A graphormer-based cell-free network power control method

Abstract

This invention discloses a cellless network power control method based on Graphormer, comprising: constructing a cellless network using time-division duplex mode; defining an uplink training model for channel estimation; defining a downlink data transmission model for precoding downlink data symbols based on the estimated channel; constructing graph structure data based on the cellless network, distributed access points, and user equipment; building a Graphormer-based neural network model; encoding the graph structure information according to the constructed graph structure data to fully extract global and local network information; training the Graphormer-based neural network to obtain a trained Graphormer-based neural network model; and using the trained Graphormer-based neural network model to achieve cellless network power control based on the transmitted power of the distributed access points, the received noise of the user equipment, and the channel between the distributed access points and the user equipment.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and more particularly to a cellless network power control method based on Graphormer. Background Technology

[0002] To meet the ever-growing demand for mobile user equipment (UE) in terms of both quantity and capacity, mobile communication systems are undergoing upgrades and evolution. Cellular-free networks, due to their advantages such as uniform signal coverage and avoidance of handover, have become one of the important candidate architectures for 6G networks. A cellless network consists of multiple access points (APs) randomly distributed across the coverage area. Each AP is connected to a central processing unit (CPU) via a fronthaul link, and the CPU coordinates cooperation between APs. All APs share the same time-frequency resources to provide services to each UE. However, in this architecture, multi-user interference in the communication network increases significantly, leading to a decrease in the signal-to-interference-plus-noise ratio (SNR). To address this issue, power control has become one of the key technologies for cellless networks.

[0003] Traditional power control methods based on optimization algorithms typically require numerous iterations, resulting in high computational complexity and hindering real-time application in future large-scale networks. Therefore, leveraging intelligent technologies—especially deep learning—to improve the efficiency of power control algorithms has become a hot research topic. In recent years, graph neural networks (GNNs) have been widely applied to resource scheduling and allocation in wireless communication due to their powerful ability to process graph-structured data. Graphormer, as an innovative architecture combining Transformer and GNNs, can extract global and local information from complex graph-structured data, making it suitable for modeling interference relationships in cell-free networks. However, current research based on Graphormer mainly focuses on general graph learning tasks, and its application in wireless communication is still in its early exploratory stages. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention employs the following technical means: a cellless network power control method based on Graphormer, comprising the following steps:

[0005] A cellless network using time-division duplex mode is constructed, an uplink training model is defined for channel estimation, and a downlink data transmission model is defined to precode downlink data symbols based on the estimated channel.

[0006] Based on cellless networks, distributed access points, and user equipment, construct graph-structured data;

[0007] Build a neural network model based on Graphormer;

[0008] Based on the constructed graph structure data, the graph structure information is encoded to fully extract global and local information of the network. The Grapher-based neural network is then trained to obtain a trained Grapher-based neural network model.

[0009] Based on the transmit power of the distributed access point, the receive noise of the user equipment, and the channel between the distributed access point and the user equipment, a pre-trained Graphormer-based neural network model is used to achieve cellless network power control.

[0010] Furthermore, the graph structure data includes topological relationships, node and edge features and variables, as detailed below:

[0011] Cellular-free networks are modeled using a heterogeneous undirected bipartite graph, where distributed access points (APs) and user equipment (UEs) are considered as two types of nodes, namely AP nodes and UE nodes, respectively. The channel between AP nodes and UE nodes is treated as an edge. This heterogeneous undirected bipartite graph is represented as follows: in, Let ε represent the set of nodes, and ε represent the set of edges. From the set of AP nodes and UE node set Composition, AP node set It consists of M AP nodes, and the UE node set is... It consists of K UE nodes, and the edge set ε consists of M×K edges. The elements in ε are denoted as (m,k).

