Balanced clustering method for decellularized massive MIMO systems

Abstract

This invention discloses a balanced clustering method for decellularized massive MIMO systems. The method aims to maximize the system's spectral efficiency. It establishes a spectral efficiency maximization optimization problem P1 by clustering access points and users, constraining each access point and user to belong to only one cluster. Based on the access point-user connection relationship, the system is transformed into a bipartite graph, further transforming the spectral efficiency maximization optimization problem P1 into a bipartite graph partitioning problem P2 with a minimum maximization segmentation objective. The bipartite graph is then transformed into a traditional graph, and based on this, the bipartite graph partitioning problem P2 is further transformed into a traditional graph segmentation problem P3. The optimal cluster set is obtained by solving this problem using a normalized spectral clustering algorithm. During the solution process, the number of clusters is adaptively determined based on the feature gap vector in the normalized spectral clustering algorithm. This invention's method is more efficient in controlling interference and significantly improves the system's spectral efficiency.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, specifically relating to a balanced clustering method for decellularized massive MIMO systems. Background Technology

[0002] In traditional cellular communication networks, users are typically served by base stations located at the center of the cellular structure. However, this architecture suffers from two main problems: firstly, users at the cellular edge are susceptible to severe interference; and secondly, each base station can only serve a limited number of users, thus restricting the overall performance of the wireless communication system. To overcome these bottlenecks, decellularized massively multi-input multiple-output (MIMO) systems have emerged. This system eliminates traditional cellular boundaries, allowing users to simultaneously access multiple distributed access points (APs), effectively mitigating inter-cell interference. Furthermore, decellularized massively multi-output systems, combined with space division multiple access (SDMA) technology, can simultaneously serve multiple users with the same time-frequency resources, significantly improving spectrum utilization. However, for large-scale user scenarios, achieving an efficient and feasible decellularized massively multi-output system requires ensuring system scalability, i.e., continuously optimizing system performance while maintaining low computational complexity.

[0003] In decellularized massive MIMO systems, designing a joint clustering scheme for access points (APs) and users to maximize the objective function (spectral efficiency) while ensuring system scalability is a key challenge. Current clustering algorithms for decellularized massive MIMO systems mainly include k-means clustering, hierarchical clustering, and machine learning. k-means clustering divides users into multiple clusters using distance metrics, ensuring that users within the same cluster have similar channel characteristics, thus achieving user clustering in decellularized massive MIMO systems. 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, achieving intelligent dynamic clustering and resource allocation.

[0004] Existing clustering algorithms in decellularized massive MIMO systems can be categorized into traditional clustering and learning-based intelligent clustering algorithms. Traditional clustering can be further divided into AP-centric and user-centric clustering. Learning-based intelligent clustering algorithms typically require real-time clustering based on the channel state at each time step. However, this design not only consumes significant resources but also ignores the randomness caused by channel estimation errors and small-scale fading, thus having certain limitations. In traditional AP-centric clustering, because the clustering design mainly considers the connectivity between APs, users are easily placed at the edge of clusters, resulting in significant interference and further degrading system performance. Traditional user-centric clustering methods usually pre-allocate APs and then perform clustering by fusing user-AP data. However, it does not fully consider the dynamic connectivity between APs and users, only considering the connectivity in the pre-design stage, making it difficult to effectively improve system performance. Furthermore, the above clustering algorithms do not consider the impact of imbalanced clustering, which may lead to some clusters having too many users, affecting system scalability and performance. Therefore, in order to better improve the scalability and performance of the system, it is necessary to comprehensively consider the connection relationship between the AP and the user and design a more effective clustering algorithm. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a balanced clustering method for decellularized large-scale MIMO systems. With maximizing system spectral efficiency as the optimization objective, this invention proposes a novel clustering algorithm to efficiently solve the optimization problem and improve overall system performance.

