Optimization Method for Multi-RIS-Assisted MIMO-NOMA System Based on Power Minimization

Abstract

The present invention relates to an optimization method for a multi-RIS-assisted MIMO-NOMA system based on power minimization, belonging to the field of wireless communication technologies. The method includes: S1: constructing a multi-RIS-assisted MIMO-NOMA system; S2: by jointly optimizing the transmit beamforming matrix V of the base station and the RIS phase shift matrix Φ, expressing the beamforming design method as a constrained optimization problem P1, and minimizing the total transmit power of the base station in the MIMO-NOMA system under the constraints of RIS phase shifts and the minimum rate constraints of users; S3: solving the optimization problem P1 by an alternating optimization method. The present invention can solve the problem that in future scenarios, the excessive number of co-cluster users leads to inaccurate base station power allocation mechanisms, and complete the differentiation of intra-cluster users by using RIS assistance to achieve efficient SIC.

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 MIMO-NOMA system based on power minimization. Background Art

[0002] The system capabilities of the current 5G network have been greatly improved. However, due to the extensive use of mobile devices such as mobile phones, tablets, wearable devices, and vehicle networking devices in daily life, users' demand for high data transmission is increasing day by day. Therefore, the academic community is urgently seeking new technologies in Beyond 5G (B5G) and Sixth Generation (6G) mobile communication networks to meet the growing communication bandwidth requirements. To solve this problem, some scholars have proposed combining Non-Orthogonal Multiple Access (NOMA) technology with Multiple-Input Multiple-Output (MIMO) technology. Although MIMO-NOMA systems have some potential advantages, there are still some limitations. Problems such as random fluctuations in wireless channels, signal path loss, high mobility of users, and atmospheric absorption may seriously affect the performance of MIMO-NOMA systems, and the impact of these problems becomes more serious at high frequencies. In view of this, engineers and researchers have begun to search for new energy-saving technologies to exceed 5G and build 6G. In particular, due to the latest progress in the field of electromagnetic metamaterials, Reconfigurable Intelligent Surface (RIS) technology has attracted great attention from the academic and industrial communities. By combining RIS with MIMO-NOMA technology, RIS can adjust the channel by adjusting the phase shift of each element, which will greatly improve the quality of the signals received by users.

[0003] Currently, many valuable research results have been obtained for the research of RIS-assisted NOMA scenarios. Some scholars have studied ideal and non-ideal RIS scenarios and proposed a new decoding order. Some scholars have studied a multi-user RIS-NOMA network and proposed joint user association, sub-channel allocation, power allocation, phase shift design, and decoding order optimization problems to improve the achievable rate. However, these studies are all based on the relatively small number of users in the same cluster. In the MIMO-NOMA scenario, the power allocation problem for a relatively large number of users in the same cluster has not been well studied. Based on this, the present invention, namely the power minimization optimization method for a multi-RIS-assisted MIMO-NOMA system, provides a feasible idea.

[0004] In traditional application scenarios, to correctly apply NOMA technology within a cluster, it is necessary to correctly execute the Successive Interference Cancellation (SIC) technique. At the same time, to jointly implement NOMA technology among multiple clusters, that is, there must be unbalanced received power within the clusters to distinguish the signals of devices. However, in the case of the increasing number of users, the power allocation may not be very effective.

[0005] Therefore, what this invention considers is to optimize the power allocation within each cluster through multiple RISs within multiple clusters, to assist the base station in completing the power allocation within the cluster to achieve efficient SIC, and beamforming is considered to solve the inter-cluster interference. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide an optimization method for a multi-RIS-assisted MIMO-NOMA system based on power minimization, to solve the problem that the base station power allocation mechanism is inaccurate due to the excessive number of users in the same cluster in future scenarios, so as to use RIS assistance to complete the differentiation of users within the cluster to achieve efficient SIC.

