Reconfigurable multifunctional intelligent metasurface and application thereof

Abstract

The application discloses a reconfigurable multifunctional intelligent metasurface and application thereof, and the multifunctional intelligent metasurface can be used for actively changing a wireless signal propagation environment, thereby improving signal transmission performance of a wireless communication system. In view of a resource allocation problem in a non-orthogonal multiple access network assisted by an MF-RIS, a non-convex optimization problem of jointly designing base station beamforming and MF-RIS coefficients is constructed with the aim of maximizing user sum rate. In view of the constructed optimization problem, firstly, a penalty function method and a continuous convex approximation method are used to convert the original optimization problem into a plurality of semi-definite programming sub-problems, then an alternating optimization method is used to obtain a suboptimal solution of the base station beamforming vector and the MF-RIS coefficient, so as to maximize the user sum rate in the NOMA system.

Description

Technical Field

[0001] This invention relates to the field of wireless resource allocation technology, and in particular to a reconfigurable multi-functional intelligence surface (MF-RIS) and its applications. Background Technology

[0002] Compared to Orthogonal Multiple Access (OMA), Non-Orthogonal Multiple Access (NOMA) achieves higher spectral efficiency and supports massive connectivity. Previous studies have shown that differences in user channel conditions can be used to enhance NOMA system performance. However, users in large-scale networks may have poor or similar channel conditions, which hinders the application of Successive Interference Cancellation (SIC) and the effective deployment of NOMA. Therefore, in practical networks, adjusting channel conditions and enhancing channel differences can effectively realize the potential of NOMA.

[0003] Recently, reconfigurable intelligence surfaces (RIS) have become a key technology for improving the performance of NOMA networks due to their ability to reconfigure the wireless propagation environment. By appropriately designing the reflection coefficient, RIS can flexibly adjust combined channel conditions to enhance the differences between users, thereby improving the performance of NOMA in large-scale networks. The combination of NOMA and RIS has been extensively studied in the literature, validating the advantages of RIS-assisted NOMA networks in enhancing signal strength, secure communication, and reducing transmit power. The power consumption issues in RIS-assisted NOMA and OMA networks have also been compared. However, most existing technologies for RIS-assisted NOMA networks use single-function RIS (SF-RIS) that only support signal reflection. This means that users on the other side cannot be effectively served by the SF-RIS.

[0004] To overcome this limitation, the concept of a dual-functional RIS (DF-RIS) has been proposed. Unlike SF-RIS, DF-RIS refers to a reconfigurable dual-functional surface capable of simultaneously reflecting and refracting signals, such as the Simultaneous Transmitting and Reflecting RIS (STAR-RIS) and the Intelligent Omni-Surface (IOS). Due to its advantageous characteristic of supporting full-space coverage, DF-RIS has attracted considerable attention. However, signals relayed by DF-RIS need to pass through cascaded channels, leading to a severe double fading problem. This problem can severely limit the performance of RIS-assisted NOMA networks because the quality degradation of the cascaded channels makes the differences between channels less pronounced than expected. Therefore, it is necessary to design new RIS architectures to improve the channel quality of wireless channels while mitigating the double fading problem faced by existing passive RISs. Summary of the Invention

[0005] This invention addresses the quality degradation and double fading issues of existing cascaded channels by proposing a reconfigurable multifunctional smart metasurface and its application in NOMA network resource allocation. The constructed multifunctional smart metasurface can not only divide the incident signal into refracted and reflected parts based on the field equivalence principle, but also amplify the input signal with the help of an active load. Therefore, MF-RIS can achieve full-space coverage and overcome the double fading problem.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] On the one hand, the present invention provides a reconfigurable multifunctional smart metasurface, which is based on the field equivalence principle, uses the surface equivalent impedance and magnetoresistance to realize the reflection and refraction of incident signals, and uses negative resistance elements to realize signal amplification.