[0006] The technical solution of the present invention is as follows:

[0007] A balanced clustering method for decellularized large-scale MIMO systems includes the following steps:

[0008] 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 processing unit through the backhaul link;

[0009] With the goal of maximizing the system's spectrum efficiency, we establish the spectrum efficiency maximization optimization problem P1 by clustering each access point and user and constraining each access point and user to belong to only one cluster.

[0010] Based on the access point-user connection relationship, the system is transformed into a bipartite graph, thereby further transforming the spectrum efficiency maximization optimization problem P1 into a bipartite graph partitioning problem P2 with a minimum maximization cutting objective;

[0011] The bipartite graph is converted into a traditional graph. Based on the traditional graph, the bipartite graph partitioning problem P2 is further converted into a traditional graph segmentation problem P3. The optimal cluster set is obtained by solving the problem using a normalized spectral clustering algorithm. During the solution process, the number of clusters is adaptively determined based on the feature gap vector in the normalized spectral clustering algorithm.

[0012] A further technical solution of the present invention is: the optimization problem P1 for maximizing spectral efficiency, specifically expressed as follows:

[0013] ,

[0014] in, Represents the set of access points. N Indicates the number of clusters. Represents a set of users. , This indicates access point clustering. , This represents user clustering. SE This represents the system's spectral efficiency. , The effective signal-to-noise ratio is represented by constraints C1 and C2, which indicate that all access points and user nodes in the decellularized 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.

[0015] A further technical solution of the present invention is: a bipartite graph partitioning problem P2 with a minimum-maximum cutting target, the specific expression of which is as follows:

[0016] ,

[0017] in, Indicates the similarity between clusters. In a decellularized massive MIMO system, the first Joint access point-user clustering, N Indicates the number of clusters. Indicating clustering The sum of the inner edges, This represents a set of access points and user nodes. Indicates the number of access points. Indicates the number of users. This indicates that the bipartite diagram is divided into... A collection of portions.

[0018] A further technical solution of the present invention is: in P2 The specific expression is: , , Represents the cluster set of access points. Represents a user cluster set. N Indicates the number of clusters. Describes the edges of a bipartite graph. , Represents all given users After all The maximum value in, This indicates a large-scale fading factor that simultaneously considers the effects of path loss and shadow fading. Clustering The supplement, This represents the total set of access points and users.

[0019] A further technical solution of the present invention is: in P2 The specific expression is: , Describes the edges of a bipartite graph. , Represents all given users After all The maximum value in, This represents a large-scale fading factor that takes into account both path loss and shadow fading effects.

[0020] A further technical solution of the present invention is: to obtain the optimal cluster set by solving the traditional graph segmentation problem P3 using a normalized spectral clustering algorithm, specifically including:

[0021] The unnormalized Laplace matrix Defined as: ,in This represents an adjacency matrix with weights of 10 ... This refers to the edge weights in a traditional graph, where m and k represent the m-th access point and the k-th user, respectively, in a matrix. Each element on its diagonal is represented as: , Indicates the number of access points. This represents the combined set of access points and user nodes after converting the bipartite graph into a traditional graph. express The j-th element,

[0022] Normalized Laplace matrix for ;

[0023] Define the normalized Laplace matrix eigenvalues The corresponding feature vector is Select and combine from them The eigenvectors are ;

[0024] right Execute the k-means algorithm to transform the traditional graph Divided into Part, specifically: , Indicates will Clustering results after dividing into N groups express The row vector;

[0025] Will Simply convert it to the original bipartite diagram: , Indicates access point m , Indicates user k .

[0026] A further technical solution of the present invention is: adaptively determining the number of clusters based on the feature gap vector in the normalized spectral clustering algorithm, specifically including:

[0027] According to the perturbation theory, the former The sorted feature values ​​have similar feature values, and are similar to There are significant differences between the eigenvalues;

[0028] The specific expression for the feature gap vector is: ,in It is the normalized Laplace matrix After sorting, the first One eigenvalue;

[0029] The number of clusters can be determined by finding the index of the first local maximum based on the feature gap vector. .

