Large-scale wireless network parameter optimization method based on graph neural network

By adopting a graph neural network-based method in wireless networks, building a base station-raster two-part graph and training a graph neural network model, the problems of poor model migration capabilities and insufficient optimization results in traditional methods are solved, and synchronous optimization of multiple base station parameters and better migration capabilities are achieved.

CN119653388APending Publication Date: 2025-03-18TONGJI UNIV
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Patent Information

Application Number
CN202411612404.6
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-13
Publication Date
2025-03-18

AI Technical Summary

Technical Problem

The existing wireless network parameter optimization method based on machine learning has the problem of fixed input and output dimensions, which leads to the inability to migrate between wireless network scenarios of different sizes, increasing the cost of training and data acquisition; at the same time, traditional models cannot learn the potential topological relationship between various elements in the wireless network, and the optimization results are poorly robust.

Method used

A large-scale wireless network parameter optimization method based on graph neural network is adopted. By dividing the grid area into a grid, and building a two-part base station-raster graph, the distributed computing cluster training graph neural network model is used to optimize the base station parameters.

Benefits of technology

The base station parameters are synchronously optimized for multiple base stations in the network area, which improves the model's migration ability between wireless network scenarios of different scales, and enhances the robustness of the optimization results.

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Abstract

The invention provides a large-scale wireless network parameter optimization method based on a graph neural network, and the method is characterized in that the training process of a graph neural network model comprises the following steps: T1, constructing the graph neural network model, and setting the graph neural network model in each calculation unit and a parameter server; t2, sampling the base station-grid bipartite graph by a sampling unit to obtain sub-graphs; step T3, the calculation unit performs multiple iterations through the graph neural network model according to the corresponding sub-graph, and calculates the gradient of each parameter of the graph neural network model; step T4, the parameter server updates the graph neural network model according to all gradients, and transmits the updated graph neural network model to each calculation unit; and T5, judging whether a preset training termination condition is met or not, if so, obtaining a trained graph neural network model, and if not, executing the step T3. In a word, the method can perform base station parameter optimization on a plurality of base stations in the network area.
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Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication transmission, and in particular relates to a large-scale wireless network parameter optimization method based on graph neural network. Background Art

[0002] Wireless network parameter optimization aims to improve overall network performance, resource utilization, and user satisfaction by reasonably configuring base station parameters in the network.

[0003] Current wireless network parameter optimization methods can be roughly divided into two categories: methods based on operations research and optimization and methods based on machine learning. Among them, methods based on operations research and optimization usually require the cooperation of complex network simulators, which have very high time complexity, and existing network simulators cannot accurately estimate network performance and cannot be truly put into use. Machine learning-based methods use neural networks to autonomously learn the relationship between network parameters and network performance indicators in a data-driven manner, and adjust network parameters, thus eliminating the need for complex network simulators.

[0004] However, there are some problems with the current machine learning-based methods. First, the input and output dimensions of traditional product neural networks are fixed, which makes it impossible to migrate the model between wireless network scenarios of different scales, greatly increasing the cost of training and data collection. Second, traditional machine learning models cannot learn the potential topological relationships between elements in wireless networks, and the robustness of the optimization results is poor. Summary of the invention

[0005] The present invention is made to solve the above-mentioned problems, and its purpose is to provide a large-scale wireless network parameter optimization method based on graph neural network.

[0006] The present invention provides a large-scale wireless network parameter optimization method based on graph neural network, which is used to optimize base station parameters of M base stations in a network area according to a distributed computing cluster, and has the following characteristics, including the following steps: step S1, dividing the grid area into N grids, and setting sampling points for the N grids respectively to obtain wireless network road test data; step S2, constructing a base station-grid bipartite graph including M base station nodes and N grid nodes according to the wireless network road test data; step S3, inputting the base station-grid bipartite graph into a trained graph neural network model to obtain optimized base station parameters corresponding to the M base stations respectively, wherein the distributed computing cluster includes multiple sampling units, multiple computing units and 1 parameter server, and the training process of the graph neural network model includes the following steps: step T1, constructing a graph neural network model, and The graph neural network model is set in each computing unit and parameter server; in step T2, each sampling unit samples the base station-grid bipartite graph respectively, and obtains a subgraph containing M base station nodes and multiple grid nodes respectively; in step T3, each computing unit performs multiple rounds of iterations through the graph neural network model according to the subgraph sampled by the corresponding sampling unit, and calculates the gradient of each parameter of the corresponding graph neural network model respectively; in step T4, the parameter server integrates all gradients of all computing units to obtain an integration result, updates the graph neural network model according to the integration result, and passes the updated graph neural network model to each computing unit; in step T5, it is determined whether the preset training termination condition is met. If so, the updated graph neural network model is used as the trained graph neural network model. If not, step T3 is executed.

