STAR-RIS assisted cellular removal large-scale MIMO beam forming method and system based on sequence rank-one constraint relaxation, and storage medium

Abstract

The invention provides an STAR-RIS assisted cellular-removal large-scale MIMO beam forming method and system based on sequence rank-one constraint relaxation, and a storage medium. The method comprises the following steps: step 1, utilizing a fractional programming method to carry out beam forming; an original non-convex problem is decoupled into an active beam forming design of an access point and a passive beam forming design of a simultaneous transmission and reflection reconfigurable intelligent surface, and the active beam forming design and the passive beam forming design are alternately optimized; and 2, for a matrix rank-one constraint existing in the passive beam forming design, gradually relaxing the constraint through a relaxation algorithm based on a sequence rank-one constraint, finding a local optimal solution meeting a constraint relaxation problem, and gradually tightening a feasible solution until the matrix rank is a one solution. The method disclosed by the invention has the beneficial effects that the method disclosed by the invention has the same performance as a traditional penalty operator algorithm under the condition of not updating a penalty term, the operation complexity is lower, and the reliability is higher.

Description

Technical Field

[0001] This invention relates to the field of communication technology, and in particular to a STAR-RIS-assisted decellularized large-scale MIMO beamforming method, system, and storage medium based on sequence rank-one constraint relaxation. Background Technology

[0002] 1. Current architecture of simultaneous transmission and reflection reconfigurable smart surface-assisted decellularized large-scale MIMO system. Cellular massive multiple-input multiple-output (CF-mMIMO) systems employ a user-centric network architecture, allowing multiple neighboring access points (APs) to collaboratively serve users. This effectively avoids the severe inter-cell interference problems of traditional cellular networks, making it one of the key technologies for 6th generation mobile networks (6G). However, the large-scale deployment of APs inevitably leads to a surge in system power consumption and backhaul overhead, reducing energy efficiency. To alleviate this contradiction, Simultaneously Transmitting and Reflecting Reconfigurable Intelligent Surface (STAR-RIS), another key 6G technology, has been introduced into CF-mMIMO systems. Unlike traditional amplified repeaters, STAR-RIS requires no signal transmission or reception capabilities, relying solely on reflected incident signals for communication, thus offering significant low-power advantages. Compared to Reconfigurable Intelligence Surfaces (RIS), STAR-RIS overcomes the limitation of traditional RIS signal reflection covering only 180°, achieving 360° coverage without requiring the transmitter and receiver to be on the same side of the reconfigurable intelligence surface simultaneously. STAR-RIS-assisted CF-mMIMO systems not only improve system energy efficiency and reduce power consumption but also extend coverage, providing reliable communication for users in signal "shadow areas."

[0003] 2. Analysis of beamforming algorithms for various simultaneous transmission and reflection reconfigurable smart surface-assisted decellularized large-scale MIMO systems. In CF-mMIMO systems, designing the phase shift parameters of STAR-RIS to maximize the objective function, WSR, is a key issue. Since the constraints of the optimization problem include non-convex signal-to-interference-plus-noise ratio (SINR) expressions and unit-mode phase constraint expressions, obtaining the optimal solution is difficult and the solution complexity is high. Currently, the main beamforming algorithm for STAR-RIS is the penalty operator method. This method first transforms the original non-convex optimization problem into a semi-deterministic programming problem by introducing auxiliary variables. For non-convex constraints with a rank of one in the phase shift parameter matrix, the algorithm first converts the rank-one constraints into non-constitutive constraints where the nuclear norm and spectral norm are equal. Then, it uses a continuous convex approximation method to convert the constraints into convex constraints. Finally, the convex constraints with equal nuclear and spectral norms, processed by the continuous convex approximation, are moved into the objective function, and a penalty operator with exponentially increasing penalty strength is introduced to force the nuclear and spectral norms to be equal. The transformed expression is a convex optimization and can be solved using a traditional convex optimization solver. Some beamforming algorithms, when dealing with matrix rank-one constraints, first relax the rank-one constraints to obtain a suboptimal solution, and then reconstruct the solution satisfying the rank-one constraints from the suboptimal solution, such as the positive semidefinite relaxation-Gaussian randomization algorithm. This algorithm introduces a very large error when reconstructing the solution satisfying the matrix rank-one constraints from the suboptimal solution.

