A multi-intelligent element surface assisted MIMO network resource allocation optimization method

Abstract

The application discloses a kind of optimization methods of multi-intelligent meta-surface assisted MIMO network resource allocation, comprising: step 1, the communication rate of all users is modeled as optimization problem and maximum problem;Step 2, the optimization problem proposed is restructured conversion;Step 3, the optimization problem after conversion is decomposed into two sub-optimization problems: base station beamforming optimization problem and the transmission reflection coefficient optimization problem of multiple synchronous transmission reflection intelligent surfaces;Step 4, base station beamforming optimization problem is solved;Step 5, the transmission reflection coefficient optimization problem of multiple synchronous transmission reflection intelligent surfaces is solved;Step 6, finally, the optimization algorithm of resource allocation problem based on multiple synchronous transmission-reflection intelligent surface assisted MIMO communication network is obtained.The method of the application can improve the resource allocation of the system, improve the communication quality of users.

Description

Technical Field

[0001] This invention relates to a resource allocation optimization method, and more particularly to an optimization method for resource allocation in a multi-smart element surface-assisted MIMO network. Background Technology

[0002] With the rapid development of metasurfaces and corresponding manufacturing technologies, reconfigurable smart surfaces (RIS) and their various variants have become promising technologies for sixth-generation (6G) wireless networks. Generally, RIS are two-dimensional structures composed of a large number of low-cost reconfigurable elements. Given these beneficial properties of RIS, industry and academia are dedicated to researching RIS, including but not limited to designing high-quality communication, reducing transmit power consumption, improving spectral and energy efficiency, establishing unobstructed communication links, and further investigating the operation of multiple RIS in wireless communication systems.

[0003] While some recent research has considered transmissive and reflective metasurfaces for wireless communication, existing contributions have primarily focused on RISs used only for reflecting incident signals; therefore, both the signal source and target must be located on the same side of the RIS, i.e., within the same half of the smart wireless environment. This topological constraint limits the flexibility of traditional RISs. To address this issue, the concept of Synchronous Transmissive-Reflective RISs (STAR-RIS) has been proposed, in which incident wireless signals can be reflected within the same half of the smart wireless environment on the same side of the RIS, but they can also be transmitted to the other side of the RIS. Therefore, STAR-RISs can create a fully spatial smart wireless environment.

[0004] Currently, considering the complex and ever-changing nature of actual communication environments and the rapidly growing demand for wireless data transmission from terrestrial user equipment, many problems still need to be solved. For example, terrain obstructions can cause signals to be affected by multipath fading, potentially leading to signal distortion, fading, and interference. Therefore, MIMO (Multiple-Input Multiple-Output) technology has become a research hotspot as a wireless communication technology that can effectively solve these problems.

[0005] Deploying STAR-RIS in complex communication environments is an effective solution to address poor user communication quality. MIMO communication networks assisted by STAR-RIS can effectively avoid signal reflection, refraction, and scattering during propagation, preventing multipath fading that negatively impacts user communication quality. Furthermore, introducing passive STAR-RIS to improve channel conditions can effectively reduce the burden on base stations.

[0006] Current STAR-RIS-based resource allocation optimization problems often only consider the impact of a single STAR-RIS on the communication system, failing to account for scenarios where multiple STAR-RIS collaborate to provide services to users in real-world situations. From a structural perspective, a MIMO communication network assisted by multiple STAR-RIS is a more complex and coupled non-convex optimization problem. Summary of the Invention

[0007] Purpose of the invention: The technical problem to be solved by the present invention is to provide an optimization method for resource allocation in multi-smart element surface-assisted MIMO networks, which addresses the shortcomings of the existing technology.

[0008] To address the aforementioned technical problems, this invention discloses an optimization method for resource allocation in multi-intelligent element surface-assisted MIMO networks, comprising the following steps:

[0009] Step 1: Model the MIMO communication network resource allocation optimization problem as a problem of maximizing the communication rate of all users, that is, the resource allocation optimization objective is to maximize the communication rate of all users in the MIMO communication network;

[0010] Step 2: Reconstruct and transform the optimization problem described in Step 1;

[0011] Step 3: Decompose the optimization problem after reconstruction and transformation in Step 2 into two sub-optimization problems: the base station beamforming optimization problem and the TRC matrix optimization problem of the transmission and reflection coefficients of multiple smart element surfaces STAR-RIS.

[0012] Step 4: Solve the base station beamforming optimization problem;

[0013] Step 5: Solve the optimization problem of the transmission and reflection coefficient TRC matrix for multiple STAR-RIS;

[0014] Step 6: Based on the solutions obtained in Steps 4 and 5, the MIMO communication network resource allocation optimization is finally completed.

[0015] Beneficial effects:

[0016] This invention investigates an optimization method for resource allocation in MIMO communication networks assisted by multiple synchronous transmission-reflection smart surfaces. By increasing the number of synchronous transmission-reflection smart surfaces in the communication system, the communication rate of users in this scenario is improved. In a MIMO communication system scenario with multiple STAR-RIS-assisted multi-user communication, multiple STAR-RIS improve user channel conditions. The communication rate of users is maximized by optimizing the base station beamforming strategy and the reflection and transmission coefficients of the STAR-RIS, while simultaneously satisfying the energy conservation constraints of the base station transmit power and the transmission and reflection coefficients of the STAR-RIS. Experimental results show that this invention can effectively improve the user's communication rate, reduce the impact of the channel environment on the user's communication rate, and provide a closed-form solution for base station beamforming, effectively reducing the overall algorithm complexity. It is applicable to MIMO wireless communication scenarios with multiple users. Attached Figure Description

[0017] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, and the advantages of the present invention in the above and / or other aspects will become clearer.

[0018] Figure 1 This is a schematic diagram of a MIMO communication network model assisted by multiple synchronous transmission and reflection smart surfaces.

[0019] Figure 2 A schematic diagram of the method flow for optimizing base station beamforming and STAR-RIS transmission and reflection coefficients to maximize user communication rates.

[0020] Figure 3 Curves showing the relationship between user communication rate and algorithm iteration number under different environments in a multi-STAR-RIS assisted MIMO communication network.