[0012]

[0013] Define the feature matrix as consisting of the feature vectors of all AP nodes. The node feature corresponding to the m-th AP is f. m =P max ; where f1,…,f M The characteristic matrix F AP M elements; Let represent the set of all M×1 dimensional matrices in the real number field;

[0014] Define the feature matrix as consisting of the feature vectors of all UE nodes. The node feature corresponding to the kth UE is f. k =σ 2 ;f1,…,f K The characteristic matrix F UE K elements, Let be the set of all K×1 dimensional matrices in the real number field;

[0015] Define the feature matrix as consisting of all edge feature vectors. The edge characteristic corresponding to edge (m,k) is e. (m,k) =β m,k ; where β m,k Let be the large-scale fading coefficient of the channel between the m-th AP and the k-th UE. Let be the set of all M×K×1 dimensional matrices over the real number field;

[0016] Define a vector consisting of the variables on all AP nodes as follows: p m p1, ..., p represents the total transmit power of the m-th AP; M For vector p AP M elements; It is an M-dimensional real space;

[0017] Define the matrix consisting of the variables on all edges as follows: This represents the power ratio allocated by the m-th AP to the k-th UE;

[0018] Therefore, the power allocated by the m-th AP to the k-th UE is expressed as:

[0019] Furthermore, the neural network model of the Graphormer includes:

[0020] The preprocessing layer is used to map AP node features, UE node features, and edge features from 1×1 dimension to 1×d dimension using three different MLPs;

[0021] The update layer is used to receive the preprocessed feature vectors of AP nodes, UE nodes and edges transmitted by the preprocessing layer, and update the node features of AP and UE nodes using message passing mechanism and type encoding respectively.

[0022] The post-processing layer receives the updated node features transmitted by the update layer, processes the node features and edge features, and obtains the power allocation result.

[0023] Furthermore, the encoding of the graph structure information includes using the following formula:

[0024]

[0025] The process of updating the features of AP nodes is as follows: the m-th AP node aggregates the features of all edges adjacent to it. This indicates that the first-order neighbor node operator is used for the m-th AP node. The aggregation operator uses the averaging operation, and then the resulting 1×d-dimensional feature vector is input. Will The output and the 0th layer feature vector of the m-th AP obtained from the preprocessing layer The feature vectors of the introduced 1×d type encoding are added together to obtain the first-layer feature vector of the m-th AP.

[0026] The process of updating UE node characteristics is as follows: Aggregate the features of all edges adjacent to the k-th UE node. This indicates that the first-order neighbor node operator is used for the k-th UE node. The aggregation operator uses the averaging operation, and then the resulting 1×d-dimensional feature vector is input. Will The output and the 0th layer feature vector of the m-th AP obtained from the preprocessing layer The 1×d type encoded feature vectors are added together to obtain the final first-layer feature vector of the k-th UE.

[0027] Where δ AP δ UE Different 1×d-dimensional learnable vectors are used to distinguish different node types, which is the type encoding in graph structure information encoding;

[0028] Attention coefficient A with graph structure information encoding i,j The calculation method is as follows:

[0029]

[0030] The first term is the traditional self-attention mechanism, using a 1×d-dimensional query vector q. i and 1×d-dimensional bond vector k j The attention coefficient scalar based on node features is calculated, and the second term is the spatial encoding. The third term is the attention coefficient scalar that captures spatial information between nodes; A scalar of attention coefficients that can capture edge information between nodes;

[0031] The calculation method is as follows:

[0032]

[0033] Wherein, ψ(v i ,v j ) represents the shortest hop count between node i and node j; b1 and b2 are two learnable scalars;

[0034] The edge feature encoding is calculated as follows:

[0035]

[0036] Where (1,2) is defined as the weighted shortest path between nodes i and j, where the edge weights are the large-scale fading coefficients. and Let the feature vectors on edges 1 and 2 that form the weighted shortest path be... There are two learnable 1×d-dimensional vectors.

[0037] Further processing of node and edge features to obtain the power allocation results is as follows:

[0038] The node feature vector of the m-th AP is input into the MLP, where the activation function of the MLP is Sigmoid. Then, the output of the MLP is multiplied by the maximum transmit power P. max The transmit power p of the m-th AP is obtained. m ;

[0039] The node feature vector of the m-th AP, the node feature vector of the k-th UE, and the edge feature vector of edge (m,k) are concatenated and then input into the MLP. post Get p' m,k The activation function of the MLP is LeakyReLU.

[0040] Then it will be p' m,k The resulting M*K dimensional matrix P' is subjected to Sofmax row-wise to obtain an M*K dimensional matrix. The elements of this matrix represent the power ratio allocated by the m-th AP to the k-th UE.

[0041] Finally, the power p allocated by the m-th AP to the k-th UE is obtained. m,k :

[0042] Furthermore, the Graphormer-based neural network is trained using an unsupervised learning method, and the loss function is set by maximizing the spectral efficiency of the cellless network.

