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

Non-cellular network power control method based on graph neural network Download PDF

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CN117560043B
CN117560043B CN202410038629.9A CN202410038629A CN117560043B CN 117560043 B CN117560043 B CN 117560043B CN 202410038629 A CN202410038629 A CN 202410038629A CN 117560043 B CN117560043 B CN 117560043B
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CN117560043A (en
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戴燕鹏
鄢德文
吕玲
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Dalian Maritime University
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    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
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Abstract

A honeycomb-free network power control method based on a graph neural network comprises the following steps: using time division duplex operation mode, using reciprocity of non-cellular network channel, and using pilot frequency information sent by uplink to make non-cellular network channel estimation; precoding transmission symbols in a downlink data transmission stage by a maximum ratio precoding scheme based on a channel estimation value, and then transmitting signals to users by using a conjugate beam forming technology; modeling the maximized downlink minimum user communication rate, converting the maximized downlink minimum user communication rate into a graph optimization problem, and solving by adopting a power control algorithm based on a graph neural network to realize the improvement of the downlink communication rate.

Description

Non-cellular network power control method based on graph neural network
Technical Field
The invention relates to the technical field of wireless communication, in particular to a honeycomb-free network power control method based on a graph neural network.
Background
In a conventional Multiple-Input Multiple-Output (MIMO) system, a large number of antennas are intensively distributed at a base station, and user terminals are distributed around the base station, which has advantages of low data sharing overhead and front-end transmission requirements. But the distributed MIMO system can improve unified and good service for all user terminals by utilizing independent fading of signals, thereby achieving the purpose of obtaining high diversity gain against shadow fading. A non-cellular network is a deconstructment of a conventional MIMO system with a large number of antennas distributed at different locations over a wide area over which the users are also distributed. These antennas are called access points. Theoretically each user can communicate with each access point. By relying on time division duplexing, a large number of geographically dispersed antennas together serve a smaller number of user terminals by means of a forward network and a central processing unit operating in the same time frequency resource. The central processing unit transmits downlink data and power control coefficients to the access point, and the access point feeds back data received from the user terminal in the uplink to the central processing unit through the forward link. All access points are connected to the central processing unit through a backhaul link to perform phase coherent cooperation, and serve all users simultaneously on the same time-frequency resource.
Deep learning-based methods are widely used to address the wireless communication field and always achieve the desired results, and existing non-cellular network power control techniques typically employ optimization methods, which can result in increased demands on computing resources when processing large-scale data. The deep learning model may be more suitable for processing large-scale data due to the characteristics of automatic feature learning and end-to-end learning, but some conventional neural network architectures, such as multi-layer perceptrons, generally generate poorer performance in a large-scale network, and the graph neural network can effectively solve the problem of resource allocation by using the topological structure of wireless communication.
In summary, optimizing cell-free power control using a graph neural network will produce the expected results.
Disclosure of Invention
According to the technical problems, the invention adopts the following technical means: a honeycomb-free network power control method based on a graph neural network comprises the following steps:
s1, adopting a time division duplex operation mode, and carrying out non-cellular network channel estimation through pilot frequency information sent by an uplink by utilizing non-cellular network channel reciprocity;
s2, precoding transmission symbols in a downlink data transmission stage by a maximum ratio precoding scheme based on a channel estimation value, and then transmitting signals to users by using a conjugate beam forming technology;
and S3, 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 by adopting a power control algorithm based on a graph neural network to improve the communication rate of the downlink.
Further: the process of using the time division duplex operation mode and using the reciprocity of the non-cellular network channel to perform the non-cellular network channel estimation through the pilot frequency information sent by the uplink is as follows:
s11, in the considered non-cellular network system, M single-antenna access points and K single-antenna users are shared, each access point is connected with a central processing unit through a backhaul link, and the M access points serve the K users under the same time-frequency resource;
in a non-cellular network system, a time division duplex operation mode is adopted, and in an uplink training stage, all users send pilot sequences to access points, channel estimation is carried out on all users at each access point, and the obtained channel state information is used for uplink data transmission decoding and downlink data transmission coding.
