Balanced clustering method for cellular-removed large-scale MIMO system

Abstract

The invention discloses a balanced clustering method for a cellular-removed large-scale MIMO (Multiple Input Multiple Output) system, which takes the spectrum efficiency maximization of the system as an optimization target, and establishes a spectrum efficiency maximization optimization problem P1 by clustering access points and users and constraining the access points and the users to only belong to one of the clusters; the system is converted into a bipartite graph according to the access point-user connection relation, and therefore the spectrum efficiency maximization optimization problem P1 is further converted into a bipartite graph division problem P2 with the minimum and maximum cutting target; the bipartite graph is converted into a traditional graph, a bipartite graph division problem P2 is further converted into a traditional graph segmentation problem P3 based on the traditional graph, an optimal clustering set is solved through a normalized spectral clustering algorithm, and in the solving process, the clustering number is adaptively determined based on a feature gap vector in the normalized spectral clustering algorithm. The method provided by the invention is more efficient in the aspect of interference control, and the spectrum efficiency of the system is remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication, and particularly relates to an equilibrium clustering method for a de-cellular massive MIMO system. Background Art

[0002] In a traditional cellular communication network, users are usually served by a base station located at the center of the cellular structure. However, this architecture has two main problems: one is that users at the cellular edge are easily subject to severe interference, and the other is that the number of users that each base station can serve is limited, thereby restricting the overall performance of the wireless communication system. To break through the above bottleneck, a de-cellular massive multiple-input multiple-output (MIMO) system has emerged. By canceling the traditional cellular boundaries, this system enables users to simultaneously access multiple distributed access points (APs), thus effectively alleviating the inter-cell interference problem. In addition, the de-cellular massive MIMO system combines space-division multiple access (SDMA) technology and can provide services to multiple users simultaneously under the same time-frequency resources, greatly improving the spectrum utilization rate. However, when facing a large-scale user scenario, to implement an efficient and feasible de-cellular massive MIMO system, it is necessary to ensure the scalability of the system, that is, to continuously optimize the system performance while maintaining a low computational complexity.

[0003] In a de-cellular massive MIMO system, how to design a joint clustering scheme for APs and users to maximize the objective function, i.e., the spectral efficiency, while ensuring the scalability of the system is a key issue. Currently, the clustering algorithms for de-cellular massive MIMO systems mainly include k-means clustering, hierarchical clustering, machine learning, etc. K-means clustering divides users into multiple clusters through distance metrics, making the channel characteristics of users within the same cluster similar, thereby realizing the clustering of users in a de-cellular massive MIMO system. Hierarchical clustering constructs a hierarchical clustering tree structure by calculating the similarity between users, initially treating each user as an independent cluster and gradually merging clusters with high similarity. Machine learning algorithms use data such as channel characteristics and user locations to train models to achieve intelligent dynamic clustering and resource allocation.

[0004] In existing clustering algorithms for cellular-free massive MIMO systems, they can be divided into traditional clustering and learning-based intelligent clustering algorithms. Among them, traditional clustering can be further divided into two types: AP-centered and user-centered. In the design of learning-based intelligent clustering algorithms, real-time clustering usually needs to be performed for the channel state at each moment. However, this design not only consumes a large amount of resources but also ignores the randomness effects brought by channel estimation errors and small-scale fading, having certain limitations. In traditional AP-centered clustering, since the clustering design mainly considers the connection relationship between APs, it is easy to cause users to be located at the edge of the cluster, resulting in users experiencing greater interference and further reducing system performance. And traditional user-centered clustering methods usually adopt the method of pre-assigning APs and then perform clustering by fusing users-APs, but they do not fully consider the dynamic connection relationship between APs and users, only considering their connection in the pre-design stage and it is difficult to effectively improve system performance. In addition, the above clustering algorithms do not consider the impact of unbalanced clustering, which may lead to too many users in some clusters, affecting the scalability and performance of the system. Therefore, in order to better improve the scalability and performance of the system, it is necessary to comprehensively consider the connection relationship between APs and users and design a more effective clustering algorithm. Summary of the Invention

[0005] In view of the above problems, the present invention provides an equilibrium clustering method for a cellular-free massive MIMO system, aiming to maximize the system spectral efficiency as the optimization goal, and proposes a new clustering algorithm to efficiently solve the optimization problem and improve the overall system performance.

