MSE minimization beam forming method and system for user information symbols of STAR-RIS assisted ISAC system, and electronic equipment

Abstract

The invention discloses an MSE minimization beam forming method and system for user information symbols of an STAR-RIS assisted ISAC system and electronic equipment. The method comprises the following steps that S1, a base station transmits a precoding signal to STAR-RIS; s2, calculating an estimation MSE (n) of a user information symbol; s3, judging whether MSE (n) satisfies MSE (n)-MSE (n-1) < = epsilon, if not, executing S4, and if yes, executing S8; s4, taking the mean square error MSE (n) in the S3 as an input parameter, and executing an ISAC base station beam vector optimization method; s5, taking the X * in the S4 as an input parameter, and executing an RIS phase shift matrix amplitude optimization method; s6, the transmission phase shift matrix amplitude # imgabs0 # and the reflection phase shift matrix amplitude # imgabs1 # in the S5 serve as input parameters, and an RIS transmission and reflection phase shift matrix phase optimization method is executed; s7, X *, # imgabs2 # and # imgabs3 # are used as input parameters, an estimated mean square error MSE (n) of a user information symbol of the current system is calculated, n is made to be equal to n + 1, and the step S3 is executed; and S8, taking the optimal value of the estimated mean square error of the obtained user information symbol as an output result.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication, and specifically relates to a beamforming method, system, and electronic device for minimizing the mean square error (MSE) of user information symbol estimation in a transmission-reflection dual-functional reconfigurable intelligent surface (STAR-RIS)-assisted non-line-of-sight integrated sensing and communication (ISAC) system. Background Art

[0002] With the rapid development of 6G integrated sensing and communication (ISAC) technology, how to achieve joint optimization of high-precision sensing and high-efficiency communication in complex environments has become the core challenge in this field. Traditional ISAC systems rely on multi-antenna beamforming technology, but limited by hardware costs and channel complexity, there are significant bottlenecks in coverage extension, multi-user interference suppression, and energy efficiency. In recent years, reconfigurable intelligent surface (RIS) technology has provided a new path for improving ISAC performance by dynamically regulating the electromagnetic wave propagation environment. However, existing RIS-assisted ISAC research mainly focuses on single reflection or transmission modes, making it difficult to adapt to the dynamic switching scenarios of sensing and communication dual functions, and lacking targeted optimization of the estimation accuracy of user information symbols.

[0003] Currently, although the simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) has been proposed, its application in ISAC still faces key problems: First, STAR-RIS units need to support both transmission and reflection phase regulation simultaneously, resulting in a sharp increase in the dimension of beamforming design, making it difficult for traditional convex optimization methods to balance computational complexity and global convergence; Second, the coupling effect between communication channels and sensing echo signals exacerbates multi-user interference, and existing solutions have not effectively balanced the joint optimization of communication rate and sensing mean square error (MSE); In addition, the impact of hardware non-ideal characteristics on MSE has not been fully modeled. Therefore, there is an urgent need for a new type of beamforming method that can achieve efficient allocation of communication-sensing resources and minimize the MSE of user information symbol estimation in the STAR-RIS-assisted ISAC framework to meet the stringent requirements of future intelligent networks for highly reliable integrated sensing and communication. Summary of the Invention

[0004] In view of the above problems existing in the existing ISAC system that the base station cannot communicate with indoor users due to being blocked by obstacles and the perception of outdoor detection targets, the present invention proposes a method, system and electronic device for minimizing the mean square error (MSE) of estimating user information symbols in a STAR-RIS-assisted non-line-of-sight ISAC system.

[0005] The present invention adopts the following technical solutions:

[0006] A method for minimizing the MSE of estimating user information symbols in a STAR-RIS-assisted ISAC system, comprising the following steps:

[0007] S1: The base station sends a precoding signal x(l)=Ws(l) to the STAR-RIS. Wherein, is an M×K-dimensional precoding matrix with all elements being complex numbers, is a K×1-dimensional symbol matrix with all elements being complex numbers, and the subscript K represents the Kth communication user, (·) T represents the transpose of the matrix, is a K×1-dimensional matrix with all elements being complex numbers, and both M and l are integers;