[0004] The shortcomings of existing simultaneous transmission and reflection reconfigurable smart surface-assisted decellularized large-scale MIMO systems; Many STAR-RIS passive beamforming optimization algorithms first transform the phase shift matrix into a vector and then multiply it by its transpose, which leads to an additional rank-one non-convex constraint. The following two main methods are commonly used to solve rank-one non-convex constraints: 1) Abandoning the rank-one constraint to find suboptimal solutions. One approach is to completely ignore the rank-one constraint and relax the non-convex equality into an inequality, transforming it into a convex inequality constraint, such as algorithms based on Quadratic Constrained Quadratic Programming (QCQP) transformations. Another algorithm recovers solutions satisfying the rank-one constraint from the relaxation problem, such as using the Semidefinite Relaxation-Gaussian Randomness (SDR-Gaussian Randomness) method. However, a significant problem is that this method of relaxing the original rank-one constraint yields feasible solutions with excessively high rank, leading to excessive bias in recovering feasible solutions satisfying the rank-one constraint from feasible solutions. 2) Adding additional constraints to minimize the rank of the matrix. Adding extra constraints to the original problem can minimize the rank of the feasible solution, such as using a penalty operator algorithm followed by continuous convex approximation. However, the large number of access users and STAR-RIS units results in exceptionally high channel dimensionality, leading to extremely high algorithm complexity. Traditional penalty operator-based algorithms may not be suitable for large-scale STAR-RIS-assisted CF-mMIMO systems. Furthermore, the penalty operator algorithm is highly dependent on the selection of penalty parameters; different initial parameters can significantly affect the final performance. Therefore, developing a low-complexity and high-reliability algorithm for large-scale STAR-RIS-assisted CF-mMIMO systems is a significant challenge. Summary of the Invention

[0005] To address the problems in the prior art, this invention provides a STAR-RIS-assisted decellularized large-scale MIMO beamforming method based on sequence rank-constraint relaxation, comprising: Step 1: Using fractional programming, the original non-convex problem is decoupled into active beamforming design at the access point and passive beamforming design of the simultaneously transmissive and reflective reconfigurable smart surface, and these are optimized alternately. Step 2: For the matrix rank-one constraint in passive beamforming design, the constraint is gradually relaxed by using a sequential rank-one constraint relaxation algorithm to find a local optimal solution that satisfies the constraint relaxation problem, and the feasible solution is gradually tightened to the matrix rank-one solution.

[0006] As a further improvement of the present invention, step 1 includes: Step S1: With the goal of maximizing the weighted sum rate of all users, the weighted sum rate problem for all users is expressed as: (Formula 7)

[0007] in It is the joint matrix of active beamforming vectors, constrained. Set a maximum limit on the total transmit power budget for each access point to constrain [the system / entity]. and constraints The amplitude and phase of the coefficients of the reconfigurable smart surface matrix, which can be simultaneously transmitted and reflected, are limited to a feasible range. This represents the passive beamforming matrix. This represents the weighted sum rate of all users. express One user, i belong t and r , This represents the total number of users on the transmission surface. This represents the total number of users on the reflective surface; Indicates the first There are 10 users, distributed on both sides of the simultaneously transmissive and reflective reconfigurable smart surface. i belong t and r When it belongs to i = t This represents the user on the transmissive side. i = r Representing the user on the reflective side, On behalf of users The weight, Indicates the first Signal-to-interference-plus-noise ratio per user Indicates the active beamforming vector. This indicates the maximum power at each access point. This represents the conjugate transpose of matrix w. Indicates the first One access point Represents the set of indexes for access points. The total number of access points. Indicates the first r The first simultaneous transmission and reflection reconfigurable smart surface n One element, Indicates the amplitude of the transmission surface. Indicates the amplitude of the reflecting surface. n Represents the first reconstructible smart surface by simultaneous transmission and reflection. n One element, This represents the set of units on a simultaneously deployed, transmissive, reflective, reconfigurable smart surface. Indicates the first Simultaneous transmission and reflection can reconstruct smart surfaces This represents the index set of simultaneously transmitted and reflected reconstructable smart surfaces. This indicates the number of reconfigurable smart surfaces that can be simultaneously transmitted and reflected; Step S2: Decouple P1 using a fractional programming algorithm and introduce artificial variables. ,and This leads to the decoupling subproblems: (Formula 8), in for: (Formula 9), in, Indicates the first The conjugate transpose of the user's active beamforming vector Representing the User's channel, i belong t and r , i = t Users representing the transmission surface i = r The user represents the reflective surface, and H represents the conjugate transpose. Represents a function; Introducing artificial variables and Formula 9 becomes: (Formula 10), in, Artificial variables, This indicates the total number of users on the transmission surface. This indicates the total number of users on the reflective surface. yes and A collection of [items / items].