[0007] To achieve the above purpose, this invention provides the following technical solutions:

[0008] An optimization method for a multi-RIS-assisted MIMO-NOMA system based on power minimization specifically includes the following steps:

[0009] S1: Construct a multi-RIS-assisted MIMO-NOMA system;

[0010] S2: Construct the objective function and constraints, specifically including: by jointly optimizing the transmit beamforming matrix V of the base station and the RIS phase shift matrix Φ, expressing the beamforming design method as a constrained optimization problem P1, and minimizing the total transmit power of the base station of the MIMO-NOMA system under the constraints of RIS phase shift and the minimum rate constraint of users;

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

[0012] Further, in step S1, to construct a multi-RIS-assisted MIMO-NOMA system, it specifically includes: assuming that the BS is equipped with M transmit antennas and communicates with KF users equipped with L receive antennas; to improve the spectral efficiency and reduce the system load, the KF served users are divided into F clusters, with K users in each cluster; each cluster is far from other clusters, that is, the interference caused by serving RISs of other clusters is ignored;

[0013] Due to the presence of obstacles between the base station and the users, to improve the transmission performance, a RIS with N≥1 reflecting elements is installed at appropriate positions in each cluster to assist the BS in communicating with the users; the phase shift of the RIS can be programmed and configured by the RIS controller, so each user receives signals from the BS-RIS-user link;

[0014] The power-domain multiplexed signal of the users in cluster f is expressed as:

[0015]

[0016] where s f,k represents 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 in cluster f; to analyze whether the RIS can optimize the power allocation to achieve perfect SIC, the present invention considers fixing p f,k , and the signal transmitted by the base station in the downlink direction is first precoded using the beamforming filter ; correspondingly, the BS downlink transmission signal can be written as:

[0017] x = Vs (2)

[0018] where, represents the combined signal sent from the BS to all users in different clusters; s represents the power-domain multiplexed signals of all F clusters, which can be represented in matrix form as:

[0019]

[0020] The received signal of user k in cluster f is expressed as:

[0021] y f,k = G f,k Φ f H f x + n f,k (4)

[0022] where, 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 is the additive white Gaussian noise with mean 0 and variance σ 2 at the k-th user in cluster f;

[0023] Let the effective phase shift and amplitude coefficient matrix of the RIS be where β f,n ∈(0,1] represents the amplitude coefficient of the nth element of the RIS, and represents the phase shift of the nth element of the RIS; in practical applications, it is usually necessary to maximize the signal reflected by the RIS, so β f,n is taken as 1.

[0024] The signal received by user k in cluster f from the base station is reflected by the RIS in the same cluster. Therefore, the signal of user k in cluster f can be expressed as:

[0025]

[0026] where is the f-th column of the precoding matrix, i.e., the transmit beamforming matrix V;

[0027] The transmit end of the MIMO-NOMA system uses superposition coding technology, while the receive end uses SIC for user signal detection. Its main function is to successfully demodulate multiple user signals in a beam. That is, users with poor channel quality are assigned stronger transmit power and decoded preferentially. After demodulation, they are subtracted from the superimposed signal, and so on until all users in the same cluster are completely demodulated.

[0028] To simplify the analysis, assume that the users in the beam exactly satisfy the decoding order of 1,…,K. According to the demodulation rule of the downlink MIMO-NOMA system, when user k in cluster f decodes its own signal, it needs to first decode the users whose decoding order is better than its own, and then regard the signals of other users as interference. Then the signal-to-interference-plus-noise ratio SINR f,k of user k in cluster f decoding its own signal is:

[0029]

[0030] According to the SINR expression in Equation (6), the information transmission rate R f,k of user k in cluster f is:

[0031]

[0032] Furthermore, in step S2, the optimization problem P1 is:

[0033]

[0034] s.t. 0 ≤ θ f,n ≤ 2π, f = 1,..., F; n = 1,..., N (8b)

[0035]

[0036] Among them, represents the minimum transmission rate at which user k in cluster f meets the QoS condition. Equation (8b) is the phase shift constraint of the RIS, and equation (8c) is the constraint on the minimum rate that the user can accept, which is used to ensure the fairness of the user.

[0037] Furthermore, step S3 specifically includes: decomposing problem P1 into two sub-problems according to the priority, and then solving them by alternating optimization. Specifically: first fix the beamforming at the BS, and then optimize the phase shift of the RIS; on this basis, according to the phase shift matrix, then design the beamforming to eliminate the inter-cluster interference; the above two stages with a sequential order are iterated alternately until the above scheme meets the threshold requirements.