[0007] The large-scale wireless network parameter optimization method based on graph neural network provided by the present invention may also have the following characteristics: wherein the base station parameters include the downtilt angle, azimuth angle and transmission power of the base station.

[0008] In the large-scale wireless network parameter optimization method based on graph neural network provided by the present invention, it can also have the following characteristics: wherein, the wireless network road test data includes user density, each base station node corresponds to each base station, each grid node corresponds to each grid, and when the base station serves the grid, the base station node corresponding to the base station is connected to the grid node corresponding to the grid through an undirected edge, the grid node characteristics of the grid node include the grid position and user density of the corresponding grid, and the base station node characteristics of the base station node include the base station position and base station parameters of the corresponding base station.

[0009] The large-scale wireless network parameter optimization method based on graph neural network provided by the present invention may also have the following features: wherein the wireless network drive test data also includes signal strength and antenna gain, and the calculation expression of path loss is: m,n =p m +Gm,n -SI m,n , where l m,n is the path loss between base station m and grid n, p m is the transmission power of base station m, SI m,n is the signal strength of grid n received from base station m, G m,n is the antenna gain G between base station m and grid n m,n .

[0010] The large-scale wireless network parameter optimization method based on graph neural network provided by the present invention may also have the following characteristics: wherein, in step T2, each acquisition unit randomly selects some grid nodes from all grid nodes connected to each base station node, and uses all base station nodes and all selected grid nodes as subgraphs.

[0011] In the large-scale wireless network parameter optimization method based on graph neural network provided by the present invention, it can also have the following characteristics: wherein, the graph neural network model includes a first neural network, a second neural network, a third neural network and a fourth neural network, and in step T3, each computing unit calculates the gradient of each parameter of the corresponding graph neural network model according to the corresponding subgraph, and the process includes the following steps: step R1, the base station parameters, base station positions and grid positions corresponding to each undirected edge in the subgraph are respectively spliced ​​into a first feature vector, and are respectively input into the first neural network to obtain antenna gain features as edge features of the corresponding undirected edges; step R2, the path loss, antenna gain features and base station power parameters of each base station node in the subgraph and the corresponding connected grid nodes are respectively spliced ​​into a second feature vector, and are respectively input into the second neural network to obtain the base station signal strength of the corresponding connected grid nodes; step R3, for each grid node in the subgraph, according to the corresponding noise power and The signal strengths of all base stations are calculated to obtain the grid signal quality of the corresponding grid nodes; Step R4, for each base station node in the subgraph, the grid signal quality and user density of each grid node connected to the base station node are respectively spliced ​​into a third feature vector, and are respectively input into the third neural network to obtain the signal quality characteristics of each grid node corresponding to the base station node; Step R5, for each base station node in the subgraph, all signal quality characteristics corresponding to the base station node are summed to obtain the signal quality characteristics of the base station node; Step R6, the signal quality characteristics of each base station node in the subgraph are input into the fourth neural network to obtain the updated base station parameters corresponding to each base station node; Step R7, determine whether the preset iteration termination condition is met, if so, execute step R8, if not, execute step R1; Step R8, calculate the network performance index according to all updated base station parameters in the subgraph, and obtain the gradient through backward transfer calculation according to the network performance index.

[0012] In the large-scale wireless network parameter optimization method based on graph neural network provided by the present invention, it can also have the following characteristics: wherein the grid signal quality includes RSRP and SINR, and the calculation expressions thereof are respectively: Where RSRP n is the RSRP corresponding to grid node n, To select the maximum base station signal strength corresponding to the base station node from all base station nodes connected to grid node n, SINR n is the SINR corresponding to grid node n, is the noise power at grid n corresponding to grid node n.