[0021] Figure 4 The graph shows the relationship between user communication rate and algorithm iteration number in a multi-STAR-RIS assisted MIMO communication network and a traditional single STAR-RIS or RIS-assisted MIMO communication network under different STAR-RIS operating modes. Detailed Implementation

[0022] This invention primarily proposes an optimization method for resource allocation in multiple STAR-RIS assisted MIMO communication networks. By jointly optimizing the base station beamforming matrix and the TRC coefficient matrix of each STAR-RIS, the sum of user communication rates in the communication system is improved. This invention aims to improve the sum of user communication rates in a multi-STAR-RIS assisted MIMO communication network scenario by using the base station beamforming matrix and the TRC coefficient matrix of each STAR-RIS, while simultaneously constraining the base station's transmit power and the energy conservation constraints of the transmission and reflection coefficients of each STAR-RIS. Compared to other STAR-RIS and RIS strategies, this invention effectively improves the sum of system communication rates and reduces the impact of channel loss caused by reflection, refraction, and scattering during signal transmission. The specific technical solution includes the following steps:

[0023] Step 1: Model the optimization problem as a problem of maximizing the communication rate for all users;

[0024] Step 2: The proposed optimization problem is reconstructed and transformed using the Weighted Minimum Mean-Square Error (WMMSE) algorithm;

[0025] Step 3: Decompose the transformed optimization problem into two sub-optimization problems: the base station beamforming optimization problem and the transmission and reflection coefficient optimization problem of multiple synchronous transmission and reflection smart surfaces;

[0026] Step 4, Solve the base station beamforming optimization problem: Reduce the high computational complexity of the transformed second-order cone programming problem by using the Lagrange duality algorithm, and derive a closed-form solution to the problem. Then, calculate the optimal base station beamforming by using complementary relaxation conditions and the bisection method.

[0027] Step 5, solve the optimization problem of transmission and reflection coefficients of multiple synchronous transmission and reflection smart surfaces: by introducing auxiliary variables, decouple the same TRC matrix problem of multiple STAR-RIS among users, and transform the problem into CCCP form through equivalent transformation and solve it;

[0028] Step 6 finally yields an optimized algorithm for resource allocation in a MIMO communication network assisted by multiple synchronous transmission-reflection smart surfaces.

[0029] Step 1 includes:

[0030] Step 1-1: Establish multiple MIMO communication models assisted by synchronous transmission and reflection smart surfaces;

[0031] Step 1-2, establish the optimization problem: maximize the sum of communication rates for all users by optimizing the beamforming matrix and transmission / reflection matrix coefficients, while ensuring that the maximum transmit power constraint of the base station and the energy conservation constraint of the synchronous transmission / reflection smart surface are met.

[0032] Step 1-1 includes: The MIMO communication model assisted by multiple STAR-RIS includes 1 base station, K ground users, and L STAR-RIS, each STAR-RIS consisting of M patch antennas. These STAR-RIS coordinate with the base station to serve the users;

[0033] STAR-RIS operates in energy-split mode. In this mode, the transmission and reflection coefficient (TRC) of each STAR-RIS patch antenna can be expressed as: as well as in, and This represents the transmission coefficient and transmission phase offset angle of the m-th antenna of the l-th STAR-RIS. and Let represent the reflection coefficient and reflection phase offset angle of the m-th antenna of the l-th STAR-RIS. Considering the energy conservation constraint, and Must meet The proposed system deploys multiple STAR-RIS systems; therefore, the TRC matrix for each STAR-RIS is independent, denoted as follows: Where ξ∈{t, r} indicates whether the user is on the transmission or reflection side of the l-th STAR-RIS. Based on this, for user k, its equivalent TRC matrix can be expressed as: The symbol Diag(·) represents taking the diagonal elements of the diagonal matrix and recombining them into a new diagonal matrix. In practice, when the positions of the user and STAR-RIS are determined, the value of the user's equivalent TRC matrix can be determined.

[0034] The channel from the base station to the l-th STAR-RIS and the channel from the l-th STAR-RIS to the k-th user are respectively used as... and This indicates that all channels simultaneously follow a narrowband quasi-static fading mode. Therefore, the channel from the base station to the l-th STAR-RIS, and the channel from the l-th STAR-RIS to the k-th user, can be simulated as a Ricean fading model channel, comprising both line-of-sight and non-line-of-sight transmission components.

[0035]

[0036]

[0037] Among them, and d RU，k This represents the distance between BS and the first STAR-RIS, and the distance between the l-th STAR-RIS and the k-th user, α. BR and α RU K represents the corresponding path loss exponent. BR and K RU F represents the Rice factor, ρ0 represents the path loss when the reference distance is 1 meter, and F represents the path loss when the reference distance is 1 meter. LoS and It is a deterministic line-of-sight component, F NLoS and It is a random non-line-of-sight component, modeled as Rayleigh fading. Among them, And the guiding vector and They are defined as follows:

[0038]

[0039]

[0040] Similarly, for deterministic line-of-sight components Where the guiding vector a U (θ AoA ) and a RU (θ AoD It can be defined as:

[0041]

[0042]

[0043] Among them, M and N a and N t These are the number of patch antennas on the STAR-RIS side, the number of base station antennas, and the number of user receiving antennas, respectively. and θ AoA These are the angles of arrival from BS to STAR-RIS and from STAR-RIS to the user. Furthermore, and θ ZoD It refers to the angles away from BS and STAR-RIS. d is the antenna spacing, and v is the wavelength.

[0044] In practical scenarios, considering that the locations of the BS and STAR-RIS are fixed, and that for any user, the channel from the BS to all STAR-RIS is the same, we can use... Let represent the channels from BS to all STAR-RIS. Similarly, the channels from all STAR-RIS to user k can be equivalent to .

[0045] use and Let represent the symbol vector and active beamforming matrix of user k on the BS. The signal transmitted from the BS can be represented as:

[0046]

[0047] Therefore, the signal received by user k can be represented as:

[0048]

[0049] in It is the noise vector of the k-th user, and its value follows... in, This indicates that the expression follows a pattern with a mean of 0 and a variance of . The complex normal distribution is given by I, where I represents the identity matrix. It is the noise power of the kth user;

[0050] Define intermediate variables The original expression is simplified. Now, the data rate of user k can be expressed as:

[0051]

[0052] in, The interference plus noise covariance matrix of the k-th user can be written as:

[0053]

[0054] Where I represents the identity matrix.