[0008] On the other hand, the present invention also provides the application of the above-mentioned reconfigurable multifunctional smart metasurface in NOMA network resource allocation, including the following steps:

[0009] S1. Design coefficients including base station active beamforming vectors and MF-RIS, with the goal of maximizing the feasibility and rate for all users, and construct an optimization problem and constraints.

[0010] S2. Determine the initial user and rate expressions based on the constraints constructed in step S1. For the highly coupled MF-RIS coefficients and base station active beamforming vectors, convert them into semidefinite programming subproblems using continuous convex approximation and penalty function methods.

[0011] S3. Alternately optimize the semidefinite programming subproblem transformed in step S2. When the sum and rate change satisfy the convergence condition, obtain the active beamforming vector and the coefficients of MF-RIS, thereby achieving optimal performance.

[0012] Furthermore, the optimization problem for step S1 is as follows:

[0013]

[0014] The constraints are:

[0015]

[0016]

[0017]

[0018]

[0019] Where M represents the number of components in the MF-RIS, N represents the number of base station antennas, and K represents the number of users. These represent the channels between the base station and the user, the base station and the RIS, and the RIS and the user, respectively. and Let β represent the amplitude and phase shift response of the m-th element, respectively. max P represents the maximum magnification factor. max P represents the maximum transmit power of the base station. o R represents the maximum amplification power of MF-RIS. k This represents the data rate of user k. w represents the minimum rate requirement for user k. k Θ represents the beam vector of user k. k This represents the coefficient matrix of the MF-RIS for user k. h represents the additive white Gaussian noise introduced at MF-RIS. k This is the equivalent combined channel of base station-MF-RIS-user.

[0020] Furthermore, the beam vector w of user k k The coefficient matrix Θ of MF-RIS for user k k In the optimization problem, the MF-RIS coefficients are highly coupled, for w k and Θ k Optimize them separately.

[0021] Furthermore, regarding w k The objective function in the subproblem, and the semidefinite programming subproblem transformation method in step S2, is as follows: using auxiliary variable A k and B k Replace w kand h k The equivalent expression for the active beamforming problem is introduced by... D k =(H H Θ k (H) H Θ k ) H W k =w k w k H The expression is further represented, where W k ≥0 and there exists a non-convex rank-1 constraint rank(W) k ) = 1, then perform a first-order Taylor expansion on the transformed expression, separating A k and B k For W k =w k w k H The non-convex rank-one constraint is introduced by ‖W k || * -‖W k ||2 = 0 transforms this into a penalty term in the objective function, where and ||W k ||2=ε1(W k ) respectively represent W k The nuclear norm and spectral norm are then used to obtain the convex upper bound of the penalty term using a first-order Taylor expansion: in In the τ1st iteration The eigenvector corresponding to the largest eigenvalue is introduced into the objective function as a penalty function to obtain a vector about w. k The standard semidefinite programming subproblem of the subproblem.

[0022] Furthermore, regarding w k The solution process for the semidefinite programming subproblem is as follows: First, initialize the penalty factor η, η = μη, μ < 1. Then, gradually decrease η to obtain a suboptimal overall solution. The process terminates when the penalty term meets the following criteria: Where ∈1 is the predefined maximum violation amount.

[0023] Furthermore, for the coefficient matrix Θ of MF-RIS k The subproblem, step S2, semidefinite programming subproblem transformation method is as follows: Define v k and V k , where v k =[u k ;1], rank(V k) = 1, define g k and G k g k =[g k,1 ,g k,2 ,...,g k,M ] H G k =Hw k Q k =diag([|g k,1 | 2 ,|g k,2 | 2 ,...,|g k,M | 2 ]), get and definition use Instead of constraints on P0, for rank-one constraints, based on the MF-RIS coefficient expression, the following form is used as a replacement: Where ||V k || * and ||V k ||2 represents matrix V k nuclear norm and spectral norm, and This corresponds to the τ2th iteration. The eigenvector of the largest eigenvalue is introduced into the objective function as a penalty function, resulting in a standard semidefinite programming subproblem of the coefficient matrix subproblem of MF-RIS.

