Optimization Method for Multi-RIS-Assisted Downlink MIMO-NOMA System Based on Sum Rate Maximization

Abstract

The present invention relates to an optimization method for a multi-RIS-assisted downlink MIMO-NOMA system based on sum rate maximization, belonging to the field of wireless communication technologies. The method includes: S1: constructing a multi-RIS-assisted downlink MIMO-NOMA system; S2: constructing an objective function and constraint conditions: by jointly optimizing the transmit beamforming matrix V of the base station, the RIS phase shift matrix Φ, and the intra-cluster power allocation p, the joint solution of the three is expressed as a constrained optimization problem P1, and under the constraints of RIS phase shift, user rate, and transmit power, the sum rate of the MIMO-NOMA system is maximized; S3: solving the optimization problem P1 by an alternating optimization method. The present invention can solve the problem that in the traditional signal model, the number of users served by a single RIS is too large, so that all user channels cannot be effectively configured.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication, and relates to an optimization method for a multi-RIS-assisted downlink MIMO-NOMA system based on sum rate maximization. Background Art

[0002] Multi-RIS-assisted MIMO-NOMA is an emerging technology that combines two powerful communication technologies, namely multiple-input multiple-output (MIMO) and non-orthogonal multiple access (NOMA). In recent years, due to its potential to improve the capacity and spectral efficiency of wireless communication systems, it has attracted great attention. MIMO is a technology that uses multiple antennas at both the transmitter and receiver to improve the quality and reliability of wireless communication. MIMO technology utilizes the spatial diversity of the wireless channel by transmitting multiple data streams over multiple antennas. Due to its ability to improve the capacity and reliability of wireless communication systems, this technology has become increasingly popular in recent years. Compared with traditional single-input single-output (SISO) systems, MIMO technology has several advantages. First, MIMO systems provide spatial multiplexing, which means that multiple data streams can be transmitted simultaneously over the same frequency band. This improves the data rate and spectral efficiency of wireless communication systems. Second, MIMO systems provide diversity, which helps to mitigate the effects of fading and interference in the wireless channel. Finally, MIMO systems provide beamforming, allowing focused beams to be transmitted to specific users, increasing signal strength and reducing interference. Non-orthogonal multiple access (NOMA) is a technology that uses superposition coding and successive interference cancellation (SIC) techniques to allow multiple users to share the same frequency band. In traditional orthogonal multiple access (OMA) systems, each user is assigned a separate frequency band, which may result in underutilization of the available spectrum. NOMA technology solves this problem by allowing multiple users to share the same frequency band, improving the spectral efficiency of wireless communication systems.

[0003] A reconfigurable intelligent surface (RIS) is a thin planar structure composed of a large number of reflecting elements. The RIS can be used to enhance the performance of wireless communication systems by reflecting, refracting, or diffracting wireless signals in a specific direction, and then optimizing the wireless channel by adjusting the phase and amplitude of the reflected signals in real time. The reflection coefficient of each element in the RIS can be controlled by adjustment to control the direction and amplitude of the reflected signal. By optimizing the reflection coefficient of the RIS, the signal strength and quality of wireless communication systems can be improved. The RIS-assisted MIMO-NOMA system can significantly improve performance and provide a potential technical solution for next-generation wireless communication systems.

[0004] Although many achievements have been made in the current research on RIS-assisted NOMA, most of the traditional signal models consider a single RIS to complete the channel configuration for all users, and the effect may not be ideal when the number of users is too large. Even if some articles consider the research on multiple RISs, there are only two users for the in-cluster power allocation. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide an optimization method for a multi-RIS-assisted downlink MIMO-NOMA system based on sum-rate maximization, which solves the problem that a single RIS in the traditional signal model serves too many users and thus cannot effectively configure the channels of all users. The present invention constructs a more general signal model and simultaneously considers using multiple RISs to assist in completing the channel configuration of all users, thereby solving the problems of RIS phase shift joint in-cluster power allocation and beamforming to maximize the system sum-rate.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] An optimization method for a multi-RIS-assisted downlink MIMO-NOMA system based on sum-rate maximization specifically includes the following steps:

[0008] S1: Construct a multi-RIS-assisted downlink MIMO-NOMA system;

[0009] To improve the transmission performance, KF users are divided into F clusters according to a certain user clustering rule, and a RIS is deployed at an appropriate position in the cluster.