[0006] The technical solution of the present invention is as follows: An equilibrium clustering method for a cellular-free massive MIMO system, comprising the following steps: Construct a cellular-free massive MIMO system, including M access points, each access point has S antennas, K single-antenna users, and the access points realize data interaction with the central processor through the backhaul link; Taking the maximization of the system spectral efficiency as the optimization goal, by clustering each access point and user and restricting that each access point and user can only belong to a certain cluster in the clustering, establish an optimization problem P1 for maximizing the spectral efficiency; According to the access point-user connection relationship, convert the system into a bipartite graph, thereby further converting the optimization problem P1 for maximizing the spectral efficiency into a bipartite graph partitioning problem P2 with a minimum-maximum cut target; Convert the bipartite graph into a traditional graph, and further convert the bipartite graph partitioning problem P2 into a traditional graph segmentation problem P3 based on the traditional graph and solve it through a normalized spectral clustering algorithm to obtain the optimal clustering set, where the number of clusters is adaptively determined based on the eigen-gap vector in the normalized spectral clustering algorithm during the solving process.

[0007] A further technical solution of the present invention is: the spectrum efficiency maximization optimization problem P1, and the specific expression is as follows: , wherein, represents the set of access points, N represents the number of clusters, represents the set of users, , represents the access point cluster, , represents the user cluster, SE represents the spectrum efficiency of the system, , represents the effective signal-to-noise ratio. Constraints C1 and C2 indicate that clustering needs to be performed on all access points and user nodes in the cell-free massive MIMO system; C3 and C4 indicate that each access point and user can only belong to a certain cluster in the clustering.

[0008] A further technical solution of the present invention is: the bipartite graph partitioning problem P2 with the minimum-maximum cut objective, and the specific expression is as follows: , wherein, represents the similarity between clusters, represents the -th joint access point-user cluster in the cell-free massive MIMO system, N represents the number of clusters, represents the sum of edges within the cluster , represents the set of combinations of access points and user nodes, represents the number of access points, represents the number of users, represents the set that partitions the bipartite graph into parts.

[0009] A further technical solution of the present invention is: the specific expression of in P2 is: , , represents the set of access point clusters, represents the set of user clusters, N represents the number of clusters, represents the graph edges of the bipartite graph, , represents the maximum value among all given users after all , represents the large-scale fading factor that simultaneously considers the effects of path loss and shadow fading, represents the clustering complement of, represents the total set of access points and users.

[0010] A further technical solution of the present invention is: In P2 The specific expression is: , represents the graph edge of the bipartite graph, , represents all given users after all the maximum value in, represents the large-scale fading factor that simultaneously considers the effects of path loss and shadow fading.

[0011] A further technical solution of the present invention is: Solve the traditional graph segmentation problem P3 through the normalized spectral clustering algorithm to obtain the optimal clustering set, specifically including: Define the unnormalized Laplacian matrix as: , where represents the adjacency matrix, and its weight is that is, the edge weight of the traditional graph. m and k respectively represent the mth access point and the kth user. The matrix , and each element on its diagonal is expressed as: , represents the number of access points, represents the combined set of access point and user nodes after converting the bipartite graph into a traditional graph, represents the jth element in, The normalized Laplacian matrix is ; Define the eigenvalues of the normalized Laplacian matrix as , and the corresponding eigenvectors are . Select and combine the first eigenvectors as ; Perform the k-means algorithm on so as to divide the converted traditional graph into parts, specifically expressed as: , represents the clustering situation after dividing into N parts, represents the row vector of; Divide Convert it to the original bipartite graph as follows: , denotes an access point m , denotes a user k .