[0055] Steps 1-2 include: The optimization problem is defined by the following optimization model P1:

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062] Wherein, objective function The sum of communication data rates for all users. Representation matrix The m-th diagonal element. Constraint C1 is the constraint on the maximum transmit power on the base station side, P max The maximum transmit power that the base station can provide is represented; constraint C2 is the equivalent TRC matrix composed of multiple STAR-RIS affecting the user side, which represents the constraint relationship between the user and the STAR-RIS; constraint C3 is the constraint on the value of the transmission and reflection coefficient of each STAR-RIS; constraint C4 is the range constraint on the transmission and reflection coefficient and phase offset of the STAR-RIS operating in energy split mode; constraint C5 is the energy conservation constraint for each STAR-RIS.

[0063] Step 2 includes introducing the Weighted Minimum Mean Square Error (WMMSE) method to transform the original optimization problem P1 into an equivalent convex form. First, we introduce a linear decoding matrix, thus estimating the signal vector for each user. It can be represented as:

[0064]

[0065] in, This is the linear decoding matrix for user k. Since the signal vector sk and the noise nk are independent, we can derive the mean square error matrix for user k as follows:

[0066]

[0067] in, This represents the average of the symbol vector and the noise, where sk represents the symbol vector transmitted by the base station;

[0068] Based on this, we introduce the auxiliary variable Z. k ≥0, the optimization problem P1 is rewritten in the following form:

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075] C6:Z k ≥0

[0076] Among them, f k (V k Qk U k Z k It can be determined by the following expression:

[0077] f k (Vk, Q) k U k Z k )=log|Z k |-Tr(Z k E k )+d k .

[0078] Where, d k This is a constant term generated during the transformation process. Unlike the original objective function, by introducing more optimization variables into P2, the original problem becomes easier to solve. For a given TRC matrix Q... k In other words, when the other two optimization matrices are fixed, f k (V k Q k U k Z k For each set of optimization matrices, it is a concave function. Based on this, a block coordinate descent algorithm is used to alternately optimize the various variables. The specific steps include:

[0079] First, with V fixed k Q k Z k In the case of solving U k The optimal solution. At this point, f k (V k Q k U k Z k ) can be seen as only related to U k The relevant functions. Therefore, for f k (V k Q k U k Z k (relative to U) k Find its first derivative and obtain the optimal U by finding the extreme points. k , denoted as U k ★ And there are:

[0080]

[0081] Secondly, with a fixed V k Q k U k In the case of solving Z k The optimal solution. And the solution for U.k The approach is consistent, and we also have Z k The optimal Z is obtained by finding the first derivative and then finding the extreme points. k The value is denoted as Z. k ★ And there are:

[0082]

[0083] Then, fix Q. k U k Z k And solve V k The optimal solution;

[0084] Finally, fix V k U k Z k And solve Q k The optimal solution;

[0085] Step 3, which transforms the original optimization problem into optimizing the base station beamforming matrix, includes:

[0086] Based on the optimization problem P2, with Q fixed... k U k Z k And solve V k The optimal solution. Considering that the main problem addressed in this step is the beamforming matrix V... k The optimization problem, and the objective function in P2 at this moment with respect to V. k It does not possess perfect concavity and convexity, therefore the objective function of P2 needs to be transformed, taking into account the mean square error E introduced in the WMMSE algorithm. k Substituting these terms into the objective function of P2, and ignoring the constant terms that do not affect the concavity or convexity of the function, the original objective function can be equivalently replaced with the following form:

[0087]

[0088] Introducing auxiliary variables and Based on this, the optimization problem P3 for this optimization variable can be obtained as follows:

[0089]

[0090]

[0091] Here, constraint C1 represents the maximum transmit power constraint of the base station. Optimization problem P3 is a second-order cone programming problem. Considering the high time complexity of computing second-order cone programming problems, a low-complexity method is proposed to solve the problem by using the Lagrange dual algorithm to find the approximately optimal closed-form solution.

[0092] Step 4, which involves solving the optimal base station beamforming problem based on the Lagrangian duality algorithm, includes: The Lagrangian cost function of optimization problem P3 can be expressed as:

[0093]

[0094] Here, λ > 0 is the Lagrangian dual variable relating to the maximum transmit power of the base station. This is achieved by considering the cost function with respect to V. k By finding the first derivative and the extrema, we can obtain the closed-form solution of the optimal solution for the beamforming matrix as follows:

[0095]

[0096] in, This represents finding the pseudo-inverse of a matrix. This is combined with constraints on the base station's transmit power. The complementary relaxation condition, λ, can be solved using the following expression:

[0097]

[0098] The optimal solution for λ can be found using a binary search algorithm, as follows:

[0099] First, if the auxiliary variable matrix A is a full-rank matrix, then it can be proven that matrix A is a positive definite matrix. This can be achieved through singular value decomposition, where A = SΞS. H ,in Ξ is a diagonal matrix where all diagonal elements are positive. Based on the form of the complementary relaxation condition, it is defined as follows:

[0100]

[0101] in, [Ω]i,i and [Ξ]i,i represent the i-th diagonal elements of matrices Ω and Ξ, respectively;

[0102] It can be proven that g(λ) is a monotonically decreasing function. Therefore, if .9(0)≤Pm ax The optimal beamforming matrix can be obtained through We obtain the result. Otherwise, we can use a binary search-based algorithm to find the solution to the following equation, thus obtaining the optimal λ:

[0103]

[0104] Due to the monotonicity of g(λ) and The equation must have a solution, which we represent as λ. ＊If we need to find the upper bound of λ using a binary search method, and Ξ is a diagonal matrix with positive diagonal elements, then we have:

[0105]

[0106] Based on this, the upper bound λ can be derived. up for:

[0107]

[0108] At this point, setting the lower bound of λ to a number close to 0 allows us to find the optimal λ using a binary search query.