[0010] S2: Construct an objective function and constraint conditions: By jointly optimizing the transmit beamforming matrix V of the base station, the RIS phase shift matrix Φ, and the in-cluster power allocation p, the solution of the three jointly is expressed as a constrained optimization problem P1, and under the constraints of RIS phase shift, user rate, and transmit power, the sum-rate of the MIMO-NOMA system is maximized;

[0011] S3: Solve the optimization problem P1 by an alternating optimization method.

[0012] Further, in step S1, a multi-RIS-assisted downlink MIMO-NOMA system is constructed, specifically including: assuming that there are KF users equipped with L antennas, F RISs, and a BS equipped with M transmit antennas in the system; to improve the spectral efficiency, the KF served users are divided into F clusters, with K users in each cluster; each RIS is equipped with N≥1 reflecting elements to assist users in receiving signals from the BS; the phase shift of the RIS can be programmed and configured by the RIS controller, so each user receives the superimposed signal from the BS-user (direct) link and the RIS-user (reflected) link; each cluster is far from other clusters, so the interference caused by the RIS serving other clusters can be reasonably ignored; let the effective phase shift and amplitude coefficient matrix of the RIS be β f,n ∈(0,1] represents the amplitude coefficient of RIS element n, j represents the imaginary unit, θ n ∈(0,2π] represents the phase shift of RIS element n; in practical applications, it is usually necessary to maximize the signal reflected by the RIS, so β f,n is taken as 1;

[0013] Assuming that each node has perfect CSI, the signal of user k in cluster f can be expressed as:

[0014]

[0015] where s f,k is the useful information signal to be transmitted to user k in cluster f, where (·) H and represent conjugate transpose and the expectation of a random variable respectively; represents the power allocated by the BS to user k corresponding to cluster f, is the f-th column of the precoding matrix V, G f,k is the Rayleigh channel matrix between the RIS and user k in cluster f, and Φ f is the effective phase shift and amplitude coefficient matrix of the RIS in cluster f, H f is the Rice channel matrix of the link from the BS to the RIS in the f-th cluster, and W f,k is the Rayleigh channel matrix between the BS and user k in cluster f, and is the additive white Gaussian noise with a mean of 0 and a variance of σ 2 at the k-th user in cluster f;

[0016] In the downlink MIMO-NOMA communication network, the user with the strongest signal strength decodes first and eliminates the interference of the user with weak signal strength through the serial interference cancellation technology; for the sake of simplified analysis, it is assumed that the order of the user channel gains is:

[0017] |(G f,1 Φ f H f +W f,1 )v f | 2 ≥…≥|(G f,k Φ f H f +W f,k )v f | 2 ≥…≥|(G f,K Φ f H f +W f,K )v f | 2 (2)

[0018] According to the principle that the user with a smaller channel gain should be allocated more power, the power allocated to each user within the beam should satisfy:

[0019] p f,1 ≤…≤p f,k ≤…≤p f,K , (3)

[0020] According to the demodulation rules of the downlink MIMO-NOMA system, before demodulating its own signal, user k in cluster f needs to first demodulate all users in the same cluster with weaker channel gains than its own, that is, user k in cluster f needs to sequentially decode the data stream of user t in the same cluster, where t = k + 1, …, K. The signal-to-interference-plus-noise ratio (SINR) of user k in cluster f for decoding the t-th user in the same cluster is expressed as:

[0021]

[0022] where 1 ≤ k < t ≤ K;

[0023] After eliminating the interference signals of all users with weaker channels in the same cluster, when user k in cluster f decodes its own signal and regards the signals of other users as interference, the signal-to-interference-plus-noise ratio (SINR) of user k in cluster f for decoding its own signal is:

[0024]

[0025] In the downlink MIMO-NOMA system, the signal-to-interference-plus-noise ratio (SINR) of user k in cluster f for decoding the t-th user should be greater than or equal to the SINR threshold of the t-th user, so as to correctly demodulate the signal of user t and facilitate the implementation of the serial interference cancellation technology.