Using channel coefficients between kth user and mth access pointThe representation is:
where m=1, …, M, k=1, K,is an access pointmAnd a userkBetween which are locatedMainly reflecting the influence of path loss and shadow fading on the channel, +.>Is a small-scale fading coefficient, each small-scale fading coefficient +>Are all independently and equidistributed, are->A complex gaussian random variable representing a mean value of 0 and a variance of 1;
large scale fading coefficient by path loss and uncorrelated lognormal shadowingModeling:
wherein:representing path loss, ++>For having standard deviation->And->Shadow fading of (1), wherein path loss +.>This can be represented as follows:
wherein:，/>is the carrier frequency, < >>Is the antenna height of the access point, +.>Is the antenna height of the user, < >>Is the distance from the mth access point to the kth user, < >>And->Is the reference distance;
shadow fading is interrelated, and a model comprising two components is used to calculate shadow fading coefficients：
Wherein,，/>is two independent random variables, +.>Gaussian random variable representing mean 0 and variance 1,/->，/>Is a parameter;
and->Is:
wherein,is->Access point and->Distance between access points, +.>Is->Individual user and->Distance between individual users->Is the relevant distance;
by channel conditionsObtain the firstmEach access point receives users on the uplinkkTransmitted pilot information->The method comprises the following steps:
wherein,for uplink pilot transmission duration, +.>Is the firstkPilot sequence for individual users, wherein +.>Is a random variable +.>，/>Expressed in plural domains->Vector of dimension,/->Is the euclidean norm,is the normalized signal-to-noise ratio of each pilot, +.>Is the firstmAdditional noise at the individual access points;
based on the received pilot sequence, the thmThe channel estimation is performed by the individual access points,at->Projection on +.>The method comprises the following steps:
wherein the method comprises the steps ofIs->Conjugate transpose of->Represents the conjugate transpose->Indicate->Individual users, here k and +>Are all included in the user set K, < >>For user->Random variable of>。
S12, according to the minimum mean square error criterion, the channel coefficient can be calculatedThe estimation is:
wherein,representing mth access point toFirst->Large scale fading coefficients between individual users, +.>The mean value is represented as such,representing conjugation.
Further: the process of precoding the transmission symbols in the downlink data transmission stage by the maximum ratio precoding scheme based on the channel estimation value and then transmitting the signals to the user by using the conjugate beam forming technology is as follows:
s21, in the downlink data transmission stage, the access pointmUsing beamforming pairs to be transmitted to users based on the results of the channel estimationkPre-coding the data of (a):
wherein,is sent to the firstkSign of individual user, and->，/>Is normalized downlink signal-to-noise ratio, +.>Is the power control coefficient of the downlink between the mth access point and the kth user; />Conjugate beam technique is used, in signal transmission part,/->Representation ofConjugate form of channel estimation;
the selection of the power control coefficients requires that the power constraints of each access point be satisfied:
also denoted as:，/>expressed as channel coefficient estimation value +.>Is the mean square of (2);
in the downlink data transmission phase in a cellular-free system, all access points transmit data signals to users on the same time-frequency resource at the same time;
s22, the firstkThe signals received by the individual users are:
wherein,is the firstkAdditive noise of individual users->Is sent to the firstk'The sign of the individual user is given by the symbol,is the power control coefficient of the downlink between the mth access point to the kth' user, and>from the mth access point to the mth access pointk'Channel estimation coefficients between individual users;
receiving signals assuming that each user knows channel statisticsWriting:
here the number of the elements is the number,
wherein,represent the firstkIntensity of the individual user desired signal,/-, for example>Representing the uncertainty of the beamforming gain,the representation comes from->Interference of individual users;
to the firstkThe expression of the downlink communication rate of each user is as follows:
the formula is developed and the formula is developed,refers to the achievable rate of the kth user in downlink, the achievable rate +.>The expression is as follows.
Wherein,expressed as channel coefficient estimation +.>Is the mean square of (c).