[0012] A further technical solution of the present invention is: adaptively determine the number of clusters based on the eigen-gap vector in the normalized spectral clustering algorithm, specifically including: According to perturbation theory, the first sorted eigenvalues have similar eigenvalues and there is an obvious gap with the eigenvalues; The specific expression of the eigen-gap vector is: , where is the normalized Laplacian matrix and the th sorted eigenvalue in it; Find the index of the first local maximum according to the eigen-gap vector to determine the number of clusters .

[0013] The balanced clustering method for the de-cellularized massive MIMO system provided by the present invention considers the randomly distributed AP-user connection characteristics in the de-cellularized massive MIMO system and solves it through bipartite graph modeling, effectively solving the problem of insufficient utilization of AP-user connection relationships by traditional clustering algorithms. At the same time, by controlling the similarity within and between clusters, the balance of the clustering results is ensured, avoiding the performance degradation caused by imbalance in traditional clustering. In addition, relying on the characteristics of the spectral clustering algorithm, the method of the present invention also proposes a method for adaptively determining the number of clusters, further optimizing the interference management within and between clusters. The simulation results show that compared with traditional clustering algorithms, the method of the present invention is more efficient in controlling interference and significantly improves the spectral efficiency of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 is a schematic structural diagram of a de-cellularized massive MIMO system based on clustering in an embodiment of the present invention; Figure 2 is a graph showing the change of the balance index with the number of users in an embodiment of the present invention; Figure 3 is a graph showing the change of the spectral efficiency with the number of users in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0015] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It can be understood that the specific embodiments described herein are only for explaining the present invention, rather than limiting the present invention. In addition, it should be noted that, for the sake of convenience of description, only the parts related to the present invention rather than all the structures are shown in the drawings.

[0016] Before discussing the exemplary embodiments in more detail, it should be mentioned that some exemplary embodiments are described as processes or methods depicted as flowcharts. Although the flowcharts depict the steps as sequential processes, many of the steps can be implemented in parallel, concurrently, or simultaneously. In addition, the order of the steps can be rearranged. The process can be terminated when its operation is completed, but it can also have additional steps not included in the drawings. The process can correspond to a method, function, procedure, subroutine, subprogram, etc.

[0017] The equalized clustering method for a cellular-free massive MIMO system in the embodiment aims to maximize the spectral efficiency and ensure the system scalability. According to the random distribution characteristics of APs and users in the cellular-free massive MIMO system, a bipartite graph partitioning problem is constructed based on the AP-user connection relationship to achieve the joint clustering of APs and users; in addition, considering the influence of the similarity within and between clusters on the system performance, a new optimization objective is introduced to ensure the balance of clustering; meanwhile, considering the influence of the number of clusters on the interference within and between clusters, a method for adaptively determining the number of clusters is proposed to manage the interference within and between clusters and effectively improve the system performance. Specifically, it includes the following steps: Construct a cellular-free massive MIMO system, including M access points, each access point has S antennas, and K single-antenna users. The access points realize data interaction with the central processor through the backhaul link; Taking the maximization of the spectral efficiency of the system as the optimization objective, by clustering each access point and user and restricting that each access point and user can only belong to a certain cluster in the clustering, an optimization problem P1 for maximizing the spectral efficiency is established; According to the AP-user connection relationship, the system is converted into a bipartite graph, so that the optimization problem P1 for maximizing the spectral efficiency is further converted into a bipartite graph partitioning problem P2 with a minimum-maximum cut objective; The bipartite graph is converted into a traditional graph, and based on the traditional graph, the bipartite graph partitioning problem P2 is further converted into a traditional graph segmentation problem P3 and solved by a normalized spectral clustering algorithm to obtain the optimal clustering set. Among them, the number of clusters is adaptively determined based on the eigen-gap vector in the normalized spectral clustering algorithm during the solving process.