[0026] Therefore, it is necessary to ensure that

[0027] According to the SINR expression in Equation (5), the information transmission rate R of user k in cluster f is obtained f,k as:

[0028]

[0029] Furthermore, in step S2, under the constraints of user rate and transmit power, the sum rate is maximized by jointly designing the phase shift matrix of the RIS, the transmit beamforming at the BS, and the power allocation. That is, the optimization problem P1 is formulated as:

[0030]

[0031]

[0032]

[0033]

[0034] 0 ≤ θ f,n ≤ 2π, f = 1,..., F; n = 1,..., N (7e)

[0035] where is the minimum transmission rate that the k-th user in the f-th cluster satisfies the QoS condition, P0 is the maximum transmit power, is the maximum transmit power of the beam; (7b) is the constraint of the minimum rate that the user can accept, which is used to ensure the fairness of the user; (7c) is the total transmit power constraint of the BS; (7d) is the total transmit power constraint within the BS beam; (7e) is the phase shift constraint of the RIS.

[0036] Furthermore, in step S3, to solve the optimization problem P1, it specifically includes: first, the optimization problem P1 is equivalent to optimizing the signal-to-interference-plus-noise ratio;

[0037]

[0038]

[0039]

[0040]

[0041] 0 ≤ θ f,n ≤ 2π, f = 1,..., F; n = 1,..., N (8e)

[0042] Then, the optimization problem P2 is decomposed into three sub-problems according to the priority, and then the alternating optimization is used to solve it. Specifically, first fix the power allocation and beamforming, and then determine the RIS phase shift matrix; on this basis, according to the phase shift matrix, then design the beamforming to eliminate the inter-cluster interference; furthermore, weaken the inter-cluster interference through the optimal power allocation within the cluster; the above three stages with a sequential order are iterated alternately until the threshold requirement is met.

[0043] The beneficial effect of the present invention is that: in view of the problem that most of the traditional signal models consider a single RIS to complete the channel configuration of all users, and the effect may not be ideal when the number of users is too large, the present invention uses multiple RISs to assist in completing the channel configuration of all users.

[0044] Other advantages, objectives and features of the present invention will be described to some extent in the subsequent specification, and to some extent, will be obvious to those skilled in the art based on the study of the following text, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following specification. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be described in detail preferably with reference to the accompanying drawings, where:

[0046] Figure 1 It is a schematic diagram of the signal model of the multi-RIS assisted downlink MIMO-NOMA system in the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0047] The following specific examples illustrate the embodiments of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the drawings provided in the following embodiments only illustrate the basic concept of the present invention schematically, and the following embodiments and the features in the embodiments can be combined with each other without conflict.

[0048] Please refer to Figure 1 , the present invention considers the MIMO-NOMA system in the multi-RIS assisted downlink communication, such as Figure 1As shown in the figure. There are KF users equipped with L antennas, F RISs, and a BS equipped with M transmit antennas in the system. To improve the spectral efficiency, the KF served users are divided into F clusters, with K users in each cluster. Each RIS is equipped with N reflecting elements (N≥1) to assist users in receiving signals from the BS. The phase shift of the RIS can be programmed and configured by the RIS controller, so each user receives the superimposed signals from the BS-user (direct) link and the RIS-user (reflected) link. Each cluster is far from other clusters, so the interference caused by the RIS serving other clusters can be reasonably ignored. Let the effective phase shift and amplitude coefficient of the RIS be β f,n ∈(0,1] denote the amplitude coefficient of RIS element n, j denote the imaginary unit, and θ n ∈(0,2π] denote the phase shift of RIS element n. In practical applications, it is usually necessary to maximize the signal reflected by the RIS, so β f,n is taken as 1.

