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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戴燕鹏
鄢德文
吕玲
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Abstract

一种基于图神经网络的无蜂窝网络功率控制方法,包括如下步骤:采用时分双工操作模式,利用无蜂窝网络信道互易性,通过上行链路发送的导频信息进行无蜂窝网络信道估计;通过基于信道估计值的最大比率预编码方案,对下行链路数据传输阶段的传输符号进行预编码,然后利用共轭波束成形技术向用户发送信号;对最大化下行链路最小用户通信速率进行建模,再通过将最大化下行链路最小用户通信速率的问题转化为图优化问题,采用一种基于图神经网络的功率控制算法进行求解,实现下行链路的通信速率的提高。

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

一种基于图神经网络的无蜂窝网络功率控制方法A cellular network power control method based on graph neural network

技术领域Technical Field

本发明涉及无线通信技术领域,具体而言,尤其涉及一种基于图神经网络的无蜂窝网络功率控制方法。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.

背景技术Background Art

在传统的多输入多输出(Multiple-Input Multiple-Output,MIMO)系统中,大量的天线集中分布在基站,用户终端分布在基站周围,具有低数据共享开销和前端传输要求的优势。但是分布式MIMO系统可以通过利用信号的独立衰落为所有用户终端提高统一良好的服务,进而达到获取抵抗阴影衰落的高分集增益的目的。无蜂窝网络是对传统MIMO系统的解构,大量天线分布在一个广域上的不同位置,用户同样分布在这个广域上。这些天线被称为接入点。理论上每个用户可以与每一个接入点通信。通过依靠时分双工操作,借助于在相同时频资源中运行的前传网络和中央处理单元,地理上分散的大量天线共同为较少数量的用户终端服务。中央处理单元将下行链路数据和功率控制系数发送给接入点,而接入点通过前传链路将从上行链路中的用户终端处接收到的数据反馈给中央处理单元。全部的接入点通过回程链路连接到中央处理器进行相位相干协作,在同一时间频率资源上同时服务于所有用户。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.

基于深度学习的方法被广泛用于解决无线通信领域,并总能得到期望的结果,现有的无蜂窝网络功率控制技术通常采用的是优化方法,在处理大规模数据时,会导致计算资源的需求增加。深度学习模型由于其自动特征学习和端到端学习的特性可能更适合处理大规模数据,但一些常规的神经网络架构,如多层感知机,通常在大规模网络中产生较差的性能了,而图神经网络可以利用无线通信的拓扑结构,有效解决资源分配问题。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.

综上所述,利用图神经网络优化无蜂窝的功率控制将会产生预期的结果。In summary, optimizing power control without cells using graph neural networks will produce the desired results.

发明内容Summary of the invention

根据上述提出的技术问题,本发明采用的技术手段如下:一种基于图神经网络的无蜂窝网络功率控制方法,包括如下步骤: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、采用时分双工操作模式,利用无蜂窝网络信道互易性,通过上行链路发送的导频信息进行无蜂窝网络信道估计;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、通过基于信道估计值的最大比率预编码方案,对下行链路数据传输阶段的传输符号进行预编码,然后利用共轭波束成形技术向用户发送信号;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、对最大化下行链路最小用户通信速率问题进行建模,再通过将最大化下行链路最小用户通信速率的问题转化为相应的图优化问题,采用一种基于图神经网络的功率控制算法进行求解,实现下行链路的通信速率的提高。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.

进一步地:所述采用时分双工操作模式,利用无蜂窝网络信道互易性,通过上行链路发送的导频信息进行无蜂窝网络信道估计的过程如下: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、在所考虑的无蜂窝网络系统中,共有M个单天线接入点和K个单天线用户,每个接入点都通过回程链路与中央处理器连接,M个接入点在相同的时间频率资源下为K个用户服务;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.

在无蜂窝网络系统中采用时分双工操作模式,利用信道互易性,在上行链路训练阶段,所有用户向接入点发送导频序列,在每个接入点处进行到所有用户的信道估计,获取到的信道状态信息用于上行链路数据传输解码和下行链路数据传输编码。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.