[0043] Furthermore, the process of mapping AP node features, UE node features, and edge features from 1×1 dimension to 1×d dimension using three different MLPs is as follows:

[0044]

[0045] For the features of the m-th AP node after preprocessing, f AP,m Let m represent the node characteristics of the m-th AP. This indicates the MLP used in the preprocessing layer to process the features of AP nodes;

[0046] For the features of the k-th UE node after preprocessing, f UE,k This represents the node characteristics of the k-th UE. This indicates the MLP used in the preprocessing layer to process the features of AP nodes;

[0047] Features of the preprocessed edge (m,k); MLP pre For use in the preprocessing layer MLP that processes features;

[0048] After this operation, the AP node features, UE node features, and edge features have the same dimension and contain richer information.

[0049] This invention proposes a graph-based power control method for cellless networks. It constructs graph-structured data of the cellless network and designs a graph-based neural network architecture to fully extract global and local information. Finally, the power control result is obtained by jointly analyzing the outputs of nodes and edges. Compared to traditional optimization algorithms, the proposed method reduces computational complexity and provides a feasible approach for power control in future large-scale networks.

[0050] To address this, this invention proposes a power control method for cellless networks based on Graphormer, aiming to leverage Graphormer's powerful feature learning capabilities to extract the spatial distribution and intensity of multi-user interference, and improve downlink spectrum efficiency in cellless networks by optimizing power control between AP and UE. Attached Figure Description

[0051] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 This is a flowchart of the method of the present invention.

[0053] Figure 2 This is a scenario diagram used in an embodiment of the present invention.

[0054] Figure 3 This is a data modeling diagram of a cellless network graph structure provided in an embodiment of the present invention.

[0055] Figure 4 The algorithm flowchart provided for the embodiments of the present invention.

[0056] Figure 5 The neural network convergence curve provided in the embodiment of the present invention.

[0057] Figure 6 The cumulative distribution of user spectrum efficiency is provided for embodiments of the present invention.

[0058] Figure 7 Box plot of spectrum efficiency for cellless networks provided in an embodiment of the present invention. Detailed Implementation

[0059] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0060] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0061] Figure 1 This is a flowchart of the method of the present invention.

[0062] like Figure 1 As shown, this embodiment of the invention provides a cellless network power control method based on Graphormer, including the following steps:

[0063] A cellless network power control method based on Graphormer, characterized by the following steps:

[0064] S1. Construct a cellless network using time-division duplex mode, define an uplink training model for channel estimation, and define a downlink data transmission model to precode downlink data symbols based on the estimated channel.

[0065] S2: Construct graph-structured data based on cellless networks, distributed access points, and user equipment;

[0066] S3: Build a neural network model based on Graphormer;

[0067] S4: Based on the constructed graph structure data, the graph structure information is encoded to fully extract the global and local information of the network, and the Grapher-based neural network is trained to obtain a trained Grapher neural network model.

[0068] S5: Based on the transmit power of the distributed access point, the receive noise of the user equipment, and the channel between the distributed access point and the user equipment, a pre-trained Graphormer-based neural network model is used to implement cellless network power control.

[0069] Steps S1 / S2 / S3 / S4 / S5 are executed sequentially;

[0070] Figure 2 This is a scene diagram used in an embodiment of the present invention;

[0071] Furthermore, a cell-free network employing time-division duplex mode is constructed, defining an uplink training model for channel estimation and a downlink data transmission model to precode downlink data symbols using the estimated channel. The specific details are as follows:

[0072] S11. Consider a cellless network consisting of M distributed access points (APs) and K user equipment (UEs). Describes the set of APs. This represents a set of UEs. APs and UEs are randomly distributed within the coverage area. APs are connected to the CPU via a fronthaul network, which is assumed to have unlimited capacity and be capable of error-free data transmission. Each AP is equipped with N antennas, and each UE is equipped with a single antenna. All APs use the same time-frequency resources to provide services to all UEs.

[0073] Cellular networks using Time Division Duplex (TDM) protocols, focusing on downlink data transmission, divide a coherent block into two phases: uplink pilot training and downlink data transmission. First, in the uplink phase, each UE uploads a length of τ. p The pilot sequence is used, and channel estimation is performed at the AP. Then, in the downlink phase, the AP uses τ d =τ c -τ p Each sample transmits UE data.