[0013] In the large-scale wireless network parameter optimization method based on graph neural network provided by the present invention, it can also have the following characteristics: wherein, there are K sampling units and K computing units, each sampling unit corresponds to each computing unit one-to-one, and the sum of the computing resources of all computing units is half of the total available computing resources of the distributed computing cluster.

[0014] In the large-scale wireless network parameter optimization method based on graph neural network provided by the present invention, it can also have the following characteristics: wherein, the total number of computing units and sampling units makes the time consumption of a training process equal to the time consumption of a sampling process.

[0015] Functions and Effects of the Invention

[0016] According to the large-scale wireless network parameter optimization method based on graph neural network involved in the present invention, based on the base station-grid bipartite graph containing topological relationship, the base station parameters, base station location and grid location are input into the first neural network to calculate the antenna gain characteristics, the antenna gain characteristics, path loss and base station power parameters are input into the second neural network to calculate the base station signal strength, and the grid signal quality mean, base station parameters and user density calculated according to the base station signal strength are input into the third neural network to obtain updated base station parameters. Therefore, the large-scale wireless network parameter optimization method based on graph neural network of the present invention can optimize the base station parameters of multiple base stations in the network area synchronously. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of a large-scale wireless network parameter optimization method based on a graph neural network in an embodiment of the present invention;

[0018] Figure 2 is a schematic diagram of a grid and a base station in an embodiment of the present invention;

[0019] Figure 3 is a schematic diagram of a base station-grid bipartite graph in an embodiment of the present invention;

[0020] Figure 4 is a schematic diagram of a process for training a graph neural network model in an embodiment of the present invention;

[0021] Figure 5 It is a schematic diagram of a flow chart of a calculation unit calculating a gradient of a parameter in an embodiment of the present invention. DETAILED DESCRIPTION

[0022] In order to make the technical means, creative features, objectives and effects achieved by the present invention easy to understand, the following embodiments and the accompanying drawings specifically illustrate the large-scale wireless network parameter optimization method based on graph neural network of the present invention.

[0023] This embodiment provides a large-scale wireless network parameter optimization method based on a graph neural network, which is used to optimize base station parameters of M base stations in a network area according to a distributed computing cluster.

[0024] Among them, the base station parameters include the downtilt angle, azimuth angle and transmission power of the base station. The distributed computing cluster includes multiple sampling units, multiple computing units and 1 parameter server. In this embodiment, there are K sampling units and K computing units, each sampling unit corresponds to each computing unit, and the sum of the computing resources of all computing units is half of the total available computing resources of the distributed computing cluster. In other embodiments, the number of sampling units and computing units can be set according to the following conditions: the sum of the number of computing units and sampling units makes the time consumed by a training process equal to the time consumed by a sampling process.

[0025] Figure 1 It is a flow chart of a large-scale wireless network parameter optimization method based on graph neural network in an embodiment of the present invention.

[0026] like Figure 1 As shown, the large-scale wireless network parameter optimization method based on graph neural network includes the following steps:

[0027] Step S1, divide the grid area into N grids, and set sampling points for each of the N grids to obtain wireless network drive test data, wherein the wireless network drive test data includes user density, signal strength and antenna gain.

[0028] Figure 2 Schematic diagram of a grid and a base station in an embodiment of the present invention.

[0029] like Figure 2As shown, the signal of the base station can cover multiple grids, that is, the base station can serve multiple grids, and one grid can receive signals from multiple base stations at the same time. Gain beam is the signal beam of the actual service base station corresponding to the grid, and Interference beam is the signal of the base station that interferes, that is, does not serve the grid. In this embodiment, the sampling points collect signal data, that is, wireless network drive test data, and then calculate the base station corresponding to each grid and the grid corresponding to each base station based on the signal data.

[0030] Step S2: constructing a base station-grid bipartite graph including M base station nodes and N grid nodes according to wireless network drive test data.

[0031] Figure 3 Schematic diagram of a base station-grid bipartite graph in an embodiment of the present invention.