将第k个用户到第m个接入点间的信道系数用表示:The channel coefficient between the kth user and the mth access point is expressed as express:

其中,m=1,…,M,k = 1,..,K,是接入点m和用户k之间的大尺度衰落系数,主要反映的是路径损耗和阴影衰落对信道的影响,是小尺度衰落系数,每一个小尺度衰落系数都是独立同分布的,表示均值为0和方差为1的复高斯随机变量;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;

通过路径损耗和不相关的对数正态阴影对大尺度衰落系数进行建模:Large-scale fading coefficients via path loss and uncorrelated log-normal shadowing To model:

其中:表示路径损失,为具有标准方差的阴影衰落,其中路径损失可由如下表示:in: represents the path loss, With standard deviation and The shadow fading of It can be expressed as follows:

其中:是载波频率,是接入点的天线高度,是用户的天线高度,是第m个接入点到第k个用户间的距离,为参考距离;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;

阴影衰落是相互关联的,使用一个包含两个分量的模型来计算阴影衰落系数Shadow fading is interrelated and a two-component model is used to calculate the shadow fading coefficients: :

其中,,是两个独立的随机变量,表示均值为0和方差为1的高斯随机变量,是一个参数;in, , , are two independent random variables, represents a Gaussian random variable with mean 0 and variance 1, , is a parameter;

的协方差函数为: and The covariance function of is:

其中,是第个接入点和第个接入点之间的距离,是第个用户和第个用户间的距离,是相关距离;in, It is access point and The distance between access points, It is Users and The distance between users, is the correlation distance;

通过信道条件,得到第m个接入点在上行链路接收到用户k发送的导频信息为:By channel conditions , we get the pilot information sent by user k received by the mth access point in the uplink for:

其中,为上行链路导频传输持续时间,为第k个用户使用的导频序列,其中为随机变量,表示在复数域维的向量,.是欧几里得范数,是每个导频归一化信噪比,是第m个接入点处的附加噪声;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;

基于接收到的导频序列,第m个接入点进行信道估计,上的投影为:Based on the received pilot sequence, the mth access point performs channel estimation. exist Projection on for:

其中的共轭转置,表示共轭转置,表示第个用户,这里的k和都包含在用户集合K中,为用户的随机变量,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、依据最小均方误差准则,可将信道系数估计为:S12, according to the minimum mean square error criterion, the channel coefficient Estimated to be:

其中,表示第m个接入点到第个用户间的大尺度衰落系数,表示均值,表示共轭。in, Indicates the distance from the mth access point to the The large-scale fading coefficient between users, represents the mean, Indicates conjugation.

进一步地:所述通过基于信道估计值的最大比率预编码方案,对下行链路数据传输阶段的传输符号进行预编码,然后利用共轭波束成形技术向用户发送信号的过程如下: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、在下行链路数据传输阶段,接入点m处根据信道估计的结果使用波束成形对将要传输给用户k的数据进行预编码: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:

其中,是发送给第k个用户的符号,并且是归一化下行链路信噪比,是第m个接入点到第k个用户间下行链路的功率控制系数;采用了共轭波束技术,在信号传输部分中,表示对信道估计的共轭形式;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;

功率控制系数的选择需要满足每个接入点的功率约束:The selection of the power control coefficient needs to satisfy the power constraint of each access point:

也表示为:,表示为信道系数估计值的均方;Also expressed as: , , expressed as the channel coefficient estimate The mean square of

在无蜂窝系统中的下行链路数据传输阶段,所有接入点同时在同一时间频率资源上发送数据信号到用户;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、第k个用户接收到的信号为:S22, the signal received by the kth user is:

其中,是第k个用户的加性噪声,是发送给第k'个用户的符号,是第m个接入点到第k'个用户间下行链路的功率控制系数,为第m个接入点到第k'个用户间的信道估计系数;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;

假设每个用户都知道信道统计信息,接收信号写成:Assuming that each user knows the channel statistics, the received signal Written as:

这里,here,

其中,表示第k个用户期望信号的强度,表示波束成形增益的不确定性,表示来自个用户的干扰;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;

到第k个用户下行通信速率表达式为:The expression of downlink communication rate to the kth user is:

将公式展开,指的是第k个用户在下行链路的可达速率,可达速率表达式如下所示。Expand the formula, Refers to the achievable rate of the kth user in the downlink. The expression is as follows.

其中,表示为信道系数估计值的均方。in, Expressed as the channel coefficient estimate The mean square of .

进一步地:对最大化下行链路最小用户通信速率问题进行建模,再通过将最大化下行链路最小用户通信速率的问题转化为相应的图优化问题,采用一种基于图神经网络的功率控制算法进行求解,实现下行链路的通信速率的提高的过程如下: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、优化接入点发射功率控制,最大化最小用户通信速率,如下:S31, optimize the access point transmission power control to maximize the minimum user communication rate as follows:

对通信速率最大化的约束优化问题进行建模,如下所示:The constrained optimization problem of maximizing the communication rate is modeled as follows:

其中,C1为发射功率约束;Among them, C1 is the transmit power constraint;

图优化模型的图通常由表示,其中表示节点集合,表示相邻节点构成边的集合,xy表示集合中的节点。节点和边分别具有不同的特征,所以图的表示可以由表示,将节点映射到其特征,节点特征,将边映射到其特征,边特征表示为节点特征和边特征的维度大小;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;

