A user clustering and topology optimization method for a distributed irregular RIS-assisted NOMA system

Abstract

The application relates to a user clustering and topology optimization method for a distributed irregular RIS-assisted NOMA system, and belongs to the technical field of wireless communication. For a distributed RIS-assisted NOMA communication model, firstly, an improved spectral clustering algorithm (B-SPC) is applied to realize non-uniform distribution NOMA user clustering (UC) in the scene, and irregular RIS-assisted communication is matched for each UC based on the fairness principle. Then, based on the NOMA user clustering mechanism, a tabu search algorithm (TS) is applied to dynamically optimize the topology structure of the irregular RIS, and a fractional programming method (FP) is adopted to jointly optimize the topology structure of the irregular RIS, the user power allocation in the UC and the reflection surface beam forming, so as to maximize the total spectral efficiency of the system. Compared with the traditional regular RIS deployment, the B-SPC clustering algorithm improves the uniformity of the UC clustering and the user service fairness, significantly improves the total spectral efficiency of the distributed irregular RIS-assisted NOMA system, and meanwhile, the FP method can realize more optimal resource allocation among different users.

Description

TECHNICAL FIELD

[0001] The application relates to a user clustering and topology optimization method for a distributed irregular RIS assisted NOMA system and belongs to the technical field of wireless communication. BACKGROUND

[0002] A reconfigurable intelligent surface (RIS) is composed of a large number of elements with controllable phase shifts. By optimizing the direction and phase of the reflected beam, the RIS can significantly enhance the spectral efficiency and energy efficiency of the communication system. In addition, the RIS has attracted widespread attention due to its low cost, low power consumption, ability to overcome signal blockage, improvement of channel capacity, and reduction of transmission power in future communication systems. Non-orthogonal multiple access (NOMA) has become an important technology for future wireless communication networks due to its ability to enhance user connectivity, improve system throughput, provide fair resource allocation, and enhance anti-interference capability. The combination of RIS and NOMA can achieve synergistic effects. On the one hand, RIS can improve the channel conditions of users by adjusting the coefficients of the reflecting elements, so that the users meet the requirements of NOMA for channel diversity. On the other hand, RIS can effectively reduce the interference caused by multiple users sharing the spectrum in the NOMA system by precisely controlling the signal reflection and beamforming, thereby improving the SINR of the users.

[0003] Most existing research focuses on centralized regular RIS, in which the elements are regularly arranged in a grid with constant element spacing. This configuration results in a large amount of pilot overhead, which is proportional to the product of the number of reflecting elements and the number of users, and can affect the communication quality. At the same time, centralized regular RIS has the problem of insufficient layout flexibility and coverage in non-uniform user distribution scenarios. Irregular RIS can be regarded as an application of mobile antennas. By adjusting the topology of the reflecting elements, it can achieve the effect of "virtual movement" and flexibly control the spatial domain degrees of freedom. This flexibility allows the irregular RIS to dynamically adjust the reflection path and signal coverage range without physically moving the antenna array, making it more suitable for NOMA systems based on channel condition decoding. The irregular RIS can provide additional degrees of freedom for the system, further optimizing the channel conditions and spectral efficiency. Therefore, based on the NOMA signal decoding mechanism, the application proposes a user clustering and topology optimization method for a distributed irregular RIS assisted NOMA system. The method optimizes the topology of the irregular RIS, analyzes the influence of RIS topology optimization on user clustering in the NOMA system, and realizes the effective integration of RIS assisted communication and user clustering in the NOMA system. This method can dynamically control the channel conditions to optimize interference management and resource allocation, thereby improving the spectral utilization efficiency and overall performance of the system. SUMMARY

[0004] The technical problem to be solved by the present application is to provide a user clustering and topology optimization method for a distributed irregular RIS assisted NOMA system, so as to overcome the resource allocation unfairness problem caused by the non-uniform distribution of users in the NOMA system and the limitations of the flexibility and coverage of the centralized regular RIS layout, improve the user communication effect and improve the resource utilization efficiency of the system.