[0008] S2: The communication user and the sensing target respectively receive the precoding signal in step S1 transmitted and reflected by the STAR-RIS. As input parameters, according to the definition that the estimated MSE of the user information symbol is the MSE between the received symbol and the desired symbol, calculate the estimated MSE of the user information symbol (n) . Wherein, MSE (n) represents the mean square error obtained in the nth calculation, and n is a constant;

[0009] S3: Judge whether the MSE (n) obtained in step S2 satisfies |MSE (n) -MSE (n-1) |≤ε, where the initial value of the mean square error MSE (0) =0; ε is a constant and can take any real number between 0.0001 and 0.1. If not satisfied, execute step S4. If satisfied, jump to and execute step S8;

[0010] S4: Take the mean square error MSE (n) obtained in step S3 as the input parameter, execute the ISAC base station beam vector optimization method, and output an M×L-dimensional matrix X * with all elements being complex numbers. Wherein, M and L are natural numbers, representing the number of rows and columns of the matrix respectively, and the superscript * represents the optimal value of X;

[0011] S5: Take the ISAC base station beam vector X *, as input parameters, execute the RIS phase shift matrix amplitude optimization method, and output the transmission phase shift matrix amplitude with all elements being real numbers and the reflection phase shift matrix amplitude The superscript * represents and optimal values;

[0012] S6: Take the RIS transmission phase shift matrix amplitude obtained in step S5 and the reflection phase shift matrix amplitude as input parameters, execute the RIS transmission and reflection phase shift matrix phase optimization method, and output the N c ×N c dimensional transmission matrix and the reflection matrix where N c is the number of reflection-transmission units of the RIS, representing the number of rows and columns of the matrix, and the superscript * represents and optimal values;

[0013] S7: Take the X obtained in step S4 * , the obtained in step S5 and the obtained in step S6 as input parameters, calculate the estimated mean square error MSE (n) of the system user information symbol, let n = n + 1, and return to execute step S3;

[0014] S8: Take the minimum value MSE (n) of the estimated mean square error of the system user information symbol obtained in step S3 as the final output result of the present invention. The present invention realizes the performance compromise between communication and sensing of the ISAC system.

[0015] Preferably, in step S4, for the optimization method of the ISAC base station beam vector X * , the following steps are adopted to implement:

[0016] The RIS-assisted integrated communication and sensing system for non-line-of-sight communication includes a base station equipped with a uniform linear array and having M antennas, K single-antenna communication users, T detection targets, a STAR-RIS with a positive integer N c of reflection-transmission units and a positive integer N s of sensing units, and an obstacle that blocks the line of sight between the communication users and the sensing targets and the base station. Among them, since the ISAC base station is blocked by the obstacle, it cannot communicate with the indoor users and sense the outdoor targets, and must rely on the transmission and reflection of the STAR-RIS to achieve communication and sensing.

[0017] The communication channel coefficient matrix is expressed as follows: is an N×M dimensional matrix whose elements are all complex numbers, representing the channel coefficient matrix from the ISAC base station to STAR-RIS; is an N×1 dimensional vector whose elements are all complex numbers, representing the channel from STAR-RIS to the kth communication user. Among them, the phase shift transmission matrix of STAR-RIS is and the reflection matrix Defined as where ρ i,n ∈[0,1] and θ i,n ∈[0,2π] represents the amplitude and phase shift response of the nth element, and satisfies N c is a positive integer, and diag(·) represents a diagonal matrix. After L time slots, in the STAR-RIS assisted non-line-of-sight ISAC system, the ISAC base station sends s k The symbol is transmitted through the RIS to the communication user, and the signal received by the communication user can be expressed as:

[0018]

[0019] in, is a K×L dimensional matrix whose elements are all complex numbers; is N whose elements are all complex numbers c ×K-dimensional matrix, representing the joint channel from RIS to the communication user, F H is the conjugate transpose of F; is a K×M-dimensional matrix whose elements are all complex numbers, representing the joint channel from the ISAC base station to K users through L frame time slots; is the RIS phase-shift transmission matrix; The precoding signal matrix sent by the ISAC base station; is a K×L dimensional matrix whose elements are all complex numbers, indicating that the communication user receives additive noise that obeys Gaussian distribution. The symbol to be received by the communication user is The signal Y received by the communication user can be re-expressed as:

[0020]