[0018] During the specific implementation process, as Figure 1 shown, it is a cellular-free massive MIMO system model based on clustering. The system includes one , where each has antennas, single-antenna users, and the AP realizes data interaction with the central processor through the backhaul link. The entire cell-free massive MIMO system is divided into clusters, where the set of APs is defined as , and the set of users is defined as . In each cluster , all the APs in serve all the users in . The channel between the AP and the user (1) where represents the large-scale fading factor that simultaneously considers the effects of path loss and shadow fading, represents the small-scale fading factor, which is independent and identically distributed over the complex normal distribution .

[0019] The cell-free massive MIMO system adopts a time-division duplex model, where the coherence interval can be divided into two parts, is used for uplink training, is used for downlink data transmission. In the uplink training phase, all users simultaneously transmit pilots of length , and the pilots between different users are either different or orthogonal to each other. After passing through the channel, the data received by the AP is expressed as: (2) where represents the transmission power of the uplink pilots, represents the precoding matrix and satisfies , represents the noise power at the AP end, and each element follows . By mapping to , define as: (3) Given a , the minimum mean square error method can be used to perform channel estimation. Specifically, the channel estimation between the AP and the user is: (4) In addition, in the scenario considering imperfect Channel State Information (CSI), the channel estimation error is expressed as: (5) , . Specifically: (6) (7) In the downlink data transmission phase, the data pre-transmitted by the AP side is expressed as: (8) Among them, represents the transmission power of each AP in the downlink transmission, represents the power allocation factor, represents the precoding matrix, represents the information of user , satisfying . Different from the traditional cellular communication network, the cellular massive MIMO system needs to consider the power constraint of each AP, that is . After passing through the channel, the information transmitted by the APs is received at the user side as: (9) Among them, represents the channel set of user , represents the noise of user , represents the precoding set for user , represents the power allocation factor set for user , represents the information of user , satisfying . In the cellular massive MIMO system, SDMA is used to transmit data. Specifically, when decoding the user data, the data of other users is regarded as interference. Thus, the instantaneous signal-to-interference-plus-noise ratio (SINR) of user can be expressed as: (10) Among them, . Therefore, the expression of the instantaneous rate is: (11) Due to the randomness of imperfect CSI and channel realizations, the above instantaneous rate is random and unattainable (because accurate estimation errors and small-scale fading values in channel realizations cannot be obtained). To solve this problem, the concept of ergodic rate is introduced and defined as: (12) where the inner mean considers the randomness of imperfect CSI, and the outer mean considers the randomness of channel realizations caused by small-scale fading.

[0020] Regarding the randomness caused by inner-layer imperfect CSI, the statistical information of the estimation error is used to estimate its impact, and the specific average SINR can be derived as: (13) Thus, the impact of imperfect CSI is eliminated. Regarding the randomness of outer-layer channel realizations, it is derived using the principle of "use and forget", and the specific effective SINR (signal-to-noise ratio) can be expressed as: (14) Therefore, the spectral efficiency of the system can be expressed as: (15) By effectively optimizing the design of clustering, the spectral efficiency of the cell-free massive MIMO system is maximized. Therefore, this maximization problem can be expressed as: (16) where represents the set of access points, N represents the number of clusters, represents the set of users, 、 represent the access point clusters, 、 represent the user clusters, SE represents the spectral efficiency of the system, , represents the effective signal-to-noise ratio. Constraints C1 and C2 mean that all access points and user nodes in the cell-free massive MIMO system need to be clustered; C3 and C4 mean that each access point and user can only belong to a certain cluster in the clustering. At the same time, due to the non-convexity of the constraints, this clustering problem is a NP-hard mixed integer non-linear programming problem. To solve this problem, the embodiment proposes a long-term clustering design.

[0021] To solve P1, a balanced clustering algorithm is proposed next to address the above issues. Specifically, in the cellular-free massive MIMO system, there are two types of nodes, including APs and users, and communication occurs only between these two. The system can be further represented as a weighted undirected bipartite graph , where represents the set of nodes (including APs and users), represents the set of edges, representing the communication channel between an AP and a user . Therefore, by converting the cellular-free massive MIMO system into a bipartite graph, the above clustering problem can be further transformed into a graph partitioning problem.