[0005] The technical solution of the present application is: a user clustering and topology optimization method for a distributed irregular RIS assisted NOMA system. The specific steps are:

[0006] Step 1: Establish a network model for distributed irregular RIS assisted downlink NOMA communication, the model comprising a base station, a plurality of distributed irregular RIS and a plurality of non-uniformly distributed users;

[0007] Step 2: Establish a problem of maximizing the total spectral efficiency of the system for the model, and decouple the problem into four sub-problems, namely: user uniform clustering, irregular RIS topology search, user cluster (UC) user power allocation and irregular RIS passive beamforming;

[0008] Step 3: Apply an improved spectral clustering algorithm to realize the uniform clustering of non-uniformly distributed NOMA users in the model, and match irregular RIS assisted communication for each UC based on the fairness principle, and based on the NOMA user clustering mechanism, apply a tabu search algorithm to dynamically optimize the topology structure of the irregular RIS;

[0009] Step 4: Design an alternating optimization scheme to jointly optimize the irregular RIS topology structure, the user power allocation in the UC and the irregular RIS beamforming to maximize the total spectral efficiency of the system.

[0010] The Step 1 is specifically:

[0011] Step 1.1: Establish a network model for distributed irregular RIS assisted downlink NOMA communication, in which a block of irregular RIS is distributed on the link from the base station to the user to communicate with K single-antenna users, and blocks the LOS link from the base station to the user, and the two-dimensional rectangular coordinates k j =[x j ,y j ] T ,j∈[1,…,K] represent the known position information of user k j , a clustering algorithm is used to divide the users into L UCs, and each UC is matched with a block of irregular RIS for service, wherein L=R;

[0012] Step 1.2: and respectively represent the channel matrix from the BS to the rth block of irregular RIS and from the rth block of irregular RIS to the kth user, where r ∈ [1, …, R], k ∈ [1, …, K], and Ns represents the number of grid points on the RIS surface; the reflection coefficient matrix of the rth block of irregular RIS is represented by r φ r represents the phase shift of the rth block of irregular RIS; the topology matrix of the rth block of irregular RIS is represented by Z r = diag(z), where z = [z r,1 ,z r,2 ,…,z r,Ns ], and z r,n ∈ {1, 0}, n = 1, …, Ns, indicates whether an element on the rth block of irregular RIS is deployed on the nth grid point, z n = 1 indicates that the position is selected, and z n = 0 indicates that the position is not selected;

[0013] Step 1.3: The signal y l,k received by the kth user in the lth UC is modeled as follows:

[0014]

[0015] where the superscript H represents the conjugate transpose operation of a matrix; the subscripts l, r, and k represent the indices of the UC, the irregular RIS, and the user, respectively; represents the users excluding the kth user; Cl represents the set of all users in the lth UC, Cl / { k} represents the set of users remaining after the kth user is excluded from the lth UC; P l,k , S l,k represent the power and the signal of the kth user in the lth UC, respectively; represent the power and the signal of the users remaining after the kth user is excluded from the lth UC, respectively, n l,k ~ CN(0, σ 2 ) represents additive white Gaussian noise with a mean of zero and a variance of σ 2 at the kth user;

[0016] Step 1.4: In downlink NOMA communication, the sending end transmits multiple user signals superimposed, and the receiving end uses successive interference cancellation (SIC) technology to recover each user signal one by one. By knowing the channel state information (CSI) of each user, the power gain is sorted in descending order as the SIC decoding order, and the signal-to-interference-and-noise ratio (SINR) of the kth user in the lth UC is:

[0017]

[0018] where |Cl | represents the number of users in the lth UC; P l,i represents the power of user i in the lth UC; B represents the available bandwidth, and the spectral efficiency of user k in the lth UC is:

[0019]

[0020] The total spectral efficiency of all users in the system is:

[0021]

[0022] where R sum is the total spectral efficiency.