[0074] In a coherent block, the correlated Rayleigh fading channel between the m-th AP and the k-th UE is an N×1-dimensional complex vector, denoted as h m,k It follows a complex Gaussian distribution and can be expressed as:

[0075]

[0076] Among them, 0 N It is an N×N dimensional matrix of all zeros. R is an N×N complex matrix. m,k The spatial correlation matrix is ​​determined by the channel gain between the m-th AP and the k-th UE and the spatial correlation among the N antennas equipped on the m-th AP. The channel gain depends on the path loss. Similar to uncorrelated Rayleigh fading channels, the large-scale fading coefficient β is... mk Defined as:

[0077]

[0078] Where tr() represents the expression for matrix R m,k The trace calculation operation is performed, where N is the number of antennas equipped on the m-th AP.

[0079] Assume the number of available orthogonal pilots τ p If the number of users K in a cellless network is less than τ, then τ = ... p <K orthogonal pilot sequences The pilot sequence is assigned to K UEs in a fixed and known manner, and this sequence satisfies:

[0080]

[0081] in,() H Let t represent the Helmet transpose operator. k ∈{1,…,τ p} represents the pilot sequence number assigned to the k-th UE. The set of UEs that use the same pilot sequence as the k-th UE. Defined as:

[0082]

[0083] S12, the pilot signal received by the m-th AP during an uplink phase. It can be represented as:

[0084]

[0085] Where, η k Let be the transmit power of the pilot sequence for the k-th UE. Let be the received noise of the m-th AP, whose elements have a mean of 0 and a variance of σ. 2 The complex Gaussian distribution, i.e. Using the received pilot signal, the AP performs channel estimation using the minimum mean square error algorithm. The estimated channel for the k-th UE at the m-th AP is... It can be represented as:

[0086]

[0087] Among them, I N It is an N×N dimensional identity matrix. -1 The operator for finding the inversion of a matrix is ​​(). * This represents the conjugate transpose operator.

[0088] S13, transfer the downlink data symbol s of the kth UE. k Recorded as: It is a complex scalar, and its average power is 1, that is... The m-th AP receives the data symbol s of the k-th UE transmitted by the CPU. k Then, using the locally computed N×1 dimensional precoding vector w m,k For s k Perform precoding, i.e., use w m,k Multiply by s k , denoted as w m,k s k A modified local partial minimum mean square error precoding algorithm is used, with the precoding vector w... m,k It is based on the channel estimation at the m-th AP. Calculated. For the k-th UE served by the m-th AP, the precoding vector for:

[0089]

[0090] The purpose of the first formula is to... Normalization facilitates subsequent power control; |||| is the L2 norm operator, and:

[0091]

[0092] This represents the set of UEs with the maximum channel gain in each pilot signal at the m-th AP. Indicates the use of pilot frequency φ ε A collection of users. Z m,u Indicates channel estimation error The correlation matrix, The expression is: Therefore Z m,u It can be represented as:

[0093]

[0094] Let p be the downlink transmission power allocated by the m-th AP to the k-th UE. m,k If ≥0, then the sum of the precoded signals of all UEs transmitted by the m-th AP is:

[0095]

[0096] Power control must meet the following constraints:

[0097]

[0098] Among them, P max Maximum transmit power for each AP.

[0099] The signal received by the kth UE The expression is:

[0100]

[0101] Among them, DS k MUI represents the signal that the k-th user expects to receive. k This represents the interference signal from other users to the k-th user. The noise at the k-th UE has a mean of 0 and a variance of σ. 2 The complex Gaussian distribution.

[0102] According to the above expression, in a coherent block, the downlink achievable spectral efficiency SE of the k-th UE is... k It can be represented as:

[0103]

[0104] Among them, instantaneous signal-to-interference-plus-noise ratio (SINR) k for:

[0105]

[0106] Based on the above modeling considerations, this invention designs a Graphormer-based neural network using power control as a method to maximize the downlink spectral efficiency of cellless networks under the finite downlink transmit power constraint of each AP.