[0021] Where S is a K×L dimensional matrix whose elements are all complex numbers. The second term represents multi-user interference (MUI). Therefore, the total power of MUI is:

[0022]

[0023] in, is the Frobenius norm operation; the signal interference plus noise ratio of each frame of the kth user can be expressed as:

[0024]

[0025] Among them, h k represents the k-th row of H, and s k,j represents the symbol at the j-th column of the k-th row. E(·) represents the expected value of the independent variable with respect to j, is a constant and is the variance of the complex additive white Gaussian noise at user k. The total rate can be calculated as By minimizing the received interference of user k, the achievable data rate of user k can be maximized. Since P MUI is closely related to the mean square error between the received symbol and the desired symbol. Therefore, the MSE is defined as:

[0026]

[0027] Among them, y l is the l-th column of Y. For the target sensing part in the system, an RIS with N s sensing units is used to estimate the directions of arrival of T targets located at different angles After L time slots, the signals received by the N s sensing units can be expressed as:

[0028]

[0029] Among them, α t represents the reflection coefficient of the t-th target, is an N c ×1 dimensional vector with all elements being complex numbers, representing the steering vector of the RIS reflection unit; λ is a positive integer representing the normalized element spacing. is an N s ×1 dimensional vector with all elements being complex numbers, representing the steering vector of the RIS sensing unit. is an N s ×L dimensional matrix, representing the additive white Gaussian noise with zero mean and covariance matrix R N . And the Cramer-Rao bound (CRB) of the azimuth angle estimation and the direction determination of other targets are as follows:

[0030]

[0031] Among them, Tr(·) is the trace operation of the matrix, <s

[0032] represents the derivative of, represents the derivative of, b i and a i represent respectively and the i-th entry of. Azimuth angle The estimated CRB of satisfies being less than a very small threshold Γ t , and its relational expression is as follows:

[0033]

[0034] The problem of minimizing the estimated mean square error MSE of user information symbols is modeled as:

[0035]

[0036] where x m,l represents the entry at (m, l) in X, and P t is the maximum transmit power of the ISAC base station. C1 constrains the ISAC waveform to a constant modulus constraint; C2 and C3 are the phase constraints of the RIS phase shift matrix during transmission and reflection; C4 is the constraint for estimating the arrival angle direction of the sensing target. Define η t = 1 / (2|α t | 2 Γ t ); C5 is the amplitude constraint of the RIS phase shift matrix during transmission and reflection; C6 and C7 are the same amplitude representations of the RIS phase shift matrix. Fix to optimize X, which completes the constant modulus design of the ISAC waveform. Therefore, this problem can be reformulated as:

[0037]

[0038] where C1 and C4 are the constraints in Equation (9).

[0039] Vectorize X into Therefore, the mean square error of the information symbol estimation and the constraint C4 can be reformulated respectively as:

[0040]

[0041] where is the Kronecker product operation, vec(·) is vectorization, Re{·} is the operation of taking the real part of a complex number, and (·) H is the conjugate transpose of a matrix, represents being defined. Since the constraint C4 in Equation (10) is non-convex, introduce an auxiliary variable μ = [μ1,..., μ T , and the constraint C4 can be reformulated as:

[0042]

[0043] Where μ is a T-by-1-dimensional array whose elements are all positive real numbers.

[0044] According to formula (13), formula (10) can be restated as:

[0045]

[0046] Among them, C1 is the constraint condition of formula (10), and C4 is the constraint condition for simplifying the solution in formula (10).

[0047] Introducing the penalty function method described in the background technology, the specific expression is:

[0048]

[0049] Among them, the penalty coefficient υ t Need to satisfy υ in each iteration t > 0. Therefore, in each iteration To update t Under the condition of determining x, μ t It can be expressed as:

[0050] μ t =max[x H Φ t x-η t ,0] (16)

[0051] Among them, max[·] means taking the maximum value in the set.