[0023] The Step2 is specifically:

[0024] In the scenario of non-uniform user distribution, the users are uniformly clustered, the topology of the irregular RIS is optimized, the channel difference of the users in the UC is constructed, and the total spectral rate of all users in the system is maximized by performing step-by-step power allocation and beamforming for the users in the UC, and the problem is modeled as follows:

[0025]

[0026] where, αl is the power allocation factor in the UC, P max is the maximum transmit power of the base station (BS), Θ l is the beamforming matrix of the irregular RIS; C1 and C2 are the BS transmit power constraints; C3 and C4 are the power allocation factor constraints in the UC; C5 is the RIS phase shift constraint; C6 is the quality of service (Qos) constraint of the user, γ min is the minimum signal-to-interference-and-noise ratio requirement for correctly performing SIC; C7-C9 are the topology constraints of the irregular RIS, and N is the number of sparse elements on the surface of the irregular RIS.

[0027] The Step3 is specifically:

[0028] Step3.1: Set the user distribution to follow the rule that the density gradually decreases from the center to the edge, simulate the distribution situation that the users are dense in the center area and sparse in the edge area in the actual communication environment;

[0029] Step3.2: Convert the user coordinates into polar coordinates to consider both the distance and direction between users in clustering, construct a distance similarity matrix and a direction similarity matrix based on the distance and direction between user positions and irregular RIS, obtain a final similarity matrix and a degree matrix, construct a Laplacian matrix according to the similarity matrix and the degree matrix, perform eigenvalue decomposition on the Laplacian matrix, extract eigenvalues and corresponding eigenvectors, select the eigenvectors corresponding to the L smallest eigenvalues to form a matrix U, and then divide the data into L clusters by the Balanced K-means algorithm;

[0030] Step3.3: After dividing the users into several UCs, match each user in the UC with an irregular RIS for service, search for the minimum average distance between the UC centroid and the single irregular RIS centroid as the matching basis by using a brute-force search method, and dynamically optimize the topology of the irregular RIS based on the NOMA user grouping mechanism and the tabu search algorithm.

[0031] The Step4 is specifically:

[0032] Step4.1: After solving the problems of UC and RIS matching and topology search, search for the irregular RIS topology Z l 0 Fixed, for the rth RIS serving the lth UC, at this time the UC subscript and the RIS subscript are the same, l=r, based on the fairness principle, the power allocation of each UC is calculated by the ratio of the number of users in the UC to the total number of users l , The problem P1 of power allocation and beamforming for a single UC is reconstructed as:

[0033]

[0034] where R l is the total spectral efficiency of the users in the lth UC;

[0035] Step4.2: Use fractional programming method to decouple the variables in problem P2, and perform Lagrange dual transformation on problem P2 to obtain:

[0036]

[0037] where is the power allocation vector, is the Lagrange auxiliary variable of γ k ;

[0038] Step4.3: After FP and removing the constant term, the problem f1 is reconstructed as:

[0039]

[0040] Solving the variable P by using an alternating optimization method l With Θ l Coupling problems.

[0041] The present application has the beneficial effects that: the present application uses distributed irregular RIS to assist NOMA system communication, and uses an improved spectral clustering algorithm according to the non-uniformity of user distribution to cluster NOMA users, so that more uniform user clustering effect is achieved, and the performance is better than that of the traditional spectral clustering algorithm and the k-means algorithm; in combination with the irregular RIS topology optimization scheme, resource allocation is performed by using greater spatial degrees of freedom, user-to-user interference is reduced, it is ensured that users under different channel conditions can correctly decode signals, and the fairness and stability of the NOMA system are improved; in addition, fractional programming (FP) method is used for power allocation and irregular RIS beamforming optimization of users in the cluster, further enhancing the power gain and channel gain of the system, significantly improving the overall communication performance, and realizing comprehensive improvement of spectral efficiency and system performance. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 is a system model diagram of the present application;

[0043] Figure 2 is a clustering effect diagram of the improved spectral clustering algorithm of the present application;

[0044] Figure 3 is a spectral efficiency diagram under different transmit powers of the present application;

[0045] Figure 4 is a spectral efficiency diagram under different reflection units of the present application with RIS grid points Ns=110. DETAILED DESCRIPTION

[0046] The present application will be further described below in combination with the drawings and specific embodiments.