[0049] This invention mainly studies beamforming, power allocation, and phase shift design, and assumes that each node has perfect CSI. Therefore, the signal of user k in cluster f can be expressed as:

[0050]

[0051] where s f,k is the useful information signal to be transmitted to user k in cluster f, where (·) H and denote conjugate transpose and the expectation of a random variable, respectively. is the power allocated by its corresponding BS. is the f-th column of the precoding matrix V, G f,k is the Rayleigh channel matrix between the RIS and user k in cluster f, and Φ f is the effective phase shift and amplitude coefficient matrix of the RIS in cluster f, H f is the Rice channel matrix of the link from the BS to the RIS in the f-th cluster, and W f,k is the Rayleigh channel matrix between the BS and user k in cluster f, and is the additive white Gaussian noise with mean 0 and variance σ 2 at the k-th user in cluster f.

[0052] In the downlink MIMO-NOMA communication network, the user with the strongest signal strength decodes first and eliminates the interference of the user with weak signal strength through the successive interference cancellation technique. To simplify the analysis, assume that the order of the user channel gains is:

[0053] |(G f,1 Φ f H f +W f,1 )v f | 2 ≥...≥|(G f,k Φ f H f +W f,k )v f | 2 ≥…≥|(G f,K Φ f H f +W f,K )v f | 2 (2)

[0054] According to the principle that users with smaller channel gains should be allocated more power, the power allocated to each user within the beam should satisfy:

[0055] p f,1 ≤…≤p f,k ≤…≤p f,K , (3)

[0056] According to the demodulation rules of the downlink MIMO-NOMA system, before demodulating its own signal, user k in cluster f needs to first demodulate all users in the same cluster with weaker channel gains than its own, that is, user k in cluster f needs to sequentially decode the data stream of user t in the same cluster, t = k + 1,…,K. The signal-to-interference-plus-noise ratio (SINR) for user k in cluster f to decode the data stream of the t-th user in the same cluster is expressed as:

[0057]

[0058] where 1 ≤ k < t ≤ K.

[0059] After eliminating the interference signals of all users with weaker channels in the same cluster, when user k in cluster f demodulates its own signal, it regards the signals of other users as interference. Then the signal-to-interference-plus-noise ratio (SINR) for user k in cluster f to decode its own signal is:

[0060]

[0061] In the downlink MIMO-NOMA system, the signal-to-interference-plus-noise ratio (SINR) for user k in cluster f to decode the t-th user should be greater than or equal to the SINR threshold of the t-th user, so as to correctly demodulate the signal of user t and facilitate the implementation of the successive interference cancellation technique. Therefore, it is necessary to ensure

[0062] According to the SINR expression in Equation (5), the information transmission rate R of user k in cluster f can be obtained f,k as:

[0063]

[0064] In the present invention, our goal is to maximize the sum rate by jointly designing the phase shift matrix of the RIS, the transmit beamforming at the BS, and the power allocation under the constraints of the user rate and transmit power. Therefore, the optimization problem P1 is formulated as:

[0065]

[0066]

[0067]

[0068]

[0069] 0 ≤ θ f,n ≤ 2π, f = 1, ..., F; n = 1, ..., N (7e)

[0070] where is the minimum transmission rate that the k-th user in the f-th cluster satisfies the QoS condition, P0 is the maximum transmit power, is the maximum transmit power of the beam. (7b) is the constraint on the minimum rate that the user can accept to ensure fairness among users, (7c) is the constraint on the total transmit power of the BS, (7d) is the constraint on the total transmit power within the BS beam, and (7e) is the phase shift constraint of the RIS.

