into a corresponding graph optimization problem, using a power control algorithm based on a graph neural network to solve it, so as to improve the communication rate of the downlink; The process of modeling the problem of maximizing the minimum user communication rate of the downlink, converting the problem of maximizing the minimum user communication rate of the downlink into a corresponding graph optimization problem, and solving it using a power control algorithm based on a graph neural network to improve the communication rate of the downlink is as follows: S31, optimize the access point transmission power control to maximize the minimum user communication rate as follows: The constrained optimization problem of maximizing the communication rate is modeled as follows: Among them, C1 is the transmit power constraint; The graph of the graph optimization model is composed of Indicates that Represents a collection of nodes. represents the set of adjacent nodes that form the edge, x and y represent the set The nodes and edges in the graph have different characteristics, so the graph can be represented by Represents, mapping nodes to their features, node features , mapping edges to their features, edge features ,in, Represented as a complex field, and Represented as the dimension size of node features and edge features; Define node feature matrix ,in , represented as the i-th row of the node feature matrix Z, that is, the node feature of the i-th node, Represented as the i-th node, adjacent feature tensor ,in , represented as the feature of the edge between node i and node j, where , Represented as the edge between node i and node j; S32, solving the established downlink minimum user communication rate maximization problem model to obtain an access point transmission power control scheme that maximizes the minimum user communication rate: Let M access points and K users be nodes, and construct the non-cellular system model as a bipartite graph; use the large-scale fading coefficient As input to the neural network, the optimization variable It is expressed as: represents a real number; The large-scale fading matrix is defined as ,in , the adjacency feature tensor of the bipartite graph is ,in ; By replacing the communication rate expression Replace with , and the large-scale fading coefficient Replace with , the optimization problem of maximizing the minimum downlink user communication rate can be transformed into the following graph optimization problem: S33. Define the loss function as the negative value of the objective function: Graph neural networks extend convolutional neural networks to graphs. In a graph neural network layer, each node updates its hidden state based on aggregated information from neighboring nodes. Assume that the node feature on node v is , the node feature on node u is , the feature of the edge e formed by nodes v and u is , Representing complex numbers, the message passing paradigm defines the following node-by-node and edge-by-edge computations: in, is the message aggregated on the edge in the t+1th layer of the neural network, is the feature of the neural network at the node v in the t+1th layer, where t is the number of layers of the neural network. is the set of edges, It is a message function defined on each edge, which generates messages by combining the features on the edge with the features of the nodes at both ends. The aggregation function Aggregate the messages received by the node and update the function The node’s features are updated by combining the aggregated messages with the node’s own features; S34. Heterogeneous neural networks are used in non-cellular network systems. Each layer of the neural network contains two types of message transmission, namely, messages transmitted from the access point to the user and messages transmitted from the user to the access point. Therefore, different weight matrices are used to parameterize different message transmission processes; the feature of node m is Initialized to an empty vector, where is an empty vector in the real field; For a T-layer graph neural network, the update of node m in layer t for: That is, the node feature of node m in the t-th layer network is ; in, are the learnable weights in the t-th layer of the neural network, , is the node feature of node m in the T-th layer network, is the activation function, is the node feature of node m in the t-1th layer of the graph neural network, is the node feature of node k in the t-1th layer of the graph neural network, is a multilayer perceptron that maps the final hidden state to the transmit power, and the aggregation function The choice is to sum; S35. Improve the graph neural network architecture according to the graph neural network design guidelines and the characteristics of the downlink data transmission model without cellular network; run the message passing from user to access point only in the first iteration: That is, the node feature of node m in the first layer of the neural network is ; For aggregate functions Select Average Aggregation, are the learnable weights in the first layer of the neural network, is the activation function. For the subsequent message passing process, only the message passing between users is considered: That is, the node feature of node m in the t-th layer network is ; in, , is