[0109] If A is a low-rank matrix, then g(λ) = Tr((Ξ+λI) cannot be obtained through singular value decomposition. -2 In this case, first check if λ = 0 is the optimal solution; if g(0) < P max Then the optimal beamforming matrix is ​​given by Give;

[0110] Otherwise, by defining the rank of A as r A =rank(A)<N a Using singular value decomposition, we can obtain:

[0111] A = [S1, S2]Ξ[S1, S2] H

[0112] Wherein, S1 contains the first r A Each and r A S2 contains the singular vectors corresponding to the last N positive eigenvalues. a -r A One and N a -r A The singular vectors corresponding to zero eigenvalues. Where Ξ1 is a group containing the first r A A diagonal matrix of positive eigenvalues. Define S = [S1, S2] to obtain:

[0113]

[0114] The case where Ω is full rank is consistent with the case where A is full rank. Furthermore, g(λ) is a monotonically decreasing function when λ > 0, and the optimal λ can be obtained using a bisection method. The upper bound of λ is... The lower bound is set to a small positive value;

[0115] Step 5, which describes the problem of decoupling multiple STAR-RIS systems with identical TRC matrices among users, involves transforming the problem into CCCP form through equivalent transformation and then solving it.

[0116] Based on problem P2, with a fixed beamforming matrix V k and auxiliary variable U k Z k Considering the equivalent matrix of the transmission and reflection smart surface for user k, the problem can be described in the form of P4:

[0117]

[0118]

[0119]

[0120]

[0121]

[0122] TRC matrix Q k Passive beamforming was performed on the signal during transmission. To address this non-convexity issue, it will be combined with Q... k Separate the irrelevant terms and only consider Q. k Related content. Substituting into the objective function, we get:

[0123]

[0124]

[0125] By performing an equivalent substitution, the two expressions can be written as:

[0126]

[0127]

[0128] Where, q k =diag(Q k ), as well as

[0129]

[0130] Therefore, optimization problem P4 can be equivalently rewritten as P5:

[0131]

[0132] stC1:q k =diag(Q k ),

[0133]

[0134]

[0135]

[0136] Constraint C1 represents the relationship between the TRC matrix of each STAR-RIS and the user. The main difficulty of problem P5 lies in C4, which shows that the transmission and reflection coefficients are coupled. Unlike the case of a single STAR-RIS, resource allocation involving multiple STAR-RIS is more challenging. This is because each user may be located on the reflection side of one STAR-RIS but on the transmission side of another. Depending on their location, the TRC matrix Q of different users will vary. k It could also be coupled;

[0137] Introduce an auxiliary variable ζ, where ζ∈{t, r} and That is, when ξ = r, ζ = t; otherwise, ζ = r. We define a matrix... Let represent the TRC matrix with state ζ. Definition Therefore, we have This is done in order to reconstruct constraint C4 into a solvable form;

[0138] Based on the above analysis, we introduce Therefore, diag(Θ) can be used k Let ) represent the TRC matrix of user k, and This indicates that it is related to diag(Θ). k The opposite state. According to constraint C4, we can restate it as follows: This allows us to transform problem P5 into P6:

[0139]

[0140]

[0141]

[0142] For the constraint C1, which is still nonconvex, we introduce the lemma:

[0143] For any condition satisfying W = ww H The matrix can be equivalently replaced by:

[0144]

[0145] Based on the above lemma, optimization problem P6 can be transformed into P7:

[0146]

[0147]

[0148]

[0149]

[0150]

[0151]

[0152] in, It is an auxiliary variable. Let represent an N×N Hermitian matrix. For the still non-convex constraints C3 and C4, we relax these constraints using a continuous convex approximation algorithm, obtaining:

[0153]

[0154]

[0155] At this point, optimization problem P7 can be transformed into P8:

[0156]

[0157]

[0158]

[0159]

[0160]

[0161]

[0162] Problem P8 is a constrained concave-convex programming problem that can be solved using algorithms such as convex optimization.

[0163] Step 6 includes:

[0164] Alternate optimization of auxiliary variable U k Z k Passive beamforming matrix V k and the equivalent TRC matrix Q k Until convergence, the optimal beamforming matrix V is finally obtained. k and the equivalent matrix Q of the transmission and reflection coefficients k And calculate the maximum downlink speed for all users at this time.

[0165] Example:

[0166] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0167] Figure 1 A MIMO communication model assisted by multiple synchronous transmission and reflection smart surfaces is described. The communication model includes one base station, K ground users, and L STAR-RIS, each of which consists of M patch antennas. These STAR-RIS coordinate with the base station to serve the users.

[0168] STAR-RIS operates in energy-split mode. In this mode, the transmission and reflection coefficient (TRC) of each STAR-RIS patch antenna can be expressed as: as well as and [0, 2π) represents the transmission coefficient and transmission phase offset angle of the m-th antenna of the l-th STAR-RIS. and Let represent the reflection coefficient and reflection phase offset angle of the m-th antenna of the l-th STAR-RIS. Considering the energy conservation constraint, and Must meet The proposed system deploys multiple STAR-RIS systems; therefore, the TRC matrix for each STAR-RIS is independent, denoted as follows: Where ξ∈{t, r} indicates whether the user is on the transmission or reflection side of the l-th STAR-RIS. Based on this, for user k, its equivalent TRC matrix can be expressed as: The symbol Diag(·) represents taking the diagonal elements of the diagonal matrix and recombining them into a new diagonal matrix. In practice, when the positions of the user and STAR-RIS are determined, the value of the user's equivalent TRC matrix can be determined.

[0169] The channel from the base station to the l-th STAR-RIS and the channel from the l-th STAR-RIS to the k-th user are respectively used as... and This indicates that all channels simultaneously follow a narrowband quasi-static fading mode. Therefore, the channel from the base station to the first STAR-RIS, and the channel from the l-th STAR-RIS to the k-th user, can be simulated as a Ricean fading model channel, comprising both line-of-sight and non-line-of-sight transmission components.

[0170]

[0171]

[0172] Among them, and d RU，kThis represents the distance between the BS and the l-th STAR-RIS, and the distance between the l-th STAR-RIS and the k-th user, α. BR and α RU K represents the corresponding path loss exponent. BR and K RU Rho0 represents the Rice factor, rho0 represents the path loss at a reference distance of 1 meter, and F represents the path loss at a reference distance of 1 meter. Los and It is a deterministic line-of-sight component, F NLoS and It is a random non-line-of-sight component, modeled as Rayleigh fading. Among them, And the guiding vector and They are defined as follows:

[0173]

[0174]

[0175] Similarly, for the channel Where the guiding vector a U (θ AoA ) and a RU (θ AoD It can be defined as:

[0176]

[0177]

[0178] Among them, M and N a and N t These are the number of patch antennas on the STAR-RIS side, the number of base station antennas, and the number of user receiving antennas, respectively. and θ AoA These are the angles of arrival from BS to STAR-RIS and from STAR-RIS to the user. Furthermore, and θ AoD It refers to the angles away from BS and STAR-RIS. d is the antenna spacing, and v is the wavelength.