定义节点特征矩阵,其中,表示为节点特征矩阵Z的第i行,即第i个节点的节点特征,表示为第i个节点。邻接特征张量,其中,表示为节点i和节点j之间边的特征,其中表示为节点i和节点j之间构成的边;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、对建立的最大化下行链路最小用户通信速率问题模型进行求解,获得使最小用户通信速率最大的接入点发射功率控制方案: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:

令M个接入点和K个用户作为节点,将无蜂窝系统模型构建为二部图;使用大尺度衰落系数作为神经网络的输入,优化变量表示为: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:

表示实数; represents a real number;

定义大尺度衰落矩阵为,其中,二部图的邻接特征张量为,其中The large-scale fading matrix is defined as ,in , the adjacency feature tensor of the bipartite graph is ,in ;

通过将通信速率表达式中的替换为,以及大尺度衰落系数替换为,可将最大化下行链路最小用户通信速率优化问题转化为如下的图优化问题: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、将损失函数定义为目标函数的负值:S33. Define the loss function as the negative value of the objective function:

图神经网络将卷积神经网络扩展到图中,在一个图神经网络层中,每个节点根据来自邻居节点的聚合信息更新自己的隐藏状态;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.

假设节点v上的节点特征为,节点u上的节点特征为,节点v和u组成的边e上的特征为表示复数,消息传递范式定义了以下逐节点和边上的计算: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:

其中,是在第t+1层神经网络中边上聚合后的消息,是在节点v在第t+1层神经网络的特征,t为所处神经网络的层数,t+1表示所处在第t+1层神经网络,为边的集合,是定义在每条边上的消息函数,通过将边上特征与其两端节点的特征相结合来生成消息,聚合函数会聚合节点接受到的消息,更新函数会结合聚合后的消息和节点本身的特征来更新节点的特征;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、无蜂窝网络系统中使用的是异构神经网络,每一层神经网络包含两种消息传递的类型,分别是接入点向用户传递的消息,以及用户向接入点传递的消息,因此要使用不同的权重矩阵来参数化不同的消息传递过程;将节点m的特征初始化为空向量,其中为实数域的空向量;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;

对于一个T层的图神经网络,节点m在第t层的更新为:For a T-layer graph neural network, the update of node m in the tth layer is:

即在第t层网络中节点m的节点特征为That is, the node feature of node m in the t-th layer network is ;

其中,是第t层神经网络中的可学权重,是在第T层网络中节点m的节点特征,是激活函数,为节点m在第t-1层图神经网络的节点特征,为节点k在第t-1层图神经网络的节点特征,是将最终隐藏状态映射到发射功率的多层感知机,聚合函数选择的是求和;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、根据图神经网络设计指南以及无蜂窝网络的下行数据传输模型的特点对图神经网络架构进行改进;仅在第一次迭代中运行从用户到接入点的消息传递: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:

即第一层神经网络中节点m的节点特征为That is, the node feature of node m in the first layer of the neural network is .

对于聚合函数选择平均聚合,是第一层神经网络中的可学权重,是激活函数,对于之后的消息传递过程,只考虑用户间的消息传递: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:

即在第t层网络中节点m的节点特征为That is, the node feature of node m in the t-th layer network is .

其中,是在第t层神经网络中可学参数,是一个将隐藏层映射到发射功率的可学习多层感知机。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.

本发明提供的一种基于图神经网络的无蜂窝网络功率控制方法,能够根据上行链路信道估计,对下行链路数据传输进行预编码,通过图神经网络对下行链路发射功率进行优化,有效地提高了系统的通信。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.

基于上述理由本发明可在无线通信等领域广泛推广。Based on the above reasons, the present invention can be widely promoted in fields such as wireless communication.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

为了更清楚地说明本发明实施例或现有技术中的技术方案,下面将对实施例或现有技术描述中所需要使用的附图做以简单地介绍,显而易见地,下面描述中的附图是本发明的一些实施例,对于本领域普通技术人员来讲,在不付出创造性劳动性的前提下,还可以根据这些附图获得其他的附图。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.

图1是本发明方法流程图。FIG. 1 is a flow chart of the method of the present invention.

图2为本发明实施例使用的场景图。FIG. 2 is a scene diagram used in an embodiment of the present invention.

图3为本发明实施例提供的图优化模型图。FIG3 is a diagram of a graph optimization model provided by an embodiment of the present invention.

图4为本发明实施例提供的神经网络流程图。FIG4 is a flowchart of a neural network provided by an embodiment of the present invention.

图5为本发明实施例提供的通过训练后的神经网络经过测试集的结果图;FIG5 is a graph showing the results of a test set of a trained neural network provided by an embodiment of the present invention;

图6为基于图神经网络的无蜂窝网络功率控制方法与多层感知机方法比较图。FIG6 is a comparison chart between the non-cellular network power control method based on graph neural network and the multi-layer perceptron method.