[0008] The beneficial effects of this invention are: the method disclosed in this invention has the same performance as the traditional penalty operator algorithm without updating the penalty term, and not only has lower computational complexity, but also higher reliability. Attached Figure Description

[0009] Figure 1 This is the STAR-RIS-assisted CF-mMIMO system model of the present invention; Figure 2 This is a schematic diagram of the user summation rate vs. the number of iterations in this invention; Figure 3This is a schematic diagram of the user combined rate vs. the transmission power at the AP in this invention; Figure 4 This is a schematic diagram showing the number of components at the user combined rate vs. STAR-RIS in this invention. Detailed Implementation

[0010] This invention explores a more general scenario for a large-scale STAR-RIS-assisted CF-mMIMO system, aiming to maximize the weighted sum rate (WSR) by jointly designing active beamforming at the access points and passive beamforming on the phase shift coefficient matrix of STAR-RIS. This joint design must satisfy the transmit power limits of each access point (AP) and the energy conservation constraints of the phase shift coefficient matrix on STAR-RIS. For this system, this invention proposes a novel low-complexity beamforming algorithm to solve the corresponding optimization problem, with the goal of maximizing the weighted sum rate (WSR).

[0011] This invention presents a STAR-RIS-assisted decellularized large-scale MIMO beamforming method based on sequential rank-one constraint relaxation. First, it utilizes fractional programming (FP) to decouple the original non-convex problem into two sub-problems: active beamforming design (AP) and passive beamforming design (STAR-RIS), and then alternately optimizes them. Addressing the matrix rank-one constraint in passive beamforming design, this invention proposes a novel low-complexity algorithm based on Sequential Rank-One Constraint Relaxation (SROCR). Unlike traditional methods that completely relax this constraint, the proposed algorithm gradually relaxes the constraint, finding a general local optimum that satisfies the matrix rank-one constraint, and progressively narrowing the feasible solution to a matrix rank-one solution. This method eliminates the need to pre-set initial penalty parameters that could severely affect the final solution.

[0012] 1. Simultaneous transmission and reflection reconfigurable smart surface-assisted decellularized large-scale MIMO system model This invention considers a multi-STAR-RIS assisted CF-mMIMO system, such as Figure 1 As shown. The system comprises a large number of access points (APs), which are connected to a CPU used for network backhaul. Users located on the STAR-RIS transmission side and reflection side are respectively referred to as… Users and Users. They can be defined as... and Specifically, the system includes One AP, One STAR-RIS, and Individual users. (This appears to be a fragment of a larger text, possibly related to a user or a command.) and These represent the index sets for AP and STAR-RIS, respectively. The AP and the first Each user is equipped with M antennas and U antennas respectively, while the first... Each STAR-RIS contains One unit. Let This represents the set of all units deployed on the STAR-RIS surface. Let... Indicates the first The signal symbols of each user, and satisfying The symbol Firstly in Each AP uses active beamforming vector Precoding is performed, therefore in the first... The precoded signal of each AP It can be represented as: (Formula 1), STAR-RIS is a planar array composed of a large number of reconfigurable passive cells. Each of these cells is connected by multiple controllable photodiodes. By applying different bias voltages to the photodiodes through a DC feed line, the photodiodes can be switched to an "on" or "off" state. To simplify the representation of STAR-RIS, this invention sets the phase shift parameters of STAR-RIS to a continuous case. The model of STAR-RIS can be represented as: (Formula 2), The amplitudes at the transmitting and reflecting ends satisfy: Phase shift satisfies .in Indicates the transpose operation; This is the conjugate transpose operation; Indicates when When the vector is a vector, transform the vector into a diagonal matrix, or when When the matrix is ​​in the form of a vector, extract the elements on the diagonal and transform them into a vector.

[0013] STAR-RIS-assisted CF-mMIMO systems utilize STAR-RIS components to establish combined communication paths between the access point (AP) and the user. Specifically, each AP-to-user channel comprises two links: a direct link and an access point-reflector-user cascaded indirect link. Each indirect link can be further decomposed into an access point-reflector link and a reflector-user link. The AP and the first A combined channel between multiple users can be written as: (Formula 3), in Each represents the first. AP to the first The link of the user, the first AP to the first The first STAR-RIS link, the... The first STAR-RIS to the 1st The connection of each user. The received signal can be represented as: (Formula 4), in ; ; ; . This represents Gaussian white noise, with a mean of 0 and a variance expressed as... . No. The signal-to-interference-plus-noise ratio (SIR) of an individual user can be expressed as: (Formula 5), Meanwhile, the WSR of all users can be represented as: (Formula 6), in On behalf of users The weight.

