User clustering and topological optimization method for distributed irregular RIS-assisted NOMA system

Abstract

The invention relates to a user clustering and topological optimization method for a distributed irregular RIS-assisted NOMA system, and belongs to the technical field of wireless communication. Aiming at a distributed RIS auxiliary NOMA communication model, firstly, an improved spectral clustering algorithm (B-SPC) is applied to realize non-uniformly distributed NOMA user clustering (UC) under the scene, and irregular RIS auxiliary communication is matched for each UC based on a fairness principle. Then, based on an NOMA user clustering mechanism, a taboo search algorithm (TS) is applied to dynamically optimize the topological structure of the irregular RIS, and then a fractional programming method (FP) is adopted to jointly optimize the topological structure of the irregular RIS, user power distribution in a UC and reflector beam forming to maximize the total spectral efficiency of the system. Compared with traditional rule RIS deployment, the B-SPC clustering algorithm improves the uniformity of UC clustering and the fairness of user service, the total spectrum efficiency of the distributed irregular RIS auxiliary NOMA system is remarkably improved, and meanwhile, the FP method can achieve better resource allocation among different users.

Description

Technical Field

[0001] The invention 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 communications. Background Art

[0002] Reconfigurable smart surface (RIS) is composed of a large number of elements with controllable phase shift. By optimizing the direction and phase of the reflected beam, it can not only significantly enhance the spectrum efficiency and energy efficiency of the communication system, but also attracts extensive attention due to its low cost, low power consumption, ability to overcome signal blocking, increase channel capacity and reduce the transmission power of future communication systems. Non-orthogonal multiple access (NOMA) has become an important technology for future wireless communication networks due to its advantages of increasing the number of user connections, improving system throughput, providing fair resource allocation and enhancing anti-interference capabilities. The combination of RIS and NOMA can achieve synergistic effects. On the one hand, RIS can improve the user's channel conditions by adjusting the coefficients of the reflection unit to meet the requirements of NOMA for user channel differences. On the other hand, RIS can effectively reduce the interference caused by multiple users sharing the spectrum in the NOMA system by precisely controlling signal reflection and beamforming, thereby improving the user's SINR.

[0003] Most existing studies focus on centralized regular RIS in which elements are regularly arranged on a grid with constant element spacing. This configuration will generate a large amount of pilot overhead, and the overhead is proportional to the product of the number of reflective elements and the number of users, which will affect the communication quality. At the same time, centralized regular RIS has the problem of insufficient layout flexibility and coverage in the scenario of non-uniform user distribution. Irregular RIS can be regarded as an application of movable antennas. By adjusting the topological structure of the reflective unit, the effect of "virtual movement" can be achieved, and the degree of freedom in the spatial domain can be flexibly controlled. It is this flexibility that allows it to dynamically adjust the reflection path and signal coverage without physically moving the antenna array. This also makes irregular RIS more suitable for NOMA systems based on channel condition decoding, which can provide additional degrees of freedom for the system and further optimize channel conditions and spectrum efficiency. Therefore, based on the NOMA signal decoding mechanism, the present invention proposes a user clustering and topology optimization method for a distributed irregular RIS-assisted NOMA system, optimizes the topological structure of the irregular RIS, analyzes the impact of RIS topology optimization on user clustering in the NOMA system, and realizes the effective integration between RIS-assisted communication and user clustering in the NOMA system. This method can dynamically control channel conditions to optimize interference management and resource allocation to improve system spectrum utilization efficiency and overall performance. Summary of the invention

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

[0005] The technical solution of the present invention 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 including a base station, multiple distributed irregular RISs, and multiple non-uniformly distributed users;

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

[0008] Step 3: Apply the improved spectral clustering algorithm to achieve uniform clustering of non-uniformly distributed NOMA users under the model, and match irregular RIS to assist communication for each UC based on the principle of fairness. Based on the NOMA user clustering mechanism, the taboo search algorithm is applied to dynamically optimize the topological structure of irregular RIS.