[0030] This invention provides a balanced clustering method for decellularized massive MIMO systems. Considering the randomly distributed AP-user connection characteristics in these systems, it solves the problem through bipartite graph modeling, effectively addressing the insufficient utilization of AP-user connection relationships by traditional clustering algorithms. Simultaneously, by controlling the similarity within and between clusters, the method ensures the balance of clustering results, avoiding the performance degradation caused by imbalance in traditional clustering. Furthermore, leveraging the characteristics of spectral clustering algorithms, this invention proposes an adaptive method for determining the number of clusters, further optimizing interference management within and between clusters. Simulation results show that compared to traditional clustering algorithms, this invention is more efficient in controlling interference and significantly improves the system's spectral efficiency. Attached Figure Description

[0031] Figure 1This is a schematic diagram of the cluster-based decellularized large-scale MIMO system structure in an embodiment of the present invention;

[0032] Figure 2 This is a graph showing how the equilibrium index changes with the number of users in an embodiment of the present invention;

[0033] Figure 3 This is a graph showing the change in spectral efficiency with the number of users in an embodiment of the present invention. Detailed Implementation

[0034] The present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are intended only to illustrate the present invention and are not intended to limit the present invention. It should also be noted that, for ease of description, the accompanying drawings only illustrate portions relevant to the present invention, rather than all structures.

[0035] Before discussing the exemplary embodiments in more detail, it should be noted that some exemplary embodiments are described as processes or methods depicted as flowcharts. Although the flowcharts describe the steps as sequential processes, many of these steps can be performed in parallel, concurrently, or simultaneously. Furthermore, the order of the steps can be rearranged. The process can be terminated when its operation is complete, but may also have additional steps not included in the figures. The process can correspond to a method, function, procedure, subroutine, subroutine, etc.

[0036] The balanced clustering method for decellularized massive MIMO systems described in this embodiment aims to maximize spectral efficiency and ensure system scalability. Based on the random distribution characteristics of APs and users in decellularized massive MIMO systems, a bipartite graph partitioning problem is constructed according to the AP-user connection relationship to achieve joint clustering of APs and users. Furthermore, considering the impact of intra-cluster and inter-cluster similarity on system performance, a novel optimization objective is introduced to ensure cluster balance. Simultaneously, considering the impact of the number of clusters on intra-cluster and inter-cluster interference, an adaptive method for determining the number of clusters is proposed to manage intra-cluster and inter-cluster interference and effectively improve system performance. Specifically, the method includes the following steps:

[0037] 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 processing unit through the backhaul link;

[0038] With the goal of maximizing the system's spectrum efficiency, we establish the spectrum efficiency maximization optimization problem P1 by clustering each access point and user and constraining each access point and user to belong to only one cluster.

[0039] Based on the access point-user connection relationship, the system is transformed into a bipartite graph, thereby further transforming the spectrum efficiency maximization optimization problem P1 into a bipartite graph partitioning problem P2 with a minimum maximization cutting objective;

[0040] The bipartite graph is converted into a traditional graph. Based on the traditional graph, the bipartite graph partitioning problem P2 is further converted into a traditional graph segmentation problem P3. The optimal cluster set is obtained by solving the problem using a normalized spectral clustering algorithm. During the solution process, the number of clusters is adaptively determined based on the feature gap vector in the normalized spectral clustering algorithm.

[0041] In the specific implementation process, such as Figure 1 The figure shows a cluster-based model of a decellularized large-scale MIMO system, which includes... indivual Each of them have One antenna, For a single-antenna user, the AP interacts with the central processing unit via a backhaul link. The entire decellularized massive MIMO system is divided into... There are clusters, where the AP set is defined as follows: The user set is defined as In each cluster middle, All APs simultaneously serve All users in AP. With users The channel between them can be represented as:

[0042] (1)

[0043] in, This indicates a large-scale fading factor that simultaneously considers the effects of path loss and shadow fading. This represents the small-scale fading factor, which is independent and identically distributed according to a complex normal distribution. .