Further: 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, solving by adopting a power control algorithm based on a graph neural network, and realizing the improvement of the communication rate of the downlink, wherein the process comprises the following steps of:
s31, optimizing the control of the transmitting power of the access point, and maximizing the minimum user communication rate, wherein the control comprises the following steps:
modeling a constraint optimization problem for communication rate maximization, as follows:
wherein C1 is the transmit power constraint;
the graph of the graph optimization model is generally defined byRepresentation of->A set of nodes is represented and,representing that neighboring nodes constitute a set of edges,xandyrepresentation set->Is included in the node (a). The nodes and edges have different characteristics, respectively, so that the representation of the graph can be made of +.>Representing, map node to its feature, node feature +.>Mapping edges to their features, edge features +.>，/>And->Dimension size expressed as node features and edge features;
defining a node feature matrixWherein->The ith row, i.e. the node characteristics of the ith node, denoted as node characteristics matrix Z,/>Denoted as the i-th node. Adjacency feature tensor->WhereinFeatures expressed as edges between node i and node j, wherein +.>，/>Represented as an edge formed between node i and node j;
s32, solving the established maximum downlink minimum user communication rate problem model to obtain an access point transmitting power control scheme for maximizing the minimum user communication rate:
m access points and K users are used as nodes, and a non-cellular system model is constructed into a bipartite graph; using large scale fading coefficientsAs input to the neural network, the optimization variable +.>Expressed as:
representing a real number;
defining a large-scale fading matrix asWherein->The adjacent characteristic tensor of the bipartite graph isWherein->；
By incorporating into the communication rate expressionReplaced by->And a large scale fading coefficient +.>Replaced byThe maximized downlink minimum user communication rate optimization problem may be translated into a graph optimization problem as follows:
s33, defining the loss function as a negative value of the objective function:
the convolutional neural network is expanded into a graph by the graph neural network, and in one graph neural network layer, each node updates the hidden state of the node according to the aggregation information from the neighbor nodes;
assume that the node on node v is characterized byThe node on node u is characterized by +.>The feature on edge e consisting of nodes v and u is +.>，/>Representing complex numbers, the messaging paradigm defines the following node-by-node and edge-by-edge calculations:
wherein,is a message aggregated on the edge in the layer t+1 neural network,/for>Is the characteristic of the neural network at the (t+1) th layer at the node v, t is the layer number of the neural network, t+1 represents the neural network at the (t+1) th layer, and the neural network is a->For the collection of edges, +.>Is a message function defined on each edge, the message is generated by combining features on the edge with features of nodes at both ends thereof, an aggregation function +.>The messages received by the nodes are aggregated, and the function is updated>The characteristics of the node are updated by combining the aggregated message and the characteristics of the node;
s34, heterogeneous neural networks are used in the non-cellular network system, each layer of neural network comprises two types of message transmission, namely a message transmitted by an access point to a user and a message transmitted by the user to the access point, so that different weight matrixes are used for parameterizing different message transmission processes; initializing the features of node m to null vectorsWherein->Null vectors that are real number fields;
for a T-layer graph neural network, the update of node m at the T-th layer is:
i.e. node m in the layer t network is characterized by；
Wherein,is a academic weight in the layer t neural network,/->，/>Is a node characteristic of node m in the layer T network,/->Is an activation function->For node m to be a node characteristic of the neural network at layer t-1, +.>For node k to be node characteristic of the neural network at layer t-1, +.>Is a multi-layer perceptron mapping the final hidden state to the transmit power, aggregation function +.>The choice is summation;
s35, improving the structure of the graphic neural network according to the design guideline of the graphic neural network and the characteristics of a downlink data transmission model of the non-cellular network; messaging from the user to the access point is only run in the first iteration:
i.e. the node characteristic of node m in the first layer neural network is。
For aggregate functionsSelecting average aggregation +.>Is a academic weight in the first layer neural network,/->Is an activation function that considers only the messaging between users for the subsequent messaging process:
i.e. node m in the layer t network is characterized by。
Wherein,，/>is a learning parameter in the layer t neural network, < >>Is a learnable multi-layer perceptron that maps hidden layers to transmit power.
The honeycomb-free network power control method based on the graph neural network provided by the invention can pre-encode downlink data transmission according to uplink channel estimation, and optimize downlink transmitting power through the graph neural network, thereby effectively improving the communication of a system.
For the reasons, the invention can be widely popularized in the fields of wireless communication and the like.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to the drawings without inventive effort to a person skilled in the art.
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a scene graph used in an embodiment of the invention.
Fig. 3 is a diagram of a graph optimization model provided in an embodiment of the present invention.
Fig. 4 is a flowchart of a neural network according to an embodiment of the present invention.