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

[0010] The Step 1 is specifically as follows:

[0011] Step 1.1: Establish a network model for distributed irregular RIS-assisted downlink NOMA communication. In the model, R blocks of irregular RIS are 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. The two-dimensional rectangular coordinate k j =[x j ,y j ] T ,j∈[1,…,K] represents user k j Based on the known location information, the user is divided into L UCs using a clustering algorithm, and an irregular RIS is matched to each UC for service, where L = R;

[0012] Step 1.2: and denote the channel matrices from BS to the rth irregular RIS and from the rth irregular RIS to user k, respectively, where r∈[1,…,R], k∈[1,…,K], and Ns denotes the number of grid points on the RIS surface; the reflection coefficient matrix of the rth irregular RIS is Indicates that φ r represents the phase shift of the rth irregular RIS; the topological matrix of the rth irregular RIS is Z r =diag(z), where z = [z r,1 ,z r,2 ,…,z r,Ns ], define z r,n ∈{1,0}, n=1,...,Ns to indicate whether the element on the rth irregular RIS is deployed on the nth grid point, z n =1 means the position is selected, z n =0 means the position is not selected;

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

[0014]

[0015] Wherein, the superscript H represents the conjugate transpose operation of the matrix; the subscripts l, r, and k represent the indexes of UC, irregular RIS, and user, respectively; represents the users after removing user k; Cl represents the set of all users in the lth UC, Cl / { k} represents the set of users remaining after removing user k from the lth UC; P l,k , S l,k denote the power and signal of user k in the lth UC respectively; They represent the power and signal of the remaining users after removing user k from the lth UC, n l,k ~CN(0,σ 2 ) means that the mean at user k is zero and the variance is σ 2 Additive Gaussian white noise;

[0016] Step 1.4: In downlink NOMA communication, the transmitter superimposes multiple user signals and transmits them. The receiver uses the successive interference cancellation (SIC) technology to restore each user signal one by one. By knowing the channel state information (CSI) of each user, the power gain is descending as the SIC decoding order. The signal-to-interference-plus-noise ratio (SINR) of user k in the lth UC is:

[0017]

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

[0019]

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

[0021]

[0022] Among them, R sum is the overall spectral efficiency.

[0023] The Step 2 is specifically as follows:

[0024] In the scenario of uneven user distribution, users are evenly clustered, the topology of irregular RIS is optimized, the channel differences of users in UC are constructed, and step-by-step power allocation and beamforming are performed for users in UC to maximize the total spectrum rate of all users in the system. The problem is modeled as follows:

[0025]

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

[0027] The Step 3 is specifically as follows:

[0028] Step 3.1: Set the user distribution to follow the rule of gradually decreasing density from the center to the edge, simulating the actual communication environment, where the center area has dense users and the edge area has sparse users;

[0029] Step 3.2: Convert user coordinates into polar coordinates so that the distance and direction between users can be considered simultaneously in clustering. Construct distance similarity matrix and direction similarity matrix based on the distance and direction between user location and irregular RIS to obtain the final similarity matrix and degree matrix. Construct Laplace matrix based on similarity matrix and degree matrix, perform eigenvalue decomposition on Laplace matrix, extract eigenvalues ​​and corresponding eigenvectors, select eigenvectors corresponding to the first L smallest eigenvalues ​​to form matrix U, and then divide the data into L clusters using Balanced K-means algorithm;

[0030] Step 3.3: After dividing the users into several UCs, an irregular RIS is matched for each user in each UC for service. The brute force search method is used to search for the minimum average distance between the centroid of the UC and the centroid of a single irregular RIS as the basis for matching. Based on the NOMA user grouping mechanism, the taboo search algorithm is applied to dynamically optimize the topological structure of the irregular RIS.