[0038] Step S3 specifically includes the following steps:

[0039] S31: First fix the beamforming at the BS and optimize the phase shift of the RIS, which specifically includes:

[0040]

[0041] s.t. 0 ≤ θ f,n ≤ 2π, f = 1,..., F; n = 1,..., N

[0042]

[0043] Among them, W f,k = G f,k diag(H f v f );

[0044] Before solving problem P2, first find the tight concave lower bound of the information transmission rate R f,k of user k in cluster f through iterative solution of the following formula, and then solve the optimization problem through SDR;

[0045] S32: According to the RIS phase shift solved in step S32, rewrite the P1 optimization problem as:

[0046]

[0047]

[0048] Then transform the optimization problem P4 into a convex optimization problem, and then introduce a relaxation method to solve it.

[0049] The beneficial effects of the present invention are as follows: The present invention can use multiple RISs simultaneously to assist users in multiple clusters to complete power differentiation, so as to perfectly implement SIC. Compared with the prior art that relies on the power allocation of the base station to complete the differentiation of users within a cluster, the power consumption is lower and it has better development prospects.

[0050] 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

[0051] 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:

[0052] Figure 1 It is a schematic diagram of a multiple RIS-assisted downlink MIMO-NOMA communication system considered by the present invention; Detailed Embodiments

[0053] 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. The 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 diagrams provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner. Without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0054] Please refer to Figure 1 , the present invention considers a multiple RIS-assisted downlink MIMO-NOMA communication system, where the BS is equipped with M transmit antennas and communicates with KF users equipped with L receive antennas. To improve the spectral efficiency and reduce the system load, the KF served users are divided into F clusters, with K users in each cluster. Each cluster is far from other clusters, so the interference caused by RISs serving other clusters can be reasonably ignored.

[0055] Due to obstacles between the base station and the users, to improve the transmission performance, a RIS with N reflection elements (N≥1) is installed at a suitable position in each cluster to assist the BS in communicating with the users. The phase shift of the RIS can be programmed and configured by the RIS controller, so each user receives signals from the BS-RIS-user link.

[0056] The power-domain multiplexing signal of the users in cluster f is expressed as:

[0057]

[0058] 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. is the power allocated by its corresponding BS. To analyze whether the RIS can optimize the power allocation to achieve perfect SIC, the present invention considers fixing p f,k . The signal transmitted by the base station in the downlink direction is first precoded using the beamforming filter . Accordingly, the BS downlink transmission signal can be written as:

[0059] x = Vs (2)

[0060] where is the combined signal sent from the BS to all users in different clusters; s represents the power-domain multiplexing signals of all F clusters, which can be expressed in matrix form as:

[0061]

[0062] The received signal of user k in cluster f is given by

[0063] y f,k = G f,k Φ f H f x + n f,k (4)

[0064] where 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 is the additive white Gaussian noise with mean 0 and variance σ 2 at the k-th user in cluster f.

[0065] Let the effective phase shift and amplitude coefficient matrix of the RIS be: represents the amplitude coefficient of the n-th element of the RIS, represents the phase shift of the n-th element of the RIS. In practical applications, it is usually necessary to maximize the signal reflected by the RIS, so take β f,n = 1.

[0066] The signal received by user k in cluster f from the base station is reflected by the RIS in the same cluster. Therefore, the signal of user k in cluster f can be expressed as:

[0067]

[0068] where is the f-th column of the precoding matrix V.

[0069] The transmitting end of the MIMO-NOMA system adopts superposition coding technology, while the receiving end uses SIC for user signal detection. Its main function is to successfully demodulate multiple user signals in a beam. That is, users with poor channel quality are assigned stronger transmission power and decoded first. After demodulation, they are subtracted from the superimposed signal, and so on until all users in the same cluster are demodulated.