[0022] According to the graph partitioning theory in graph theory, the -th combined AP-user clustering in the cellular-free massive MIMO system is defined as , and the mathematical expression for partitioning the graph into parts is . Since this patent takes into account the effects of imperfect CSI and the randomness of channel realizations, a long-term clustering design based on large-scale fading parameters is considered. Specifically, the graph edges can be defined as: (17) where represents the maximum value among all given for all . The similarity between clusters is defined as: (18) where represents the complement of cluster .

[0023] Unbalanced clustering results will lead to problems such as decreased spectral efficiency and poor scalability. On the contrary, balanced clustering results will lead to more balanced intra-cluster and inter-cluster interference, thus creating a more suitable environment for implementing the cellular-free massive MIMO system. To achieve this balance, it is necessary to simultaneously minimize the similarity between clusters and maximize the similarity within clusters, while traditional clustering designs only focus on the intra-cluster similarity related to intra-cluster interference. Therefore, different from traditional objectives such as minimum cut or ratio cut used in previous studies, the present invention first adopts a balance metric in the cellular-free massive MIMO system, namely the min-max cut objective. Specifically, the above spectral efficiency maximization problem can be further transformed into a bipartite graph partitioning problem with a min-max cut objective: (19) where represents the similarity between clusters, represents the \(i\)-th joint access point-user clustering in the cellular massive MIMO system, where \(i\) represents the number of clusters, N denotes the number of clusters, represents the sum of the edges within the cluster where \(i\) is the cluster index, represents the set of combined access points and user nodes, denotes the number of access points, denotes the number of users, represents the set that divides the bipartite graph into \(k\) parts.

[0024] The specific expression of \(P_2\) is: \[P_2 = \frac{1}{2}\sum_{i = 1}^{k}\frac{e_i}{|S_i^a||S_i^u|}\sum_{(m,n)\in S_i^a\times S_i^u}w_{mn}\] where \[S_i^a\] represents the set of access point clusters, \[S_i^u\] N represents the set of user clusters, \(e_i\) represents the number of edges in the bipartite graph, \[w_{mn} = \frac{1}{L_{mn}}\] where \(L_{mn}\) represents the maximum value among all given users after considering all path loss and shadow fading effects, \(L_{mn}\) represents the large-scale fading factor considering both path loss and shadow fading effects, \(\overline{S}_i\) represents the complement of the cluster \(S_i\), and \(\mathcal{V}\) represents the total set of access points and users.

[0025] To solve the above problem, the bipartite graph needs to be first converted into a traditional graph. Specifically, first, the nodes at both ends of the edge with a weight of 1 are fused into a new node, defined as \(v_{mn}\). The converted graph is denoted as \(\mathcal{G}'\), and the weight of the edge after conversion is: \((20)\) Based on the converted graph, \(P_2\) is further converted into a traditional graph segmentation problem: \((21)\) where the traditional graph segmentation problem can be solved by the normalized spectral clustering algorithm. The specific process is as follows: First, the unnormalized Laplacian matrix is defined as: \((22)\) where \(A\) is the adjacency matrix, and its specific weight is \[A_{mn} = \begin{cases}1, & \text{if} (m,n)\in\mathcal{E}\\0, & \text{otherwise}\end{cases}\] and each element on its diagonal can be expressed as: (23) Based on the above process, the normalized Laplacian matrix can be further defined as: (24) Define the eigenvalues of the normalized Laplacian matrix as , and the corresponding eigenvectors as . Select and combine the first eigenvectors as: (25) Finally, perform the k-means algorithm on so as to divide into parts, specifically expressed as: (26) Convert it to the original bipartite graph: (27) In addition, to achieve the best performance of the above clustering design, it is necessary to determine the appropriate number of clusters . It can be observed that a smaller number of clusters will pose a greater challenge to the interference suppression mechanism within each cluster due to the high correlation of interference signals. On the contrary, a larger number of clusters will lead to higher inter-cluster interference, but reduce the computational complexity, thus ensuring the scalability of the system. Therefore, in the cellular-free massive MIMO system, the number of clusters should be determined to achieve a balance between intra-cluster and inter-cluster interference.