[0047] Embodiment 1: As shown in the figure, R pieces of irregular RIS are distributed on the link from the base station to the user in the system, and K single-antenna users are communicated. N reflection elements are sparsely distributed on Ns grid points on the surface of the RIS (Ns>N). Figure 1

[0048] A user clustering and topology optimization method of a distributed irregular RIS assisted NOMA system. The specific steps are as follows:

[0049] Step 1: Establish a network model of a distributed irregular RIS assisted downlink NOMA communication, which includes a base station, multiple distributed irregular RIS, and multiple non-uniformly distributed users;

[0050] ​Step 1.1: Establish a network model for distributed irregular RIS-assisted downlink NOMA communication. In this model, R blocks of irregular RIS are distributed along the link from the base station to the user to communicate with K single-antenna users, while blocking the LOS link from the base station to the user. This is represented by two-dimensional Cartesian coordinates k. j =[x j ,y j ] T j∈[1,…,K] represents user k j Given the location information, the user is divided into L UCs using a clustering algorithm, and each UC is matched with an irregular RIS block for service, where L = R;

[0051] Step 1.2: and Let Ns represent the channel matrices from BS to the r-th irregular RIS block and from the r-th irregular RIS block to user k, respectively, where r∈[1,…,R], k∈[1,…,K], and Ns represents the number of grid points on the RIS surface; the reflection coefficient matrix of the r-th irregular RIS block is represented by Ns. It means that φ r The phase shift of the r-th irregular RIS is represented by Z; the topological matrix of the r-th irregular RIS is represented by Z. r =diag(z) means, where z = [z r,1 ,z r,2 ,...,z r,Ns ], define z r,n Let z ∈ {1,0}, n = 1,...,Ns to indicate whether an element on the r-th irregular RIS block is deployed at the n-th grid point. n =1 indicates that the position is selected, z n =0 indicates that the position was not selected;

[0052] Step 1.3: The signal y received by user k in the l-th UC l,k The model is as follows:

[0053]

[0054] Wherein, the superscript H denotes the conjugate transpose operation of the matrix; the subscripts l, r, and k represent the indices of UC, irregular RIS, and user, respectively; This represents the user group after removing user k; Cl Let represent the set of all users in the l-th UC. Cl / { k} represents the set of users remaining after removing user k from the l-th UC; P l,k S l,k Let represent the power and signal strength of user k in the l-th UC, respectively; respectively represent the power and signal of the remaining users in the lth UC after removing user k, n l,k ~CN(0,σ 2 represents an additive white Gaussian noise with mean zero and variance σ 2 at user k;

[0055] Step 1.4: In downlink NOMA communication, the sending end transmits a plurality of user signals after superposition, and the receiving end recovers each user signal one by one by using successive interference cancellation (SIC) technology. By knowing the channel state information (CSI) of each user, the power gain is in descending order as the SIC decoding order, and the signal-to-interference-and-noise ratio (SINR) of user k in the lth UC is:

[0056]

[0057] where |C l | represents the number of users in the lth UC; P l,i represents the power of user i in the lth UC; B represents the available bandwidth, and the spectral efficiency of user k in the lth UC is:

[0058]

[0059] The total spectral efficiency of all users in the system is:

[0060]

[0061] where R sum is the total spectral efficiency.