[0071] Since R f,k = log2(1 + SINR f,k ) is a monotonic function of SINR f,k , maximizing the sum signal-to-interference-plus-noise ratio of the system can maximize the sum rate of the system. The optimization problem P1 can be equivalently optimized for the signal-to-interference-plus-noise ratio

[0072]

[0073]

[0074]

[0075]

[0076] 0 ≤ θ f,n ≤ 2π, f = 1, ..., F; n = 1, ..., N (8e)

[0077] Due to the non-convexity of Problem P2, and involving the optimization of the RIS phase shift matrix, power allocation, and beamforming, it is difficult to directly obtain the analytical solution or the optimal solution of Problem P2 through optimization algorithms. Therefore, we decompose the above optimization problem into the following three sub-problems according to the priority, and then use alternating optimization to solve it. Specifically, first fix the power allocation and beamforming, and then determine the RIS phase shift matrix; on this basis, according to the phase shift matrix, then design the beamforming to eliminate the inter-cluster interference; furthermore, weaken the inter-cluster interference through the optimal power allocation within the cluster; the above three stages with a sequential order are iterated alternately until the above scheme meets the threshold requirements.

[0078] 1) Determine the RIS phase shift matrix

[0079] After fixing the power allocation and the beamforming at the BS, optimize the phase of the RIS. The problem of P2 can be expressed as:

[0080]

[0081]

[0082]

[0083] 0 ≤ θ f,n ≤ 2π (9d)

[0084] where ξ = [ξ f,1 , …, ξ f,K T , ξ f,k are slack variables to ensure that the constraint (9b) always holds equal for the optimal solution. When maximizing the introduced variables, it is equivalent to optimizing the lower bound of the system user and the signal-to-interference-plus-noise ratio. Therefore, the transformed optimization problem P3 is equivalent to the original problem.

[0085] Let u f = [u f,1 , …, u f , N T , a f,k = W f,k v f , B f,k = G f,k diag(H f v f ) We can obtain: |(G f,k Φ f H f + W f,k )v f | 2 = |a f,k + B​​f,k u f | 2 Then, constraints (9b) and (9c) can be rewritten as:

[0086]

[0087]

[0088] Simplifying the above equation gives:

[0089]

[0090]

[0091] Then, the optimization problem P3 can be rewritten as:

[0092]

[0093] s.t. |u f,n | = 1, (14b)

[0094] (12), (13) (14c)

[0095] By introducing a penalty factor, P3 can be rewritten as:

[0096]

[0097] s.t. |u f,n | ≤ 1, (15b)

[0098] (12), (13) (15c)

[0099] where μ is a large constant. To solve the non-convex parts in equations (12), (13), and (15a), we use the SCA algorithm. The first-order Taylor series of equations (15a), (12), and (13) can be expressed as:

[0100]

[0101]

[0102]

[0103] With the above approximations, the non-convex problem P4 can be rewritten as:

[0104]

[0105] s.t., (19b), (21), (22) (19b) So far, the original problem P2 has been transformed into a convex optimization problem and can be solved using a convex optimization toolbox.

[0106] 2) Determine the beamforming vector at the BS

[0107] In order to decode the received symbols from the multiplexed signals, the SIC technique is adopted to eliminate the intra-cluster interference, and the inter-cluster interference can be optimized by beamforming. Therefore, the present invention considers designing a beamforming matrix V to eliminate the inter-cluster interference. In the present invention, it is assumed that the downlink channel state information CSI of the channel is completely known, and the inter-cluster interference can be eliminated at the BS side through BD precoding, reducing the interference received by the receiving end and simultaneously reducing the complexity of the terminal processing.

[0108] The channel of the k-th user in the f-th cluster is To simplify the analysis, it is assumed that the channel similarity of the users in the same cluster is the highest, that is, it is assumed that the channel of the k-th user in the f-th cluster is the channel of all users in the f-th cluster. Then, equation (1) can be rewritten as:

[0109]

[0110] To eliminate the inter-cluster interference, the precoding matrix needs to satisfy the following conditions:

[0111]

[0112] The above equation can also be expressed as:

[0113]

[0114] where h n,fk (n = 1, 2,..., F) is the n-th column of is a subset obtained by removing 1 column. v f,k can be obtained from the null space of Performing SVD decomposition on can obtain

[0115]

[0116] where is the right singular matrix corresponding to the non-zero singular values, is the right singular matrix corresponding to the zero singular values; constitutes the null space of f,k The precoding matrix v can be designed based on Applying the matrix When the precoding is the singular vector corresponding to the larger singular value, the channel capacity of the system can be increased. Therefore, the equivalent channel is decomposed by SVD again.