[0024] Furthermore, regarding Θ k The solution process for the semidefinite programming subproblem is as follows: First, initialize the penalty factor ξ, where ξ > 0 to ensure V k A penalty factor of rank 1 is applied, and then ξ is gradually decreased to obtain a suboptimal global solution. The process terminates when the penalty term meets the following criterion: Where ∈2 is the predefined maximum violation amount.

[0025] Furthermore, the method for alternately optimizing the MF-RIS coefficients and the base station active beamforming problem in step S3 is as follows: Initialization Error tolerance Δ, maximum number of iterations T 0,max The penalty factors η and ξ, and the predefined threshold ∈; set the iteration exponent τ0 = 0, given Updated by solving the base station active beamforming problem The value, then given Updated by solving the MF-RIS coefficient subproblem Update τ0 = τ0 + 1 to the value of τ0, and repeat the above process until... Or τ0 > T 0,max Then use renew The output converges until the constraints of the MF-RIS coefficients and the active beamforming vector satisfy a predefined threshold ∈.

[0026] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0027] The reconfigurable multifunctional smart metasurface proposed in this invention can not only divide the incident signal into refracted and reflected parts based on the field equivalence principle, but also amplify the output signal with active loads, actively changing the wireless signal propagation environment, thereby improving the signal transmission performance of the wireless communication system, achieving full-space coverage and overcoming the double fading problem. Furthermore, addressing the resource allocation problem in Non-Orthogonal Multiple Access (NOMA) networks, the MF-RIS of this invention is applied to NOMA networks. With the goal of maximizing users and rates, a non-convex optimization problem is constructed that jointly designs base station beamforming and MF-RIS coefficients. For the constructed optimization problem, the original optimization problem is first transformed into multiple semidefinite programming subproblems using the penalty function method and the Successive Convex Approximation (SCA) method. Then, an alternating optimization method is used to obtain suboptimal solutions for the base station beamforming vector and MF-RIS coefficients, which can adjust the channel conditions between users, thereby increasing the difference in channel gain between different users and ultimately improving the reachability and rate of all NOMA users. Simulation results show that the proposed MF-RIS-assisted NOMA network can provide a sum rate that is about 57% higher than that of traditional RIS, and MF-RIS is more likely to be deployed on the user side to obtain better performance. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0029] Figure 1 A schematic diagram of the MF-RIS-assisted NOMA network principle provided in an embodiment of the present invention.

[0030] Figure 2 A simulation diagram illustrating the application of MF-RIS in a simulated scenario, provided as an embodiment of the present invention.

[0031] Figure 3 This is a schematic diagram of the power results obtained by MF-RIS simulation in a simulated scenario, as provided in an embodiment of the present invention. Detailed Implementation

[0032] To better understand this technical solution, the method of the present invention will be described in detail below with reference to the accompanying drawings.

[0033] Please see Figure 1 This invention first proposes a reconfigurable multifunctional smart metasurface (MF-RIS), which, based on the field equivalence principle, uses the surface equivalent impedance and magnetoresistance to realize the reflection and refraction of incident signals, and uses negative resistance elements to realize signal amplification, thereby achieving full space coverage and overcoming the double fading problem.

[0034] We then investigate the resource allocation problem in downlink multi-user NOMA networks, where MF-RIS is deployed to assist communication between base stations and users, widening the difference in channel gain between different users, thereby improving the reachability and sum rate for all NOMA users. Specifically, we jointly optimize the active beamforming vector and MF-RIS coefficients using SCA and a penalty function to maximize the achievable sum rate.

[0035] The steps for applying MF-RIS to resource allocation in downlink multi-user NOMA networks are as follows:

[0036] The S1 design includes active beamforming vectors for the base station and coefficients of MF-RIS, aiming to maximize the feasibility and rate for all users, and constructs an optimization problem and constraints.