FIG. 5 is a graph of the results of a test set through a trained neural network according to an embodiment of the present invention;
fig. 6 is a diagram of a comparison of a non-cellular network power control method and a multi-layer perceptron method based on the neural network of fig. 6.
Detailed Description
In order that those skilled in the art will better understand the present invention, a technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in which it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and the claims of the present invention and the above figures are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged where appropriate such that the embodiments of the invention described herein may be implemented in sequences other than those illustrated or otherwise described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
FIG. 1 is a flow chart of the method of the present invention.
As shown in fig. 1, an embodiment of the present invention provides a method for controlling power of a non-cellular network based on a graph neural network, which is characterized by comprising the following steps:
s1, adopting a time division duplex operation mode, and carrying out non-cellular network channel estimation through pilot frequency information sent by an uplink by utilizing non-cellular network channel reciprocity;
s2, precoding transmission symbols in a downlink data transmission stage by a maximum ratio precoding scheme based on a channel estimation value, and then transmitting signals to users by using a conjugate beam forming technology;
and S3, 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 by adopting a power control algorithm based on a graph neural network to improve the communication rate of the downlink.
The steps S1/S2/S3 are sequentially executed;
FIG. 2 is a scene graph used in an embodiment of the invention;
further, the specific content of performing the channel estimation of the non-cellular network through the pilot frequency information sent by the uplink by using the channel reciprocity of the non-cellular network in the time division duplex operation mode is as follows:
FIG. 2 is a scene graph used in an embodiment of the invention; s11, in the considered non-cellular network system, M single-antenna access points and K single-antenna users are all arranged, each access point is connected with a central processing unit through a backhaul link, and the M access points serve the K users under the same time-frequency resource.
The process of signal transmission from an access point to a user is called downlink and vice versa is uplink.
In the non-cellular network system, a time division duplex operation mode is adopted, and in an uplink training stage, all users send pilot sequences to access points, channel estimation is carried out on all users at each access point, and the acquired channel state information is used for uplink data transmission decoding and downlink data transmission encoding.
Using channel coefficients between kth user and mth access pointThe representation is:
where m=1, …, M, k=1, K,is the large scale fading coefficient between access point m and user k, mainly reflecting the influence of path loss and shadow fading on the channel, +.>Is a small-scale fading coefficient, each small-scale fading coefficient +>Are all independently and equidistributed, are->Representing a complex gaussian random variable with a mean value of 0 and a variance of 1.
Large-scale fading system by path loss and uncorrelated lognormal shadowingNumber of digitsModeling:
wherein:representing path loss, ++>For having standard deviation->And->Shadow fading of (1), wherein path loss +.>This can be represented as follows:
wherein:，/>is the carrier frequency, < >>Is the antenna height of the access point, +.>Is the antenna height of the user, < >>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 a common obstacle, so shadow fading is interrelated, and a model comprising two components is used to calculate the shadow fading coefficients：
Wherein,，/>is two independent random variables, +.>Complex Gaussian random variable representing mean 0 and variance 1,/A>，/>Is a parameter.
And->Is:
wherein,is->Access point and->Distance between access points, +.>Is->Individual user and->Distance between individual users->Is a relevant distance, typically between 20m and 200m, depending on the circumstances.
By channel conditionsCan obtain the firstmEach access point receives users on the uplinkkTransmitted pilot information->The method comprises the following steps:
wherein,for uplink pilot transmission duration, +.>Is the firstkPilot sequence for individual users, wherein +.>Is a random variable +.>，/>Expressed in plural domains->Vector of dimensions, & gt>Is the euclidean norm,is the normalized signal-to-noise ratio of each pilot, +.>Is the firstmAdditional noise at the individual access points.
Based on the received pilot sequence, the thmThe channel estimation is performed by the individual access points,at->Projection on +.>The method comprises the following steps:
wherein the method comprises the steps ofIs->Is a common component of (2)Yoke transpose, ->Represents the conjugate transpose->Indicate->Individual users, here k and +>Are all included in the user set K, < >>For user->Random variable of>。
S12, according to the minimum mean square error criterion, the channel coefficient can be calculatedThe estimation is:
wherein,representing the mth access point to +.>Large scale fading coefficients between individual users, +.>The mean value is represented as such,representing conjugation.