[0044] Cellular-free massive MIMO systems employ a time-division duplex model, where the correlation interval... It can be divided into two parts. It was used for uplink training. It was used for downlink data transmission. During the uplink training phase, all users simultaneously transmitted a length of... The pilot signals must be different for each user, or they must be orthogonal to each other. After transmission through the channel, the AP... The received data is represented as follows:

[0045] (2)

[0046] in This indicates the transmit power of the uplink pilot. Represent the precoding matrix and satisfy , Indicates AP The noise power at the end, where each element obeys By Mapped to ,definition for:

[0047] (3)

[0048] By the given Channel estimation can be performed using the least mean square error method. Specifically, AP With users The channel estimation between them is as follows:

[0049] (4)

[0050] Furthermore, in scenarios considering imperfect channel state information (CSI), the channel estimation error is expressed as:

[0051] (5)

[0052] , . Specifically:

[0053] (6)

[0054] (7)

[0055] During the downlink data transmission phase, the data pre-sent by the AP is represented as follows:

[0056] (8)

[0057] in, This represents the transmission power of each AP in the downlink transmission. Indicates the power allocation factor. Represents the precoding matrix, Indicates user Information to satisfy Unlike traditional cellular communication networks, decellularized massive MIMO systems need to consider the power constraints of each access point (AP), i.e. After transmission through the channel, the information transmitted by the APs is received by the user as follows:

[0058] (9)

[0059] in, Indicates user The set of channels, Indicates user noise, Indicates targeting users The precoding set, Indicates targeting users The set of power allocation factors, Indicates user Information to satisfy In decellularized massive MIMO systems, SDMA is used to transmit data. Specifically, when decoding user data, other user data is treated as interference, thereby allowing the user's data to be transmitted. The instantaneous signal-to-interference-plus-noise ratio (SINR) can be expressed as:

[0060] (10)

[0061] in, Therefore, the expression for instantaneous rate is:

[0062] (11)

[0063] Due to imperfect CSI and the randomness of channel implementation, the aforementioned instantaneous rate is random and unreachable (due to the inability to obtain accurate estimation errors and small-scale fading values ​​in the channel implementation). To address this issue, the concept of ergodic rate is introduced, defined as:

[0064] (12)

[0065] The inner layer takes the average value. The randomness of imperfect CSI is considered, and the outer layer takes the mean. The randomness of channel implementation caused by small-scale fading is taken into consideration.

[0066] To address the randomness caused by imperfect CSI in the inner layer, the statistical information of the estimation error is used to estimate its impact. The specific average SINR can be derived as follows:

[0067] (13)

[0068] This eliminates the impact of imperfect CSI. Regarding the randomness of the outer channel implementation, the effective SINR (signal-to-noise ratio) can be derived using the use-and-forget principle:

[0069] (14)

[0070] Therefore, the spectral efficiency of the system can be expressed as:

[0071] (15)

[0072] By effectively optimizing the clustering design, the spectral efficiency of the decellularized massive MIMO system can be maximized. Therefore, this maximization problem can be expressed as:

[0073] (16)

[0074] in, Represents the set of access points. N Indicates the number of clusters. Represents a set of users. , This indicates access point clustering. , This represents user clustering. SE This represents the system's spectral efficiency. , Let C represent the effective signal-to-noise ratio. Constraints C1 and C2 indicate that all access points and user nodes in the decellularized 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. Furthermore, due to the non-convexity of the constraints, this clustering problem is an NP-hard mixed-integer nonlinear programming problem. To solve this problem, the embodiment proposes a long-term clustering design.