[0031] The Step 4 is specifically as follows:

[0032] Step 4.1: After solving the UC and RIS matching and topology search problems, the irregular RIS topology Z l 0 Fixed, for the rth RIS serving the lth UC, the UC subscript and RIS subscript are the same, l = r, based on the principle of fairness, by calculating the ratio of the number of users in the UC to the total number of users α l , to allocate power to each UC, The problem P1 of power allocation and beamforming for a single UC can be reconstructed as:

[0033]

[0034] Among them, R l is the total spectrum efficiency of users in the lth UC;

[0035] Step 4.2: Use the fractional programming method to decouple the variables in problem P2, and perform Lagrangian dual transformation on problem P2 to obtain:

[0036]

[0037] in, is the power allocation vector, For γ k Lagrange auxiliary variables of ;

[0038] Step 4.3: After performing FP and removing the constant term, problem f1 is reconstructed as:

[0039]

[0040] Use alternating optimization to solve the variable P l With Θ l Coupling problem.

[0041] The beneficial effects of the present invention are as follows: the present invention uses distributed irregular RIS to assist NOMA system communication, and adopts an improved spectral clustering algorithm to cluster NOMA users according to the non-uniformity of user distribution, thereby achieving a more uniform user clustering effect, and having better performance than the traditional spectral clustering algorithm and the k-means algorithm; combined with the irregular RIS topology optimization scheme, it utilizes a larger spatial degree of freedom for resource allocation, reduces interference between users, and ensures that users under different channel conditions can correctly decode signals, thereby improving the fairness and stability of the NOMA system; in addition, the fractional programming (FP) method is used to perform power allocation and irregular RIS beamforming optimization for users within the cluster, thereby further enhancing the power gain and channel gain of the system, significantly improving the overall communication performance, and achieving a comprehensive improvement in spectrum efficiency and system performance. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0044] Figure 3 is a spectrum efficiency diagram of the present invention at different transmission powers;

[0045] Figure 4 It is a spectrum efficiency diagram of the RIS grid point Ns=110 under different reflection units of the present invention. DETAILED DESCRIPTION

[0046] The present invention will be further described below in conjunction with the accompanying drawings and specific implementation methods.

[0047] Example 1: Figure 1 As shown, in this system, R irregular RIS blocks are distributed on the link from the base station to the user to communicate with K single-antenna users. N reflective elements are sparsely distributed on Ns grid points on the RIS surface (Ns>N).

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

[0049] Step 1: Establish a network model for distributed irregular RIS-assisted downlink NOMA communication, the model including a base station, multiple distributed irregular RISs, and multiple non-uniformly distributed users;

[0050] Step 1.1: Establish a network model for distributed irregular RIS-assisted downlink NOMA communication. In the model, R blocks of irregular RIS are 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. The two-dimensional rectangular coordinate k j =[x j ,y j ] T ,j∈[1,…,K] represents user k j Based on the known location information, the user is divided into L UCs using a clustering algorithm, and an irregular RIS is matched to each UC for service, where L = R;

[0051] Step 1.2: and denote the channel matrices from BS to the rth irregular RIS and from the rth irregular RIS to user k, respectively, where r∈[1,…,R], k∈[1,…,K], and Ns denotes the number of grid points on the RIS surface; the reflection coefficient matrix of the rth irregular RIS is Indicates that φ r represents the phase shift of the rth irregular RIS; the topological matrix of the rth irregular RIS is Z r =diag(z), where z = [z r,1 ,z r,2 ,...,z r,Ns ], define z r,n ∈{1,0}, n=1,...,Ns to indicate whether the element on the rth irregular RIS is deployed on the nth grid point, z n =1 means the position is selected, z n =0 means the position is not selected;

[0052] Step 1.3: Signal y received by user k in the lth UC l,k The modeling is as follows:

[0053]