[0107] Furthermore, the graph structure data includes topological relationships, node and edge features and variables, specifically:

[0108] Figure 3 This is a data modeling diagram of a cellless network graph structure provided in an embodiment of the present invention;

[0109] S21. The above cellless network is modeled using a heterogeneous undirected bipartite graph, where AP and UE are considered as two types of nodes, namely AP nodes and UE nodes, respectively. The channel between AP nodes and UE nodes is regarded as an edge. This heterogeneous undirected bipartite graph can be represented as follows: in, Let ε represent the set of nodes, and ε represent the set of edges. From the set of AP nodes and UE node set Composition, AP node set It consists of M AP nodes, and the UE node set is... A system consists of K UE nodes, and its edge set ε consists of M×K edges. The elements in ε are denoted as (m,k). The above description can be expressed as:

[0110]

[0111] Define the feature matrix as consisting of the feature vectors of all AP nodes. The node feature corresponding to the m-th AP is f. m =P max ; where f1,…,f M The characteristic matrix F AP M elements; Let represent the set of all M×1 dimensional matrices in the real number field;

[0112] Define the feature matrix as consisting of the feature vectors of all UE nodes. The node feature corresponding to the kth UE is f. k =σ 2 ;f1,...,f K The characteristic matrix F UE K elements, Let be the set of all K×1 dimensional matrices in the real number field;

[0113] Define the feature matrix as consisting of all edge feature vectors. The edge characteristic corresponding to edge (m,k) is e. (m,k) =β m,k , where β m,k Let be the large-scale fading coefficient of the channel between the m-th AP and the k-th UE. Let be the set of all M×K×1 dimensional matrices over the real number field;

[0114] Define a vector consisting of the variables on all AP nodes as follows: p m Let p1,...,p represent the transmit power of the m-th AP. M For vector p AP M elements; It is an M-dimensional real space;

[0115] Define the matrix consisting of the variables on all edges as follows: Its elements are This represents the power allocation ratio of the m-th AP to the k-th UE. Therefore, the power allocated by the m-th AP to the k-th UE can be expressed as the product of the transmit power of the m-th AP and the power allocation ratio of the m-th AP to the k-th UE, i.e.

[0116] Figure 4 The algorithm flowchart provided for the embodiments of the present invention;

[0117] Furthermore, the aforementioned graphormer-based neural network architecture mainly includes a preprocessing layer, an update layer, and a post-processing layer. Based on the constructed graph data structure, three graph structure information encoding methods are designed to better extract global and local network information. Unsupervised learning is used to train the neural network, improving the downlink spectral efficiency of the cell-free network. The specific content is as follows:

[0118] The graphormer-based neural network model includes:

[0119] The preprocessing layer is used to map AP node features, UE node features, and edge features from 1×1 dimension to 1×d dimension using three different MLPs;

[0120] The update layer is used to receive the preprocessed feature vectors of AP nodes, UE nodes and edges transmitted by the preprocessing layer, and update the node features of AP and UE nodes using message passing mechanism and graph structure information encoding respectively.

[0121] The post-processing layer receives the updated node features transmitted by the update layer, processes the node features and edge features, and obtains the power allocation result.

[0122] The preprocessing layer is constructed by using three different MLPs to map AP node features, UE node features, and edge features from 1×1 dimension to 1×d dimension:

[0123]

[0124] For the features of the m-th AP node after preprocessing, f AP,m Let m represent the node characteristics of the m-th AP. This indicates the MLP used in the preprocessing layer to process the features of AP nodes;

[0125] For the features of the k-th UE node after preprocessing, f UE,k This represents the node characteristics of the k-th UE. This indicates the MLP used in the preprocessing layer to process the features of AP nodes;

[0126] Features of the preprocessed edge (m,k); MLP pre For use in the preprocessing layer MLP that processes features;

[0127] After this operation, the AP node features, UE node features, and edge features have the same dimension and contain richer information, which facilitates subsequent processing.

[0128] The construction and update layer consists of two steps. First, the AP node and UE node are updated with node characteristics using a message passing mechanism and type encoding, respectively:

[0129]

[0130] The process of updating the features of AP nodes is as follows: the m-th AP node aggregates the features of all edges adjacent to it. This indicates that the first-order neighbor node operator is used for the m-th AP node. The aggregation operator uses the averaging operation, and then the resulting 1×d-dimensional feature vector is input. Will The output and the 0th layer feature vector of the m-th AP obtained from the preprocessing layer The feature vectors of the introduced 1×d type encoding are added together to obtain the first-layer feature vector of the m-th AP.