the learnable parameter in the t-th layer of the neural network, is a learnable multilayer perceptron that maps hidden layers to transmit powers; The process of adopting the time division duplex operation mode, utilizing the reciprocity of the non-cellular network channel, and performing non-cellular network channel estimation through the pilot information sent in the uplink is as follows: S11. In the non-cellular network system under consideration, there are M single-antenna access points and K single-antenna users. Each access point is connected to the central processor via a backhaul link. The M access points serve K users under the same time and frequency resources. In the non-cellular network system, the time division duplex operation mode is adopted, and the channel reciprocity is utilized. In the uplink training phase, all users send pilot sequences to the access point, and the channel estimation to all users is performed at each access point. The acquired channel state information is used for uplink data transmission decoding and downlink data transmission encoding; The channel coefficient between the kth user and the mth access point is expressed as express: Where, m = 1,…,M, k = 1,..,K, is the large-scale fading coefficient between access point m and user k , which mainly reflects the impact of path loss and shadow fading on the channel. is the small-scale fading coefficient, each small-scale fading coefficient are all independent and identically distributed, represents a complex Gaussian random variable with mean 0 and variance 1; Large-scale fading coefficients via path loss and uncorrelated log-normal shadowing To model: in: represents the path loss, With standard deviation and shadow fading coefficient The shadow fading of It can be expressed as follows: in: , is the carrier frequency, is the antenna height of the access point, is the user's antenna height, is the distance from the mth access point to the kth user, and is the reference distance; Shadow fading is interrelated and a two-component model is used to calculate the shadow fading coefficients: : in, , , are two independent random variables, represents a Gaussian random variable with mean 0 and variance 1, , is a parameter; and The covariance function of is: in, It is access point and The distance between access points, It is Users and The distance between users, is the correlation distance; By channel conditions , we get the pilot information sent by user k received by the mth access point in the uplink : in, is the uplink pilot transmission duration, is the pilot sequence used by the kth user, where is the random variable of user k, , Representation in the complex domain dimensional vector, . is the Euclidean norm, is the normalized signal-to-noise ratio of each pilot, is the additional noise at the mth access point; Based on the received pilot sequence, the mth access point performs channel estimation. exist Projection on for: in: for The conjugate transpose of represents the conjugate transpose, Indicates users, where k and are all included in the user set K, For users A random variable, ; S12, according to the minimum mean square error criterion, the channel coefficient Estimated to be: in, Indicates the distance from the mth access point to the The large-scale fading coefficient between users, represents the mean, denotes conjugation; The process of precoding the transmission symbols in the downlink data transmission phase by using the maximum ratio precoding scheme based on the channel estimation value and then sending the signal to the user by using the conjugate beamforming technology is as follows: S21. In the downlink data transmission phase, access point m uses beamforming to precode the data to be transmitted to user k according to the channel estimation result. The signal sent by the mth access point for: in, is the symbol sent to the kth user, and , is the normalized downlink signal-to-noise ratio, is the power control coefficient of the downlink from the mth access point to the kth user; The conjugate beam technology is used. In the signal transmission part, represents the conjugate form of the channel estimate; The selection of the power control coefficient needs to satisfy the power constraint of each access point: Also expressed as: , , expressed as the channel coefficient estimate The mean square of During the downlink data transmission phase in a non-cellular system, all access points send data signals to users simultaneously on the same time-frequency resources; S22, the signal received by the kth user is: in, is the additive noise of the kth user, is the symbol sent to the k'th user, is the power control coefficient of the downlink from the mth access point to the k'th user, is the channel estimation coefficient between the mth access point and the k'th user; Assuming that each user knows the channel statistics, the received signal Written as: here, in, represents the strength of the desired signal of the kth user, represents the uncertainty in the beamforming gain, Indicates from Interference of individual users; The expression of downlink communication rate to the kth user is: Expand the formula, Refers to the achievable rate of the kth user in the downlink. The expression is as follows; in, Expressed as the channel coefficient estimate The mean square of .