[0075] To address P1, a balanced clustering algorithm is proposed to solve the aforementioned problem. Specifically, in decellularized massive MIMO systems, there are two types of nodes: access points (APs) and users, and communication occurs only between these two. The system can be further represented as a weighted undirected bipartite graph. ,in This indicates a combination of nodes (including APs and users). Let AP be the set of edges. With users Inter-cell communication channels. Therefore, by converting the decellularized massive MIMO system into a bipartite graph, the above clustering problem can be further transformed into a graph partitioning problem.

[0076] According to graph partitioning theory in graph theory, the first... A joint AP-user cluster is defined as , the diagram Divided into The mathematical expression for the portion is: Since this patent considers the impact of imperfect CSI and the randomness of channel implementation, it proposes a long-term clustering design based on large-scale fading parameters. Specifically, the graph edges can be defined as follows:

[0077] (17)

[0078] in Represents all given After all The maximum value in the cluster. The similarity between clusters is defined as:

[0079] (18)

[0080] in, Clustering The supplement to .

[0081] Imbalanced clustering results in decreased spectral efficiency and poor scalability. Conversely, balanced clustering leads to more balanced intra- and inter-cluster interference, creating a more suitable environment for decellularized massive MIMO systems. To achieve this balance, it is necessary to simultaneously minimize inter-cluster similarity and maximize intra-cluster similarity, whereas traditional clustering designs only focus on intra-cluster similarity related to intra-cluster interference. Therefore, unlike traditional objectives such as minimum cut or ratio cut used in previous studies, this invention first employs an equilibrium metric in decellularized massive MIMO systems, namely, a minimum-maximum cut objective. Specifically, the aforementioned spectral efficiency maximization problem can be further transformed into a bipartite graph partitioning problem with a minimum-maximum cut objective:

[0082] (19)

[0083] in, Indicates the similarity between clusters. In a decellularized massive MIMO system, the first Joint access point-user clustering, N Indicates the number of clusters. Indicating clustering The sum of the inner edges, This represents a set of access points and user nodes. Indicates the number of access points. Indicates the number of users. This indicates that the bipartite diagram is divided into... A collection of portions.

[0084] P2 The specific expression is: , , Represents the cluster set of access points. Represents a user cluster set. N Indicates the number of clusters. Describes the edges of a bipartite graph. , Represents all given users After all The maximum value in, This indicates a large-scale fading factor that simultaneously considers the effects of path loss and shadow fading. Clustering The supplement, This represents the total set of access points and users.

[0085] To solve the above problem, it is necessary to first convert the bipartite graph into a traditional graph. Specifically, the nodes at both ends of an edge with a weight of 1 are first merged into a new node, defined as... The converted graph is represented as follows: The weights after conversion are:

[0086] (20)

[0087] Based on the transformed graph, P2 is further transformed into a traditional graph partitioning problem:

[0088] (twenty one)

[0089] The traditional graph segmentation problem can be solved using a normalized spectral clustering algorithm. The specific process is as follows:

[0090] First, the unnormalized Laplace matrix is ​​defined as:

[0091] (twenty two)

[0092] in It is an adjacency matrix, and its specific weights are: , Each element on its diagonal can be represented as:

[0093] (twenty three)

[0094] Based on the above process, the normalized Laplace matrix can be further defined as:

[0095] (twenty four)

[0096] Define the eigenvalues ​​of the normalized Laplace matrix as follows: The corresponding feature vector is Before selecting and combining The eigenvectors are:

[0097] (25)

[0098] Finally, Execute the k-means algorithm to thus Divided into Part, specifically:

[0099] (26)

[0100] Simply convert it back to the original bipartite diagram:

[0101] (27)

[0102] Furthermore, to achieve the optimal performance of the above clustering design, it is necessary to determine an appropriate number of clusters. It can be observed that a smaller number of clusters presents a greater challenge to the interference suppression mechanism within each cluster due to the high correlation of interfering signals. Conversely, a larger number of clusters leads to higher cross-cluster interference but reduces computational complexity, thus ensuring system scalability. Therefore, in decellularized massive MIMO systems, the number of clusters should be determined to achieve a balance between intra-cluster and inter-cluster interference.