[0054] Wherein, the superscript H represents the conjugate transpose operation of the matrix; the subscripts l, r, and k represent the indexes of UC, irregular RIS, and user, respectively; represents the users after removing user k; Cl represents the set of all users in the lth UC, Cl / { k} represents the set of users remaining after removing user k from the lth UC; P l,k , S l,k denote the power and signal of user k in the lth UC respectively; They represent the power and signal of the remaining users after removing user k from the lth UC, n l,k ~CN(0,σ 2 ) means that the mean at user k is zero and the variance is σ 2 Additive Gaussian white noise;

[0055] Step 1.4: In downlink NOMA communication, the transmitter superimposes multiple user signals and transmits them. The receiver uses the successive interference cancellation (SIC) technology to restore each user signal one by one. By knowing the channel state information (CSI) of each user, the power gain is descending as the SIC decoding order. The signal-to-interference-plus-noise ratio (SINR) of user k in the lth UC is:

[0056]

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

[0058]

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

[0060]

[0061] Among them, R sum is the overall spectral efficiency.

[0062] Step 2: Establish the problem of maximizing the total spectrum efficiency of the system for the model, and decouple the problem into four sub-problems, namely: user uniform clustering, irregular RIS topology search, user power allocation within user cluster (UC), and irregular RIS passive beamforming;

[0063] In the scenario of uneven user distribution, users are evenly clustered, the topology of irregular RIS is optimized, the channel differences of users in UC are constructed, and step-by-step power allocation and beamforming are performed for users in UC to maximize the total spectrum rate of all users in the system. The problem is modeled as follows:

[0064]

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

[0066] Step 3: Apply the improved spectral clustering algorithm to achieve uniform clustering of non-uniformly distributed NOMA users under the model, and match irregular RIS to assist communication for each UC based on the principle of fairness. Based on the NOMA user clustering mechanism, the taboo search algorithm is applied to dynamically optimize the topological structure of irregular RIS.

[0067] Step 3.1: Set the user distribution to follow the rule of gradually decreasing density from the center to the edge, simulating the actual communication environment, where the center area has dense users and the edge area has sparse users;

[0068] Specifically, users are distributed within a range of 1km with (0m, 0m) as the center. Considering that in practice, the line-of-sight link between the BS and the user is blocked, and the user density in the central area increases, the channel fades faster; in the case of uneven user distribution, users far from the BS or in poor channel conditions receive weak signals, which can easily lead to unfair resource allocation and affect the overall system performance. Based on this, multiple irregular RIS distributions are deployed above the central user, and their deployment locations are distributed as (0.1km, 0), (-0.1km, 0), (0, 0.1km) and (0, -0.1km).

[0069] Step 3.2: Convert user coordinates into polar coordinates so that the distance and direction between users can be considered simultaneously in clustering. Construct distance similarity matrix and direction similarity matrix based on the distance and direction between user location and irregular RIS to obtain the final similarity matrix and degree matrix. Construct Laplace matrix based on similarity matrix and degree matrix, perform eigenvalue decomposition on Laplace matrix, extract eigenvalues ​​and corresponding eigenvectors, select eigenvectors corresponding to the first L smallest eigenvalues ​​to form matrix U, and then divide the data into L clusters using Balanced K-means algorithm;

[0070] Step 3.3: After dividing the users into several UCs, an irregular RIS is matched for each user in each UC for service. The brute force search method is used to search for the minimum average distance between the centroid of the UC and the centroid of a single irregular RIS as the basis for matching. Based on the NOMA user grouping mechanism, the taboo search algorithm is applied to dynamically optimize the topological structure of the irregular RIS.

[0071] Step 4: Design an alternating optimization scheme to jointly optimize the irregular RIS topology, user power allocation within the UC, and irregular RIS beamforming to maximize the overall spectral efficiency of the system.