[0179] In practical scenarios, considering that the locations of the BS and STAR-RIS are fixed, and that for any user, the channel from the BS to all STAR-RIS is the same, we can use... Let represent the channels from BS to all STAR-RIS. Similarly, the channels from all STAR-RIS to user k can be equivalent to .

[0180] use and Let represent the symbol vector and active beamforming matrix of user k on the BS. The signal transmitted from the BS can be represented as:

[0181]

[0182] Therefore, the signal received by user k can be represented as:

[0183]

[0184] in It is the noise vector of the k-th user, and its value follows... in, This indicates that the expression follows a pattern with a mean of 0 and a variance of . The complex normal distribution is given by I, where I represents the identity matrix. It is the noise power of the kth user;

[0185] Define here The original expression is simplified. Now, the data rate for user k can be expressed as:

[0186]

[0187] in, The interference plus noise covariance matrix of the k-th user can be written as:

[0188]

[0189] Where I represents the identity matrix.

[0190] Optimization problem modeling:

[0191] The optimization problem is defined by the following optimization model P1:

[0192]

[0193]

[0194]

[0195]

[0196]

[0197]

[0198] Wherein, objective function The sum of communication data rates for all users. Representation matrix The m-th diagonal element. Constraint C1 is the constraint on the maximum transmit power on the base station side, Pmax The maximum transmit power that the base station can provide is represented; constraint C2 is the equivalent TRC matrix composed of multiple STAR-RIS affecting the user side, which represents the constraint relationship between the user and the STAR-RIS; constraint C3 is the constraint on the value of the transmission and reflection coefficient of each STAR-RIS; constraint C4 is the range constraint on the transmission and reflection coefficient and phase offset of the STAR-RIS operating in energy split mode; constraint C5 is the energy conservation constraint for each STAR-RIS.

[0199] The optimization problem proposed in this invention is a non-convex problem involving multiple coupled STAR-RIS systems. To solve this non-convex problem, the weighted minimum mean square error (WMMSE) algorithm is first introduced to transform the original optimization problem P1 into an equivalent convex form. Secondly, this optimization problem is further divided into two sub-problems: the base station beamforming optimization problem and the TRC coefficient matrix optimization problem for each STAR-RIS system.

[0200] Step 1: First, we introduce a linear decoding matrix, thus estimating the signal vector for each user. It can be represented as:

[0201]

[0202] in, It is the linear decoding matrix introduced by user k. Due to the signal vector s k and noise n k Since they are independent, we can derive the mean square error matrix for user k as follows:

[0203]

[0204] in, This represents the mean of the symbol vector and the noise, s. k Represents the symbol vector transmitted by the base station;

[0205] Based on this, we introduce the auxiliary variable Z. k ≥0, the optimization problem P1 is rewritten in the following form:

[0206]

[0207]

[0208]

[0209]

[0210]

[0211]

[0212] C6:Z k ≥0

[0213] Among them, f k (V k Q k U k Z k It can be determined by the following expression:

[0214] f k (V k Q k U k Z k )=log|Z k |-Tr(Z k E k )+d k .

[0215] Unlike the original objective function, P2 introduces more optimization variables, making the original problem easier to solve. For a given TRC matrix Q... k In other words, when the other two optimization matrices are fixed, f k (V k Q k U k Z k For each set of optimization matrices, it is a concave function. Based on this, a block coordinate descent algorithm is used to alternately optimize the various variables. The specific steps include:

[0216] First, with a fixed V k Q k Z k In the case of solving U k The optimal solution. At this point, f k (V k Q k U k Z k ) can be seen as only related to U k The relevant functions. Therefore, for f k (V k Q k U k Z k (relative to U) k Find its first derivative and obtain the optimal U by finding the extreme points. k :

[0217]

[0218] Secondly, with a fixed V k Q k U k In the case of solving Z k The optimal solution. And the solution for U. k The approach is consistent, and we also have Z k The optimal Z is obtained by finding the first derivative and then finding the extreme points. k The value is:

[0219]

[0220] Then, fix Q. k U k Z k And solve V k The optimal solution;

[0221] Finally, fix V k U k Z k And solve Q k The optimal solution;

[0222] Step 2: Optimization of Base Station Beamforming Problem

[0223] Based on the optimization problem P2, with Q fixed... k U k Z k And solve V k The optimal solution. Considering that the main problem addressed in this step is the beamforming matrix V... k The optimization problem, and the objective function in P2 at this moment with respect to V. k It does not possess perfect concavity and convexity, therefore the objective function of P2 needs to be transformed, taking into account the mean square error E introduced in the WMMSE algorithm. k Substituting these terms into the objective function of P2, and ignoring the constant terms that do not affect the concavity or convexity of the function, the original objective function can be equivalently replaced with the following form:

[0224]

[0225] Introducing auxiliary variables and Based on this, the optimization problem P3 for this optimization variable can be obtained as follows:

[0226]

[0227]

[0228] Here, constraint C1 represents the maximum transmit power constraint of the base station. Optimization problem P3 is a second-order cone programming problem. Considering the high time complexity of computing second-order cone programming problems, a low-complexity method is proposed to solve the problem by using the Lagrange dual algorithm to find the approximately optimal closed-form solution.

[0229] The Lagrangian cost function for optimization problem P3 can be expressed as:

[0230]

[0231] Here, λ > 0 is the Lagrangian dual variable relating to the maximum transmit power of the base station. This is achieved by considering the cost function with respect to V. k By finding the first derivative and the extrema, we can obtain the closed-form solution of the optimal solution for the beamforming matrix as follows:

[0232]

[0233] in, This represents finding the pseudo-inverse of a matrix. This is combined with constraints on the base station's transmit power. The complementary relaxation condition, λ, can be solved using the following expression:

[0234]

[0235] The optimal solution for λ can be found using a binary search algorithm, as follows:

[0236] First, if the auxiliary variable matrix A is a full-rank matrix, then it can be proven that matrix A is a positive definite matrix. This can be achieved through singular value decomposition, where A = SΞS. H ,in Ξ is a diagonal matrix where all diagonal elements are positive. Based on the form of the complementary relaxation condition, it is defined as follows:

[0237]

[0238] in, [Ω] i，i and [Ξ] i，i Let i and represent the i-th diagonal elements of matrices Ω and Ξ, respectively.