[0032] like Figure 3 As shown, the base station-grid bipartite graph contains M base station nodes, namely BS1, BS 2, ..., BS M and N grid nodes, namely Grid 1, Grid 2, ..., GridN, and undirected edges connecting the base station nodes and the grid nodes, such as l 1,1 , l 2,1 , l 1,3 , l 2,3 wait.

[0033] In the base station-grid bipartite graph, each base station node corresponds to each base station, and each grid node corresponds to each grid. When a base station serves a grid, the base station node corresponding to the base station and the grid node corresponding to the grid are connected by an undirected edge.

[0034] The grid node features of the grid node include the grid position and user density of the corresponding grid. The base station node features of the base station node include the base station position and base station parameters of the corresponding base station. The edge features of the undirected edge include the path loss between the corresponding base station and the corresponding grid. In this embodiment, the base station position, base station power parameters, base station parameters before optimization and grid position are all existing data, which can be obtained by querying the service provider, for example.

[0035] The calculation expression of path loss is:

[0036] l m,n =p m +G m,n -SI m,n ,

[0037] Where l m,n is the path loss between base station m and grid n, p m is the transmission power of base station m, SIm,n is the signal strength of grid n received from base station m, G m,n is the antenna gain G between base station m and grid n m,n .

[0038] Step S3, input the base station-grid bipartite graph into the trained graph neural network model to obtain the optimized base station parameters corresponding to the M base stations.

[0039] In this embodiment, the methods for obtaining the trained graph neural network model include the following: first, building a graph neural network model based on an existing pre-trained model, and training the graph neural network model through a distributed computing cluster according to the base station-grid bipartite graph corresponding to the network area; second, fine-tuning the graph neural network model trained according to the base station-grid bipartite graph corresponding to other network areas through a distributed computing cluster according to the base station-grid bipartite graph corresponding to the network area; third, directly applying the trained graph neural network model corresponding to the network area to the wireless network parameter optimization of the network area this time.

[0040] The first method mentioned above is described in detail below in conjunction with the accompanying drawings. In addition, the graph neural network model constructed in the first method can be replaced with a graph neural network model trained according to the base station-grid bipartite graph corresponding to other network areas, thereby realizing the second method mentioned above.

[0041] Figure 4 It is a schematic diagram of the process of training a graph neural network model in an embodiment of the present invention.

[0042] like Figure 4 As shown in the figure, the training process of the graph neural network model includes the following steps:

[0043] Step T1, construct a graph neural network model, and set the graph neural network model in each computing unit and parameter server. The graph neural network model includes a first neural network, a second neural network, a third neural network and a fourth neural network.

[0044] Step T2: Each sampling unit samples the base station-grid bipartite graph to obtain a subgraph including M base station nodes and a plurality of grid nodes.

[0045] Each acquisition unit randomly selects some grid nodes from all grid nodes connected to each base station node, and uses all base station nodes and all selected grid nodes as subgraphs. That is, each subgraph contains all base station nodes and some grid nodes, and each base station node has an undirected edge with at least one grid node.

[0046] In step T3, each computing unit performs multiple rounds of iterations through the graph neural network model according to the subgraph sampled by the corresponding sampling unit, and calculates the gradient of each parameter of the corresponding graph neural network model.

[0047] Figure 5 It is a schematic diagram of a flow chart of a calculation unit calculating a gradient of a parameter in an embodiment of the present invention.

[0048] like Figure 5 As shown, in step T3, each computing unit calculates the gradient of each parameter of the corresponding graph neural network model according to the corresponding subgraph, including the following steps:

[0049] Step R1, the base station parameters, base station positions and grid positions corresponding to each undirected edge in the subgraph are respectively spliced ​​into the first feature vector, and are respectively input into the first neural network to obtain the antenna gain feature as the edge feature of the corresponding undirected edge. That is, the first feature vector corresponding to each undirected edge is respectively input into the first neural network to obtain the antenna gain feature corresponding to the undirected edge.

[0050] Step R2, the path loss, antenna gain characteristics and base station power parameters of each base station node in the subgraph and the corresponding connected grid node are spliced ​​into the second feature vector, and are respectively input into the second neural network to obtain the base station signal strength of the corresponding connected grid node. That is, the second feature vector corresponding to each undirected edge is input into the second neural network to obtain a base station signal strength of the grid node corresponding to the undirected edge.

