A clustering and de-hopping networking method based on adjustable weighting kernel k-means

Abstract

The application provides a clustering and cell removal networking method based on an adjustable weighted kernel k-means, the method is based on a clustering and cell removal networking problem modeled by a graph representation of a wireless communication network and a graph partitioning theory, in consideration of network structure balance, replaces an existing minimum k-cut problem with a normalized minimum k-cut problem, converts the normalized minimum k-cut problem into a trace maximization problem, and establishes an equivalent relationship with a weighted kernel k-means, improves the weighted kernel k-means by introducing two hyperparameters, realizes control on the number of activated beams, designs a clustering and cell removal networking algorithm based on the adjustable weighted kernel k-means, reduces the calculation complexity of an existing networking algorithm, and realizes adjustment on the network structure between system performance and system overhead.

Description

Technical Field

[0001] The present invention relates to the field of 5G / 6G wireless communication network optimization, and provides a clustering and cellular networking method based on adjustable weighted kernel k-means. Background Art

[0002] In the decellularized massive MIMO scenario, the system overhead caused by the joint transmission of all base stations / APs increases rapidly as the density of base stations and users increases. The difficulty of system operation caused by the difficulty of base station synchronization, the number of channels to be estimated, the number of signaling exchanges, and the complexity of signal processing cannot be ignored. A large number of studies have begun to focus on the formation method of virtual cells. The core idea can be summarized as follows: (1) Each user selects a subset of base stations / APs with which its channel gain is greater than a set threshold or a given size; (2) Each base station only serves the subset of users with the largest channel gain or within a given coverage range. The algorithm for forming virtual cells based on the above idea is easy to implement, but the virtual cells formed generally overlap with each other. Due to the limited power of a single base station, the downlink transmission becomes complicated and the coupling between users is high. In addition, although users in the virtual cell are served by the surrounding base stations, they are still interfered by adjacent virtual cells and need to be managed. As a result, the downlink transmission requires a large amount of signaling exchanges and the computational complexity is extremely high.

[0003] Because these methods urgently need improvement, a network architecture that performs interference cancellation and downlink transmission within a tolerable complexity has recently been widely researched. Specifically, the entire network is divided into multiple non-overlapping subnets, where users with strong mutual interference are grouped together, while interference between different subnets is relatively weak. This subnetting approach is known as clustered decellularized networking. With clustered decellularized networking, interference cancellation techniques are independently implemented within each subnet, making interference between subnets almost negligible.

[0004] Numerous studies have proposed subnet partitioning methods for users and base stations / APs, primarily categorized as "user-centric" and "base station / AP-centric." Considering user-centric subnet partitioning, this method selects a subset of base stations with the highest channel gain to serve each user and merges virtual cells that share at least one base station. Base station / AP-centric methods, on the other hand, subnet the base stations and associate each user with the base station with the highest channel gain, forming a non-overlapping subnet. However, the "user-centric" subnet partitioning method inevitably leads to an imbalance in subnet size, resulting in a single subnet containing the majority of base stations and users. This topology still results in frequent Channel State Information (CSI) exchanges and complex signal processing techniques. The "base station / user-centric" subnet partitioning method also introduces "unlucky users," where the base station with the highest channel gain for the user is not in the subnet associated with the user, or the user is near the edge of the subnet, subjecting the user to severe interference from neighboring subnets. Furthermore, many studies on clustered decellularized networks employ single-antenna base stations / APs. To establish a more reasonable subnet partitioning model and theory, L. Dai et al. proposed applying graph partitioning theory to model clustered decellularized networks, considering subnet partitioning from both the base station and user sides. Building on this, J.-Y. Wang et al. considered multi-base station, multi-antenna clustered decellularized networks and proposed beam-level clustered decellularized networks. Subnet partitioning methods based on graph partitioning theory have been proven to achieve better system performance than "user-centric" and "base station-centric" subnet partitioning methods. Currently, most clustered decellularized networking algorithms based on graph partitioning theory are based on spectral clustering methods, which have high computational and time complexity, making it difficult to update networking solutions in real systems in a timely manner. Researching low-complexity beam-level clustered decellularized networks has important practical significance. Summary of the Invention