[0052] According to formula (15), formula (14) can be restated as:

[0053]

[0054] in, Since the only constraint of this problem is the constant modulus constraint C1, the Riemannian manifold optimization algorithm described in the background art can be used to solve it. Where x is optimized on the ML-dimensional complex circle. Definition is the feasible domain of the problem, that is Assumptions for The point on The tangent space can be expressed as

[0055]

[0056] Where ⊙ represents the Hadamard product. The Riemann gradient is the steepest ascending direction on the Riemann manifold. It can be obtained by projecting the Euclidean gradient and is often used for manifold optimization. It can be expressed as:

[0057]

[0058] Among them, is the projection towards the tangent space. is the objective function of the Euclidean gradient, and its expression is:

[0059]

[0060] Among them, the expression of ζ'(x) is:

[0061]

[0062] Iteratively update according to the Riemannian steepest descent algorithm. The descent direction of the nth iteration is selected as the negative counterpart of the Riemannian gradient. Therefore, the x of the (n + 1)th iteration is updated as:

[0063]

[0064] Among them, δ n is the step size, represents the retraction operation, which is used to map the points in the tangent space to the manifold . For a circular sphere, the contraction operation can be expressed as:

[0065]

[0066] Solve equation (22) to obtain the optimal ISAC base station beam vector X * .

[0067] Preferably, in step S5, the optimization method of the amplitude of the RIS transmission phase shift matrix and the reflection phase shift matrix amplitude is realized by the following steps:

[0068] S5.1: Fix X, and Optimize and The purpose is to realize the optimal allocation of the amplitude of the RIS phase shift matrix Θ between perspective and reflection. Therefore, equation (9) can be reformulated as:

[0069]

[0070] Among them, C4, C5, C6, and C7 are all constraint conditions in equation (10).

[0071] S5.2: Vectorize and into and Therefore, the minimum mean square error of the information symbol estimation and constraint C4 are respectively reformulated as:

[0072]

[0073] Where Tr(·) represents the trace operation of the matrix, ⊙ represents the Hadamard product operation, (·) T represents the transpose of the matrix, (·) H represents the conjugate transpose of the matrix, e * represents the conjugate of e; definition C=FF H , D=GXX H G H , E=GXS H F H and

[0074] S5.3: According to equations (25) and (26), the minimum mean square error of the estimated information symbol and the constraint C4 can be restated as:

[0075]

[0076]

[0077] S5.4: In equations (27) and (28), let and Then formula (24) can be restated as:

[0078]

[0079] in, and C4 are the objective function and constraints obtained by simplifying formula (24), and C5 is the constraint condition of formula (24).

[0080] S5.5: Equation (29) can be solved using the Karush-Kuhn-Tucker (KKT) condition. To obtain the KKT condition, first find the Lagrangian function of Equation (29), which is expressed as follows:

[0081]

[0082] in, is the Lagrange multiplier. Then the KKT condition can be written as:

[0083]

[0084] in, represents the Lagrangian function right Find the partial derivative.

[0085] S5.6: Analyze Equation (31). When and hold, When and hold, where min{·} represents taking the minimum value in the set. In summary, we can obtain which is expressed as follows:

[0086]

[0087] S5.7: According to and Equation (32), we can obtain

[0088] Preferably, in step S6, the optimization method for the phase of the RIS transmission phase shift matrix and the phase of the reflection phase shift matrix is implemented by the following steps:

[0089] S6.1: Fix X, and Optimize and aiming to achieve the optimal design of the phase of the RIS phase shift matrix Θ between transmission and reflection. According to Equations (27) and (28), the problem is reformulated as follows:

[0090]

[0091] where the objective function in Equation (33) is the objective function obtained by simplifying and solving Equation (27), C2 and C6 are the constraint conditions in Equation (9); the objective function in Equation (34) is a newly defined auxiliary variable, and C3, C4, and C7 are the constraint conditions in Equation (9).

[0092] S6.2: The only constraint of Equation (33) is the constant modulus constraint C2. The Riemannian manifold algorithm can be used, where is optimized on the N c dimensional complex circle. Define as the feasible region of the problem, that is, Assume is a point on , then the tangent space of can be expressed as:

[0093]

[0094] where Re{·} represents the operation of taking the real part of a complex number, and ⊙ represents the Hadamard product operation.

[0095] S6.3: Obtain the objective function by projecting the Euclidean gradient The Riemannian gradient is expressed as follows:

[0096]

[0097] where is the projection onto the tangent space, is the Euclidean gradient of the objective function which is expressed as follows:

[0098]

[0099] S6.4: Iteratively update according to the Riemannian steepest descent algorithm. The descent direction at the n-th iteration is chosen as the negative counterpart of the Riemannian gradient. Therefore, the update at the (n + 1)-th iteration is:

[0100]

[0101] where δ n is the step size, denotes the retraction operation, which is used to map a point in the tangent space to the manifold .