[0131] The process of updating UE node characteristics is as follows: Aggregate the features of all edges adjacent to the k-th UE node. This indicates that the first-order neighbor node operator is used for the k-th UE node. The aggregation operator uses the averaging operation, and then the resulting 1×d-dimensional feature vector is input. Will The output and the 0th layer feature vector of the m-th AP obtained from the preprocessing layer The 1×d type encoded feature vectors are added together to obtain the final first-layer feature vector of the k-th UE.

[0132] Where, δ AP δ UE Different 1×d-dimensional learnable vectors are used to distinguish different node types. This is the type encoding in graph structure information encoding. The updated AP node features and UE node features contain local information and can reflect the surrounding channel conditions.

[0133] Next, the AP node features and UE node features are concatenated, while edge features are preserved, to facilitate further updating of node features using Graphormer, thus enriching the node feature information. This process is as follows:

[0134]

[0135] in, The feature matrix is ​​a (M+K)×d-dimensional real feature matrix composed of the first-layer feature vectors of M APs and the first-layer feature vectors of K UEs. It is an M×K×d-dimensional real feature matrix composed of the first-layer feature vectors of M×K edges.

[0136] On this graph, node features are updated using a Graphormer layer. The architecture of the Graphormer layer can be represented as follows:

[0137]

[0138] In this architecture, MHA stands for Multi-Head Attention, LN for Layer Normalization, FFN for Feedforward Neural Network, and l represents the l-th Graphormer layer. This architecture is also a classic architecture of the Transformer layer. The Graphormer layer, based on this, introduces graph structure information encoding during the attention coefficient calculation process to capture the graph structure information between node i and node j, as well as the relationships between node pairs, rather than focusing solely on the semantic similarity between node pairs. Inspired by this, this invention sets three graph structure information encoding methods based on the established graph structure data, and the above-mentioned encoding type is one of them.

[0139] The following introduces two other encoding methods. First, the attention coefficient matrix A∈ is encoded using graph structure information. (M+K)×(M+K) The element, namely the attention coefficient, is calculated as follows:

[0140]

[0141] The first term is the traditional self-attention mechanism, using a 1×d-dimensional query vector q. i and 1×d-dimensional bond vector k j The attention coefficient scalar based on node features is calculated, and the second term is spatial encoding, specifically, the attention coefficient scalar that can capture spatial information between nodes. The calculation method is as follows:

[0142]

[0143] Wherein, ψ(v i ,v j Let represent the shortest hop count between node i and node j. Based on the established heterogeneous undirected bipartite graph, the shortest hop count between any two nodes is at most 2 and at least 1, so only the range of two hops needs to be considered; b1 and b2 are two learnable scalars;

[0144] The third term is the edge feature encoding, which is an attention coefficient scalar that captures edge information between nodes. The calculation method is as follows:

[0145]

[0146] Where (1,2) is defined as the weighted shortest path between nodes i and j, where the edge weights are the large-scale fading coefficients. and Let the feature vectors on edges 1 and 2 that form the weighted shortest path be... There are two learnable 1×d-dimensional vectors.

[0147] The node features updated by the Grapher layer, that is, the node features output by the update layer, can be represented as:

[0148]

[0149] S33. Finally, in the post-processing layer, the node features and edge features are processed to obtain the power allocation result.

[0150] First, the node feature vector of the m-th AP enter The activation function of the MLP is Sigmoid, and then the output of the MLP is multiplied by the maximum transmit power P of the m-th AP. max The transmit power p of the m-th AP is obtained. m ;after,

[0151] The node feature vector of the m-th AP The node feature vector of the k-th UE The edge eigenvectors of edge (m,k) Input MLP after splicing post Get p' m,k The activation function of this MLP is LeakyReLU; then, it will be determined by p' m,k The resulting M×K dimensional matrix P' is subjected to Sofmax row-wise to obtain the M×K dimensional matrix. The elements of the matrix are This represents the power ratio allocated by the m-th AP to the k-th UE; finally, the transmit power p of the m-th AP is... m Multiply by the power ratio allocated by the m-th AP to the k-th UE

[0152] The final power p allocated by the m-th AP to the k-th UE is obtained. m,k : That is, the power control result p m,k .