[0014] 2. Maximizing the WSR in a Simultaneously Transmittance-Reflectance Reconfigurable Smart Surface-Assisted Decellularized Massive MIMO System This invention aims to maximize WSR (Wait and See) and the WSR problem for all users can be expressed as: (Formula 7), in It is the joint matrix of active beamforming vectors. Constraints Set a maximum limit on the total transmit power budget for each AP. Constraint and Limit the amplitude and phase adjustment of the STAR-RIS matrix coefficients to an achievable range. This represents the passive beamforming matrix. This represents the weighted sum rate of all users. express One user, i belong t and r , This represents the total number of users on the transmission surface. This represents the total number of users on the reflective surface; Indicates the first There are [number] users, distributed on both sides of STAR-RIS. i belong t and r When it belongs to i = t This represents the user on the transmissive side. i = r Representing the user on the reflective side, On behalf of users The weight, Indicates the first Signal-to-interference-plus-noise ratio per user Indicates the active beamforming vector. This indicates the maximum power at each access point. This represents the conjugate transpose of matrix w. Indicates the first One access point Represents the set of indexes for access points. The total number of access points. Indicates the first r The first on STAR-RIS n One element, Indicates the amplitude of the transmission surface. Indicates the amplitude of the reflecting surface. n Indicates the first on STAR-RIS n One element, This represents the set of units on a simultaneously deployed, transmissive, reflective, reconfigurable smart surface. This invention assumes that the scenario has more than one STAR-RIS. Indicates the first One STAR-RIS, This represents the index set of simultaneously transmitted and reflected reconstructable smart surfaces. This indicates the number of STAR-RIS, where N represents the number of elements on a single STAR-RIS.

[0015] Decouple it using the FP algorithm and introduce artificial variables. The purpose of introducing artificial variables here is to separate the optimization variables from log(·). In P1, the variables are written below max, in the form of log[f(W,Θ) / g(W,Θ)]. In P2, artificial variables are introduced for equivalent transformation. Using the fractional programming algorithm, introducing artificial variables is an intermediate step in fractional programming. Its purpose is to separate f(W,Θ) / g(W,Θ) from log and transform it into an addition / subtraction form, which is beneficial for subsequent differentiation and can yield decoupled subproblems: (Formula 8), in for: (Formula 9), in, Indicates the first The conjugate transpose of the user's active beamforming vector, h k i Representing the k i User's channel, i belong t and r , i = t Users representing the transmission surface i = r The user represents the reflective surface, and H represents the conjugate transpose. Represents a function that indicates extracting from P2. To optimize. Because in P2, only It contains variables, and the other terms either have closed-form solutions or are constants.

[0016] Introducing artificial variables and Then formula 9 (while ignoring the constant term) can be transformed into: (Formula 10), in, These are artificial variables. The algorithm comes from a paper and aims to decouple the formulas. The proof is quite complex, so only the conclusion of that paper is used here. This indicates the total number of users on the transmission surface. This indicates the total number of users on the reflective surface. yes and A collection of [items], used here. j In order to be with Make distinctions.

[0017] The reformulated optimization problem is then decoupled into several subproblems, and the optimal solution for each optimization variable is derived through the following steps using alternating optimization across variables.

[0018] Step y1: Fix And optimize

[0019] Taking the partial derivative of Equation 9, i.e. , can get optimal solution (Formula 11), Step y2: Fix And optimize

[0020] Taking the partial derivative of the formula, i.e. , Indicates the introduced artificial variables, resulting in optimal solution (Formula 12), Step y3: Fix And optimize

[0021] Introduce the following formula: (Formula 13), in, It is the user channel. It is an artificial variable, h j Representing the j The user's channel, where H represents the conjugate transpose; (Formula 14), Where m is a variable substitution; (Formula 15), in, For variable substitution, The representative size is k i The identity matrix, I represents a column vector where only the b-th row is 1 and the other rows are 0. N This represents an identity matrix of size N*N, where N represents the total number of elements on a single STAR-RIS. (Formula 16), in, Variable substitution; (Formula 17), in, For variable substitution, It is a substitution of Formula 14; Substituting Equations 13-17 into Equation 10, and then deleting P3 with a constant term (since this is an extremum problem, the constant term does not affect the final extremum calculation), we can solve for the active beamforming variables: (Formula 18), This is clearly a convex problem, which can be solved using readily available tools, including Equation 18. Let W represent a function of the variable W, which is the variable that P1 wants to optimize, namely the active beamforming joint matrix.

[0022] Step y4: Fix And optimize

[0023] Introducing artificial variables , Then the original problem can be transformed into: (Formula 19), in, This represents a function, used to distinguish it from the previous functions. It is the conjugate transpose that introduces artificial variables. It's a variable substitution, specifically a variable substitution for the passive beamforming vector. k i and j Representing the k i For each user, i = t / r; in Then, taking the derivative of Equation 19, we get... Get variables The optimal solution is (Formula 20), Here k i = j ; The following definition is then introduced: (Formula 21), in, c It is an intermediate replacement variable. It is about introducing artificial variables. transpose, It is from the bth access point to the... k i Channel transposition for individual users; (Formula 22), Where g is an intermediate substitution variable. represent From r simultaneously transmissive and reflective reconfigurable smart surfaces to the nth k i Channels for each user, G b represent The channel from the b-th access point to the r-th simultaneously transmitted and reflected reconfigurable smart surface; (Formula 23), in, As an intermediate variable, i =t / r; (Formula 24), in, As an intermediate variable, For formula 22 whenk i = j In this situation, It is the conjugate of Formula 21; Introduction The formula for passive beamforming is obtained as follows: (Formula 25), in, Representative on The function, i =t / r; for The conjugate transpose, 1 RN This represents a column vector of length R*N containing only 1s, where R is the total number of STAR-RIS; and N is the total number of elements in a single STAR-RIS. Here, it is assumed that all STAR-RIS have the same elements. Constraints and constraints Transform into a clearer form: (Formula 26), in, Indicates the phase shift at the transmission end. The phase shift at the reflecting end is represented by H, which represents the conjugate rotation; where the constraint... and constraints This will make the original expression non-convex, so we need to introduce... We have the following equation: (Formula 27), in, , , , All are introduced intermediate variables, where T represents transpose; .