[0103] The optimal number of clusters can be determined by... The optimal number of clusters is determined through iterations. In each iteration, the aforementioned spectral clustering method is used. However, especially when dealing with large-scale data, exhaustive searching for the optimal number of clusters leads to high computational complexity. To address this issue, a low-complexity adaptive clustering design is employed based on the feature gaps in the spectral clustering method to determine the number of clusters. Specifically, according to perturbation theory, the first... The eigenvalues ​​of the sorted eigenvalues ​​have similar eigenvalues, and are similar to the eigenvalues ​​of the sorted eigenvalues. There are significant differences between the feature values.

[0104] (28)

[0105] in It is the sorted number of normalized Laplace matrices. Each feature value. Therefore, this patent can adaptively determine the number of clusters. This process involves dividing the data into corresponding clusters. The specific steps are summarized in Table 1 below:

[0106]

[0107] To better demonstrate the effectiveness of this invention, simulation experiments were conducted in the embodiments to verify the proposed balanced clustering scheme for solving the spectral efficiency maximization problem. It is assumed that there are 10 APs in this scenario, each with 4 antennas. Furthermore, the pilot length is 6, and the pilot transmit power and downlink data transmit power are 100mW and 200mW, respectively.

[0108] Figure 2 The results show a comparison using a balanced metric, namely the minimum-maximum cut objective, in relation to the number of users. It can be seen that the proposed balanced clustering algorithm, due to its use of the minimum-maximum cut objective, outperforms traditional k-means clustering, hierarchical clustering, and user-centric clustering algorithms in decellularized large-scale MIMO systems. This is because, in traditional clustering algorithms, users and access points (APs) within a specific cluster may be highly concentrated, leading to abnormally large cut values ​​in other clusters. Furthermore, as the system size increases, the size of this specific user cluster also increases, thus widening the performance gap between these clustering algorithms.

[0109] Figure 3 The relationship between spectral efficiency and the number of users is demonstrated. It can be seen that the proposed clustering algorithm outperforms traditional clustering algorithms in decellularized massive MIMO systems. Compared to traditional algorithms, the proposed clustering can more efficiently manage intra- and inter-cluster interference without significantly increasing computational complexity, thus improving spectral efficiency. As the number of users increases, the imbalanced clustering results of traditional algorithms become more severe, leading to limited spectral efficiency. Furthermore, the low-complexity operations introduced by clustering, combined with the continuous improvement in spectral efficiency, validate the scalability of decellularized massive MIMO systems.

[0110] As can be seen from the embodiments, the balanced clustering method for decellularized massive MIMO systems provided by this invention considers the connection characteristics of randomly distributed access points (APs) to users in decellularized massive MIMO systems and solves the problem through bipartite graph modeling, effectively addressing the problem of insufficient utilization of AP-user connection relationships in traditional clustering algorithms. Simultaneously, by controlling the similarity within and between clusters, the balance of clustering results is ensured, avoiding the performance degradation caused by imbalance in traditional clustering. Furthermore, leveraging the characteristics of spectral clustering algorithms, this invention also proposes an adaptive method for determining the number of clusters, further optimizing interference management within and between clusters. Simulation results show that compared to traditional clustering algorithms, this invention's method is more efficient in controlling interference and significantly improves the system's spectral efficiency.

[0111] In this document, the terms “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that a step or method that comprises a list of elements includes not only those elements but also other elements not expressly listed or inherent to such a step or method.