具体实施方式DETAILED DESCRIPTION

为了使本技术领域的人员更好地理解本发明方案,下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例仅仅是本发明一部分的实施例,而不是全部的实施例。基于本发明中的实施例,本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例,都应当属于本发明保护的范围。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.

需要说明的是,本发明的说明书和权利要求书及上述附图中的术语“第一”、“第二”等是用于区别类似的对象,而不必用于描述特定的顺序或先后次序。应该理解这样使用的数据在适当情况下可以互换,以便这里描述的本发明的实施例能够以除了在这里图示或描述的那些以外的顺序实施。此外,术语“包括”和“具有”以及他们的任何变形,意图在于覆盖不排他的包含,例如,包含了一系列步骤或单元的过程、方法、系统、产品或设备不必限于清楚地列出的那些步骤或单元,而是可包括没有清楚地列出的或对于这些过程、方法、产品或设备固有的其它步骤或单元。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.

图1是本发明方法流程图。FIG. 1 is a flow chart of the method of the present invention.

如图1所示,本发明实施例提供了一种基于图神经网络的无蜂窝网络功率控制方法,其特征在于,包括如下步骤: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、采用时分双工操作模式,利用无蜂窝网络信道互易性,通过上行链路发送的导频信息进行无蜂窝网络信道估计;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、通过基于信道估计值的最大比率预编码方案,对下行链路数据传输阶段的传输符号进行预编码,然后利用共轭波束成形技术向用户发送信号;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、对最大化下行链路最小用户通信速率问题进行建模,再通过将最大化下行链路最小用户通信速率的问题转化为相应的图优化问题,采用一种基于图神经网络的功率控制算法进行求解,实现下行链路的通信速率的提高。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.

步骤S1/S2/S3顺序执行;Steps S1/S2/S3 are executed sequentially;

图2为本发明实施例使用的场景图;FIG2 is a scene diagram used in an embodiment of the present invention;

进一步的,所述采用时分双工操作模式,利用无蜂窝网络信道互易性,通过上行链路发送的导频信息进行无蜂窝网络信道估计的具体内容为: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:

图2为本发明实施例使用的场景图;S11、在所考虑的无蜂窝网络系统中,共有M个单天线接入点和K个单天线用户,每个接入点都通过回程链路与中央处理器连接,M个接入点在相同的时间频率资源下为K个用户服务。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.

信号从接入点传到用户的过程被称为下行链路,反之则为上行链路。The process of signal transmission from access point to user is called downlink, and the reverse is uplink.

在本无蜂窝网络系统中采用时分双工操作模式,利用信道互易性,在上行链路训练阶段,所有用户向接入点发送导频序列,在每个接入点处进行到所有用户的信道估计,获取到的信道状态信息用于上行链路数据传输解码和下行链路数据传输编码。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.

将第k个用户到第m个接入点间的信道系数用表示:The channel coefficient between the kth user and the mth access point is expressed as express:

其中, m=1,…,M,k = 1,..,K,是接入点m和用户k之间的大尺度衰落系数,主要反映的是路径损耗和阴影衰落对信道的影响,是小尺度衰落系数,每一个小尺度衰落系数都是独立同分布的,表示均值为0和方差为1的复高斯随机变量。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.

通过路径损耗和不相关的对数正态阴影对大尺度衰落系数进行建模:Large-scale fading coefficients via path loss and uncorrelated log-normal shadowing To model:

其中:表示路径损失,为具有标准方差的阴影衰落,其中路径损失可由如下表示:in: represents the path loss, With standard deviation and The shadow fading of It can be expressed as follows:

其中:是载波频率,是接入点的天线高度,是用户的天线高度,是第m个接入点到第k个用户间的距离,为参考距离。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.

在现实世界中,相邻的发射机和接收机可能会被共同的障碍物包围,因此,阴影衰落是相互关联的,使用一个包含两个分量的模型来计算阴影衰落系数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. :

其中,,是两个独立的随机变量,表示均值为0和方差为1的复高斯随机变量,是一个参数。in, , , are two independent random variables, represents a complex Gaussian random variable with mean 0 and variance 1, , is a parameter.

的协方差函数为: and The covariance function of is:

其中,是第个接入点和第个接入点之间的距离,是第个用户和第个用户间的距离,是相关距离,取决于环境,一般在20m—200m之间。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.

通过信道条件,可以得到第m个接入点在上行链路接收到用户k发送的导频信息为:By channel condition , we can get the pilot information sent by user k received by the mth access point in the uplink for:

其中,为上行链路导频传输持续时间,为第k个用户使用的导频序列,其中为随机变量,表示在复数域维的向量,.是欧几里得范数,是每个导频归一化信噪比,是第m个接入点处的附加噪声。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.