[0062] Step 2: A problem of maximizing the total spectral efficiency of the system is established for the model, and the problem is decoupled into four sub-problems, which are user uniform clustering, irregular RIS topology search, user power allocation in user cluster (UC), and irregular RIS passive beamforming;

[0063] In the scenario of non-uniform user distribution, the users are uniformly clustered, the topology of the irregular RIS is optimized, the channel difference in the UC is constructed, and the power allocation and beamforming in the UC are performed step by step to model the problem of maximizing the total spectral rate of all users in the system as follows:

[0064]

[0065] where, αl is the power allocation factor in the UC, P max is the maximum transmit power of the base station (BS), and Θ lis the beamforming matrix of irregular RIS; C1, C2 are the BS transmit power constraints; C3, C4 are the UC inner power allocation factor constraints; C5 is the RIS phase shift constraint; C6 is the quality of service (Qos) constraint of users, γ min is the minimum signal-to-interference-and-noise ratio requirement for correct SIC implementation; C7-C9 are the topology constraints of irregular RIS, N is the number of sparse elements on the surface of irregular RIS.

[0066] Step 3: Apply the improved spectral clustering algorithm to realize the uniform clustering of NOMA users with non-uniform distribution under the model, and match each UC with irregular RIS assisted communication based on the fairness principle; based on the NOMA user clustering mechanism, apply the tabu search algorithm to dynamically optimize the topology structure of irregular RIS.

[0067] Step 3.1: Set the user distribution to follow the rule that the density gradually decreases from the center to the edge, simulate the distribution situation that the user density is high in the center area and low in the edge area in the actual communication environment;

[0068] Specifically, the users are distributed within a range of 1 km in radius with (0m, 0m) as the center. Considering that the line-of-sight link between the BS and the user is blocked in practice, and the user density increases in the center area, the channel fading is faster; in the case of non-uniform user distribution, users far from the BS or in poor channel conditions receive weak signals, which easily leads to unfair resource allocation and affects the overall system performance. Based on this, multiple irregular RISs are distributed and deployed above the center users, and the deployment positions are distributed as (0.1km, 0), (-0.1km, 0), (0, 0.1km) and (0, -0.1km).

[0069] Step 3.2: Convert the user coordinates to polar coordinates to consider both the distance and direction between users in clustering, construct a distance similarity matrix and a direction similarity matrix based on the distance and direction between the user position and the irregular RIS, obtain the final similarity matrix and degree matrix, construct a Laplacian matrix according to the similarity matrix and the degree matrix, perform eigenvalue decomposition on the Laplacian matrix, extract the eigenvalues and the corresponding eigenvectors, select the eigenvectors corresponding to the first L smallest eigenvalues to form a matrix U, and then divide the data into L clusters through the Balanced K-means algorithm;

[0070] Step 3.3: After dividing the users into several UCs, match a piece of irregular RIS to serve each user in the UC, use the brute force search method to search for the minimum average distance between the UC centroid and the single irregular RIS centroid as the matching basis, and based on the NOMA user grouping mechanism, apply the tabu search algorithm to dynamically optimize the topology structure of irregular RIS.

[0071] Step4: An alternating optimization scheme is designed to jointly optimize the irregular RIS topology, the power allocation of intra-UC users, and the irregular RIS beamforming to maximize the total spectral efficiency of the system.

[0072] Step4.1: After solving the UC and RIS matching and topology search problems, the obtained irregular RIS topology Z l 0 Fixedly, for the rth block of RIS serving the lth UC, at this time the UC index and the RIS index are the same, l = r, based on the fairness principle, the power allocation of each UC is calculated by calculating the ratio of the number of intra-UC users to the total number of users l The power allocation and beamforming problem P1 of a single UC is reconstructed as:

[0073]

[0074] where R l is the total spectral efficiency of the lth intra-UC user;

[0075] Step4.2: Use the fractional programming method to decouple the variables in problem P2, and perform Lagrangian dual transformation on problem P2 to obtain:

[0076]

[0077] where is the power allocation vector, is the Lagrange auxiliary variable of k ;

[0078] Step4.3: After FP and removing the constant term, problem f1 is reconstructed as:

[0079]

[0080] The alternating optimization method is used to solve the problem of coupling variables P l and l .