[0102] S6.5: Solve equations (38) and C6 to obtain the optimal phase of the RIS transmission phase shift matrix

[0103] S6.6: In equation (34), C4 is a non-convex constraint. To solve it, let Then According to the successive linearization method described in the background art, rewrite C4 as:

[0104]

[0105] where is the result of the previous iteration. According to equation (39), equation (34) can be transformed as follows:

[0106]

[0107] S6.7: Solving equation (40) is a linear problem, which can be solved by the convex optimization solver described in the background art to obtain According to C7, obtain the optimal phase of the RIS reflection phase shift matrix

[0108] The present invention also discloses a beamforming system for minimizing the MSE of user information symbols in a STAR-RIS assisted ISAC system, which is used to execute the above method and includes the following modules:

[0109] Precoding signal transmission module: used for the base station to transmit precoding signals to the STAR-RIS;

[0110] Mean square error estimation module: taking the precoding signals respectively received by the communication user and the sensing target as input parameters, defining the MSE of the received symbol and the desired symbol according to the estimated MSE of the user information symbol, and calculating the estimated MSE of the user information symbol (n) ; where, MSE (n) represents the mean square error obtained in the nth calculation;

[0111] Judgment module: judging whether the MSE obtained by the mean square error estimation module (n) satisfies |MSE (n) -MSE (n-1) |≤ε, where the initial value of the mean square error MSE (0) =0, and ε is a constant; if not satisfied, it is executed by the ISAC base station beam vector optimization module, and if satisfied, it jumps and is executed by the output module;

[0112] ISAC base station beam vector optimization module: taking the mean square error MSE obtained by the judgment module (n) as an input parameter, executing the ISAC base station beam vector optimization method, and outputting an M×L-dimensional matrix X whose elements are all complex numbers * ; where, M and L are natural numbers, representing the number of rows and columns of the matrix respectively, and the superscript * represents the optimal value of X;

[0113] RIS phase shift matrix amplitude optimization module: taking X obtained by the ISAC base station beam vector optimization module * as an input parameter, executing the RIS phase shift matrix amplitude optimization method, and outputting the transmission phase shift matrix amplitude and the reflection phase shift matrix amplitude whose elements are all real numbers and the reflection phase shift matrix amplitude

[0114] RIS transmission and reflection phase shift matrix phase optimization module: taking the transmission phase shift matrix amplitude and the reflection phase shift matrix amplitude obtained by the RIS phase shift matrix amplitude optimization module and the reflection phase shift matrix amplitude as input parameters, executing the RIS transmission and reflection phase shift matrix phase optimization method, and outputting an N c ×N c [[ID=……]] dimensional transmission matrix and reflection matrix where, N c is the number of reflection-transmission units of the RIS, representing the number of rows and columns of the matrix;

[0115] Current mean square error estimation module: taking the obtained X * , and It should be noted that there seems to be some incomplete or unclear parts in the original text, especially around the ellipsis part. The translation is done as accurately as possible based on the available content.As an input parameter, calculate the estimated mean square error (MSE) of the user information symbol of the current system. (n) Let n = n + 1, and jump to the judgment module for execution.

[0116] Output module: Use the optimal value of the estimated mean square error of the user information symbol obtained by the judgment module as the output result.

[0117] The present invention also discloses an electronic device, including:

[0118] A processor;

[0119] A memory for storing a program, which, when called and executed by the processor, causes the processor to execute the above method or system.

[0120] The technical introduction related to the present invention is as follows:

[0121] 1. Alternating optimization method

[0122] Alternating optimization is a typical optimization strategy, especially suitable for complex systems that can be decomposed into multiple sub-problems. For system design problems with non-convex objective functions or constraint conditions, this method significantly reduces the complexity of global optimization by optimizing each sub-problem in stages. Its core mechanism is to fix other variables during the iteration process and only optimize the current target variable, and explore the global optimal solution through a step-by-step approximation strategy. This technology has been successfully applied to practical scenarios such as beamforming design, resource dynamic allocation in the communication field, and multi-parameter collaborative optimization of reconfigurable intelligent surface-assisted systems. See specifically: "Luo Z Q, Ma W K, So A M C, et al. Semidefinite relaxation of quadratic optimization problems[J]. IEEE Signal Processing Magazine, xx, xx(xx): xx-xx."