[0005] The present invention aims to overcome the shortcomings of the prior art by disclosing a clustering and decellularizing networking method based on adjustable weighted kernel k-means. This method addresses the problem of beam-level clustering and decellularizing networking, using a graph representation of a wireless communication network with a large-scale antenna array at the base station transmitter end. By leveraging the equivalence of weighted kernel k-means with the normalized minimum k-cut problem, the method improves weighted kernel k-means by introducing two hyperparameters, achieving more flexible algorithmic performance. Based on this improved adjustable kernel k-means, a networking acceleration algorithm is designed to optimize the wireless communication network. By adjusting different hyperparameters, network structures with varying preferences between system spectral efficiency and joint processing complexity and signaling overhead can be obtained.

[0006] Technical solution:

[0007] A clustering and decellularizing networking method based on adjustable weighted kernel k-means is proposed. This method is based on the clustering and decellularizing networking problem modeled based on graph representation of wireless communication networks and graph segmentation theory. While considering the balance of network structure, the existing minimum k-cut problem is replaced by a normalized minimum k-cut problem. The normalized minimum k-cut problem is transformed into a trace maximization problem, and an equivalent relationship with weighted kernel k-means is established. Two hyperparameters are introduced to improve the weighted kernel k-means and achieve control over the number of activated beams. A clustering and decellularizing networking algorithm based on adjustable weighted kernel k-means is designed to reduce the computational complexity of existing networking algorithms and achieve adjustment of the network structure to balance system performance and system overhead.

[0008] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0009] (1) Realize network acceleration: Compared with the existing networking algorithm based on spectral clustering, the algorithm proposed in this invention greatly reduces the computational complexity and can realize real-time network update.

[0010] (2) Realize beam activation-sleep control: Through the proposed two-batch initialization method and two hyperparameters, the number of activated beams in the wireless communication network can be controlled. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 Flowchart of the method of the present invention.

[0012] Figure 2 Diagram of the beam-level clustering and cellular network model.

[0013] Figure 3 Schematic diagram of the structure of a weighted undirected graph.

[0014] Figure 4 Schematic diagram of graph partitioning theory.

[0015] Figure 5 Principle of the beam activation-steering function.

[0016] Figure 6 Relationship between the number of initial groups and the number of activated beams for different hyperparameters ∈: As the hyperparameter ∈ decreases, the number of activated beams increases.

[0017] Figure 7 Relationship between the number of initial groups and the number of activated beams under different hyperparameters Υ: When the hyperparameter ∈>0, as the hyperparameter Υ decreases, the number of activated beams decreases.

[0018] Figure 8The relationship diagram of the initial group number, running time and iteration number under different networking algorithms: the algorithm proposed in the application has shorter running time and fewer iteration numbers than the spectral clustering method.

[0019] Figure 9 The relationship diagram of the initial group number and system spectral efficiency under different hyperparameters ∈.

[0020] Figure 10 The relationship diagram of the initial group number and system spectral efficiency under different hyperparameters ∈. DETAILED DESCRIPTION

[0021] The application models the clustering cell-free networking problem based on the graph partition theory based on the graph representation of the wireless communication network, studies the algorithm framework with lower complexity and more flexible networking, and realizes the optimization of the wireless communication network structure. Considering the balance of network division, the existing minimum k-cut problem is converted into a normalized minimum k-cut problem, based on which the equivalence relationship between the weighted kernel k-means and the clustering cell-free networking problem is studied, and the preliminary design of the algorithm is completed. Through the characteristics of the weighted kernel k-means algorithm, two hyperparameters are introduced to improve the flexibility of the algorithm, and different clustering results are obtained by changing the hyperparameters. The improved adjustable kernel k-means is applied to complete the design of the clustering cell-free networking acceleration algorithm, so as to realize the adjustment of the trade-off between the system spectral efficiency and the joint processing complexity and the signaling overhead.