[0072] Step 4.1: After solving the UC and RIS matching and topology search problems, the irregular RIS topology Z l 0 Fixed, for the rth RIS serving the lth UC, the UC subscript and RIS subscript are the same, l = r, based on the principle of fairness, by calculating the ratio of the number of users in the UC to the total number of users α l , to allocate power to each UC, The problem P1 of power allocation and beamforming for a single UC can be reconstructed as:

[0073]

[0074] Among them, R l is the total spectrum efficiency of users in the lth UC;

[0075] Step 4.2: Use the fractional programming method to decouple the variables in problem P2, and perform Lagrangian dual transformation on problem P2 to obtain:

[0076]

[0077] in, is the power allocation vector, For γ k Lagrange auxiliary variables of ;

[0078] Step 4.3: After performing FP and removing the constant term, problem f1 is reconstructed as:

[0079]

[0080] Use alternating optimization to solve the variable P l With Θ l Coupling problem.

[0081] Specifically, the specific steps for clustering users using the improved spectral clustering algorithm in Step 3.2 are as follows:

[0082] First, the user coordinates are converted to polar coordinates so that the distance and direction between users can be considered simultaneously in clustering. The distance similarity matrix W is constructed based on the distance and direction between the user location and the irregular RIS. dist (i,j), direction similarity matrix W cos (i,j) get the total similarity matrix W i,j Sum degree matrix D i,j for:

[0083]

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

[0085]

[0086] Among them, u k is the coordinate of user k; s l is the coordinate of the lth irregular RIS; θ i and θ j is the direction angle between users i and j and RIS; σ dist and σ cos is the Gaussian kernel function;

[0087] Then, the Laplacian matrix is ​​constructed according to the similarity matrix and the degree matrix:

[0088]

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

[0090] Finally, the Laplace matrix L sym Perform eigenvalue decomposition to extract eigenvalues ​​and corresponding eigenvectors. Select the eigenvectors corresponding to the first L smallest eigenvalues ​​to form the matrix U, and then divide the data into L clusters using the Balanced K-means algorithm.

[0091] Specifically, for the variable P in Step 4.3 l With Θ l The coupling problem is solved by alternating optimization. The specific steps are as follows:

[0092] In formula (8), To simplify the formula, fix Θ l and Solving for P l The problem is refactored as:

[0093]

[0094] Perform a secondary transformation on equation (14) to further reconstruct f3 as follows:

[0095]

[0096] in, is a secondary auxiliary variable. l Find the partial derivative, let Get X l The optimal solution is:

[0097]

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

[0099] In formula (8), Fixed P l and Solving for Θ l The problem is refactored as:

[0100]

[0101] Performing a secondary transformation on equation (17) yields:

[0102]

[0103] in, is a secondary auxiliary variable. l Find the partial derivative, let Get Y l The optimal solution is:

[0104]

[0105] At this point, f5 is a standard quadratic constrained quadratic programming (QCQP) problem. The objective function and constraints of the QCQP problem are both quadratic. To solve this problem, f5 is reconstructed as:

[0106]

[0107] in, To obtain the real part, is a constant term. At this time, problem f6 is strictly convex and can be solved using the CVX toolbox.

[0108] In this implementation case, the number of users K=29; the number of irregular RIS and the number of user clusters l=r=4; the number of effective elements of each RIS N=30, the number of grids of sparse RIS Ns=60, the system bandwidth B=20MHz, 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 settings of these parameters, the system is simulated using MATLAB.

[0109] like Figure 2As shown in the figure, the improved spectral clustering algorithm (B-SPC) introduces cosine similarity and constructs a similarity matrix based on user distance and direction similarity. Then, the balanced constraint is introduced through Balanced-Kmeans to achieve balanced resource allocation, ensuring that the number of users in each cluster is relatively uniform while making the similarity between user clusters low and the similarity within clusters high. However, in the scenario of uneven user distribution, the traditional SPC clustering scheme may cause some clusters to contain a large number of users because it does not consider the balance of the number of users. The k-means algorithm clusters users with similar Euclidean distances, which will lead to uneven distribution of the number of users in the scenario of uneven user distribution, and the interference between clusters is large, affecting the performance of the NOMA communication system.