基于接收到的导频序列,第m个接入点进行信道估计,上的投影为:Based on the received pilot sequence, the mth access point performs channel estimation. exist Projection on for:

其中的共轭转置,表示共轭转置,表示第个用户,这里的k和都包含在用户集合K中,为用户的随机变量,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、依据最小均方误差准则,可将信道系数估计为:S12, according to the minimum mean square error criterion, the channel coefficient Estimated to be:

其中,表示第m个接入点到第个用户间的大尺度衰落系数,表示均值,表示共轭。in, Indicates the distance from the mth access point to the The large-scale fading coefficient between users, represents the mean, Indicates conjugation.

所述通过基于信道估计值的最大比率预编码方案,对下行链路数据传输阶段的传输符号进行预编码,然后利用共轭波束成形技术向用户发送信号的过程如下: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、在下行链路数据传输阶段,接入点m处根据信道估计的结果使用波束成形对将要传输给用户k的数据进行预编码: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:

其中,是发送给第k个用户的符号,并且是归一化下行链路信噪比,是第m个接入点到第k个用户间下行链路的功率控制系数。功率控制系数的选择需要满足每个接入点的功率约束: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:

也可以表示为:,表示为信道系数估计值的均方。It can also be expressed as: , , expressed as the channel coefficient estimate The mean square of .

在无蜂窝系统中的下行链路数据传输阶段,所有接入点同时在同一时间频率资源上发送它们的数据信号到用户;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、第k个用户接收到的信号为:S22, the signal received by the kth user is:

其中,是第k个用户的加性噪声,是发送给第k'个用户的符号,是第m个接入点到第k'个用户间下行链路的功率控制系数,为第m个接入点到第k'个用户间的信道估计系数。假设每个用户都知道信道统计信息,接收信号可以写成: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:

这里,here,

其中,表示第k个用户期望信号的强度,表示波束成形增益的不确定性,表示来自个用户的干扰。可以得到第k个用户下行通信速率表达式为: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:

将公式展开,可得到用户k的完整通信速率表达式:Expanding the formula, we can get the complete communication rate of user k expression:

其中,表示为信道系数估计值的均方。in, Expressed as the channel coefficient estimate The mean square of .

根据要求1所述一种基于图神经网络的无蜂窝网络功率控制方法,对最大化下行链路最小用户通信速率问题进行建模,再通过将最大化下行链路最小用户通信速率的问题转化为相应的图优化问题,采用一种基于图神经网络的功率控制算法进行求解,实现下行链路的通信速率的提高的过程如下: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、优化接入点发射功率控制,最大化最小用户通信速率:S31. Optimize access point transmission power control to maximize the minimum user communication rate:

对通信速率最大化的约束优化问题进行建模,如下所示:The constrained optimization problem of maximizing the communication rate is modeled as follows:

其中,C1为发射功率约束。Among them, C1 is the transmission power constraint.

图3为本发明实施例提供的图优化模型图;FIG3 is a graph optimization model diagram provided by an embodiment of the present invention;

图优化模型的图通常由表示,其中表示节点集合,表示相邻节点构成边的集合,xy表示集合中的节点。节点和边分别具有不同的特征,所以图的表示可以由表示,将节点映射到其特征,节点特征,将边映射到其特征,边特征表示为节点特征和边特征的维度大小。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.

定义节点特征矩阵,其中,表示为节点特征矩阵Z的第i行,即第i个节点的节点特征,表示为第i个节点。邻接特征张量,其中,表示为节点i和节点j之间边的特征,其中表示为节点i和节点j之间构成的边。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、对建立的最大化下行链路最小用户通信速率问题模型进行求解,获得使最小用户通信速率最大的接入点发射功率控制方案。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.

为了将最大化下行链路最小用户通信速率优化问题转化为图优化问题,令M个接入点和K个用户作为节点,将无蜂窝系统模型构建为二部图。使用大尺度衰落系数作为神经网络的输入,优化变量表示为: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:

表示实数; represents a real number;

定义大尺度衰落矩阵为,其中,二部图的邻接特征张量为,其中The large-scale fading matrix is defined as ,in , the adjacency feature tensor of the bipartite graph is ,in .

通过将通信速率表达式中的替换为,以及大尺度衰落系数替换为,可将最大化下行链路最小用户通信速率优化问题转化为图优化问题: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、将损失函数定义为目标函数的负值:S33. Define the loss function as the negative value of the objective function:

图神经网络将卷积神经网络扩展到图中,在一个图神经网络层中,每个节点根据来自邻居节点的聚合信息更新自己的隐藏状态。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.