[0022] Step 1. Beam-level clustering cell-free network model establishment and graph representation

[0023] Through theoretical modeling of the beam-level clustering cell-free wireless communication network (physical object), the physical object is represented as a weighted undirected graph by using the knowledge of graph theory.

[0024] Interpretation: The beam-level clustering cell-free networking breaks the current traditional mobile cell boundary, clusters (or groups) the fixed beams of the user and the base station transmitting end in the wireless communication system, and forms multiple non-overlapping subnets. Since the subnets are non-overlapping, each subnet can operate independently. And, individual joint processing can be performed within each subnet. At the same time, the beam-level clustering cell-free networking divides the users with strong mutual interference into the same subnet, so that the interference between subnets can be regarded as noise, and the interference cancellation technology can be applied within the subnet to eliminate strong interference. The beam-level clustering cell-free network model is shown in Figure 2 .

[0025] Step (1.1)

[0026] The specific scenario of the beam-level clustering cell-free wireless communication network is described, including the number of users, the number of base stations, the number of base station transmitting beams, etc.

[0027] Consider a downlink transmission scenario of a beam-level clustered cellular network, where K single-antenna users share time-frequency resources and M base stations are equipped with large-scale antenna arrays at the transmitting end. Assume that the mth base station pre-forms N m fixed beams, and the total number of fixed beams at all base station transmitters is The base station set is represented as The user set is represented as The beam set is represented as Where M, K, and N are all natural numbers, representing the number of base stations, the number of users, and the number of fixed beams at all base station transmitters, respectively. K with b N Denote the Kth user and the Nth beam respectively. Due to the limitation of hardware cost, the number of RF chains at the base station transmitter is much smaller than the number of antenna array elements, that is, N m <<N RF , m=1, 2, ..., M.

[0028] Step (1.2)

[0029] By using graph theory knowledge, the beam-level clustering cellular network (physical object) is modeled as a weighted undirected graph, and the constituent elements and meanings of the weighted undirected graph are described, including nodes, edges and edge weights.

[0030] According to graph theory, the beam-level clustering cellular network can be modeled as a weighted undirected graph in Represents a set of points. Each point v i is the beam b i It is combined with one or more users who regard it as the optimal beam (i.e., the beam with the largest beam domain channel gain), which is expressed as

[0031]

[0032] Among them, h k，n Indicates that the beam b n To user u k beam domain channel.

[0033] The set ε represents the set of edges between each point.

[0034] The matrix representing the weight value on the edge, where the element a in the i-th row and j-th column is i，j Represents point v i and dot v j The weight of the edge between

[0035]

[0036] Assume that the entire wireless communication network is divided into G non-overlapping subnets, and the user set in the g-th subnet is expressed as The number of users in the set is denoted as K g , the beam set in the g-th subnet The number of beams in the set is denoted as B g Based on graph partitioning theory, It is used to represent the beam-level clustering and cellular networking results, where the user set and beam set in each subnet can be expressed as

[0037]

[0038] and

[0039]

[0040] Where G is a natural number, representing the number of subnets in the beam-level clustering cellular network.

[0041] Step 2. Modeling the beam-level clustering and cellular networking problem based on graph partitioning theory

[0042] We propose a beam-level clustering decellularization optimization problem: how to group users and beams to form subnets. This problem is modeled as a graph partitioning problem (a theoretical problem). Specifically, we partition the weighted undirected graph from step 1 into multiple subgraphs, each corresponding to a subnet in the beam-level clustering decellularization network.

[0043] Step (2.1)

[0044] According to existing research work, in order to ensure that the sizes of subnets are basically balanced, the beam-level clustering and cellular networking optimization problem is modeled as a normalized k-cut problem (graph theory knowledge / theoretical problem), among which the normalized k-cut problem is a classic problem type in graph segmentation problems.