[0026] The optimal number of clusters can be determined through iterations. In each iteration, the above spectral clustering method is adopted. However, especially when dealing with large-scale data, an exhaustive search for the optimal number of clusters will lead to a very high computational complexity. To solve this problem, based on the eigengap in the spectral clustering method, a low-complexity adaptive clustering design is adopted to determine the number of clusters. Specifically, according to the perturbation theory, the first sorted eigenvalues have similar eigenvalues and there is an obvious gap with the th eigenvalue. The eigengap vector is expressed as: (28) where is the th sorted eigenvalue in the normalized Laplacian matrix. Therefore, this patent can determine the number of clusters in an adaptive manner, and then divide the corresponding clusters. Its specific process is summarized into the following Table 1 algorithm:

[0027] To better demonstrate the effectiveness of the present invention, simulation experiments were conducted in the embodiments, and the proposed balanced clustering scheme was verified through simulation to solve the problem of maximizing spectral efficiency. It is assumed that there are 10 APs in this scenario, and each AP has 4 antennas. Additionally, the pilot length is 6, and the pilot transmission power and downlink data transmission power are 100 mW and 200 mW respectively.

[0028] Figure 2 The comparison results of the balanced metric, i.e., the min-max cut objective and the number of users, are shown. It can be seen that the proposed balanced clustering algorithm, due to adopting the min-max cut objective, is superior to the traditional k-means clustering, hierarchical clustering, and user-centric clustering algorithms in the de-cellular massive MIMO system. This is because, in the traditional clustering algorithms, the users and APs within a specific cluster may be highly concentrated, resulting in an abnormally large cut value in other clusters. In addition, as the system scale increases, the size of this specific user cluster also increases, thereby expanding the performance gap between these clustering algorithms.

[0029] Figure 3 The relationship between spectral efficiency and the number of users is shown. It can be seen that the proposed clustering algorithm is superior to the traditional clustering algorithms in the de-cellular massive MIMO system. Compared with the traditional algorithms, the proposed clustering can manage the intra-cluster and inter-cluster interference more efficiently without significantly increasing the computational complexity, thereby improving the spectral efficiency. As the number of users increases, the unbalanced clustering results of the traditional algorithms become more serious, resulting in limited spectral efficiency. In addition, based on the low-complexity operations introduced by clustering and the continuous improvement of spectral efficiency, the scalability of the de-cellular massive MIMO system is verified.

[0030] It can be seen from the embodiments that the balanced clustering method for the de-cellular massive MIMO system provided by the present invention considers the characteristics of the randomly distributed access point AP-user connections in the de-cellular massive MIMO system and solves it through bipartite graph modeling, effectively solving the problem of insufficient utilization of the AP-user connection relationship by the traditional clustering algorithms. At the same time, by controlling the intra-cluster and inter-cluster similarities, the balance of the clustering results is ensured, avoiding the performance degradation caused by imbalance in the traditional clustering. In addition, relying on the characteristics of the spectral clustering algorithm, the method of the present invention also proposes a method for adaptively determining the number of clusters, further optimizing the interference management within and between clusters. The simulation results show that, compared with the traditional clustering algorithms, the method of the present invention is more efficient in controlling interference and significantly improves the spectral efficiency of the system.

[0031] In this text, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, such that a step, method comprising a series of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such step, method.

[0032] The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can be made, and all should be regarded as falling within the protection scope of the present invention.