The process of precoding the transmission symbols in the downlink data transmission stage by the maximum ratio precoding scheme based on the channel estimation value and then transmitting the signals to the user by using the conjugate beam forming technology is as follows:
s21, in the downlink data transmission stage, the access pointmUsing beamforming pairs to be transmitted to users based on the results of the channel estimationkPre-coding the data of (a):
wherein,is sent to the firstkSign of individual user, and->，/>Is normalized downlink signal-to-noise ratio, +.>Is the power control coefficient of the downlink between the mth access point and the kth user. The selection of the power control coefficients requires that the power constraints of each access point be satisfied:
can also be expressed as:，/>expressed as channel coefficient estimation value +.>Is the mean square of (c).
In the downlink data transmission phase in a cellular-free system, all access points transmit their data signals to the user simultaneously on the same time-frequency resource;
s22, the firstkThe signals received by the individual users are:
wherein,is the firstkAdditive noise of individual users->Is sent to the firstk'The sign of the individual user is given by the symbol,is the power control coefficient of the downlink between the mth access point to the kth' user, and>from the mth access point to the mth access pointk'Channel estimation coefficients between individual users. Assuming that each user knows the channel statistics, receive signal +.>Can be written as:
/>
here the number of the elements is the number,
wherein,represent the firstkIntensity of the individual user desired signal,/-, for example>Representing the uncertainty of the beamforming gain,the representation comes from->Interference of individual users. Can obtain the firstkThe expression of the downlink communication rate of each user is as follows:
expanding the formula to obtain the userkIs a complete communication rate of (a)The expression:
wherein,expressed as channel coefficient estimation +.>Is the mean square of (c).
The method for controlling power of a non-cellular network based on a graph neural network according to claim 1, wherein the method comprises the steps of modeling the problem of maximizing the minimum user communication rate of a downlink, converting the problem of maximizing the minimum user communication rate of the downlink into a corresponding graph optimization problem, solving by adopting a power control algorithm based on the graph neural network, and realizing the improvement of the communication rate of the downlink, wherein the process comprises the following steps:
s31, optimizing the control of the transmitting power of the access point, and maximizing the minimum user communication rate:
modeling a constraint optimization problem for communication rate maximization, as follows:
wherein C1 is the transmit power constraint.
FIG. 3 is a diagram of a graph optimization model provided by an embodiment of the present invention;
the graph of the graph optimization model is generally defined byRepresentation of->A set of nodes is represented and,representing that neighboring nodes constitute a set of edges,xandyrepresentation set->Is included in the node (a). The nodes and edges have different characteristics, respectively, so that the representation of the graph can be made of +.>Representing, map node to its feature, node feature +.>Mapping edges to their features, edge features +.>，/>And->The dimension size expressed as node features and edge features.
Defining a node feature matrixWherein->The ith row, i.e. the node characteristics of the ith node, denoted as node characteristics matrix Z,/>Denoted as the i-th node. Adjacency feature tensor->WhereinFeatures expressed as edges between node i and node j, wherein +.>，/>Represented as an edge formed between node i and node j.
S32, solving the established maximum downlink minimum user communication rate problem model to obtain an access point transmitting power control scheme which maximizes the minimum user communication rate.
In order to convert the maximized downlink minimum user communication rate optimization problem into a graph optimization problem, the non-cellular system model is constructed as a bipartite graph with M access points and K users as nodes. Using large scale fading coefficientsAs input to the neural network, the optimization variable +.>Expressed as:
representing a real number;
defining a large-scale fading matrix asWherein->The adjacent characteristic tensor of the bipartite graph isWherein->。
By incorporating into the communication rate expressionReplaced by->And a large scale fading coefficient +.>Replaced byThe maximized downlink minimum user communication rate optimization problem may be translated into a graph optimization problem:
s33, defining the loss function as a negative value of the objective function:
the graph neural network extends the convolutional neural network into the graph, and in one graph neural network layer, each node updates its hidden state according to the aggregation information from the neighbor nodes.