[0024] Substitute formula 27 into ,get (Formula 28), Among the newly added constraints arrive Because it was introduced This is caused by, among which when i = t Add C4 and C6 at the same time; i = r C5 and C7 have been added.

[0025] The main difficulty lies in handling constraints. and Because it is non-convex, a sequence rank-one constraint relaxation algorithm is introduced to replace the matrix rank-one constraint with an equivalent form.

[0026] 3. Low-complexity beamforming algorithm with rank-one constraint relaxation in sequence Then based on constraints and Solve the non-convex problem. When the following conditions are met... At that time, we had (Formula 29), Where Tr(·) represents the trace of a matrix; Maximum eigenvalue This has the following equivalent form. This can be further expressed as: (Formula 30), (Formula 31), in Let H represent the slack variable, where H is the conjugate transpose. express Maximum eigenvalues ​​and Traces. Therefore, constraints. It can be replaced with formula 30.

[0027] Suppose we find a feasible solution to the original problem with the constraint that the matrix rank is one. ,in Represents the primal problem with the constraint that the matrix rank is one. A feasible solution in the next iteration. It must satisfy (Equations 29-31). Therefore, the optimal solution to the problem in Equation 30 is: (Formula 32), In the formula This indicates the j-th iteration. Indicates the first The optimal solution of formula 29 in the second iteration. This represents the optimal solution to Equation 31. For a given... ,constraint: (Formula 33), It is about The linear constraints allow us to obtain a feasible solution for the next iteration. , express The conjugate transpose of . However, in order for Equation 26 to remain valid, The structure should be maintained at the first level, and its principal eigenvectors should be exactly equal to... .

[0028] However, the linear equality constraint is difficult to handle, so we introduce an equivalent constraint of matrix rank one with sequential relaxation, which is then reformulated as: (Formula 34), where relaxation parameter As An adaptive parameter for the ratio of the largest eigenvalue to the matrix trajectory, which gradually approaches 1. This parameter also satisfies the following inequality: (Formula 35), when This means that the rank-one constraint is ignored. When When added, it indicates that the rank of the successive approximation matrix of the feasible solution is one, constrained. At this point, the feasible solution satisfies the matrix rank-one constraint. Therefore, according to the derivation of formulas 29-35, the C2 and C3 constraints of P6 are transformed into the C2 and C3 constraints of P7, which can be expressed as: (Formula 36), in, Representative on The function.

[0029] This is a standard convex optimization problem, therefore it can be optimized in other ways. and To minimize the rank of the feasible solution, we introduce... Used as an update control variable to approximate a rank-1 solution. If the solution is infeasible, meaning the step size is too large, then reduce the step size. The design for the combined active and passive beamforming is shown in Algorithm 1.

[0030] Algorithm 1: Design of joint active and passive beamforming based on sequential rank-one constraint relaxation algorithm for passive beamforming 1. Input: All Channels , and in .

[0031] 2. Ensure: Optimized active precoding vectors Optimized passive precoding matrix Weighted sum rate .

[0032] 3. Initialization and ;make sure .

[0033] 4. While no convergence of do 5. (11) Solve ; 6. (12) Solve ; Active beamforming; 7. By solving Solve ; 8. Solve using (16) ; Passive beamforming based on sequence rank-one constraint relaxation algorithm: 9. Determine: {set} ,convergence .

[0034] use Solving relaxation problems get Obtain the initial steps. ; 10. Repeat until convergence 11. Given Solving convex problems ; 12. If question Solvable but ; otherwise ; EndIf 13. Settings ; 14. Settings ; 15. Until ; 16. From Get ; 17. EndWhile 18. Obtain .