图神经网络是一个有可学参数的消息传递过程,消息传递是实现图神经网络的一种通用框架和编程范式。假设节点v上的节点特征为,节点u上的节点特征为,节点v和u组成的边e上的特征为表示复数,消息传递范式定义了以下逐节点和边上的计算: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:

其中,是在第t+1层神经网络中边上聚合后的消息,是在节点在第t+1层神经网络上的特征,t为所处神经网络的层数,t+1表示所处在第t+1层神经网络,为边的集合,是定义在每条边上的消息函数,它通过将边上特征与其两端节点的特征相结合来生成消息,聚合函数会聚合节点接受到的消息,更新函数会结合聚合后的消息和节点本身的特征来更新节点的特征;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、在本申请的无蜂窝网络系统中使用的是异构神经网络,每一层神经网络包含两种消息传递的类型,分别是接入点向用户传递的消息,以及用户向接入点传递的消息,因此要使用不同的权重矩阵来参数化不同的消息传递过程。由于不存在节点特征,所以将节点m的特征初始化为空向量,其中为实数域的空向量。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.

对于一个T层的图神经网络,节点m在第t层的更新为:For a T-layer graph neural network, the update of node m in the tth layer is:

即在第t层网络中节点m的节点特征为That is, the node feature of node m in the t-th layer network is .

.

其中,是第t层神经网络中的可学权重,是在第T层网络中节点m的节点特征,是激活函数,为节点m在第t-1层图神经网络的节点特征,为节点k在第t-1层图神经网络的节点特征,是将最终隐藏状态映射到发射功率的多层感知机,聚合函数选择的是求和;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、但是当前消息传递过程并不是最优的,所以可以根据图神经网络设计指南以及无蜂窝网络下行数据传输模型的特点对图神经网络架构进行改进。由于用户节点上既没有节点特征,也没有优化变量,因此我们仅在第一次迭代中运行从用户到接入点的消息传递:图4为本发明实施例提供的神经网络流程图;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;

即第一层神经网络中节点m的节点特征为That is, the node feature of node m in the first layer of the neural network is .

以简化消息传递,对于初始的神经网络的输入即大尺度衰落系数,通过神经网络后,映射到本文要优化的变量:功率控制系数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 ;

对于聚合函数选择平均聚合,是第一层神经网络中的可学权重,是激活函数,对于之后的消息传递过程,只考虑用户间的消息传递: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:

即在第t层网络中节点m的节点特征为That is, the node feature of node m in the t-th layer network is .

其中,是在第t层神经网络中可学参数,是一个将隐藏层映射到发射功率的可学习多层感知机。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.

仿真条件Simulation conditions

在仿真场景中,接入点和用户随机分布在1km * 1km的矩形区域,载波频率,接入点的天线高度,用户的天线高度,阴影衰落的标准方差,每个导频归一化信噪比,归一化下行链路信噪比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 .

仿真内容与结果分析Simulation content and result analysis

仿真1:训练集训练图神经网络,并用测试集数据进行验证。Simulation 1: Train the graph neural network with the training set and verify it with the test set data.

如图5所示,将图2展示的场景系统模型构建成的图模型输入神经网络进行训练,通过训练集训练后的网络,利用测试集进行验证。训练集与测试集的数量均选取4000,接入点的个数为100,用户的个数为40。在经历50个时期后,测试集的数据具有良好的收敛性。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.

仿真2:将本申请提出的方法与多层感知机方法做对比,如图6可以看出,所提出的基于图神经网络的无蜂窝网络功率控制方法性能优于多层感知机,在训练好的网络中,所提方法性能较多层感知机提升20%,验证本发明方法的有效性。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.

最后应说明的是:以上各实施例仅用以说明本发明的技术方案,而非对其限制;尽管参照前述各实施例对本发明进行了详细的说明,本领域的普通技术人员应当理解:其依然可以对前述各实施例所记载的技术方案进行修改,或者对其中部分或者全部技术特征进行等同替换;而这些修改或者替换,并不使相应技术方案的本质脱离本发明各实施例技术方案的范围。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)