[0037] We consider an MF-RIS-assisted NOMA downlink network, where an MF-RIS consisting of M components is deployed to assist communication from an N-antenna base to K single-antenna users. (See [link to relevant documentation]). Figure 1 On the right side. The sets of components and users are respectively composed of and The channels for base station-user, base station-RIS, and RIS-user are respectively represented by... This indicates. Furthermore, we define... As the refraction (p = t) or reflection (p = r) beamforming vector, where p ∈ {t, r} represents the signal arriving at a specific user being refracted or reflected by MF-RIS. and Let represent the amplitude and phase shift responses of the m-th element, respectively, and let β be the maximum amplification factor. max ≥1. Due to the law of conservation of energy, the amplification function is limited by the energy supplied to the amplifier, that is, If user k is located in reflection space, then the diagonal matrix of user k's MF-RIS is determined by Θ.k =diag(u r ) is given, otherwise Θ k =diag(u t ).

[0038] We assume that perfect channel state information for all channels is available at the base station. Therefore, the signal received at user k is represented as:

[0039]

[0040] Where x = ∑ k w k s k x represents the transmitted signal, w k and These represent the precoded beam and information symbol transmitted by user k, respectively. This represents the noise at MF-RIS, with the noise power of each component being... This represents additive white Gaussian noise at user k, with power of

[0041] By using SIC, users with high channel quality can eliminate interference from users with poor channel quality, thereby improving the signal-to-interference-plus-noise ratio (SIR). Therefore, we assume that the user indices are arranged in ascending order relative to their channel gain, i.e.:

[0042] h1 2 ≤|h2| 2 ≤…≤‖h K || 2

[0043] in, This is an equivalent combined channel. For a fixed SIC decoding order, the reachable sum rate corresponding to user k is determined by R. k =log2(1+γ) k ) is given, where γ k It can be obtained from the following formula:

[0044]

[0045] Our goal is to maximize the sum rate for all users by jointly optimizing the active beamforming vector and MF-RIS coefficients of the base station. Under the constraints of BS transmit power, MF-RIS amplification power, and the minimum Quality of Service (QoS) for each user, the optimization problem can be formulated as follows:

[0046]

[0047]

[0048]

[0049]

[0050]

[0051] Where P max P0 and P1 represent the maximum transmit and amplify power of the base station and MF-RIS, respectively. This represents the minimum rate requirement for user k. Specifically, constraints on transmit power, amplification power, QoS requirements, and decoding order are given in formulas 2-5, respectively.

[0052] It can be observed that the optimization problem is difficult to handle due to the non-convex objective function and constraints. Furthermore, the active beamforming vector and MF-RIS coefficients are highly coupled, making direct solutions difficult. Therefore, our goal is to transform the optimization problem into some tractable convex subproblems and perform iterative, alternating optimization.

[0053] S2. Determine the initial user and rate expressions based on the constraints constructed in step S1. For the highly coupled MF-RIS coefficients and base station active beam power constraints, introduce an auxiliary variable set for transformation and apply a first-order Taylor expansion to obtain the transformed lower bound.

[0054] Given the MF-RIS coefficients, the active beamforming optimization problem remains non-convex. To facilitate the solution, we first introduce an auxiliary variable set. Where A k and B k Defined as:

[0055]

[0056]

[0057] Therefore, the data rate can be rewritten as:

[0058] R k =log2(1+(A) k B k ) -1 )

[0059] Therefore, the active beamforming optimization problem mentioned above can be equivalently represented as:

[0060]

[0061]

[0062]

[0063]

[0064]

[0065] We further define:

[0066]

[0067] D k =(H H Θ k (H) H Θ k ) H

[0068]

[0069] W k ≥0,rank(W k ) = 1

[0070] To handle non-convex constraints, we use a first-order Taylor expansion, and then we obtain the following lower bound:

[0071]

[0072] in and These are A in the τ1st iteration. k and B k Feasibility points.