[0110] like Figure 3 As shown in the figure, the spectrum efficiency of irregular RIS under the improved spectrum clustering scheme is the best. The improved spectrum clustering scheme can obtain a relatively uniform number of users in the UC and effectively balance the serial interference of each UC to improve the system performance. At the same time, by optimizing the reflector layout in combination with the taboo search algorithm, the channel difference of users in the cluster is enlarged, the discrimination of user signals is improved, and the decoding efficiency and the overall spectrum efficiency of the NOMA system are improved. In contrast, the regular RIS cannot flexibly adjust the reflector layout, resulting in relatively small channel differences among users in the cluster after clustering, which affects the effective decoding and spectrum utilization of the NOMA system. The performance of 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 each resource block in the orthogonal multiple access scheme can only be allocated to one user, the resource utilization is low, and the traditional OMA scheme is significantly lower than the NOMA scheme in terms of spectrum efficiency.

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

[0112] The specific implementation modes of the present invention are described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above implementation modes, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. A user clustering and topology optimization method for a distributed irregular RIS-assisted NOMA system, characterized by: Step 1: Establish a network model for distributed irregular RIS-assisted downlink NOMA communication, the model including a base station, multiple distributed irregular RISs, and multiple non-uniformly distributed users; Step 2: Establish the problem of maximizing the total spectrum efficiency of the system for the model, and decouple the problem into four sub-problems, namely: user uniform clustering, irregular RIS topology search, user power allocation within UC, and irregular RIS passive beamforming; Step 3: Apply the improved spectral clustering algorithm to achieve uniform clustering of non-uniformly distributed NOMA users under the model, and match irregular RIS to assist communication for each UC based on the principle of fairness. Based on the NOMA user clustering mechanism, the taboo search algorithm is applied to dynamically optimize the topological structure of irregular RIS. Step 4: Design an alternating optimization scheme to jointly optimize the irregular RIS topology, user power allocation within the UC, and irregular RIS beamforming to maximize the overall spectral efficiency of the system.

2. The user clustering and topology optimization method of the distributed irregular RIS-assisted NOMA system according to claim 1 is characterized in that: The Step 1 is specifically as follows: Step 1.1: Establish a network model for distributed irregular RIS-assisted downlink NOMA communication. In the model, R blocks of irregular RIS are 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. The two-dimensional rectangular coordinate k j =[x j ,y j ] T ,j∈[1,…,K] represents user k j Based on the known location information, the user is divided into L UCs using a clustering algorithm, and an irregular RIS is matched to each UC for service, where L = R; Step 1.2: and denote the channel matrices from BS to the rth irregular RIS and from the rth irregular RIS to user k, respectively, where r∈[1,…,R], k∈[1,…,K], and Ns denotes the number of grid points on the RIS surface; the reflection coefficient matrix of the rth irregular RIS is Indicates that φ r represents the phase shift of the rth irregular RIS; the topological matrix of the rth irregular RIS is Z r =diag(z), where z = [z r,1 ,z r,2 ,…,z r,Ns ], define z r,n ∈{1,0}, n=1,...,Ns to indicate whether the element on the rth irregular RIS is deployed on the nth grid point, z n =1 means the position is selected, z n =0 means the position is not selected; Step 1.3: Signal y received by user k in the lth UC l,k The modeling is as follows: Wherein, the superscript H represents the conjugate transpose operation of the matrix; the subscripts l, r, and k represent the indexes of UC, irregular RIS, and user, respectively; represents the users after removing user k; Cl represents the set of all users in the lth UC, Cl / { k } represents the set of users remaining after removing user k from the lth UC; P l,k , S l,k denote the power and signal of user k in the lth UC respectively; They represent the power and signal of the remaining users after removing user k from the lth UC, n l,k ~CN(0,σ 2 ) means that the mean at user k is zero and the variance is σ 2 Additive Gaussian white noise; Step 1.4: In downlink NOMA communication, the transmitter superimposes multiple user signals and transmits them. The receiver uses SIC technology to restore each user signal one by one. By knowing the CSI of each user channel, the SIC decoding order is based on the descending order of power gain. The SINR of user k in the lth UC is: Among them, |C l | represents the number of users of the lth UC; P l,i represents the power of user i in the lth UC; B represents the available bandwidth, and the spectrum efficiency of user k in the lth UC is: The total spectrum efficiency of all users in the system is: Among them, R sum is the overall spectral efficiency.