[0153] The above process can be represented as:

[0154]

[0155] Here, Sigmoid and LeakyReLU are the activation functions of the last layer of the corresponding MLP, and Softmax is performed row by row. The above two activation functions guarantee the transmit power p of the m-th AP. m Greater than or equal to 0 and less than or equal to the maximum transmit power P max It also guarantees that the sum of the transmit power allocated by the m-th AP to all UEs is 1, that is:

[0156]

[0157] S34. After constructing the Graphormer-based neural network architecture, prepare the graph structure data required for training and testing, train the neural network model using unsupervised learning, maximize the spectral efficiency of the cellless network, and set the loss function Loss of the neural network to be the negative of the sum of the downlink spectral efficiencies of all UEs:

[0158]

[0159] The Graphormer-based neural network is trained using an unsupervised learning method, and the loss function is set by maximizing the spectral efficiency of the cellless network.

[0160] Simulation conditions

[0161] In the simulation scenario, access points (APs) and user units (UEs) are randomly distributed within a 960m x 960m rectangular area. A local scattering model is used to model the spatial correlation between antennas at the APs, and a pilot allocation method is employed to prevent closely spaced UEs from using the same pilot signal. The pilot transmit power is 200mW, and the maximum downlink transmit power of the APs is 1000mW. There are 16 APs and 16 users; each AP is equipped with 4 antennas, and each UE is equipped with a single antenna.

[0162] Simulation content and result analysis

[0163] Simulation 1: The training set is used to train a Graphormer-based neural network, and the test set data is used for validation.

[0164] like Figure 5 As shown, Figure 2 The system model shown is constructed as follows Figure 3The graph-structured data shown was input into a Grapher-based neural network. The network was trained using a training set and validated using a test set. The number of cell-free networks in the training and test sets were 2048 and 512, respectively. After 20 training epochs, the neural network demonstrated good convergence.

[0165] Simulation 2: The proposed method is compared with the weighted minimum mean square error power control algorithm, the equal power control algorithm, and the fractional power control algorithm. Figure 6 and Figure 7 It can be seen that the proposed Graphormer-based power control method for cellless networks outperforms the equal power control algorithm and the fractional power control algorithm, and approximates the weighted minimum mean square error power control algorithm. This verifies the effectiveness of the method proposed in this invention.

[0166] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A cellless network power control method based on Graphormer, characterized in that, Includes the following steps: A cellless network using time-division duplex mode is constructed, an uplink training model is defined for channel estimation, and a downlink data transmission model is defined to precode downlink data symbols based on the estimated channel. Based on cellless networks, distributed access points, and user equipment, construct graph-structured data; Build a neural network model based on Graphormer; Based on the constructed graph structure data, the graph structure information is encoded to fully extract global and local information of the network. The Grapher-based neural network is then trained to obtain a trained Grapher-based neural network model. Based on the transmit power of the distributed access point, the receive noise of the user equipment, and the channel between the distributed access point and the user equipment, a pre-trained Graphormer-based neural network model is used to achieve cellless network power control. The graph structure data includes topological relationships, node and edge features and variables, as detailed below: Cellular-free networks are modeled using a heterogeneous undirected bipartite graph, where distributed access points (APs) and user equipment (UEs) are considered as two types of nodes, namely AP nodes and UE nodes, respectively. The channel between AP nodes and UE nodes is treated as an edge. This heterogeneous undirected bipartite graph is represented as follows: ,in, Represents a set of nodes. Represents the set of edges and the set of nodes. From the set of AP nodes and UE node set Composition, AP node set Depend on M Composed of AP nodes, UE node set Depend on K It consists of UE nodes, and the edge set Depend on Composed of strips, The elements in are denoted as ; Define the feature matrix as consisting of the feature vectors of all AP nodes. , of which m The node characteristics corresponding to each AP are: ;in Characteristic matrix M elements; Let represent the set of all M×1 dimensional matrices in the real number field; Define the feature matrix as consisting of the feature vectors of all UE nodes. , of which k The node characteristics corresponding to each UE are: ; Characteristic matrix K elements, Let be the set of all K×1 dimensional matrices in the real number field; Define the feature matrix as consisting of all edge feature vectors. , among which the side The corresponding edge features are ;in, Let be the large-scale fading coefficient of the channel between the m-th AP and the k-th UE. Let M be the set of all M×K×1 dimensional matrices over the real number field; Define a vector consisting of the variables on all AP nodes as follows: , Indicates the first m Total transmit power of each AP; For vectors M elements; It is an M-dimensional real space; Define the matrix consisting of the variables on all edges as follows: , , indicating the first m The AP is the first k The power allocation ratio for each UE; Therefore m The AP is the first k The power allocated to each UE is expressed as follows: ; The encoding of the graph structure information includes the following formula: The process of updating AP node characteristics is as follows: m Each AP node aggregates the features of all its adjacent edges. , Indicates the first m Each AP node takes a first-order neighbor node operator, and the aggregation operator uses an averaging operation. Then, the resulting... 3D feature vector input ,Will The output and preprocessing layer obtained from the first m The 0th layer feature vector of AP and the introduced The type-encoded feature vectors are added together to obtain the final first... m The first layer feature vector of each AP ; The process of updating UE node characteristics is as follows: For the first k Each UE node aggregates features from all its adjacent edges. Indicates the first k Each UE node takes a first-order neighbor node operator, and the aggregation operator uses an averaging operation. Then, the resulting... 3D feature vector input ,Will The output and preprocessing layer obtained from the first m The 0th layer feature vector of AP and the introduced The type-encoded feature vectors are added together to obtain the final first... k The first layer feature vector of a UE ;in , For different Dimensionally learnable vectors are used to distinguish different node types, serving as type encoding in graph structure information encoding. Attention coefficients with graph structure information encoding The calculation method is as follows: The first item is the traditional self-attention mechanism, which uses... Dimensional query vector and 3D key vector The attention coefficient scalar based on node features is calculated, and the second term is the spatial encoding. The third term is the attention coefficient scalar that captures spatial information between nodes; A scalar of attention coefficients that can capture edge information between nodes; The calculation method is as follows: in, This represents the shortest number of hops between node i and node j; , They are two learnable scalars; The edge feature encoding is calculated as follows: in, Defined as the weighted shortest path between nodes i and j, where: the edge weight is the large-scale fading coefficient. and To form the edges of the weighted shortest path and edge eigenvectors on, , For two learnable Dimensional vector.