[0035] 4. Complexity and Simulation Results Analysis The complexity comparison is shown in Table 1, where Indicates the number of iterations. During the update... hour, , , All solutions are in closed-form, so the solution is... The complexity is Solve The complexity is The time complexity of the penalty operator algorithm is O(n log n). The outer layer of the penalty operator algorithm optimizes the penalty parameters, while the inner layer finds a general solution that satisfies the matrix rank-one constraint. Clearly, compared to penalty operator-based algorithms, the sequence rank-one constraint-based relaxation algorithm achieves convergence with only one loop and avoids updating the penalty parameters. Inappropriate initial penalty parameters can lead to infeasible solutions and introduce additional complexity to adjust the penalty terms. Therefore, compared to penalty-based algorithms, the sequence rank-one constraint-based relaxation algorithm proposed in this invention has lower complexity. The complexity of the semidefinite relaxation-Gaussian randomization algorithm is... ,in Given a Gaussian random number of iterations, the complexity of the quadratic constrained quadratic programming algorithm is O(n log n). Although the semidefinite relaxation-Gaussian randomization algorithm and the algorithm based on quadratic constraint quadratic programming have low complexity, our proposed algorithm based on sequential rank-one constraint relaxation performs much better than them.

[0036] Table 1 Algorithm Complexity Analysis

[0037] This invention evaluates the performance of the proposed passive beamforming based on a sequential rank-one constraint relaxation algorithm through numerical simulation to optimize the wave retardation (WSR) of a multi-STAR-RIS assisted CF-mMIMO system. In the simulation setup, four access points (APs) are deployed along the y-axis at coordinates (0,0,5)m, (0,40,5)m, (0,80,5)m, and (0,120,5)m, respectively. Additionally, two elevated STAR-RISs are located at (-100,50,7)m and (-100,70,7)m, respectively. Users in the transmit zone are located at (-105,45,1.5)m and (-105,75,1.5)m, and users in the reflector zone are located at (-95,45,1.5)m and (-95,75,1.5)m. For the channel model, an expert fading channel is used. Reference range. When the reference path loss is 1 m, it is set to dB, reference path loss set to The noise variance is dBm. The user weight coefficient represents the priority of user access. For simplicity, all user coefficients are set to 1, meaning all users have equal access to the system. It is assumed that the system has complete knowledge of all users' CSI. For the selection of STAR-RIS optimization parameters, the step size is set. This means trading convergence speed for increased accuracy. This invention solves the relaxation problem. And parameters were set. and 0. The number of AP antennas is set to 4, and the number of user antennas is set to 2.

[0038] To highlight the advantages of the passive beamforming based on the sequential rank-one constraint relaxation algorithm proposed in this invention, this invention compares it with three passive beamforming algorithms with different baselines by combining active and passive beamforming: 1) a penalty operator algorithm, with the initial penalty term set to 0.01 and increasing at a rate of 10 times; 2) a algorithm with random number of iterations. 3) A semidefinite relaxation-Gaussian randomization algorithm; 4) An algorithm based on quadratic constraint quadratic programming: Problem Since it is a non-convex problem, this invention removes the constraints. and By relaxing the equality constraints to inequalities, it becomes a standard convex problem.

[0039] Figure 2 The convergence performance of the passive beamforming based on the sequential rank-one constraint relaxation algorithm proposed in this invention, as well as other benchmarks, is demonstrated. Figure 2 The number of STAR-RIS components was set to 40, and the maximum power of the AP was set to -23 dBm. It can be seen that all algorithms converged within 6 iterations. The proposed sequential rank-one constraint-based relaxation algorithm performs comparably to the penalty operator algorithm and exhibits significant performance advantages in other benchmark tests. The semidefinite relaxation-Gaussian randomization algorithm did not achieve ideal performance because the proportion of the principal eigenvalues ​​of the feasible solution to the total sum of eigenvalues ​​is insufficient, resulting in high-rank solutions. Although we can eventually recover the first-order solution from the relaxation problem, there is a significant gap between the recovered first-order solution and the optimal solution of the original problem. Algorithms based on quadratic constraint quadratic programming transformation suffer from severe coefficient distortion and poor performance because the optimal solutions obtained are one approaching 1 and the other approaching 0.

[0040] exist Figure 3 In this invention, the WSR performance was studied based on the transmit power of the AP. The number of elements was set to 35. For convenience, all APs were under the same power budget. As the power budget increased, the WSR showed an increasing trend because the higher transmit power enhanced the strength of the received signal, thereby improving the WSR. The sequential rank-one constraint relaxation algorithm proposed in this invention achieved the same performance as the penalty operator algorithm as the power budget increased. Furthermore, under any AP power budget, the sequential rank-one constraint relaxation algorithm outperformed both the semidefinite relaxation-Gaussian randomization algorithm and the quadratic constraint quadratic programming algorithm. This is because there is a significant difference between the solution recovered by the semidefinite relaxation-Gaussian randomization algorithm and the solution recovered by the quadratic constraint quadratic programming algorithm, resulting in a large loss.

[0041] Figure 4 This illustrates a comparison of the number of components at the user's combined rate versus the STAR-RIS. The power budget for all APs is set to -13 dBm, and all STAR-RIS components have the same number of components. Figure 4 As shown, the WSR increases with the number of STAR-RIS elements. Furthermore, because it does not strictly adhere to the matrix rank-one constraint, the algorithm of this invention outperforms algorithms based on quadratic constraint quadratic programming and semidefinite relaxation-Gaussian randomization algorithms, which limit their effectiveness. Moreover, the algorithm proposed in this invention achieves the same performance as the penalty operator algorithm without updating the penalty term, thus enhancing robustness.