[0123] 2. Penalty function method

[0124] The penalty function is a core method for transforming constrained optimization problems into unconstrained problems and is widely used in the design of systems with equality or inequality constraints. Its core idea is to introduce penalty terms related to the constraint conditions into the objective function, transforming the original constrained problem into an iterative solution of a series of unconstrained sub-problems. For solutions that violate the constraint conditions, the penalty function imposes a large cost, forcing the optimization process to gradually approach the feasible region. In the iteration, by dynamically adjusting the penalty coefficient, the relationship between constraint satisfaction and objective optimization can be effectively balanced. This method is particularly suitable for non-convex, non-linear or high-dimensional complex systems, and can simplify scenarios that are difficult to directly handle by traditional Lagrange multiplier methods, such as power allocation constraints in communication systems, regularization design of machine learning models, and physical boundary limit problems in engineering optimization. See specifically: "Boyd S, Parikh N, Chu E, et al. Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers[J]. Foundations & Trends in Machine Learning, 2010, 3(1): 1-122.".

[0125] 3. Riemannian Manifold Optimization Method

[0126] Riemannian manifold optimization is a mathematical method for constrained optimization problems defined on non-linear geometric spaces. Its core lies in extending the optimization theory in traditional Euclidean spaces to manifold spaces with specific structures, such as spherical surfaces, Stiefel manifolds or positive definite matrix spaces. This method constructs an optimization framework through differential geometry tools, uses the Riemannian gradient to replace the Euclidean gradient, which is defined as the projected gradient of the objective function on the tangent space of the manifold, and combines the retraction operation to map the iterative points back to the manifold to maintain the constraint conditions. Classical algorithms include the Riemannian conjugate gradient method, trust region method and stochastic optimization variants, which improve the convergence efficiency through the intrinsic geometric properties of the manifold. In the field of communication, this method is applied to non-convex problems such as intelligent reflecting surface phase regulation and multi-antenna beamforming. By implicitly embedding complex constraints through the manifold geometric structure, it avoids performance losses caused by traditional relaxation techniques. In machine learning, Riemannian optimization is applicable to tasks such as low-rank matrix factorization and tensor network training, effectively handling structured constraints such as orthogonality and fixed rank. See specifically: "ABSIL P A, MAHONY R, SEPULCHRER. Optimization algorithms on matrix manifolds[J]. IEEE Transactions on Automatic Control, 2008, 53(5): 1203-1218.".

[0127] 4. Successive Linearization Method

[0128] The successive linearization method is an iterative solution strategy for non-convex optimization problems. Its core idea is to gradually simplify complex non-linear constraints or objective functions into linear sub-problems through local linear approximation, thereby reducing the difficulty of global optimization. In each iteration, the method performs a first-order Taylor expansion on the non-linear terms based on the current solution, constructs a linear approximation model, and updates the solution by solving the linearized sub-problem. By continuously repeating the linear approximation and sub-problem optimization, it gradually approaches the feasible solution or optimal solution of the original problem. This method is widely used in fields such as communication systems, resource allocation, and signal processing. For example, it can be applied to non-convex scenarios such as reconfigurable intelligent surface phase optimization and multi-user interference management. By transforming non-convex constraints into sequential linear constraints, successive linearization can avoid the computational complexity brought by directly dealing with high-dimensional non-linear problems while maintaining the feasibility of the solution. See specifically: "Mao Y, Dueri D, Szmuk M, et al. Successive Convexification of Non-Convex Optimal Control Problems with State Constraints[C] / / 20th IFAC World Congress. 2017: 4063 - 4069."