[0112] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A balanced clustering method for decellularized large-scale MIMO systems, characterized in that, Includes 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 processing unit through the backhaul link; With the goal of maximizing the system's spectrum efficiency, we establish the spectrum efficiency maximization optimization problem P1 by clustering each access point and user and constraining each access point and user to belong to only one cluster. Based on the access point-user connection relationship, the system is transformed into a bipartite graph, thereby further transforming the spectrum efficiency maximization optimization problem P1 into a bipartite graph partitioning problem P2 with a minimum maximization cutting objective; The bipartite graph is converted into a traditional graph. Based on the traditional graph, the bipartite graph partitioning problem P2 is further converted into a traditional graph segmentation problem P3. The optimal cluster set is obtained by solving the problem using a normalized spectral clustering algorithm. During the solution process, the number of clusters is adaptively determined based on the feature gap vector in the normalized spectral clustering algorithm.

2. The equilibrium clustering method for decellularized large-scale MIMO systems according to claim 1, characterized in that, The optimization problem P1, which aims to maximize spectral efficiency, is expressed as follows: ,in, Represents the set of access points. N Indicates the number of clusters. Represents a set of users. , This indicates access point clustering. , This represents user clustering. SE This represents the system's spectral efficiency. , The effective signal-to-noise ratio is represented by constraints C1 and C2, which indicate that all access points and user nodes in the decellularized 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 balanced clustering method for decellularized large-scale MIMO systems according to claim 1, characterized in that, The bipartite graph partitioning problem P2, which has a minimum-maximum cutting objective, is expressed as follows: ,in, Indicates the similarity between clusters. In a decellularized massive MIMO system, the first Joint access point-user clustering, N Indicates the number of clusters. Indicating clustering The sum of the inner edges, This represents a set of access points and user nodes. Indicates the number of access points. Indicates the number of users. This indicates that the bipartite diagram is divided into... A collection of portions.

4. The balanced clustering method for decellularized large-scale MIMO systems according to claim 3, characterized in that, P2 The specific expression is: , , Represents the cluster set of access points. Represents a user cluster set. N Indicates the number of clusters. Describes the edges of a bipartite graph. , Represents all given users After all The maximum value in, This indicates a large-scale fading factor that simultaneously considers the effects of path loss and shadow fading. Clustering The supplement, This represents the total set of access points and users.

5. The balanced clustering method for decellularized large-scale MIMO systems according to claim 3, characterized in that, P2 The specific expression is: , , Represents the cluster set of access points. Represents a user cluster set. Indicates the number of clusters. Describes the edges of a bipartite graph. , Represents all given users After all The maximum value in, This represents a large-scale fading factor that takes into account both path loss and shadow fading effects.

6. The balanced clustering method for decellularized large-scale MIMO systems according to claim 1, characterized in that, The optimal cluster set is obtained by solving the traditional graph segmentation problem P3 using a normalized spectral clustering algorithm, specifically including: The unnormalized Laplace matrix Defined as: ,in This represents an adjacency matrix with weights of 10 ... This refers to the edge weights in a traditional graph, where m and k represent the m-th access point and the k-th user, respectively, in a matrix. Each element on its diagonal is represented as: , Indicates the number of access points. This represents the combined set of access points and user nodes after converting the bipartite graph into a traditional graph. express The j-th element; Normalized Laplace matrix for ; Define the normalized Laplace matrix eigenvalues The corresponding feature vector is Select and combine from them The eigenvectors are ; right Execute the k-means algorithm to transform the traditional graph Divided into Part, specifically: , Indicates will Clustering results after dividing into N groups express The row vector; Will Simply convert it to the original bipartite diagram: , Indicates access point m , Indicates user k .

7. The equilibrium clustering method for decellularized large-scale MIMO systems according to claim 6, characterized in that, The feature gap vector in the normalized spectral clustering algorithm adaptively determines the number of clusters, specifically including: According to the perturbation theory, the former The sorted feature values ​​have similar feature values, and are similar to There are significant differences between the eigenvalues; The specific expression for the feature gap vector is: ,in It is the normalized Laplace matrix After sorting, the first One eigenvalue; The number of clusters can be determined by finding the index of the first local maximum based on the feature gap vector. .

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