[0081] Specifically, the specific steps of clustering users in Step3.2 using the improved spectral clustering algorithm are as follows:

[0082] First, convert the user coordinates to polar coordinates to consider both the distance and direction between users in clustering. Based on the distance and direction between user positions and irregular RIS, construct the distance similarity matrix W dist (i,j), the direction similarity matrix W cos (i,j), and the total similarity matrix W i,j and the degree matrix D i,j are:​

[0083]

[0084] W i,j = W dist (i,j) x W cos (i,j) (11)

[0085]

[0086] where u k is the coordinate of user k; s l is the coordinate of the l-th irregular RIS; θ i and θ j are the direction angles of users i and j with the RIS; σ dist and σ cos are Gaussian kernel functions.

[0087] Then, the Laplacian matrix L is constructed according to the similarity matrix W and the degree matrix D as follows:

[0088]

[0089] where I is the identity matrix, and W and D are the similarity matrix and the degree matrix, respectively.

[0090] Finally, the eigenvalues and eigenvectors of the Laplacian matrix L sym are extracted by eigenvalue decomposition. The eigenvectors corresponding to the L smallest eigenvalues are selected to form a matrix U, and the BalancedK-means algorithm is used to divide the data into L clusters.

[0091] Specifically, to solve the coupling problem of the variables P l and Θ l in Step 4.3, an alternating optimization method is used. The specific steps are as follows:

[0092] In equation (8), let to simplify the formula, and fix Θ l and to solve the problem of P l , which is reconstructed as:

[0093]

[0094] Further reconstruct f3 as:

[0095]

[0096] where is a quadratic auxiliary variable. Take the partial derivative of X l and set X l The optimal solution of Y is:

[0097]

[0098] At this time, the problem f4 is a convex optimization problem, which is solved by using the CVX toolbox.

[0099] Let Fix P l and Solve Θ l The problem is reconstructed as:

[0100]

[0101] The second transformation of equation (17) is:

[0102]

[0103] where, is a quadratic auxiliary variable. The partial derivative of Y l is taken, and The optimal solution of Y l is:

[0104]

[0105] At this time, f5 is a standard quadratic constraint quadratic programming (QCQP) problem, and the objective function and constraint condition of the QCQP problem are quadratic. To solve this problem, f5 is reconstructed as:

[0106]

[0107] where, is the real part, is a constant term. At this time, the problem f6 is strictly convex, which is solved by using the CVX toolbox.

[0108] In this embodiment, the number of users K is set to 29; the number of irregular RISs and the number of user clusters l = r = 4; the number of effective elements of each RIS N = 30, the grid number of sparse RIS Ns = 60, the system bandwidth B = 20 MHz, the free space loss model 125 + 36.6*log10(d), the length of the taboo table Q = 10, and the number of neighborhood solutions generated each time is 15. According to the setting of these parameters, the system is simulated by using MATLAB.

[0109] As Figure 2As shown, the improved spectral clustering algorithm (B-SPC) introduces cosine similarity and constructs a similarity matrix based on user distance and direction similarity, and then introduces balanced constraints through Balanced-Kmeans to achieve balanced resource allocation, ensuring that the number of users in each cluster is relatively uniform while the similarity between user clusters is low and the similarity within the cluster is high. The traditional SPC clustering scheme may lead to a large number of users in some clusters due to the lack of consideration of the balance of the number of users in the scenario where the distribution of users is uneven. The k-means algorithm clusters users with similar Euclidean distances, which may lead to uneven distribution of the number of users and greater interference between clusters in the scenario where the distribution of users is uneven, affecting the performance of the NOMA communication system.