[0042] This invention explores a more general scenario involving a large-scale STAR-RIS-assisted CF-mMIMO system. The goal is to maximize the user's beamforming performance (WSR) by jointly designing active beamforming on the AP and passive beamforming on the STAR-RIS. To address this complex challenge, this invention decomposes the original problem into several sub-problems and proposes a novel sequential rank-one constraint relaxation algorithm for passive beamforming design. Unlike traditional methods that directly ignore the matrix rank-one constraint, the proposed sequential rank-one constraint relaxation algorithm finds a general local optimum that satisfies the matrix rank-one constraint and gradually tightens feasible solutions to satisfy it. This method does not rely on initial penalty parameters that may adversely affect the final solution. The sequential rank-one constraint relaxation algorithm of this invention achieves performance comparable to traditional penalty operator algorithms but with lower computational complexity and higher reliability.

[0043] The present invention also discloses a STAR-RIS-assisted decellularized massive MIMO beamforming system based on sequence rank-one constraint relaxation, comprising: a memory, a processor, and a computer program stored in the memory, the computer program being configured to implement the steps of the method described in the present invention when called by the processor.

[0044] The present invention also discloses a computer-readable storage medium storing a computer program configured to implement the steps of the method described in the present invention when invoked by a processor.

[0045] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A STAR-RIS-assisted decellularized large-scale MIMO beamforming method based on sequence rank-one constraint relaxation, characterized in that, include: Step 1: Using fractional programming, the original non-convex problem is decoupled into active beamforming design at the access point and passive beamforming design of the simultaneously transmissive and reflective reconfigurable smart surface, and these are optimized alternately. Step 2: For the matrix rank-one constraint in passive beamforming design, the constraint is gradually relaxed by using a sequential rank-one constraint relaxation algorithm to find the local optimal solution that satisfies the constraint relaxation problem, and the feasible solution is gradually tightened to the matrix rank-one solution.

2. The STAR-RIS-assisted decellularized massive MIMO beamforming method according to claim 1, characterized in that, Step 1 includes: Step S1: With the goal of maximizing the weighted sum rate of all users, the weighted sum rate problem for all users is expressed as: Formula (7), in It is the joint matrix of active beamforming vectors, constrained. Set a maximum limit on the total transmit power budget for each access point to constrain [the system / entity]. and constraints The amplitude and phase of the coefficients of the reconfigurable smart surface matrix, which can be simultaneously transmitted and reflected, are limited to a feasible range. This represents the passive beamforming matrix. This represents the weighted sum rate of all users. express One user, i belong t and r , This represents the total number of users on the transmission surface. This represents the total number of users on the reflective surface; Indicates the first There are 10 users, distributed on both sides of the simultaneously transmissive and reflective reconfigurable smart surface. i belong t and r When it belongs to i = t This represents the user on the transmissive side. i = r Representing the user on the reflective side, On behalf of users The weight, Indicates the first Signal-to-interference-plus-noise ratio per user Indicates the active beamforming vector. This indicates the maximum power at each access point. This represents the conjugate transpose of matrix w. Indicates the first One access point Represents the set of indexes for access points. The total number of access points. Indicates the first r The first simultaneous transmission and reflection reconfigurable smart surface n One element, Indicates the amplitude of the transmission surface. Indicates the amplitude of the reflecting surface. n Represents the first reconstructible smart surface by simultaneous transmission and reflection. n One element, This represents the set of units on a simultaneously deployed, transmissive, reflective, reconfigurable smart surface. Indicates the first Simultaneous transmission and reflection can reconstruct smart surfaces This represents the index set of simultaneously transmitted and reflected reconstructable smart surfaces. This indicates the number of reconfigurable smart surfaces that can be simultaneously transmitted and reflected; Step S2: Decouple P1 using a fractional programming algorithm and introduce artificial variables. ,and We obtain the decoupling subproblems: Formula (8), in for: Formula (9), in, Indicates the first The conjugate transpose of the user's active beamforming vector Representing the User's channel, i belong t and r , i = t Users representing the transmission surface i = r The user represents the reflective surface, and H represents the conjugate transpose. Represents a function; Introducing artificial variables and Formula (9) becomes: Formula (10), in, Artificial variables, This indicates the total number of users on the transmission surface. This indicates the total number of users on the reflective surface. yes and A collection of [items / items].