[0239] It can be proven that g(λ) is a monotonically decreasing function. Therefore, if g(0) ≤ P max The optimal beamforming matrix can be obtained through We obtain the result. Otherwise, we can use a binary search-based algorithm to find the solution to the following equation, thus obtaining the optimal λ:

[0240]

[0241] Due to the monotonicity of g(λ) and The equation must have a solution, which we represent as λ. ★ If we need to find the upper bound of λ using a binary search method, and Ξ is a diagonal matrix with positive diagonal elements, then we have:

[0242]

[0243] Based on this, we can deduce that the upper bound of λ is:

[0244]

[0245] At this point, setting the lower bound of λ to a number close to 0 allows us to find the optimal λ using a binary search query.

[0246] If A is a low-rank matrix, then g(λ) = Tr((Ξ+λI) cannot be obtained through singular value decomposition. -2 In this case, first check if λ = 0 is the optimal solution; if g(0) < P max Then the optimal beamforming matrix is ​​given by Give;

[0247] Otherwise, by defining the rank of A as r A =rank(A)<N a Using singular value decomposition, we can obtain:

[0248] A = [S1, S2]Ξ[S1, S2] H

[0249] Wherein, S1 contains the first r A Each and r A S2 contains the singular vectors corresponding to the last N positive eigenvalues. a -r A One and N a -r A The singular vectors corresponding to zero eigenvalues. Where Ξ1 is a group containing the first r A A diagonal matrix of positive eigenvalues. Define S = [S1, S2] to obtain:

[0250]

[0251] The case where Ω is full rank is consistent with the case where A is full rank. Furthermore, g(λ) is a monotonically decreasing function when λ > 0, and the optimal λ can be obtained using a bisection method. The upper bound of λ is... The lower bound is set to a small positive value;

[0252] Step 3: Optimize the TRC matrix for each STAR-RIS

[0253] Based on problem P2, with a fixed beamforming matrix V k and auxiliary variable U k Z k Considering the equivalent matrix of the transmission and reflection smart surface for user k, the problem can be described in the form of P4:

[0254]

[0255]

[0256]

[0257]

[0258]

[0259] TRC matrix Q k Passive beamforming was performed on the signal during transmission. To address this non-convexity issue, it will be combined with Q... k Separate the irrelevant terms and only consider Q. k Related content. Substituting into the objective function, we get:

[0260]

[0261]

[0262] By performing an equivalent substitution, the two expressions can be written as:

[0263]

[0264]

[0265] in, as well as

[0266]

[0267] Therefore, optimization problem P4 can be equivalently rewritten as P5:

[0268]

[0269] stC1:q k =diag(Q k ),

[0270]

[0271]

[0272]

[0273] Constraint C1 represents the relationship between the TRC matrix of each STAR-RIS and the user. The main difficulty of problem P5 lies in C4, which shows that the transmission and reflection coefficients are coupled. Unlike the case of a single STAR-RIS, resource allocation involving multiple STAR-RIS is more challenging. This is because each user may be located on the reflection side of one STAR-RIS but on the transmission side of another. Depending on their location, the TRC matrix Q of different users will vary. k It could also be coupled;

[0274] Introduce an auxiliary variable ζ, where ζ∈{t, r} and That is, when ξ = r, ζ = t; otherwise, ζ = r. We define a matrix... Let represent the TRC matrix with state ζ. Definition Therefore, we have This is done in order to reconstruct constraint C4 into a solvable form;

[0275] Based on the above analysis, we introduce Therefore, we can use diag(Θ) k Let ) represent the TRC matrix of user k, and This indicates that it is related to diag(Θ). k The opposite state. According to constraint C4, we can restate it as follows: This allows us to transform problem P5 into P6:

[0276]

[0277]

[0278]

[0279] For the constraint C1, which is still nonconvex, we introduce the lemma:

[0280] For any condition satisfying W = ww H The matrix can be equivalently replaced by:

[0281]

[0282] Based on the above lemma, optimization problem P6 can be transformed into P7:

[0283]

[0284]

[0285]

[0286]

[0287]

[0288]

[0289] in, It is an auxiliary variable. Let represent an N×N Hermitian matrix. For the still non-convex constraints C3 and C5, we relax these constraints using a continuous convex approximation algorithm, obtaining:

[0290]

[0291]

[0292] At this point, optimization problem P7 can be transformed into P8:

[0293]

[0294]

[0295]

[0296]

[0297]

[0298]

[0299] Problem P8 is a constraint-based concave-convex programming problem that can be solved using convex optimization packages such as CVX.

[0300] See Figure 2 In a specific embodiment of the present invention, the steps are as follows:

[0301] 1) The optimization problem is modeled as a user communication rate maximization problem. The user communication rate is maximized by optimizing the base station beamforming matrix and the TRC matrix of each STAR-RIS, while the base station transmit power is constrained and the energy of the STAR-RIS transmission and reflection coefficients is conserved.

[0302] 2) Optimize the problem by introducing the WMMSE algorithm to transform the original optimization problem into an optimization problem that is easier to optimize.

[0303] 3) Decompose the optimization problem into two sub-optimization problems: base station beamforming matrix optimization and TRC matrix optimization for each STAR-RIS.

[0304] 4) Solving the base station beamforming matrix optimization: The high computational complexity of the transformed second-order cone programming problem is reduced by using the Lagrange duality algorithm, and the closed-form solution is derived. Then, the optimal base station beamforming is calculated by complementary relaxation conditions and the bisection method.

[0305] 5) Solve the optimization problem of transmission and reflection coefficients of multiple synchronous transmission and reflection smart surfaces: By introducing auxiliary variables, decouple the same TRC matrix problem of multiple STAR-RIS among users, and transform the problem into the form of CCCP problem through equivalent transformation and solve it.

[0306] 6) Finally, an optimization algorithm for the resource allocation problem in a MIMO communication network based on multiple synchronous transmission-reflection smart surfaces is obtained.