[0110] As shown in Figure 3 , the irregular RIS has the best spectral efficiency under the improved spectral clustering scheme, and the improved spectral clustering scheme can obtain a relatively uniform number of users in the UC, effectively balancing the serial interference of each UC to improve system performance. At the same time, by combining the tabu search algorithm to optimize the layout of the reflecting surface, the channel difference of the users within the cluster is expanded, the discrimination of the user signal is improved, and the decoding efficiency and the overall spectral efficiency of the NOMA system are improved. In contrast, the regular RIS cannot flexibly adjust the layout of the reflecting surface, resulting in relatively small channel differences among users in the cluster after clustering, affecting the effective decoding and spectral utilization of the NOMA system. The performance of the traditional spectral clustering and k-means clustering algorithms in the irregular RIS scenario is slightly inferior to that of the improved spectral clustering algorithm. In addition, since the orthogonal multiple access scheme can only allocate one user to each resource block, the resource utilization is low, and the traditional OMA scheme is significantly lower than the NOMA scheme in terms of spectral efficiency.

[0111] As shown in Figure 4 , the irregular RIS has the highest spectral efficiency under the improved spectral clustering scheme, and significantly improves with the increase in the number of reflecting elements, which indicates that expanding the size of the reflecting array can effectively improve the system capacity. At the same time, the improved spectral clustering scheme is more effective in optimizing user clustering and resource allocation. Compared with the regular RIS, the irregular RIS optimizes the signal path through flexible layout to achieve efficient channel enhancement and signal reflection with fewer reflecting elements, thereby improving resource utilization and reducing deployment costs.

[0112] The specific embodiments of the application are described in detail above with reference to the accompanying drawings, but the application is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the purpose of the application.

Claims

1. A user clustering and topology optimization method for a distributed irregular RIS-assisted NOMA system, characterized in that: Step 1: Establish a network model for distributed irregular RIS-assisted downlink NOMA communication, which includes a base station, multiple distributed irregular RISs, and multiple non-uniformly distributed users; Step 2: Establish a problem of maximizing the total spectral efficiency of the system for the model, and decouple the problem into four sub-problems: user uniform clustering, irregular RIS topology search, UC user power allocation, and irregular RIS passive beamforming; Step 3: Apply an improved spectral clustering algorithm to achieve uniform clustering of non-uniformly distributed NOMA users in the model, and match irregular RIS-assisted communication for each UC based on the fairness principle. Based on the NOMA user clustering mechanism, apply the tabu search algorithm to dynamically optimize the topology of irregular RIS; Step 4: Design an alternating optimization scheme to jointly optimize the topology of irregular RIS, user power allocation in UC, and irregular RIS beamforming to maximize the total spectral efficiency of the system; The Step 2 is specifically: In the scenario of non-uniform user distribution, uniformly cluster users, optimize the topology of irregular RIS, construct the channel difference within UC, and perform step-by-step power allocation and beamforming for UC users to maximize the total spectral rate of all users in the system. The problem is modeled as follows: (5)； wherein, is a BS transmit power constraint, is a BS maximum transmit power, is a beamforming matrix of irregular RIS; C1, C2 are BS transmit power constraints; C3, C4 are intra-UC power allocation factor constraints; C5 is a RIS phase shift constraint; C6 is a user’s Qos constraint, is a minimum signal-to-interference-and-noise ratio requirement for correct execution of SIC; C7-C9 are topological constraints of irregular RIS, N is the number of sparse elements of the irregular RIS surface.