3. The user clustering and topology optimization method of the distributed irregular RIS-assisted NOMA system according to claim 1 is characterized in that: The Step 2 is specifically as follows: In the scenario of uneven user distribution, users are evenly clustered, the topology of irregular RIS is optimized, the channel differences of users in UC are constructed, and step-by-step power allocation and beamforming are performed for users in UC to maximize the total spectrum rate of all users in the system. The problem is modeled as follows: in, αl is the power allocation factor within UC, P max is the maximum transmission power of BS, Θ l is the beamforming matrix of irregular RIS; C1 and C2 are BS transmit power constraints; C3 and C4 are power allocation factor constraints within UC; C5 is RIS phase shift constraint; C6 is user QoS constraint, γ min The minimum signal-to-interference-noise ratio requirement for the correct execution of SIC; C7-C9 are the topological constraints of the irregular RIS, and N is the number of sparse elements on the irregular RIS surface.

4. The user clustering and topology optimization method of the distributed irregular RIS-assisted NOMA system according to claim 1 is characterized in that: The Step 3 is specifically as follows: Step 3.1: Set the user distribution to follow the rule of gradually decreasing density from the center to the edge, simulating the actual communication environment, where the center area has dense users and the edge area has sparse users; Step 3.2: Convert the user coordinates into polar coordinates, construct the distance similarity matrix and direction similarity matrix based on the distance and direction between the user location and the irregular RIS, and obtain the final similarity matrix and degree matrix. Construct the Laplace matrix based on the similarity matrix and degree matrix, perform eigenvalue decomposition on the Laplace matrix, extract the eigenvalues ​​and corresponding eigenvectors, select the eigenvectors corresponding to the first L smallest eigenvalues ​​to form the matrix U, and then divide the data into L clusters using the Balanced K-means algorithm; Step 3.3: After dividing the users into several UCs, an irregular RIS is matched for each user in each UC for service. The brute force search method is used to search for the minimum average distance between the centroid of the UC and the centroid of a single irregular RIS as the basis for matching. Based on the NOMA user grouping mechanism, the taboo search algorithm is applied to dynamically optimize the topological structure of the irregular RIS.

5. The user clustering and topology optimization method of the distributed irregular RIS-assisted NOMA system according to claim 1 is characterized in that: The Step 4 is specifically as follows: Step 4.1: After solving the UC and RIS matching and topology search problems, the irregular RIS topology obtained by the search is Fixed, for the rth RIS serving the lth UC, the UC subscript and RIS subscript are the same, l = r, based on the principle of fairness, by calculating the ratio of the number of users in the UC to the total number of users α l , to allocate power to each UC, The problem P1 of power allocation and beamforming for a single UC can be reconstructed as: Among them, R l is the total spectrum efficiency of users in the lth UC; Step 4.2: Use the fractional programming method to decouple the variables in problem P2, and perform Lagrangian dual transformation on problem P2 to obtain: in, is the power allocation vector, For γ k Lagrange auxiliary variables of ; Step 4.3: After performing FP and removing the constant term, problem f1 is reconstructed as: Use alternating optimization to solve the variable P l With Θ l Coupling problem.

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