Claims

1. An equalization clustering method for a cellular-free massive MIMO system, characterized in that It includes the following steps: Construct a cell-free massive MIMO system, including M access points, each access point has S antennas, K single-antenna users, and the access points realize data interaction with the central processor through the backhaul link; Taking the maximum spectral efficiency of the system as the optimization goal, by clustering each access point and user, and restricting that each access point and user can only belong to a certain cluster in the clustering, establish the spectral efficiency maximization optimization problem P1; According to the access point-user connection relationship, convert the system into a bipartite graph, so as to further convert the spectral efficiency maximization optimization problem P1 into a bipartite graph partitioning problem P2 with a minimum-maximum cut target; Convert the bipartite graph into a traditional graph, and further convert the bipartite graph partitioning problem P2 into a traditional graph segmentation problem P3 based on the traditional graph and solve it by the normalized spectral clustering algorithm to obtain the optimal clustering set. Among them, the number of clusters is adaptively determined based on the eigen-gap vector in the normalized spectral clustering algorithm during the solving process.

2. The equalization clustering method for a cell-free massive MIMO system according to claim 1, wherein The optimization problem P1 for maximizing spectral efficiency is as follows: , where represents the set of access points, N represents the number of clusters, represents the set of users, 、 represents the access point clusters, 、 represents the user clusters, SE represents the spectral efficiency of the system, , represents the effective signal-to-noise ratio. Constraints C1 and C2 indicate that all access points and user nodes in the cell-free massive MIMO system need to be clustered; C3 and C4 indicate that each access point and user can only belong to one of the clusters.

3. The equalization clustering method for the de-cellularized massive MIMO system according to claim 1, wherein The bipartite graph partitioning problem P2 with the min-max cut objective is as follows: , where represents the similarity between clusters, represents the th joint access point-user cluster in the cell-free massive MIMO system, N represents the number of clusters, represents the sum of edges within the cluster , represents the set of combinations of access points and user nodes, represents the number of access points, represents the number of users, represents the set that partitions the bipartite graph into parts.

4. The equalized clustering method for a cell-free massive MIMO system according to claim 3, characterized in that In P2 The specific expression is: , , represents the access point clustering set, represents the user clustering set, N represents the number of clusters, represents the graph edges of the bipartite graph, , represents all given users after all the maximum value in, represents the large-scale fading factor that takes into account both path loss and shadow fading effects, represents the cluster complement of, represents the total set of access points and users.

5. The equalized clustering method for a cell-free massive MIMO system according to claim 3, characterized in that In P2 The specific expression is as follows: , represents the graph edges of a bipartite graph, , represents all given users after all the maximum value in, represents the large-scale fading factor that takes into account the effects of both path loss and shadow fading.

6. The equalized clustering method for a de-cellularized massive MIMO system according to claim 1, characterized in that Solving the traditional graph segmentation problem P3 by the normalized spectral clustering algorithm to obtain the optimal clustering set, specifically including: The unnormalized Laplacian matrix is defined as: , where represents the adjacency matrix, whose weight is , that is, the edge weight of the traditional graph. m and k represent the m-th access point and the k-th user respectively. The matrix , and each element on its diagonal is expressed as: , represents the number of access points, represents the combined set of access points and user nodes after converting the bipartite graph into a traditional graph, represents the j-th element in; Normalized Laplacian matrix is ; Define the normalized Laplacian matrix The eigenvalues of are Select and combine the first eigenvectors as ; Pair Execute the k-means algorithm to partition the transformed traditional graph into parts, specifically represented as: , indicating the clustering situation after dividing into N parts, indicating the row vector of Convert to the original bipartite graph as follows: That is, , represents an access point m , represents a user k .

7. The equalization clustering method for the de-cellularized massive MIMO system according to claim 6, characterized in that Adaptive determination of the number of clusters based on the eigen-gap vector in the normalized spectral clustering algorithm, specifically including: According to perturbation theory, the first sorted eigenvalues have similar eigenvalues and there is a significant gap between them and the eigenvalues; The specific expression of the feature gap vector is as follows: , where is the normalized Laplacian matrix after sorting, and the th eigenvalue; The number of clusters can be determined by finding the index of the first local maximum according to the characteristic gap vector .

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