2. The user clustering and topology optimization method for distributed irregular RIS-assisted NOMA systems according to claim 1, characterized in that, The Step 1 is specifically: Step 1.1: Establish a network model of distributed irregular RIS-aided downlink NOMA communication, in which a block of irregular RIS is distributed on the link from the base station to the user to communicate with K single-antenna users, and the LOS link from the base station to the user is blocked, and the known position information of the user is represented by a two-dimensional rectangular coordinate , , , the users are divided into L UCs by clustering algorithm, and each UC is matched with a block of irregular RIS for service, where L=R; Step 1.2: and denote the channel matrix from the BS to the r-th irregular RIS and from the r-th irregular RIS to the user k, respectively, where , , Nsdenotes the number of grid points on the RIS surface; the reflection coefficient matrix of the r-th irregular RIS is denoted by , denotes the phase shift of the r-th irregular RIS; the topology matrix of the r-th irregular RIS is denoted by , where , and is defined as , to indicate whether the element on the r-th irregular RIS is deployed on the n-th grid point, denotes that the position is selected, denotes that the position is not selected; Step 1.3: The signal received by user k in the first UC is modeled as follows:​ (1)； wherein the superscript H denotes the conjugate transpose operation of a matrix; the subscript r, k represent the indices of the UCs, irregular RISs and users, respectively; represents the users after removing user k; represents the set of all users in the th UC, represents the set of all users in the th UC after removing user k; , represent the power and signal of user k in the th UC, respectively; , represent the power and signal of the remaining users in the th UC after removing user k, respectively, represents the additive white Gaussian noise with mean of zero and variance of at user k. Step 1.4: In the downlink NOMA communication, the transmitter superimposes and transmits multiple user signals, and the receiver uses the SIC technology to recover each user signal one by one. By knowing the CSI of each user channel, the power gain is arranged in descending order as the SIC decoding order, and the first user signal is decoded by the SIC technology. The SINR of user k in the first UC is: (2)； wherein, denotes the number of users in the th UC; denotes the power of user i in the th UC; B denotes the available bandwidth, and the spectral efficiency of user k in the th UC is: (3)； The total spectral efficiency of all users in the system is: (4)； wherein, is the total spectral efficiency.

3. The user clustering and topology optimization method for distributed irregular RIS-assisted NOMA systems according to claim 1, characterized in that, The Step 3 is specifically: Step 3.1: Set the user distribution to follow the rule of gradually decreasing density from the center to the edge, simulating the distribution of the actual communication environment where the users in the center area are dense and the users in the edge area are sparse; Step3.2: convert the user coordinates into polar coordinates, construct a distance similarity matrix and a direction similarity matrix based on the distance and direction between the user position and the irregular RIS, obtain a final similarity matrix and a degree matrix, construct a Laplacian matrix according to the similarity matrix and the degree matrix, perform eigenvalue decomposition on the Laplacian matrix, extract eigenvalues and corresponding eigenvectors, and select the eigenvectors corresponding to the L smallest eigenvalues to form a matrix and then divide the data into L clusters through a Balanced K-means algorithm. Step 3.3: After dividing the users into several UCs, match a piece of irregular RIS for each user in the UC to provide service. Use the brute-force search method to search for the minimum average distance between the UC centroid and the single irregular RIS centroid as the matching basis. Based on the NOMA user grouping mechanism, apply the tabu search algorithm to dynamically optimize the topology of irregular RIS.

4. The user clustering and topology optimization method for distributed irregular RIS-assisted NOMA systems according to claim 1, characterized in that, The Step 4 is specifically: Step4.1: After solving the UC and RIS matching and topology search problems, the irregular RIS topology searched is Fixed, for the rth block RIS service, the first UC, at this time the UC subscript and the RIS subscript are the same, l=r, based on the principle of fairness, the power of each UC is allocated by calculating the ratio of the number of users in the UC to the total number of users , The problem P1 of power allocation and beamforming for a single UC is reconstructed as: (6)； wherein, is the total spectral efficiency for the lth intra-UC user; Step 4.2: Use fractional programming method to decouple the variables in problem P2, and perform Lagrangian dual transformation on problem P2 to get: (7); wherein is a power allocation vector, is a Lagrange multiplier. Step 4.3: Perform FP and remove constant terms from problem Reconstruct to: (8); Solving the variables in an alternating optimization manner With Coupling problems.

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