[0307] Simulation results demonstrate that, compared to other algorithms, the proposed algorithm improves the sum of user communication rates and is suitable for scenarios with a large number of users.

[0308] Table 1 presents the system model simulation parameters for this research problem, including the configuration information of the base station, users, and STAR-RIS, as well as the channel parameters.

[0309] Table 1 Simulation Model Parameter Variables Table

[0310]

[0311]

[0312] like Figure 3 As shown, the proposed method converges under different numbers of transmit antennas, receive antennas, and STAR-RIS patch antennas, and these convergences affect the sum of the communication rates of the system users. Higher numbers of transmit antennas, receive antennas, and STAR-RIS patch antennas can effectively improve the system's channel environment, thereby increasing the sum of the system's communication rates.

[0313] like Figure 4 As shown, under different STAR-RIS operating modes and different comparative environments, the method of this invention can maximize the sum of user communication rates of the system by optimizing the beamforming matrix of the base station and the TRC of STAR-RIS under the same conditions.

[0314] In its specific implementation, this application provides a computer storage medium and a corresponding data processing unit. The computer storage medium is capable of storing a computer program, which, when executed by the data processing unit, can run the invention's content regarding an optimization method for resource allocation in a multi-intelligent element surface-assisted MIMO network, as well as some or all of the steps in various embodiments. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0315] Those skilled in the art will clearly understand that the technical solutions in the embodiments of the present invention can be implemented using computer programs and their corresponding general-purpose hardware platforms. Based on this understanding, the technical solutions in the embodiments of the present invention, or the parts that contribute to the prior art, can be embodied in the form of computer programs, i.e., software products. These computer program software products can be stored in a storage medium and include several instructions to cause a device containing a data processing unit (which may be a personal computer, server, microcontroller, MUU, or network device, etc.) to execute the methods described in various embodiments or certain parts of the embodiments of the present invention.

[0316] This invention provides an idea and method for optimizing resource allocation in multi-element surface-assisted MIMO networks. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment of the invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

Claims

1. An optimization method for resource allocation in a multi-smart element surface-assisted MIMO network, characterized in that, Includes the following steps: Step 1: Model the MIMO communication network resource allocation optimization problem as a problem of maximizing the communication rate of all users, that is, the resource allocation optimization objective is to maximize the communication rate of all users in the MIMO communication network; Step 2: Reconstruct and transform the optimization problem described in Step 1; Step 3: Decompose the optimization problem after reconstruction and transformation in Step 2 into two sub-optimization problems: the base station beamforming optimization problem and the TRC matrix optimization problem of the transmission and reflection coefficients of multiple smart element surfaces STAR-RIS. Step 4: Solve the base station beamforming optimization problem; Step 5: Solve the optimization problem of the transmission and reflection coefficient TRC matrix for multiple STAR-RIS; Step 6: Based on the solutions obtained in Steps 4 and 5, the MIMO communication network resource allocation optimization is finally completed; Specifically, step 1, which involves modeling the MIMO communication network resource allocation optimization problem as a problem of maximizing the communication rate of all users, includes: Step 1-1: Establish multiple STAR-RIS-assisted MIMO communication models; Step 1-2: Model the optimization problem: maximize the sum of communication rates for all users by optimizing the beamforming matrix and transmission / reflection matrix coefficients, while ensuring that the maximum transmit power constraint of the base station and the energy conservation constraint of STAR-RIS are met. Specifically, the establishment of multiple STAR-RIS-assisted MIMO communication models mentioned in step 1-1 includes: The multiple STAR-RIS-assisted MIMO communication models include: 1 base station, One ground user, There are 10 STAR-RIS, where each STAR-RIS is composed of 10 STAR-RIS. The STAR-RIS collaborative base station, consisting of patch antennas, serves users. The STAR-RIS operating mode is preset, and the transmission and reflection coefficient (TRC) of each STAR-RIS patch antenna is expressed as: ； ； in, and Indicates the first The first STAR-RIS The transmission coefficient and transmission phase offset angle of each antenna. and Indicates the first The first STAR-RIS The reflection coefficient and reflection phase offset angle of each antenna, and satisfying the following conditions: , Indicates the transmission phase. Indicates the reflection phase; For each STAR-RIS, its TRC matrix It is independent, represented as: ； in, This indicates that the user is in the first position. The transmission or reflection side of a STAR-RIS The dimension is The complex matrix will be used by the user Equivalent TRC matrix Represented as: ； Among them, symbols This means taking the diagonal elements of a diagonal matrix and rearranging them to form a new diagonal matrix; From base station to the The channel of the first STAR-RIS and from the first The first STAR-RIS to the 1st Each user's channel is used separately and It means that, among them, The dimension is Complex matrix, The dimension is Complex matrix, This refers to the line-of-sight transmission section. This refers to the non-line-of-sight transmission portion, as detailed below: ； ； in, This represents the path loss when the reference distance is 1 meter. Indicates the base station and the first The distance between STAR-RIS Indicates the first The first STAR-RIS and the first The distance between users and This represents the corresponding path loss index. and Represents Rice factor, and It is a deterministic line-of-sight component. and These are random non-line-of-sight components, where, And the guiding vector and They are defined as follows: ； ； Similarly, for deterministic line-of-sight components , where the guiding vector and Defined as: ； ； in, , and These are the number of patch antennas on the STAR-RIS side, the number of base station antennas, and the number of user receiving antennas, respectively. and These are the angles of arrival from the base station to STAR-RIS and from STAR-RIS to the user. and It's the angle from away from the base station and away from STAR-RIS. It is the antenna spacing. It is the wavelength; use This represents the channels from the base station to all STAR-RIS, where, Indicates from the base station to the... One STAR-RIS channel, The dimension is Complex matrices; from all STAR-RIS to users The channel is equivalent to ,in, Indicates from the first The first STAR-RIS to the 1st Channels for individual users The dimension is Complex matrix; use and To represent users on the base station The symbol vector and the active beamforming matrix, where, The dimension is Complex column vectors, The dimension is Complex matrix; signal transmitted from base station Represented as: ； user Received signal Represented as: ； in, It is the first The noise vector of each user, whose value follows... ,in, This indicates that the expression follows a pattern with a mean of 0 and a variance of . The complex normal distribution, Represents the identity matrix. It is the first Noise power per user; This is a useful signal; Interference between users; Define intermediate quantities ,user Data rate Represented as: ； in, The interference plus noise covariance matrix of the k-th user is expressed as follows: ； in, Represents the identity matrix.