[0045] The clustering and decellularization problem, aimed at maximizing system spectrum efficiency, can be modeled as the classic minimum k-cut problem. However, the optimal solution to the minimum k-cut problem often results in an extremely large subnet, leading to network imbalance. To improve balance among subnets, the normalized minimum k-cut problem is used instead of the original optimization problem:

[0046]

[0047] Among them, the cut function is defined as

[0048]

[0049] express exist The relative complement of . Capacity function Defined as

[0050]

[0051] in,

[0052]

[0053] Represents point v i degree.

[0054] Step (2.1), since the normalized minimum k-cut problem is an NP-hard problem, the indicator matrix It was introduced to solve the optimization problem Convert it to a trace maximization problem for easy solution, expressed as

[0055]

[0056] Z T Z=I G , (2.8) where I G Represents the identity matrix of size G×G, indicating that the element in the i-th row and g-th column of the matrix Z is defined as

[0057]

[0058] D=diag(d1,d2,...d N ) represents the degree matrix, and diag(·) is a function that creates a diagonal matrix.

[0059] Step 3. Design of adjustable weighted kernel k-means network acceleration algorithm

[0060] By utilizing the equivalence between weighted kernel k-means and the beam-level clustering decellularization problem in step 2 (i.e., the normalized minimum k-cut problem), and by proposing a new two-batch initialization method and introducing two hyperparameters, the present invention proposes an adjustable weighted kernel k-means networking acceleration algorithm.

[0061] The algorithm comprises the following steps:

[0062] Step (3.1)

[0063] This paper briefly introduces the principle of weighted kernel k-means algorithm and transforms it into the form of trace maximization problem.

[0064] Compared with ordinary k-means, the weighted kernel k-means algorithm uses the mapping function φ(·) to transform the sample points s iTransforming from the original space to a high-dimensional space can make the data that is nonlinearly separable in the original space linearly separable in the high-dimensional space. The optimization problem of weighted kernel k-means can be written as

[0065]

[0066] in

[0067]

[0068] Indicates a subnet The present invention introduces the kernel function κ to represent the dot product of two sample points, which is expressed as

[0069] κ(s i , s j )=φ(s i )·φ(s j ). (3.3)

[0070] Euclidean distance Expressed as

[0071]

[0072] The optimization problem of weighted kernel k-mEans in formula (3.1) can be transformed into the form of trace maximization problem.

[0073]

[0074] F T F=I G (3.6)

[0075] Among them, the indicator matrix The element in row i and column g of is defined as

[0076]

[0077] The matrix K represents the kernel matrix, and its i-th row and j-th column element K i，j =κ(s i , s j ). The diagonal matrix Ω represents the weight matrix, and its weight element in the i-th row and i-th column is ω i .

[0078] Step (3.2)

[0079] By establishing the complete equivalence between weighted kernel k-means and normalized k-cut problems, low-complexity weighted kernel k-means is used to solve the beam-level clustering and cellular networking problem, which can achieve network acceleration.

[0080] By comparison, the present invention finds that when the following conditions are met, the optimization problem and optimization problems are equivalent to:

[0081] Ω=D (3.8)

[0082] and

[0083] K=∈D -1 +D -1 AD -1 (3.9)

[0084] in, The hyperparameter ∈ is introduced Used to adjust the main diagonal displacement of the kernel matrix K.

[0085] Step (3.3)

[0086] The distance calculation in weighted kernel k-means will be affected by the hyperparameter ∈, resulting in different clustering results, that is, different subnet segmentation results.