[0070] To simplify the analysis, assume that the users in the beam exactly satisfy the decoding order of 1,..., K. According to the demodulation rule of the downlink MIMO-NOMA system, when user k in cluster f decodes its own signal, it needs to first decode the users whose decoding order is better than it, and then regard the signals of other users as interference. Then the signal-to-interference-plus-noise ratio (SINR) of user k in cluster f when decoding its own signal is:

[0071]

[0072] According to the SINR expression in Equation (6), the information transmission rate R of user k in cluster f can be obtained as f,k as follows:

[0073]

[0074] Problem formulation:

[0075] In the present invention, our goal is to minimize the total transmit power of the base station by jointly designing the phase shift matrix of the RIS and the transmit beamforming at the BS under the user rate and phase shift constraints. Therefore, the optimization problem is formulated as:

[0076]

[0077] s.t. 0 ≤ θ f,n ≤ 2π, f = 1,..., F; n = 1,..., N (8b)

[0078]

[0079] where Denote the minimum transmission rate that user \(k\) in cluster \(f\) satisfies the QoS condition. Equation (8b) is the phase shift constraint of the RIS, and equation (8c) is the constraint of the minimum rate that the user can accept, which is used to ensure the fairness of the user.

[0080] Due to the non-convexity of problem P1 and the optimization of the RIS phase shift matrix and beamforming, it is difficult to directly obtain the analytical solution or the optimal solution of problem P1 through the optimization algorithm. By carefully observing the objective function and the constraint conditions, it can be found that the downlink precoding is closely related to the channel conditions. Moreover, in the RIS-assisted MIMO-NOMA system, there is a cascaded link from the base station to the user terminal. According to the channel model, the cascaded link is closely related to the channel. Therefore, we decompose the above optimization problem into the following two sub-problems according to the priority, and then use the alternating optimization to solve it. Specifically, first fix the 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; the above two stages with a sequential order are iterated alternately until the above scheme meets the threshold requirements.

[0081] 1) Determine the RIS phase shift matrix

[0082] First, let \(W\) f,k \(=\mathbf{G}\) f,k \(\text{diag}(\mathbf{H}\) f \(\mathbf{v}\) f ), then equation (6) can be rewritten as:

[0083]

[0084] According to the SINR expression in equation (9), the information transmission rate \(R\) of user \(k\) in cluster \(f\) can be obtained as: f,k as:

[0085]

[0086] Fix the beamforming at the BS and optimize the phase shift of the RIS. Then the problem of P2 can be expressed as:

[0087]

[0088] s.t. \(0\leq\theta\) f,n \(\leq 2\pi, f = 1, \ldots, F; n = 1, \ldots, N\) (11b)

[0089]

[0090] Before solving the problem of P2, we first find the tight concave lower bound of the information transmission rate \(R\) of user \(k\) in cluster \(f\) through the following iterative solution, and then solve the optimization problem through SDR. f,k ​

[0091]

[0092] Among them, the left - hand side of the constraint (11c) can be transformed through Equation (12) to obtain:

[0093]

[0094] where t represents the t - th iteration,

[0095]

[0096]

[0097] Although is a positive - semidefinite matrix, but is not concave, so consider using the SDR method to handle the non - concave terms. First, let So the constraint of (8b) can be transformed into:

[0098]

[0099] Then Equation (10) can be rewritten as:

[0100]

[0101] Let where,

[0102] By introducing slack variables, the objective function becomes:

[0103] P3:

[0104]

[0105]

[0106]

[0107] At this point, the constraint (18c) becomes concave. By removing the rank - one constraint (18b), the above - mentioned optimization problem can be solved using standard numerical methods, such as the CVX toolbox. During the solution process, once convergence is achieved, the first - order solution can be retrieved with the help of Gaussian randomization (although a stable point cannot be guaranteed at this time).

[0108] 2) Determine the precoding matrix

[0109] According to the solved RIS phase shifts, the P1 optimization problem can be rewritten as:

[0110] P4:

[0111]

[0112] Only the constraint (19b) is a non-convex constraint, so it is considered that it can be solved by transformation:

[0113]

[0114] Let z f,k = G f,k Φ f H f , then |z f,k v f | 2 can be rewritten as where Introduce the slack matrix is a rank-one positive semi-definite matrix, then Thus, the constraint condition (20) can be equivalently rewritten as:

[0115]

[0116] rank(V f ) = 1 (22)

[0117] V f ≥ 0 (23)

[0118] So far, the optimization problem P4 has become an SDP problem, so it can be solved by the existing convex optimization solver CVX.

[0119] 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 purpose and scope of the present technical solution, and they should all be covered by the scope of the claims of the present invention.