[0073] S3. Introduce a penalty function based on the subproblem transformed in step S2. Transform this subproblem into a semidefinite programming subproblem.

[0074] For S4, W k For non-convex rank-one constraints, we assume they are transformed into penalty terms in the objective function. Therefore, we first introduce an equation:

[0075]

[0076] in and ||W k ||2=ε1(W k ) respectively represent W k The nuclear norm and spectral norm of ε. i (W k ) is matrix W k The i-th largest singular value. Therefore, when matrix W k The equation holds true when the rank is 1.

[0077] Next, we add this equation to the objective function as a penalty term. Since this equation as a penalty term makes the objective function non-convex, we apply a first-order Taylor expansion to obtain a convex upper bound, as follows:

[0078]

[0079] in In the τ1st iteration The eigenvector corresponding to the largest eigenvalue.

[0080] By introducing a convex upper bound into the objective function, we arrive at the following problem:

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] Where η > 0 is the penalty factor, if W k If the rank is not 1, then the objective function is penalized. It can be verified that when η→0, the solution to the above problem {W}... k The equation is always satisfied.

[0090] The transformed problem is a standard SDP problem, which can be efficiently solved using CVX. To obtain a high-quality solution, we first initialize a large η to find a feasible initial point, and then gradually decrease η as η = μη, μ < 1, until a sufficiently small value is obtained to obtain a suboptimal overall solution. The process terminates when the penalty term meets the following criterion:

[0091]

[0092] Where ∈1 represents the equation The predefined maximum violation value.

[0093] For the coefficient design of MF-RIS, we define it as follows:

[0094] v k=[u k ;1]

[0095]

[0096] rank(V k ) = 1

[0097] Let g k =[g k,1 ,g k,2 ,...,g k,M ] H G k =Hw k

[0098] Then Q k =diag([|g k,1 | 2 ,|g k,2 | 2 ,...,|g k,M | 2 ])

[0099]

[0100] Given

[0101]

[0102] It can be obtained

[0103]

[0104]

[0105] Therefore, based on the above transformation, non-convex constraints can be transformed into convex constraints.

[0106] To handle the nonconvex constraint ‖h1‖ 2 ≤|h2| 2 ≤...≤‖h K || 2 ,and We define Then we have:

[0107]

[0108]

[0109] Based on the above transformation, we can obtain:

[0110]

[0111]

[0112] Based on the above formula, we can define ‖h1‖ 2 ≤|h2| 2 ≤...≤‖h K || 2 The decoding order in the text is restated as follows:

[0113]

[0114] Then, given the active beamforming vector, the subproblem of MF-RIS coefficient design can be given by the following equation:

[0115]

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123]

[0124]

[0125] Where F i F represents k w in k was w i The value when used as a substitute.

[0126] Similar to the active beam power constraint in a base station, we replace the rank-one constraint in the above text with the following form:

[0127]

[0128] Where ||V k || * and ||V k ||2 represents matrix V k The nuclear norm and spectral norm. And and This corresponds to the τ2th iteration. The eigenvector of the largest eigenvalue.

[0129] By

[0130]

[0131] Introduction

[0132] The above-mentioned problems of the present invention can be restated as follows:

[0133]

[0134]

[0135]

[0136]

[0137]

[0138]

[0139]

[0140]

[0141]

[0142] Where ξ>0 is to ensure V k A penalty factor with a rank of 1.

[0143] The optimization problem after the above transformation is a standard SDP problem. CVX can solve this problem effectively. The iteration termination criterion is given by the following equation:

[0144]

[0145] Where ∈2 represents the predefined maximum violation amount.

[0146] Based on the above derivation, we propose a penalty-based iterative algorithm to effectively solve the problem. Details are given in the algorithm below.