The graph neural network is a messaging process with a learned parameter, and messaging is a general framework and programming paradigm for implementing graph neural networks. Assume that the node on node v is characterized byThe node on node u is characterized by +.>The feature on edge e consisting of nodes v and u is +.>，/>Representing complex numbers, the messaging paradigm defines the following node-by-node and edge-by-edge calculations:
/>
wherein,is a message aggregated on the edge in the layer t+1 neural network,/for>Is the characteristic of the node on the (t+1) th layer neural network, t is the layer number of the neural network, t+1 represents the (t+1) th layer neural network, and the node is added with the layer number of the neural network>For the collection of edges, +.>Is a message function defined on each edge by specifying the edgeThe sign is combined with the features of its two end nodes to generate a message, the aggregation function +.>The messages received by the nodes are aggregated, and the function is updated>The characteristics of the node are updated by combining the aggregated message and the characteristics of the node;
s34, in the non-cellular network system of the present application, heterogeneous neural networks are used, and each layer of neural network includes two types of message delivery, that is, a message delivered by an access point to a user and a message delivered by a user to an access point, so different weight matrices are used to parameterize different message delivery processes. Since there is no node feature, the feature of node m is initialized to a null vectorWherein->Is a null vector in the real number domain.
For a T-layer graph neural network, the update of node m at the T-th layer is:
i.e. node m in the layer t network is characterized by。
。
Wherein,is a academic weight in the layer t neural network,/->，/>Is a node characteristic of node m in the layer T network,/->Is an activation function->For node m to be a node characteristic of the neural network at layer t-1, +.>For node k to be node characteristic of the neural network at layer t-1, +.>Is a multi-layer perceptron mapping the final hidden state to the transmit power, aggregation function +.>The choice is summation;
s35, but the current message passing process is not optimal, so the graphic neural network architecture can be improved according to the graphic neural network design guideline and the characteristics of the non-cellular network downlink data transmission model. Since there are neither node features nor optimization variables on the user nodes, we only run messaging from the user to the access point in the first iteration: FIG. 4 is a flowchart of a neural network according to an embodiment of the present invention;
i.e. the node characteristic of node m in the first layer neural network is。
To simplify messaging, input to the initial neural network, i.e. large scale fading coefficientsAfter passing through the neural network, it maps to the variables to be optimized herein: power control coefficient->；
For aggregate functionsSelecting average aggregation +.>Is a academic weight in the first layer neural network,/->Is an activation function that considers only the messaging between users for the subsequent messaging process:
i.e. node m in the layer t network is characterized by。
/>
Wherein,，/>is a learning parameter in the layer t neural network, < >>Is a learnable multi-layer perceptron that maps hidden layers to transmit power.
Simulation conditions
In a simulation scenario, the access point and the user followThe machine is distributed in a rectangular area with the speed of 1km and the carrier frequency of 1kmAntenna height of access point +.>Antenna height of user->，/>，Standard deviation of shadow fading->Normalized signal-to-noise ratio per pilot>Normalized downlink signal-to-noise ratio +.>。
Simulation content and result analysis
Simulation 1: the training set trains the graph neural network and verifies with the test set data.
As shown in fig. 5, the graph model constructed by the scene system model shown in fig. 2 is input into a neural network for training, and the training set is used for training the trained network, and the test set is used for verification. 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 a period of 50, the data of the test set had good convergence.
Simulation 2: comparing the method proposed by the present application with the multi-layer perceptron method, as can be seen from fig. 6, the proposed non-cellular network power control method based on the graph neural network has better performance than the multi-layer perceptron, and in the trained network, the proposed method has 20% higher performance than the multi-layer perceptron, and the effectiveness of the method of the present invention is verified.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention.