[0051] Step R3: for each grid node in the subgraph, the grid signal quality of the corresponding grid node is calculated according to the corresponding noise power and the signal strength of all base stations.

[0052] Among them, the grid signal quality includes RSRP and SINR, and their calculation expressions are:

[0053]

[0054] Where RSRP n is the RSRP corresponding to grid node n, To select the maximum base station signal strength corresponding to the base station node from all base station nodes connected to grid node n, SINR n is the SINR corresponding to grid node n, is the noise power at grid n corresponding to grid node n.

[0055] Step R4, for each base station node in the subgraph, the grid signal quality and user density of each grid node connected to the base station node are respectively spliced ​​into a third feature vector, and are respectively input into the third neural network to obtain the signal quality characteristics corresponding to each grid node corresponding to the base station node.

[0056] Step R5: For each base station node in the subgraph, all signal quality features corresponding to the base station node are summed to obtain the signal quality feature of the base station node.

[0057] Step R6, inputting the signal quality characteristics of each base station node in the subgraph into the fourth neural network to obtain updated base station parameters corresponding to each base station node.

[0058] Step R7, determine whether the preset iteration termination condition is reached, if yes, execute step R8, if no, execute step R1. In this embodiment, the preset iteration termination condition is that the total number of iterations reaches a preset value.

[0059] Step R8, calculating the network performance index according to all updated base station parameters in the subgraph, and obtaining the gradient through backward transfer calculation according to the network performance index.

[0060] In step T4, the parameter server integrates all the gradients of all computing units to obtain the integration result, updates the graph neural network model based on the integration result, and passes the updated graph neural network model to each computing unit.

[0061] Step T5, determine whether the preset training termination condition is reached, if so, use the updated graph neural network model as the trained graph neural network model, if not, execute step T3. In this embodiment, the preset training termination condition is that the maximum number of training times is reached or the network performance index calculated by the base station parameters output by the updated graph neural network model no longer improves.

[0062] Functions and Effects of the Embodiments

[0063] According to the large-scale wireless network parameter optimization method based on graph neural network involved in this embodiment, based on the base station-grid bipartite graph containing topological relationship, the base station parameters, base station location and grid location are input into the first neural network to calculate the antenna gain characteristics, the antenna gain characteristics, path loss and base station power parameters are input into the second neural network to calculate the base station signal strength, and the grid signal quality mean, base station parameters and user density calculated according to the base station signal strength are input into the third neural network to obtain updated base station parameters. In short, this method can optimize the base station parameters of multiple base stations in the network area synchronously.

[0064] Furthermore, through a distributed computing cluster, a corresponding number of sampling units, computing units, and parameter servers are set up to iteratively train the graph neural network model, so that the computing power can be fully utilized and the graph neural network model that meets the performance requirements can be trained more quickly.

[0065] Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A large-scale wireless network parameter optimization method based on graph neural network, used to optimize base station parameters of M base stations in a network area according to a distributed computing cluster, characterized in that: The following steps are involved: Step S1, dividing the grid area into N grids, and setting sampling points for the N grids respectively to obtain wireless network drive test data; Step S2, constructing a base station-grid bipartite graph including M base station nodes and N grid nodes according to the wireless network drive test data; Step S3, inputting the base station-grid bipartite graph into the trained graph neural network model to obtain the optimized base station parameters corresponding to the M base stations respectively, The distributed computing cluster includes multiple sampling units, multiple computing units and a parameter server. The training process of the graph neural network model includes the following steps: Step T1, constructing a graph neural network model, and setting the graph neural network model in each of the computing units and the parameter server; Step T2, each of the sampling units samples the base station-grid bipartite graph to obtain a subgraph including M base station nodes and a plurality of grid nodes; Step T3, each of the computing units performs T rounds of iterations through the graph neural network model according to the subgraph sampled by the corresponding sampling unit, and calculates the gradient of each parameter of the corresponding graph neural network model; Step T4, the parameter server integrates all the gradients of all the computing units to obtain an integration result, updates the graph neural network model according to the integration result, and transmits the updated graph neural network model to each computing unit; Step T5, determine whether the preset training termination condition is reached. If so, use the updated graph neural network model as the trained graph neural network model. If not, execute step T3.