[0147] Specifically, the algorithm alternately optimizes the sub-problems of MF-RIS coefficients and base station active beamforming based on the penalty function method and the successive convex approximation method, and initializes... Error tolerance Δ, maximum number of iterations T 0,max The penalty factors η and ξ, and the predefined threshold ∈. The iteration count τ0 = 0 is set, given... The update is achieved by solving the subproblem of active beamforming at the base station. The value, then given Update by solving the subproblem of MF-RIS coefficients Update τ0 = τ0 + 1 to the value of τ0, and repeat the above process until... Or τ0 > T 0,max Next update and The output converges until the constraints of the MF-RIS coefficients and the active beamforming vector satisfy a predefined threshold ∈.

[0148] Since the objectives of both optimization problems are non-decreasing during iterations, and the system throughput has an upper limit, the proposed algorithm guarantees convergence. Furthermore, the algorithm's complexity is O(n log n). Among them I in and I out These represent the number of internal and external iterations required for convergence, respectively.

[0149] Please see Figure 2 In the application scenario, the base station and MF-RIS are located at (0, 0, 0) meters and (0, 50, 20) meters, respectively. Furthermore, users are divided into two groups, distributed on circles with centers at (0, 45, 0) meters and (0, 55, 0) meters, and a radius of r = 3 meters, respectively. We assume all channels experience Ricean fading and set K = 6, N = 16, M = 100, and Pmax = 20 dBm. Next, we set up three comparative schemes, deploying Reflecting-only RIS, Active RIS (a RIS element capable of simultaneously supporting signal reflection and signal amplification), and STAR-RIS to assist downlink NOMA system communication.

[0150] Please refer to the simulation results. Figure 3 Specifically, when P max At 10 dBm, the MF-RIS-assisted NOMA scheme provides a 57% higher sum rate than the RIS-only scheme. This result can be explained as follows: First, the signal reflection and refraction capabilities allow MF-RIS to serve all users throughout the space, thus achieving a higher system sum rate. Second, by providing additional power to amplify the incident signal, MF-RIS effectively improves the quality of the cascaded channel. Furthermore, the MF-RIS scheme is superior to STAR-RIS and active RIS schemes because the latter two only partially address the problems faced by RIS-only schemes (i.e., half-space coverage and double fading).

[0151] Numerical results validate the effectiveness of MF-RIS and its superiority over traditional RIS. Simulation results show that the proposed MF-RIS-assisted NOMA network can provide approximately 57% higher sum rate than traditional RIS, and MF-RIS is more suitable for deployment on the user side to achieve better performance.

[0152] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. However, these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for applying a reconfigurable multifunctional smart metasurface to resource allocation in NOMA networks, characterized in that, Includes the following steps: S1. Design coefficients including base station active beamforming vectors and MF-RIS, with the goal of maximizing the feasibility and rate for all users, and construct an optimization problem and constraints. S2. Determine the initial user and rate expressions based on the constraints constructed in step S1. For the highly coupled MF-RIS coefficients and base station active beamforming vectors, convert them into semidefinite programming subproblems using continuous convex approximation and penalty function methods. S3. Alternately optimize the semidefinite programming subproblem after the transformation in step S2. When the sum and rate change satisfy the convergence condition, obtain the active beamforming vector and the coefficients of MF-RIS, thereby achieving optimal performance. The optimization problem in step S1 is: The constraints are: Where M represents the number of components in the MF-RIS, N represents the number of base station antennas, and K represents the number of users. These represent the channels between the base station and the user, the base station and the RIS, and the RIS and the user, respectively. and Let β represent the amplitude and phase shift response of the m-th element, respectively. max P represents the maximum magnification factor. max P represents the maximum transmit power of the base station. o R represents the maximum amplification power of MF-RIS. k This represents the data rate of user k. w represents the minimum rate requirement for user k. k Θ represents the beam vector of user k. k This represents the coefficient matrix of the MF-RIS for user k. h represents the additive white Gaussian noise introduced at MF-RIS. k This is the equivalent combined channel of base station-MF-RIS-user.

Images