Claims (1)

1. The honeycomb-free network power control method based on the graph neural network is characterized by comprising the following steps of:
s1, adopting a time division duplex operation mode, and carrying out non-cellular network channel estimation through pilot frequency information sent by an uplink by utilizing non-cellular network channel reciprocity;
s2, precoding transmission symbols in a downlink data transmission stage by a maximum ratio precoding scheme based on a channel estimation value, and then transmitting signals to users by using a conjugate beam forming technology;
s3, modeling a 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 by adopting a power control algorithm based on a graph neural network to improve the communication rate of the downlink;
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, solving by adopting a power control algorithm based on a graph neural network, and realizing the improvement of the communication rate of the downlink, wherein the process comprises the following steps of:
s31, optimizing the control of the transmitting power of the access point, and maximizing the minimum user communication rate, wherein the control comprises the following steps:
modeling a constraint optimization problem for communication rate maximization, as follows:
wherein C1 is the transmit power constraint;
graph-optimization model graph-by-graphRepresentation of->Representing node set,/->Representing that neighboring nodes constitute a set of edges,xandyrepresentation set->The nodes, nodes and edges of the graph have different characteristics, respectively, so that the graph can be represented by +.>Representing, map node to its feature, node feature +.>Mapping edges to their features, edge features +.>Wherein->Represented as complex field>And->Dimension size expressed as node features and edge features;
defining a node feature matrixWherein->The ith row, i.e. the node characteristics of the ith node, denoted as node characteristics matrix Z,/>Denoted as the i-th node, adjacency feature tensor->WhereinFeatures expressed as edges between node i and node j, wherein +.>，/>Represented as an edge formed between node i and node j;
s32, solving the established maximum downlink minimum user communication rate problem model to obtain an access point transmitting power control scheme for maximizing the minimum user communication rate:
m access points and K users are used as nodes, and a non-cellular system model is constructed into a bipartite graph; using large scale fading coefficientsAs input to the neural network, the optimization variable +.>Expressed as:
representing a real number;
defining a large-scale fading matrix asWherein->The adjacent characteristic tensor of the bipartite graph isWherein->；
By incorporating into the communication rate expressionReplaced by->And a large scale fading coefficient +.>Replaced byThe maximized downlink minimum user communication rate optimization problem may be translated into a graph optimization problem as follows:
s33, defining the loss function as a negative value of the objective function:
the convolutional neural network is expanded into a graph by the graph neural network, and in one graph neural network layer, each node updates the hidden state of the node according to the aggregation information from the neighbor nodes;
assume that the node on node v is characterized byThe node on node u is characterized by +.>The feature on edge e consisting of nodes v and u is +.>，/>Representing complex numbers, the messaging paradigm defines the following node-by-node and edge-by-edge calculations:
wherein,is a message aggregated on the edge in the layer t+1 neural network,/for>Is the characteristic of the neural network at the t+1th layer at the node v, t is the layer number of the neural network, and is->For the collection of edges, +.>Is a message function defined on each edge, the message is generated by combining features on the edge with features of nodes at both ends thereof, an aggregation function +.>The messages received by the nodes are aggregated, and the function is updated>The characteristics of the node are updated by combining the aggregated message and the characteristics of the node;
s34, heterogeneous neural networks are used in the non-cellular network system, each layer of neural network comprises two types of message transmission, namely a message transmitted by an access point to a user and a message transmitted by the user to the access point, so that different weight matrixes are used for parameterizing different message transmission processes; features of node mInitialized to a null vector, whereinNull vectors that are real number fields;
for a T-layer neural network, node m is updated at the T-th layerThe method comprises the following steps:
i.e. node m in the layer t network is characterized by；
Wherein,is a academic weight in the layer t neural network,/->，/>Is a node characteristic of node m in the layer T network,/->Is an activation function->For node m to be a node characteristic of the neural network at layer t-1, +.>For node k to be node characteristic of the neural network at layer t-1, +.>Is a multi-layer perceptron mapping the final hidden state to the transmit power, aggregation function +.>The choice is summation;
s35, improving the structure of the graphic neural network according to the design guideline of the graphic neural network and the characteristics of a downlink data transmission model of the non-cellular network; messaging from the user to the access point is only run in the first iteration:
i.e. the node characteristic of node m in the first layer neural network is；
For aggregate functionsSelecting average aggregation +.>Is a academic weight in the first layer neural network,/->Is an activation function that considers only the messaging between users for the subsequent messaging process:
i.e. node m in the layer t network is characterized by；
Wherein,，/>is a learning parameter in the layer t neural network, < >>Is a learnable multi-layer perceptron mapping the hidden layer to the transmitting power;
the process of using the time division duplex operation mode and using the reciprocity of the non-cellular network channel to perform the non-cellular network channel estimation through the pilot frequency information sent by the uplink is as follows:
s11, in the considered non-cellular network system, M single-antenna access points and K single-antenna users are shared, each access point is connected with a central processing unit through a backhaul link, and the M access points serve the K users under the same time-frequency resource;
in a non-cellular network system, a time division duplex operation mode is adopted, and in an uplink training stage, all users send pilot sequences to access points, channel estimation is carried out on all users at each access point, and the obtained channel state information is used for uplink data transmission decoding and downlink data transmission encoding;
using channel coefficients between kth user and mth access pointThe representation is:
where m=1, …, M, k=1, K,is an access pointmAnd a userkThe large scale fading coefficient between them is mainly reflected by the influence of path loss and shadow fading on the channel,/>Is a small-scale fading coefficient, each small-scale fading coefficient +>Are all independently and equidistributed, are->A complex gaussian random variable representing a mean value of 0 and a variance of 1;
by logarithm of path loss and uncorrelationNormal shadow versus large scale fading coefficientModeling:
wherein:representing path loss, ++>For having standard deviation->And shadow fading coefficient->Shadow fading of (1), wherein path loss +.>This can be represented as follows:
wherein:，/>is the carrier frequency, < >>Is the antenna height of the access point, +.>Is of the userAntenna height->Is the distance from the mth access point to the kth user, < >>And->Is the reference distance;
shadow fading is interrelated, and a model comprising two components is used to calculate shadow fading coefficients：
Wherein,，/>is two independent random variables, +.>Gaussian random variable representing mean 0 and variance 1,/->，/>Is a parameter;
and->Is:
wherein,is->Access point and->Distance between access points, +.>Is->Individual user and the firstDistance between individual users->Is the relevant distance;
by channel conditionsObtain the firstmEach access point receives users on the uplinkkTransmitted pilot information->：
Wherein,for uplink pilot transmission duration, +.>Is the firstkPilot sequence for individual users, wherein +.>For the random variable of user k +.>，/>Expressed in plural domains->Vector of dimension,/->Is Euclidean norm, ++>Is the normalized signal-to-noise ratio of each pilot, +.>Is the firstmAdditional noise at the individual access points;
based on the received pilot sequence, the thmThe channel estimation is performed by the individual access points,at->Projection on +.>The method comprises the following steps:
wherein:is->Conjugate transpose of->Represents the conjugate transpose->Indicate->Individual users, here k and +>Are all included in the user set K, < >>For user->Random variable of>；
S12, according to the minimum mean square error criterion, the channel coefficient can be calculatedThe estimation is:
wherein,representing the mth access point to +.>Large scale fading coefficients between individual users, +.>Mean value->Represents conjugation;
the process of precoding the transmission symbols in the downlink data transmission stage by the maximum ratio precoding scheme based on the channel estimation value and then transmitting the signals to the user by using the conjugate beam forming technology is as follows:
s21, in the downlink data transmission stage, the access pointmUsing beamforming pairs to be transmitted to users based on the results of the channel estimationkPre-coding data of the mth access pointThe method comprises the following steps:
wherein,is sent to the firstkSign of individual user, and->，/>Is normalized downlink signal-to-noise ratio, +.>Is the power control coefficient of the downlink between the mth access point and the kth user; />Conjugate beam technique is used, in signal transmission part,/->Representing a conjugate form of the channel estimate;
the selection of the power control coefficients requires that the power constraints of each access point be satisfied:
also denoted as:，/>expressed as channel coefficient estimation value +.>Is the mean square of (2);
in the downlink data transmission phase in a cellular-free system, all access points transmit data signals to users on the same time-frequency resource at the same time;
s22, the firstkThe signals received by the individual users are:
wherein,is the firstkAdditive noise of individual users->Is sent to the firstk'Symbol of individual user->Is the power control coefficient of the downlink between the mth access point to the kth' user, and>from the mth access point to the mth access pointk'Channel estimation coefficients between individual users;
receiving signals assuming that each user knows channel statisticsWriting:
here the number of the elements is the number,
wherein,represent the firstkIntensity of the individual user desired signal,/-, for example>Representing uncertainty of beamforming gain, +.>The representation comes from->Interference of individual users;
to the firstkThe expression of the downlink communication rate of each user is as follows:
the formula is developed and the formula is developed,refers to the achievable rate of the kth user in downlink, the achievable rate +.>The expression is as follows;
wherein,expressed as channel coefficient estimation +.>Is the mean square of (c).
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