2. The large-scale wireless network parameter optimization method based on graph neural network according to claim 1 is characterized in that: in, The base station parameters include the downtilt angle, azimuth angle and transmit power of the base station.

3. The large-scale wireless network parameter optimization method based on graph neural network according to claim 1 is characterized in that: in, The wireless network drive test data includes user density, Each of the base station nodes corresponds to each of the base stations, Each of the grid nodes corresponds to each of the grids, When the base station serves the grid, the base station node corresponding to the base station and the grid node corresponding to the grid are connected via an undirected edge. The grid node features of the grid node include the grid position of the corresponding grid and the user density, The base station node characteristics of the base station section include the base station location and the base station parameters of the corresponding base station.

4. The large-scale wireless network parameter optimization method based on graph neural network according to claim 3 is characterized in that: in, The wireless network drive test data also includes signal strength and antenna gain, The edge characteristics of the undirected edge include a path loss between the corresponding base station and the corresponding grid, The calculation expression of the path loss is: it m,n =p m +G m,n -AND m,n , Where l m,n is the path loss between base station m and grid n, p m is the transmission power of base station m, SI m,n is the signal strength of grid n received from base station m, G m,n is the antenna gain between base station m and grid n.

5. The large-scale wireless network parameter optimization method based on graph neural network according to claim 3 is characterized in that: in, In the step T2, each of the acquisition units randomly selects some of the grid nodes from all the grid nodes connected to each of the base station nodes, and uses all the base station nodes and all the selected grid nodes as the subgraph.

6. The large-scale wireless network parameter optimization method based on graph neural network according to claim 3, Features: in, The graph neural network model includes a first neural network, a second neural network, a third neural network and a fourth neural network. In step T3, the process in which each computing unit calculates the gradient of each parameter of the corresponding graph neural network model according to the corresponding subgraph includes the following steps: Step R1, concatenating the base station parameters, the base station positions and the grid positions corresponding to each of the undirected edges in the subgraph into first feature vectors, and inputting them into the first neural network to obtain antenna gain features as the edge features of the corresponding undirected edges; Step R2, respectively concatenating the path loss, the antenna gain characteristics and the base station power parameters of each base station node in the subgraph and the corresponding connected grid node into a second feature vector, and respectively inputting them into the second neural network to obtain the base station signal strength of the corresponding connected grid node; Step R3, for each grid node in the subgraph, respectively calculate the grid signal quality of the corresponding grid node according to the corresponding noise power and all base station signal strengths; Step R4, for each base station node in the subgraph, respectively concatenate the grid signal quality and the user density of each grid node connected to the base station node into a third feature vector, and respectively input them into the third neural network to obtain the signal quality features corresponding to each grid node corresponding to the base station node; Step R5, for each base station node in the subgraph, summing up all the signal quality features corresponding to the base station node to obtain the signal quality feature of the base station node; Step R6, inputting the signal quality characteristics of each base station node in the subgraph into the fourth neural network to obtain the updated base station parameters corresponding to each base station node; Step R7, determine whether the preset iteration termination condition is reached, if so, execute step R8, if not, execute step R1; Step R8, calculating a network performance indicator according to all updated base station parameters in the subgraph, and obtaining the gradient through backward transfer calculation according to the network performance indicator.

7. The large-scale wireless network parameter optimization method based on graph neural network according to claim 6 is characterized in that: in, The grid signal quality includes RSRP and SINR, and the calculation expressions thereof are respectively: Where RSRP n is the RSRP corresponding to grid node n, To select the maximum base station signal strength corresponding to the base station node from all base station nodes connected to grid node n, SINR n is the SINR corresponding to grid node n, is the noise power at grid n corresponding to grid node n.

8. The large-scale wireless network parameter optimization method based on graph neural network according to claim 1, characterized in that: in, The number of the sampling units and the number of the computing units are both K, Each of the sampling units corresponds to each of the computing units one by one. The sum of the computing resources of all the computing units is half of the total available computing resources of the distributed computing cluster.

9. The large-scale wireless network parameter optimization method based on graph neural network according to claim 1, characterized in that: in, The total number of the computing units and the sampling units makes the time consumed in a training process equal to the time consumed in a sampling process.

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