[0129] 5. Convex Optimization Solver

[0130] A convex optimization solver is a computational tool designed for efficiently solving convex optimization problems. Its theoretical basis covers mathematical programming and numerical algorithms. It can automatically verify the convexity of the objective function and constraints, and standardize the problem into forms such as linear programming and second-order cone programming for analysis. Mainstream solvers are constructed based on the interior point method, active set method, or first-order gradient algorithm, approaching the optimal solution through iteration and ensuring global convergence. Typical tools include the open-source framework CVXPY and the commercial software MOSEK, which support large-scale sparse matrix operations and parallel computing acceleration. In the field of communication, such solvers are applied to scenarios such as power allocation optimization and beamforming design, relying on convexity to strictly guarantee the global optimality of the solution. See specifically: "Luo Z Q, Ma W K, So A M C, et al. Semidefinite relaxation of quadratic optimization problems[J]. IEEE Signal Processing Magazine, 2010, 27(3): 20 - 34."

[0131] The beneficial effects of the present invention are as follows:

[0132] The present invention discloses a method and system for minimizing the mean square error of estimating user information symbols in a transmit-reflect dual-functional reconfigurable intelligent surface-assisted non-line-of-sight communication and sensing integrated system. First, the present invention fixes the amplitudes of the RIS transmit and reflect phase shift matrices as well as the phases of the RIS transmit and reflect phase shift matrices and uses the penalty function and Riemannian manifold optimization algorithm to solve for the optimal ISAC base station beam vector X * . Secondly, with the ISAC base station beam vector X * and the phases of the RIS transmit and reflect phase shift matrices fixed , the KKT conditions are used to solve for the amplitudes of the RIS transmit and reflect phase shift matrices Finally, the Riemannian manifold algorithm and the successive linearization method are used to solve for the phases of the RIS transmit and reflect phase shift matrices Ultimately, the optimal mean square error value is obtained, achieving the performance trade-off between communication and sensing in the ISAC system. Description of the Drawings

[0133] Figure 1 FIG. is a model diagram of a STAR-RIS-assisted non-line-of-sight ISAC system according to a preferred embodiment of the present invention;

[0134] Figure 2 FIG. is a flowchart of a method for minimizing the mean square error of estimating user information symbols in a STAR-RIS-assisted non-line-of-sight ISAC system according to a preferred embodiment of the present invention;

[0135] Figure 3 FIG. is a comparison diagram of the algorithm convergence performance under different schemes;

[0136] Figure 4 FIG. is a comparison diagram of the relationship between the signal-to-noise ratio and the total system rate under different schemes;

[0137] Figure 5 FIG. is a comparison diagram of the relationship between the number of sensing units N s and the total system rate;

[0138] Figure 6 FIG. is a block diagram of a system for minimizing the MSE of user information symbols in a STAR-RIS-assisted ISAC system according to a preferred embodiment of the present invention. Detailed Embodiments

[0139] The present invention will be further described below in conjunction with specific embodiments. The specific embodiments of the present invention can be detailedly illustrated through the following embodiment diagrams.

[0140] Figure 1This is a model diagram of the STAR-IRS-assisted non-line-of-sight ISAC system according to an embodiment of the present invention. The system includes a base station equipped with a uniform linear array and having M antennas, K indoor communication users with single antennas, T outdoor sensing targets, and a STAR-RIS with a positive integer N of reflection-transmission units c and a positive integer N of sensing units s and an obstacle that blocks the line of sight between the communication users and the sensing targets and the base station. Among them, since the ISAC base station is blocked by the obstacle, it cannot communicate with the indoor users and sense the outdoor targets, and must rely on the transmission and reflection of the STAR-RIS to achieve communication and sensing.

[0141] Figure 2 This is a flowchart of a method for minimizing the mean square error of the estimation of user information symbols in a STAR-RIS-assisted non-line-of-sight ISAC system according to an embodiment of the present invention, which is mainly completed through the following steps:

[0142] Step 1: The base station transmits a precoded signal X to the STAR-RIS. Among them, the precoded signal X is an M×L-dimensional matrix with all elements being complex numbers;

[0143] Step 2: The communication users and the receiving ends of the sensing targets respectively receive the precoded signal in Step S1 transmitted and reflected by the STAR-RIS, and use it as an input parameter to calculate the estimated minimum mean square error MSE of the user information symbols (n) ; Initialize the iteration number n = 0 and the convergence judgment constant ε = 0.01, and input the beam vector X of the ISAC base station (0) , the amplitude of the transmission and reflection phase shift matrix of the RIS the phase of the transmission and reflection phase shift matrix of the RIS