2. The optimization method for resource allocation in a multi-element surface-assisted MIMO network according to claim 1, characterized in that, The optimization problem described in steps 1-2 is modeled as follows: the optimization problem is defined as the following optimization model P1: ； ； ； ； ； ； Wherein, the objective function is: The sum of communication data rates for all users. Representation matrix The One diagonal element; Constraint C1 is the constraint on the maximum transmit power on the base station side. This indicates the maximum transmission power that the base station can provide. This indicates finding the trace of a matrix; Constraint C2 is the equivalent TRC matrix composed of multiple STAR-RIS influences on the user side. This constraint represents the constraint relationship between the user and STAR-RIS. Constraint C3 is a constraint on the value of the transmission and reflection coefficients for each STAR-RIS; Constraint C4 is a range constraint on the transmission and reflection coefficients and phase offset values ​​of STAR-RIS operating in energy splitting mode. Constraint C5 is an energy conservation constraint for each STAR-RIS.

3. The optimization method for resource allocation in a multi-element surface-assisted MIMO network according to claim 2, characterized in that, Step 2 involves reconstructing and transforming the optimization problem described in Step 1, specifically by introducing the Weighted Minimum Mean Square Error (WMMSE) method to convert the optimization model P1 into an equivalent convex optimization model. The specific method is as follows: Step 2-1: Introduce a linear decoding matrix, and the estimated signal vector for each user. Represented as: ； in, It is the introduced user The linear decoding matrix yields the user's... Mean square error matrix for: ； in, This means taking the mean of the symbol vector and the noise. Represents the symbol vector transmitted by the base station; Step 2-2, introduce auxiliary variables The optimization model P1 is reconstructed into an optimization model. : ； ； ； ； ； ； ； in, Determined by the following expression: ； in, As an auxiliary variable, This refers to the constant term generated during the transformation process.

4. The optimization method for resource allocation in a multi-element surface-assisted MIMO network according to claim 3, characterized in that, The base station beamforming optimization problem described in step 3 refers to the problem of optimizing the beamforming matrix. The optimization problem P3 is as follows: ； ； in, The matrix represents the real part of a complex number. sum matrix These are auxiliary variables introduced during the transformation of the objective function; Constraint C1 represents the maximum transmit power constraint of the base station; The optimization problem of the transmission and reflection coefficient TRC matrix of multiple STAR-RIS mentioned in step 3 is based on the optimization model P2, with a fixed beamforming matrix. and auxiliary variables , using users The equivalent matrix of the transmission and reflection smart surface is obtained, and the optimization problem P4 of the transmission and reflection coefficient TRC matrix of multiple STAR-RIS is as follows: ； ； ； ； ； in, The matrix represents the real part of a complex number. sum matrix These are auxiliary variables introduced during the transformation of the objective function.

5. The optimization method for resource allocation in a multi-element surface-assisted MIMO network according to claim 4, characterized in that, Step 4 describes solving the base station beamforming optimization problem, which involves using the Lagrange dual algorithm to solve the closed-form solution of the beamforming matrix. Specifically, this includes: Optimize the Lagrangian cost function of problem P3 Represented as: ； in, It is the Lagrange dual variable related to the maximum transmit power of the base station; by examining this cost function with respect to... By finding the first derivative and the extrema, we obtain the closed-form solution of the optimal solution for the beamforming matrix. for: ； in, This indicates finding the pseudo-inverse of a matrix; Taking into account the constraints on base station transmit power Complementary relaxation conditions, The value of is determined by the following expression: ； The optimal solution is obtained by binary search algorithm.

6. The optimization method for resource allocation in a multi-element surface-assisted MIMO network according to claim 5, characterized in that, Step 5 describes solving the TRC matrix optimization problem for multiple STAR-RIS transmission and reflection coefficients, which involves using a constrained concave-convex programming algorithm to optimize the TRC matrix of multiple STAR-RIS. The specific method is as follows: With TRC matrix Separate the irrelevant terms and... Substituting the objective function, optimization problem P4 is equivalently rewritten as optimization problem P5: ； ； ； ； ； in, , and These are auxiliary variables used when transforming the objective function. Indicates the matrix The diagonal elements form a column vector; constraint C1 represents the relationship between the TRC matrix of each STAR-RIS and the user; For the non-convex constraint C4, an auxiliary variable is introduced. ,in and That is, when hour, ;otherwise, Define matrix To represent having a state The TRC matrix; define the user's inverse TRC matrix. To obtain the user's inverse TRC vector At this point, constraint C4 is reformed into a solvable form; thus, optimization problem P5 is transformed into optimization problem P6: ； ； ； in, Used to represent users The TRC coefficient, Used to indicate and user TRC coefficients with opposite states The dimension is A column vector in which every element is 1; For constraint C1, the lemma is introduced to transform optimization problem P6 into optimization problem P7: ； ； ； ； ； ； in, It is an auxiliary variable. Representing a dimension as Hermitian matrix; For constraints C3 and C5, the constraints are relaxed using a continuous convex approximation algorithm, transforming optimization problem P7 into optimization problem P8: ； ； ； ； ； ； in, and This indicates that the continuous convex approximation algorithm is used in the first... The value at the next iteration. Thus, optimization problem P8 is a constrained concave-convex programming problem, which is solved using a convex optimization algorithm.

7. The optimization method for resource allocation in a multi-element surface-assisted MIMO network according to claim 6, characterized in that, Step 6, which involves optimizing the MIMO communication network resource allocation, specifically includes: alternately optimizing auxiliary variables. Passive beamforming matrix and equivalent TRC matrix Until convergence, the optimal beamforming matrix is ​​finally obtained. Equivalent matrix of transmission and reflection coefficients The above matrix is ​​used to optimize the allocation of MIMO communication network resources, and the maximum downlink rate of all users at this time is calculated, which is the optimized MIMO communication network resource.

8. The optimization method for resource allocation in a multi-element surface-assisted MIMO network according to claim 7, characterized in that, The pre-setting of the STAR-RIS operating mode mentioned in step 1-1 is to set the STAR-RIS operating mode to energy splitting mode.

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