Claims

1. An optimization method for a multi-RIS-assisted MIMO-NOMA system based on power minimization, characterized in that, The method specifically includes the following steps: S1: Construct a multi-RIS assisted MIMO-NOMA system; S2: Construct the objective function and constraints, specifically including: By jointly optimizing the transmit beamforming matrix V of the base station and the RIS phase shift matrix Φ, the beamforming design method is expressed as a constrained optimization problem P1, and under the constraints of RIS phase shift and the minimum rate constraint of users, minimize the total transmit power of the base station in the MIMO-NOMA system; S3: Solve the optimization problem P1 by the method of alternating optimization; In step S1, to construct a multi-RIS assisted MIMO-NOMA system, specifically including: Assume that the BS is equipped with M transmit antennas and communicates with KF users equipped with L receive antennas; The KF served users are divided into F clusters, with K users in each cluster; Each cluster is far from other clusters, that is, the interference caused by the RIS serving other clusters is ignored; Install a RIS with N≥1 reflection elements at appropriate positions in each cluster to help the BS communicate with users; The phase shift of the RIS is programmed and configured by the RIS controller, so each user receives signals from the BS-RIS-user link; The power-domain multiplexing signal of the users in cluster f is expressed as: Among them, s f,k represents 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 corresponding to user k in cluster f; The signal transmitted by the base station in the downlink direction is first precoded using the beamforming filter Accordingly, the BS downlink transmission signal is written as: x = Vs (2) Among them, represents the combined signal sent from the BS to all users in different clusters; s represents the power-domain multiplexing signals of all F clusters, which is expressed in matrix form as: The received signal of user k in cluster f is expressed as: y f,k = G f,k Φ f H f x + n f,k (4) Among them, 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 is the additive white Gaussian noise with zero mean and variance σ 2 at the k-th user in cluster f; Let the effective phase shift and amplitude coefficient matrix of the RIS be where β f,n ∈(0, 1] represents the amplitude coefficient of RIS element n, and φ f,n = exp(jθ f,n ), θ n ∈(0, 2π] represents the phase shift of RIS element n; The signal transmitted by the base station received by user k in cluster f is reflected by the RIS in the same cluster, so the signal of user k in cluster f is expressed as: Among them, is the f-th column of the precoding matrix, i.e., the transmit beamforming matrix V; Assume that the users within the beam exactly satisfy the decoding order of 1, …, K. According to the demodulation rules of the downlink MIMO-NOMA system, when user k in cluster f decodes its own signal, it needs to first decode the users with a better decoding order than it, and then regard the signals of other users as interference. Then, the signal-to-interference-plus-noise ratio (SINR) of user k in cluster f when decoding its own signal f,k is as follows: According to the SINR expression in equation (6), the information transmission rate R of user k in cluster f is obtained f,k as follows: In step S2, the optimization problem P1 is: such that 0 ≤ θ f,n ≤ 2π, f = 1, ..., F; n = 1, ..., N(8b) where, represents the minimum transmission rate that user k in cluster f satisfies the QoS condition. Equation (8b) is the phase shift constraint of the RIS, and equation (8c) is the constraint of the minimum rate that the user can accept, which is used to ensure the fairness of the user.

2. The optimization method for the multi-RIS-assisted MIMO-NOMA system according to claim 1, characterized in that, Step S3 specifically includes: Decompose problem P1 into two sub-problems according to the priority, and then solve it by alternating optimization, specifically: First fix the beamforming at the BS, and then optimize the phase shift of the RIS; On this basis, according to the phase shift matrix, then design the beamforming to eliminate the inter-cluster interference; The above two stages with a sequential order are iterated alternately until the threshold requirement is met.

3. The optimization method for the multi-RIS-assisted MIMO-NOMA system according to claim 2, characterized in that, Step S3 specifically includes the following steps: S31: First fix the beamforming at the BS and optimize the phase shift of the RIS, specifically including: P2: s.t. 0 ≤ θ f,n ≤ 2π, f = 1, ..., F; n = 1, ..., N where W f,k = G f,k diag(H f v f ); Before solving the P2 problem, first iteratively solve the following formula to find the information transmission rate R of user k in cluster f, f,k the tight concave lower bound of, and then solve the optimization problem through SDR; S32: According to the RIS phase shift solved in step S32, rewrite the P1 optimization problem as: P4: Then transform the optimization problem P4 into a convex optimization problem, and then introduce the relaxation method to solve it.

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