[0117]

[0118] Among them, is the left singular matrix after SVD, is the diagonal matrix after SVD, is the right singular matrix corresponding to the non-zero singular value, is the right singular matrix corresponding to the zero singular value; Therefore, the precoding matrix v of user k f,k is:

[0119]

[0120] After eliminating the inter-cluster interference, the SINR of the k-th user in the f-th cluster can be rewritten as:

[0121]

[0122] Let be the equivalent channel gain, so equation (26) can be rewritten as:

[0123]

[0124] The corresponding information transmission rate R of user k in cluster f f,k is:

[0125]

[0126] 3) Power optimization and allocation

[0127] According to the solved Φ f , the P1 optimization problem can be rewritten as:

[0128]

[0129]

[0130]

[0131]

[0132] To maximize equation (29a) is equivalent to maximizing the sum rate of users within each beam. That is

[0133]

[0134]

[0135]

[0136] According to the definition of the logarithmic function, the objective function in Equation (30a) can be rewritten as:

[0137]

[0138] Let where p2 = {p f,1 , …, p f,k-1}. The first-order Taylor expansion of H(p2) can be expressed by the following formula:

[0139]

[0140] Therefore, the optimization problem P7 can be rewritten as:

[0141]

[0142] s.t. (30b), (30c) (33b)

[0143] Since the objective function is a concave function and all constraints are affine constraints, the optimization problem P8 becomes a convex optimization problem. The present invention considers using the Lagrange duality method to optimize it, and then P8 can be written as:

[0144]

[0145] where λ and μ are the Lagrange multipliers for constraints (30b) and (30c), respectively.

[0146] Then, we can obtain the dual function of problem P8:

[0147]

[0148] Taking the derivative of Equation (35) can obtain:

[0149]

[0150] Then we can obtain:

[0151]

[0152] Let A represent the coefficient matrix of the above equation, Y = (p f,1 , …, p f,K ), then Equation (38) can be rewritten as:

[0153] AY = b (38)

[0154] Thus, we can obtain the solution of Equation (39):

[0155]

[0156] The iteration formula can be expressed as:

[0157]

[0158] where η is the step size.

[0159] Optimize the dual problem:

[0160] min g(λ,μ) (41a)

[0161] s.t. λ≥0, μ≥0 (41b)

[0162] The dual problem is a convex optimization problem, and the gradient descent method can be used to optimize it.