[0087] When the kernel matrix K and the weight matrix Ω are given, the present invention calculates the reference point v by formula (3.4) i To the g-th subnet center c g The Euclidean distance. When the reference point v i Located in subnet hour,

[0088]

[0089] in,

[0090]

[0091] Indicates that when there is no main diagonal displacement, the reference point v i To the g-th subnet center c g The Euclidean distance. When the reference point v i Not in subnet hour,

[0092]

[0093] Through analysis, it can be obtained that when the hyperparameter ∈>0, there exists That is, the reference point v i Often stay in the original subnet, and when the hyperparameter ∈ < 0, the reference point v i It is more likely to choose other subnets. As |∈| increases, the above properties will be continuously enhanced. Therefore, by adjusting ∈, weighted kernel k-means can obtain different segmentation (clustering) results.

[0094] Step (3.4)

[0095] In light of these findings, the present invention proposes a two-batch initialization method (i.e., forming the initial grouping of weighted kernel l-means) so that a hyperparameter ∈ can regulate the number of active beams in a wireless communication network. Simultaneously, another hyperparameter γ is defined to implement the beam activation-sleep function.

[0096] According to the adjustable nature of the hyperparameter ∈, a classification-based initialization method is proposed to achieve the purpose of controlling the number of activated beams. First, the point set with users and the point set with only beams are defined as and The proposed classification-based initialization method mainly consists of two steps: (1) point set The points in G are randomly initialized to a <G clusters; (2) point set The points in GG are randomly initialized a Obviously, as the hyperparameter ∈ increases, the points where only beams exist tend to move to other clusters, resulting in more activated beams.

[0097] By observing equations (3.10) and (3.12), when When I was very young, and The gap will become very large. It will affect the clustering results. The value of G a There is a direct relationship. Based on this, the scale factor Υ is defined as

[0098]

[0099] The scaling factor Y is also used as a hyperparameter to directly adjust the number of active beams. For clusters initially consisting of only beams, as the scaling factor Y increases, these beams are more likely to select clusters containing users. Conversely, as the scaling factor Y increases, these beams tend to remain dormant.

[0100] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0101] Example

[0102] 1. Simulation scene settings

[0103] In order to more specifically and effectively present the content of the present application, a specific wireless communication network scenario is considered, and the adjustable weighted kernel k-means networking algorithm proposed in the present application is executed on this wireless communication network to obtain experimental data to verify the performance of the algorithm proposed in the present application.

[0104] The software platform used in this simulation experiment is MATLAB R2022a. In the considered wireless communication system, the number of base stations is set to 5, that is, M = 5, and the 5 base stations are located in a circular region and are located at (0, 0), (0, 1), (1, 0), (1, 1) and (0, 2) in the Cartesian coordinate system respectively. Users are uniformly and randomly distributed in the above-mentioned circular region. For a more realistic system structure, only path loss and beamforming gain in the wireless communication network are considered during the execution of the algorithm. In the process of joint transmission in each subnet, Zero-Forcing (ZF) precoding is applied to completely eliminate intra-subnet interference.

[0105] All experimental results are obtained using the Monte Carlo method and 1000 random user positions.

[0106] 2. Experimental data analysis

[0107] 2.1 Performance analysis of beam activation-sleep control

[0108] Figure 6 and Figure 7 respectively show the curves of the average number of activated beams with the number of subnets under different hyperparameters ∈ and different hyperparameters Y. In order to compare with the existing benchmark method, that is, the spectral clustering algorithm, the corresponding experimental data generated by the spectral clustering algorithm are also shown in Figure 6 and Figure 7 Specifically, it can be seen from Figure 6 that a negative hyperparameter ∈ can produce more activated beams for data transmission than the spectral clustering algorithm, on the other hand, a non-negative hyperparameter ∈ will cause more beam sleep. In Figure 7 , the hyperparameter ∈ is set to 0.1, at this time, the increase of the hyperparameter Y will cause the increase of the number of activated beams, which also proves the effectiveness of the theoretical design part of the algorithm. Since the more beams activated by joint transmission, more radio frequency chains and signaling overheads are needed and higher joint processing complexity is required, therefore the adjustable weighted kernel k-means algorithm proposed in the present application indeed provides a method suitable for practical wireless communication systems.