1.一种基于图神经网络的无蜂窝网络功率控制方法,其特征在于,包括如下步骤:1. A non-cellular network power control method based on graph neural network, characterized in that it includes the following steps: S1、采用时分双工操作模式,利用无蜂窝网络信道互易性,通过上行链路发送的导频信息进行无蜂窝网络信道估计;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、通过基于信道估计值的最大比率预编码方案,对下行链路数据传输阶段的传输符号进行预编码,然后利用共轭波束成形技术向用户发送信号;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、对最大化下行链路最小用户通信速率问题进行建模,再通过将最大化下行链路最小用户通信速率的问题转化为相应的图优化问题,采用一种基于图神经网络的功率控制算法进行求解,实现下行链路的通信速率的提高;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; 所述对最大化下行链路最小用户通信速率问题进行建模,再通过将最大化下行链路最小用户通信速率的问题转化为相应的图优化问题,采用一种基于图神经网络的功率控制算法进行求解,实现下行链路的通信速率的提高的过程如下: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、优化接入点发射功率控制,最大化最小用户通信速率,如下:S31, optimize the access point transmission power control to maximize the minimum user communication rate as follows: 对通信速率最大化的约束优化问题进行建模,如下所示:The constrained optimization problem of maximizing the communication rate is modeled as follows: 其中,C1为发射功率约束;Among them, C1 is the transmit power constraint; 图优化模型的图由表示,其中表示节点集合,表示相邻节点构成边的集合,xy表示集合中的节点,节点和边分别具有不同的特征,所以图的表示可以由表示,将节点映射到其特征,节点特征 ,将边映射到其特征,边特征,其中,表示为复数域,表示为节点特征和边特征的维度大小;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; 定义节点特征矩阵 ,其中,表示为节点特征矩阵Z的第i行,即第i个节点的节点特征,表示为第i个节点,邻接特征张量 ,其中 ,表示为节点i和节点j之间边的特征,其中表示为节点i和节点j之间构成的边;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、对建立的最大化下行链路最小用户通信速率问题模型进行求解,获得使最小用户通信速率最大的接入点发射功率控制方案: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: 令M个接入点和K个用户作为节点,将无蜂窝系统模型构建为二部图;使用大尺度衰落系数作为神经网络的输入,优化变量 表示为: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: 表示实数; represents a real number; 定义大尺度衰落矩阵为,其中 ,二部图的邻接特征张量为,其中The large-scale fading matrix is defined as ,in , the adjacency feature tensor of the bipartite graph is ,in ; 通过将通信速率表达式中的替换为,以及大尺度衰落系数替换为,可将最大化下行链路最小用户通信速率优化问题转化为如下的图优化问题: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、将损失函数定义为目标函数的负值:S33. Define the loss function as the negative value of the objective function: 图神经网络将卷积神经网络扩展到图中,在一个图神经网络层中,每个节点根据来自邻居节点的聚合信息更新自己的隐藏状态;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. 假设节点v上的节点特征为,节点u上的节点特征为,节点v和u组成的边e上的特征为表示复数,消息传递范式定义了以下逐节点和边上的计算: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: 其中,是在第t+1层神经网络中边上聚合后的消息,是在节点v在第t+1层神经网络的特征,t为所处神经网络的层数,为边的集合,是定义在每条边上的消息函数,通过将边上特征与其两端节点的特征相结合来生成消息,聚合函数会聚合节点接受到的消息,更新函数会结合聚合后的消息和节点本身的特征来更新节点的特征;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、无蜂窝网络系统中使用的是异构神经网络,每一层神经网络包含两种消息传递的类型,分别是接入点向用户传递的消息,以及用户向接入点传递的消息,因此要使用不同的权重矩阵来参数化不同的消息传递过程;将节点m的特征初始化为空向量,其中为实数域的空向量;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; 对于一个T层的图神经网络,节点m在第t层的更新为:For a T-layer graph neural network, the update of node m in layer t for: 即在第t层网络中节点m的节点特征为That is, the node feature of node m in the t-th layer network is ; 其中,是第t层神经网络中的可学权重,是在第T层网络中节点m的节点特征, 是激活函数,为节点m在第t-1层图神经网络的节点特征,为节点k在第t-1层图神经网络的节点特征,是将最终隐藏状态映射到发射功率的多层感知机,聚合函数选择的是求和;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、根据图神经网络设计指南以及无蜂窝网络的下行数据传输模型的特点对图神经网络架构进行改进;仅在第一次迭代中运行从用户到接入点的消息传递: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: 即第一层神经网络中节点m的节点特征为That is, the node feature of node m in the first layer of the neural network is ; 对于聚合函数选择平均聚合, 是第一层神经网络中的可学权重,是激活函数,对于之后的消息传递过程,只考虑用户间的消息传递: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: 即在第t层网络中节点m的节点特征为That is, the node feature of node m in the t-th layer network is ; 其中,是在第t层神经网络中可学参数,是一个将隐藏层映射到发射功率的可学习多层感知机;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; 所述采用时分双工操作模式,利用无蜂窝网络信道互易性,通过上行链路发送的导频信息进行无蜂窝网络信道估计的过程如下: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、在所考虑的无蜂窝网络系统中,共有M个单天线接入点和K个单天线用户,每个接入点都通过回程链路与中央处理器连接,M个接入点在相同的时间频率资源下为K个用户服务;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. 