[0163] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the present technical solution, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A multi-RIS assisted downlink MIMO-NOMA system optimization method based on sum rate maximization, characterized in that, The method specifically includes the following steps: S1: Construct a multi-RIS-assisted downlink MIMO-NOMA system; S2: Construct the objective function and constraints: By jointly optimizing the transmit beamforming matrix V of the base station, the RIS phase shift matrix Φ, and the intra-cluster power allocation p, the combined solution of the three is expressed as a constrained optimization problem P1. Under the constraints of RIS phase shift, user rate, and transmit power, maximize the sum rate of the MIMO-NOMA system; S3: Solve the optimization problem P1 by the method of alternating optimization; In step S1, a multi-RIS assisted downlink MIMO-NOMA system is constructed, which specifically includes: assuming that there are KF users equipped with L antennas, F RISs, and a BS equipped with M transmit antennas in the system; dividing the served KF users into F clusters, with K users in each cluster; each RIS is equipped with N≥1 reflecting elements to assist users in receiving signals from the BS; each user receives the superimposed signals from the BS-user link and the RIS-user link; ignoring the interference caused by the RISs serving other clusters; letting the effective phase shift and amplitude coefficient matrix of the RIS be β f,n ∈(0,1] represents the amplitude coefficient of the nth element of the RIS, j represents the imaginary unit, and θ n ∈(0,2π] represents the phase shift of the nth element of the RIS; Assume that each node has perfect CSI. Therefore, the signal of user k in cluster f is expressed as: where s f,k is the useful information signal to be transmitted to user k in cluster f, where (·) H and denote conjugate transpose and the expectation of a random variable, respectively; denotes the power allocated to user k in cluster f by the corresponding BS, is the f-th column of the precoding matrix V, G f,k is the Rayleigh channel matrix between the RIS and user k in cluster f, and Φ f is the effective phase shift and amplitude coefficient matrix of the RIS in cluster f, H f is the Rice channel matrix of the link from the BS to the RIS in the f-th cluster, and W f,k is the Rayleigh channel matrix between the BS and user k in cluster f, and is the additive white Gaussian noise with mean 0 and variance σ 2 at the k-th user in cluster f; In the downlink MIMO-NOMA communication network, the user with the strongest signal strength decodes first and eliminates the interference of the user with weak signal strength through the successive interference cancellation technique; Assume the order of user channel gains is: |(G f,1 Φ f H f +W f,1 )v f | 2 ≥…≥|(G f,k Φ f H f +W f,k )v f | 2 ≥…≥|(G f,K Φ f H f +W f,K )v f | 2 (2) According to the principle that the user with a smaller channel gain should be allocated more power, the power allocated to each user within the beam should satisfy: p f,1 ≤…≤p f,k ≤…≤p f,K , (3) According to the demodulation rule of the downlink MIMO-NOMA system, before demodulating its own signal, user k in cluster f needs to first demodulate all users in the same cluster with weaker channel gains than itself, that is, user k in cluster f needs to sequentially decode the data stream of user t in the same cluster, where t = k + 1, …, K, and the signal-to-interference-plus-noise ratio of user k in cluster f decoding the t-th user in the same cluster is expressed as: where 1 ≤ k < t ≤ K; After eliminating the interference signals of all users with weaker channels in the same cluster, when user k in cluster f decodes its own signal and regards the signals of other users as interference, the signal-to-interference-plus-noise ratio of user k in cluster f for decoding its own signal is: In the downlink MIMO-NOMA system, for the signal-to-interference-plus-noise ratio (SINR) of user k in cluster f to decode the t-th user to be greater than or equal to the SINR threshold of the t-th user, it is necessary to ensure that According to the SINR expression in formula (5), the information transmission rate R of user k in cluster f is obtained f,k as follows: In step S2, under the constraints of user rate and transmit power, maximize the sum rate by jointly designing the phase shift matrix of the RIS, the transmit beamforming at the BS, and the power allocation. That is, the optimization problem P1 is formulated as: 0 ≤ θ f,n ≤ 2π, f = 1, ..., F; n = 1, ..., N (7e) where is the minimum transmission rate that the k-th user in the f-th cluster satisfies the QoS condition, P0 is the maximum transmit power, is the maximum transmit power of the beam; (7b) is the constraint of the minimum rate that the user can accept, which is used to ensure the fairness of the user; (7c) is the total transmit power constraint of the BS; (7d) is the total transmit power constraint within the BS beam; (7e) is the phase shift constraint of the RIS.

2. The optimization method of the multi-RIS assisted downlink MIMO-NOMA system according to claim 1, wherein, In step S3, to solve the optimization problem P1, it specifically includes: first, equivalent the optimization problem P1 to the optimization of the signal-to-interference-plus-noise ratio; 0 ≤ θ f,n ≤ 2π, f = 1, ..., F; n = 1, ..., N (8e) Then, the optimization problem P2 is decomposed into three sub-problems according to the priorities, and then it is solved by using the alternating optimization method.

3. The optimization method for a multi-RIS assisted downlink MIMO-NOMA system according to claim 2, wherein In step S3, decompose the optimization problem P2 into three sub-problems according to the priority, and then solve it by alternating optimization. Specifically, it includes: first, fix the power allocation and beamforming, and then determine the RIS phase shift matrix; On this basis, according to the phase shift matrix, then design the beamforming to eliminate the inter-cluster interference; Furthermore, weaken the inter-cluster interference through the optimized intra-cluster power allocation; The above three stages with a sequential order are iterated alternately until the threshold requirement is met.

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