[0109] 2.2 Performance analysis of networking acceleration capability

[0110] Figure 8The running time of the adjustable weighted kernel k-means algorithm and spectral clustering algorithm proposed in this paper varies with the number of subnets and the number of iterations required to reach convergence. Figure 8 As can be seen from the results, the algorithm proposed in this invention executes three times faster than the spectral clustering algorithm, meaning its runtime is one-third of that of the spectral clustering algorithm. Furthermore, the algorithm proposed in this invention requires only half as many iterations as the spectral clustering algorithm. These two points demonstrate that the adjustable weighted kernel k-means algorithm proposed in this invention has the ability to accelerate networking. Combined with the theoretical analysis above, this also indicates that the theoretical computational complexity of the algorithm proposed in this invention is far lower than that of the spectral clustering algorithm. In particular, in future ultra-dense networks with a large number of base stations equipped with large-scale antenna arrays, the algorithm proposed in this invention has lower computational overhead and can better adapt to actual systems.

[0111] 2.3 Improvement of Spectrum Efficiency

[0112] Figure 9 and Figure 10 The curves of average spectrum efficiency changing with the number of subnets under different hyperparameters ∈ and Υ are shown respectively. Obviously, as the number of subnets increases, the interference between subnets in the system increases and the spectrum efficiency decreases. Figure 6 and Figure 7 Combined analysis shows that when the combinations of hyperparameters ∈ and Υ are set to ∈ = 0 / Υ = 0.5, ∈ = 0.1 / Υ = 0.5, and ∈ = 0.1 / Υ = 0.75, the proposed adjustable weighted kernel k-means algorithm can use fewer active beams and achieve higher spectral efficiency. This shows that the proposed algorithm can not only accelerate clustering and cellular networking, but also improve spectral efficiency.

[0113] The above description is only a description of the preferred embodiments of the present application and does not limit the scope of the present application. Any changes or modifications made by any person skilled in the art based on the above disclosed technical content should be regarded as equivalent valid embodiments and fall within the scope of protection of the technical solution of the present application.