2. The cellless network power control method based on Graphormer according to claim 1, characterized in that, The graphormer-based neural network model includes: The preprocessing layer is used to process AP node features, UE node features, and edge features from three different MLPs respectively. dimensional mapping as dimension; The update layer is used to receive the preprocessed feature vectors of AP nodes, UE nodes and edges transmitted by the preprocessing layer, and update the node features of AP and UE nodes using message passing mechanism and type encoding respectively. The post-processing layer receives the updated node features transmitted by the update layer, processes the node features and edge features, and obtains the power allocation result.

3. The cellless network power control method based on Graphormer according to claim 1, characterized in that, The process of processing node features and edge features to obtain the power allocation result is as follows: The node feature vector of the m-th AP is input into the MLP, where the activation function of the MLP is Sigmoid. Then, the output of the MLP is multiplied by the maximum transmit power P. max Get the first m The transmit power p of each AP m ; The node feature vector of the m-th AP, the node feature vector of the k-th UE, and the edge feature vector of edge (m,k) are concatenated and then input into the MLP. post Get p' m,k The activation function of the MLP is LeakyReLU. Then it will be p' m,k The M*K dimensional matrix formed Perform Sofmax row-wise to obtain an M*K dimensional matrix. The elements of this matrix represent the power ratio allocated by the m-th AP to the k-th UE. ; Finally, we get the first m The AP is the first k Power allocated to each UE : .

4. The cellless network power control method based on Graphormer according to claim 1, characterized in that, The Graphormer-based neural network is trained using an unsupervised learning method, and the loss function is set by maximizing the spectral efficiency of the cellless network.

5. The cellless network power control method based on Graphormer according to claim 2, characterized in that, The method uses three different MLPs to respectively extract AP node features, UE node features, and edge features from dimensional mapping as The process of dimensioning is as follows: The node features of the m-th AP after preprocessing. Indicates the first m Node characteristics of an AP This indicates the MLP used in the preprocessing layer to process the features of AP nodes; For the node features of the k-th UE after preprocessing, Indicates the first k Node characteristics of each UE This indicates the MLP used in the preprocessing layer to process the features of AP nodes; Features of the preprocessed edge (m,k); For use in the preprocessing layer MLP that processes features; Let m be the set of edges (m, k). After this operation, the AP node features, UE node features, and edge features have the same dimension and contain richer information.

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