在无蜂窝网络系统中采用时分双工操作模式,利用信道互易性,在上行链路训练阶段,所有用户向接入点发送导频序列,在每个接入点处进行到所有用户的信道估计,获取到的信道状态信息用于上行链路数据传输解码和下行链路数据传输编码;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; 将第k个用户到第m个接入点间的信道系数用表示:The channel coefficient between the kth user and the mth access point is expressed as express: 其中,m=1,…,M,k = 1,..,K, 是接入点m和用户k之间的大尺度衰落系数,主要反映的是路径损耗和阴影衰落对信道的影响,是小尺度衰落系数,每一个小尺度衰落系数都是独立同分布的,表示均值为0和方差为1的复高斯随机变量;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; 通过路径损耗和不相关的对数正态阴影对大尺度衰落系数进行建模:Large-scale fading coefficients via path loss and uncorrelated log-normal shadowing To model: 其中:表示路径损失,为具有标准方差和阴影衰落系数的阴影衰落,其中路径损失可由如下表示:in: represents the path loss, With standard deviation and shadow fading coefficient The shadow fading of It can be expressed as follows: 其中:是载波频率,是接入点的天线高度,是用户的天线高度,是第m个接入点到第k个用户间的距离,为参考距离;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; 阴影衰落是相互关联的,使用一个包含两个分量的模型来计算阴影衰落系数Shadow fading is interrelated and a two-component model is used to calculate the shadow fading coefficients: : 其中,,是两个独立的随机变量,表示均值为0和方差为1的高斯随机变量,是一个参数;in, , , are two independent random variables, represents a Gaussian random variable with mean 0 and variance 1, , is a parameter; 的协方差函数为: and The covariance function of is: 其中,是第个接入点和第个接入点之间的距离,是第个用户和第个用户间的距离,是相关距离;in, It is access point and The distance between access points, It is Users and The distance between users, is the correlation distance; 通过信道条件,得到第m个接入点在上行链路接收到用户k发送的导频信息By channel conditions , we get the pilot information sent by user k received by the mth access point in the uplink : 其中,为上行链路导频传输持续时间,为第k个用户使用的导频序列,其中为用户k的随机变量,表示在复数域维的向量,.是欧几里得范数,是每个导频归一化信噪比,是第m个接入点处的附加噪声;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; 基于接收到的导频序列,第m个接入点进行信道估计,上的投影为:Based on the received pilot sequence, the mth access point performs channel estimation. exist Projection on for: 其中:的共轭转置,表示共轭转置,表示第个用户,这里的k和都包含在用户集合K中,为用户的随机变量,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、依据最小均方误差准则,可将信道系数估计为:S12, according to the minimum mean square error criterion, the channel coefficient Estimated to be: 其中,表示第m个接入点到第 个用户间的大尺度衰落系数,表示均值,表示共轭;in, Indicates the distance from the mth access point to the The large-scale fading coefficient between users, represents the mean, denotes conjugation; 所述通过基于信道估计值的最大比率预编码方案,对下行链路数据传输阶段的传输符号进行预编码,然后利用共轭波束成形技术向用户发送信号的过程如下: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、在下行链路数据传输阶段,接入点m处根据信道估计的结果使用波束成形对将要传输给用户k的数据进行预编码,第m个接入点发送的信号为: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: 其中,是发送给第k个用户的符号,并且是归一化下行链路信噪比,是第m个接入点到第k个用户间下行链路的功率控制系数;采用了共轭波束技术,在信号传输部分中,表示对信道估计的共轭形式;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; 功率控制系数的选择需要满足每个接入点的功率约束:The selection of the power control coefficient needs to satisfy the power constraint of each access point: 也表示为:,表示为信道系数估计值的均方;Also expressed as: , , expressed as the channel coefficient estimate The mean square of 在无蜂窝系统中的下行链路数据传输阶段,所有接入点同时在同一时间频率资源上发送数据信号到用户;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、第k个用户接收到的信号为:S22, the signal received by the kth user is: 其中,是第k个用户的加性噪声,是发送给第k'个用户的符号,是第m个接入点到第k'个用户间下行链路的功率控制系数,为第m个接入点到第k'个用户间的信道估计系数;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; 假设每个用户都知道信道统计信息,接收信号写成:Assuming that each user knows the channel statistics, the received signal Written as: 这里,here, 其中,表示第k个用户期望信号的强度,表示波束成形增益的不确定性,表示来自个用户的干扰;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; 到第k个用户下行通信速率表达式为:The expression of downlink communication rate to the kth user is: 将公式展开,指的是第k个用户在下行链路的可达速率,可达速率表达式如下所示;Expand the formula, Refers to the achievable rate of the kth user in the downlink. The expression is as follows; 其中,表示为信道系数估计值的均方。in, Expressed as the channel coefficient estimate The mean square of .
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