Claims

1. A tunable kernel-based k -means clustering and cellular networking method, characterized in that: Including steps: Step 1: Establishment of beam-level clustering and cellular network model and graph representation; Step 2: Modeling the beam-level clustering and cellular networking problem based on graph partitioning theory; Step 3. Design an adjustable weighted kernel k-means network acceleration algorithm; The step 1 is to theoretically model the beam-level clustered cellular wireless communication network and use graph theory to represent the physical object as a weighted undirected graph, which specifically includes the following steps: Step 1.1: Describe the specific scenario of the beam-level clustering cellular wireless communication network, including the number of users, the number of base stations, and the number of base station transmitting beams; Consider a downlink transmission scenario of a beam-level clustered cellular network. Single-antenna users share time-frequency resources. The base station is equipped with a large-scale antenna array at the transmitting end; assuming that The base station pre-forms fixed beams, and the total number of fixed beams at all base station transmitters is ; The base station set is represented as , the user set is represented as , the beam set is expressed as ,in are all natural numbers, representing the number of base stations, the number of users, and the number of fixed beams at all base station transmitters. and Respectively represent users and beams; Due to the limitation of hardware cost, the number of RF chains at the base station transmitter is much smaller than the number of antenna array elements, that is, ; Step 1.2: Using graph theory, model the beam-level clustering and cellularization network as a weighted undirected graph and describe the components and meaning of the weighted undirected graph, including nodes, edges, and edge weights. According to graph theory, the beam-level clustering cellular network is modeled as a weighted undirected graph ,in Represents a set of points; each point It is made of beam It is combined with one or more users who regard it as the optimal beam, where the optimal beam is the beam with the largest beam domain channel gain, expressed as (1.1) in, Indicates the beam To the user Beam domain channel; gather Represents the set of edges between each point; Represents the matrix of edge weights, where its Rank Elements of a column Indicates a point and point The weight of the edge between (1.2) Assume that the entire wireless communication network is divided into non-overlapping subnets, The set of users in a subnet is represented as , the number of users in the set is expressed as , No. Beam collection in a subnet ,The number of beams in the set is expressed as ; Based on graph partitioning theory, It is used to represent the beam-level clustering and cellular networking results, where the user set and beam set in each subnet are represented as (1.3) and (1.4) in is a natural number, indicating the number of subnets in the beam-level clustering cellular network; The step 2 is to divide the weighted undirected graph in step 1 into multiple subgraphs, each subgraph corresponding to a subnet in the beam-level clustering cellular network, and specifically includes the following steps: Step 2.1: To improve the balance between subnets, normalize the minimum The cutting problem is replaced by the user's original optimization problem: (2.1) (2.2) (2.3) Among them, the cut function is defined as ，(2.4) express exist Relative complement in ; capacity function Defined as (2.5) in, (2.6) Indicates a point degree; Step 2.1, indicator matrix It was introduced to solve the optimization problem Convert it to a trace maximization problem for easy solution, expressed as (2.7) (2.8) in, Indicates size The identity matrix, indicating the matrix No. Rank The elements of a column are defined as (2.9) represents the degree matrix, is a function that creates a diagonal matrix; The step 3 specifically includes the following steps: Step 3.1: Using the mapping function , the sample points Convert the original space to a high-dimensional space, so that the data that is nonlinearly separable in the original space can be linearly separable in the high-dimensional space; weighted kernel k -means optimization problem is written as (3.1) in (3.2) Indicates a subnet Cluster center; introduce kernel function To represent the dot product of two sample points, it is expressed as (3.3) Euclidean distance Expressed as (3.4) The weighted kernel in formula (3.1) k -means optimization problem is transformed into the form of trace maximization problem. (3.5) (3.6) Among them, the indicator matrix No. Rank The elements of a column are defined as (3.7) matrix represents the kernel matrix, its Rank Column Elements ; Diagonal matrix Represents the weight matrix, its weight Rank The column elements are ; Step 3.2: Use low-complexity weighted kernel k-means to solve the beam-level clustering and cellular networking problem, achieving network acceleration; When the following conditions are met, the optimization problem and optimization problems are equivalent to: (3.8) and (3.9) Among them, the hyperparameters Introduced to adjust the kernel matrix The main diagonal displacement of Step 3.3: When the kernel matrix is ​​given and the weight matrix , calculate the reference point by formula (3.4) To Subnet Center Euclidean distance; when the reference point Located in subnet hour, (3.10) in, (3.11) Indicates that when there is no main diagonal displacement, the reference point To Subnet Center The Euclidean distance of When the reference point Not in subnet hour, (3.12) When the hyperparameters ,exist , that is, the reference point Often stay in the original subnet, and when the hyperparameters , reference point are more likely to choose other subnets; As the value of , weighted kernel k -means obtains different segmentation results; Step 3.4: Make the hyperparameters Adjust the number of active beams in wireless communication networks; at the same time, another hyperparameter Defined to implement beam activation-sleep function; According to the hyperparameters Based on the adjustable nature of , a classification-based initialization method is adopted to achieve the purpose of controlling the number of activated beams; first, the point set with users and the point set with only beams are defined as and ; The classification-based initialization method consists of two steps: (1) point set The points in are randomly initialized to clusters; (2) point sets The points in are randomly initialized to clusters; with the hyperparameters As increases, the points where only beams exist tend to move to other clusters, resulting in more activated beams. By observing equations (3.10) and (3.12), when Very small, and The gap will become huge; It will affect the clustering results. The value of There is a direct relationship; define the scaling factor for (3.13) Scale Factor It is also used as a hyperparameter to directly adjust the number of activated beams; for the initial cluster with only beams, the hyperparameter With the condition of , with the proportional factor As the factor increases, these beams are more likely to select clusters where users exist. On the contrary, when the factor When the value of increases, this part of the beam will remain dormant.

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