3. The STAR-RIS-assisted decellularized massive MIMO beamforming method according to claim 2, characterized in that, Step 1 further includes: Step y1: Fix And optimize ; Taking the partial derivative of formula (9), i.e. ,get optimal solution Formula (11), Step y2: Fix And optimize ; Taking the partial derivative of formula (10), i.e. , Indicates the introduced artificial variables, resulting in optimal solution Formula (12), Step y3: Fix And optimize ; Introduce the following formula: Formula (13), in, It is the user channel. It is an artificial variable, h j Representing the j The user's channel, where H represents the conjugate transpose; Formula (14), Where m is a variable substitution; Formula (15), in, For variable substitution, The representative size is The identity matrix, I represents a column vector where only the b-th row is 1 and the other rows are 0. N This represents an identity matrix of size N*N, where N represents the total number of elements in STAR-RIS; Formula (16), in, Variable substitution; Formula (17), in, For variable substitution, It is a substitution of formula (14); Substituting formulas (13-17) into formula (10), we can solve for the active beamforming variables: Formula (18), in, Let W be a function of the variable W, which is the variable that P1 wants to optimize, i.e., the joint active beamforming matrix. Step y4: Fix And optimize ; Introducing artificial variables The original problem then becomes: Formula (19), in, This represents a function, used to distinguish it from the previous functions. It is the conjugate transpose that introduces artificial variables. It's a variable substitution, specifically a variable substitution for the passive beamforming vector. k i and j Representing the k i One user, i =t / r; ， Differentiating formula (19), i.e. Get variables The optimal solution is Formula (20), Here k i = j ; The following definition is then introduced: Formula (21), in, It is an intermediate replacement variable. It is about introducing artificial variables. transpose, It is the first The access point to the first Channel transposition for individual users; Formula (22), Where g is an intermediate substitution variable. represent From r simultaneously transmissive and reflective reconfigurable smart surfaces to the nth k i Channels for each user, G b represent The channel from the b-th access point to the r-th simultaneously transmitted and reflected reconfigurable smart surface; Formula (23), in, As an intermediate variable, i =t / r; Formula (24), in, As an intermediate variable, For formula (22) when k i = j In this situation, It is the conjugate of formula (21); Introduction The formula for passive beamforming is obtained as follows: Formula (25), in, Representative on The function, i =t / r; for The conjugate transpose, 1 RN This represents a column vector of length R*N containing only 1s, where R is the total number of STAR-RISs and N is the total number of elements in a single STAR-RIS. Constraints and constraints Transform into a clearer form: Formula (26), in, Indicates the phase shift at the transmission end. The phase shift at the reflecting end is indicated by H, which represents the conjugate rotation. Among the constraints and constraints This will make the original expression non-convex, so we introduce... We obtain the following equation: Formula (27), in, , , , All of these are introduced intermediate variables, where T represents transpose; in ; Substitute formula (27) into ,get Official (28).

4. The STAR-RIS-assisted decellularized massive MIMO beamforming method according to claim 3, characterized in that, Step 2 includes: Based on constraints and constraints Solve the nonconvex problem when the following condition is met: have Formula (29), Where Tr(·) represents the trace of a matrix; Maximum eigenvalue The following is an equivalent form, which can be further expressed as: Formula (30), Formula (31), in Let H represent the slack variable, where H is the conjugate transpose. express Maximum eigenvalues ​​and traces, therefore, constraints Replace with formula 30; Suppose we find a feasible solution to the original problem with the constraint that the matrix rank is one. ,in Represents the primal problem with the constraint that the matrix rank is one. A feasible solution in the next iteration. Formulas (29-31) must be satisfied; therefore, the optimal solution to the problem in formula (30) is: Formula (32), In the formula Indicates the first j iteration Indicates the first j The optimal solution of the next iteration formula (29) This represents the optimal solution of formula (31) for a given condition. ,constraint: Formula (33), It is about The linear constraints are satisfied, thus yielding a feasible solution for the next iteration. , express The conjugate transpose of; Introducing an equivalent constraint that the rank of the matrix is ​​one under sequential relaxation, we can restate equation (29) as follows: Formula (34) Among them, relaxation parameter As An adaptive parameter for the ratio of the largest eigenvalue to the matrix trajectory gradually approaches 1, and this parameter also satisfies the following inequality: Formula (35), when This means ignoring the rank-one constraint when When it is increased, it indicates that the rank of the successive approximation matrix of the feasible solution is one, which is a constraint. When the feasible solution satisfies the matrix rank-one constraint, therefore, according to the derivation of formulas (29-35), the C2 and C3 constraints of P6 are transformed into the C2 and C3 constraints of P7, expressed as: Formula (36) in, Representative on The function.

5. A STAR-RIS-assisted decellularized large-scale MIMO beamforming system based on sequence rank-one constraint relaxation, characterized in that, include: A memory, a processor, and a computer program stored on the memory, the computer program being configured to implement the steps of the method of any one of claims 1-4 when invoked by the processor.

6. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program configured to implement the steps of the method according to any one of claims 1-4 when invoked by a processor.

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