[0144] Step 3: Determine whether |MSE (n) -MSE (n-1) | ≤ ε holds, where MSE (n) refers to the mean square error value obtained by the nth iteration calculation. If it holds, directly end (i.e., jump to Step 8), otherwise execute Step 4; |MSE (n) -MSE (n-1) | ≤ ε can characterize the convergence performance of this method;

[0145] Step 4: According to MSE (n) , execute the beam vector optimization method of the ISAC base station to obtain the beam vector X of the ISAC base station (n) ;

[0146] Step 5: According to X (n) , execute the amplitude optimization method of the transmission and reflection phase shift matrix to obtain the amplitude of the transmission and reflection phase shift matrix

[0147] Step 6: According to X (n) and Execute the RIS transmission and reflection phase shift matrix phase optimization method to solve the transmission and reflection phase shift matrix phases

[0148] Step 7: According to X (n) , and Calculate MSE (n) , and n = n + 1, then immediately return to execute Step 3;

[0149] Step 8: Output the estimated mean square error MSE of the minimum user information symbol of the system * .

[0150] Figure 3 is the algorithm convergence performance diagram under different schemes. Among them, the number of antennas is 20, the number of communication users is 4, the number of RIS reflection-transmission units is 40, and the base station transmission power is set to -10 dB. It can be seen from the figure that the proposed STAR-RIS scheme in the present invention has a faster convergence speed than the passive RIS scheme, and can basically reach convergence after 4 iterations, verifying the effectiveness and convergence of the method of the present invention. The final minimum mean square error of the proposed STAR-RIS scheme in the present invention is significantly lower than that of the passive RIS scheme, proving the effectiveness of the method of the present invention in minimizing the mean square error in this system.

[0151] Figure 4 is the relationship diagram between the signal-to-noise ratio of the transmitted signal and the total system rate under different schemes. It can be seen from the figure that the total system rate increases with the increase of the signal-to-noise ratio of the transmitted signal. Specifically, when the SNR increases from 0 to 5 dB, the proposed STAR-RIS scheme in the present invention has a gain of about 0.503 bps / Hz higher than the passive RIS scheme; when the SNR = 20 dB, the proposed STAR-RIS scheme in the present invention has a gain of about 1.489 bps / Hz higher than the passive RIS scheme. The results show that deploying STAR-RIS in the ISAC system can improve the communication service quality of the system compared with the passive RIS.

[0152] Figure 5 is the relationship diagram between the number of reflection-transmission units N c and the total system communication rate under different schemes. Among them, the number of antennas is 20, the number of communication users is 4, the sensing target is 2, and the threshold Γ t = 0.001. It can be seen from the figure that for the proposed STAR-RIS scheme of optimizing the phase and amplitude in the present invention, the total communication rate increases with the increase of the number of reflection-transmission units N c . Specifically, when N s = 12, N cIncreases from 28 to 36, and the corresponding total communication rate obtains a gain of 0.116 bps / Hz. When N c = 40, N s = 14, the optimization amplitude is about 0.599 bps / Hz higher than the equal-amplitude scheme, with an increase of about 15.24%. The results show that the STAR-RIS optimization phase and amplitude scheme proposed in the present invention can flexibly allocate beam energy, balance the CRB constraints of the sensing target and the communication link requirements, so that the newly added N c degrees of freedom are effectively utilized, avoiding resource occupation, that is, improving the total communication rate.

[0153] The present invention also discloses a minimum mean square error (MSE) beamforming system for user information symbols in a STAR-RIS-assisted ISAC system, which is used to execute the above method, including the following modules:

[0154] Precoded signal transmission module: used for the base station to transmit a precoded signal to the STAR-RIS;

[0155] Mean square error estimation module: taking the precoded signals respectively received by the communication user and the sensing target as input parameters, defining the MSE of the received symbol and the desired symbol according to the estimated MSE of the user information symbol, and calculating the estimated MSE of the user information symbol (n) ; where, MSE (n) represents the mean square error obtained in the nth calculation;

[0156] Judgment module: judging whether the MSE (n) obtained by the mean square error estimation module satisfies |MSE (n) - MSE (n-1) | ≤ ε, where the initial value of the mean square error MSE (0) = 0, and ε is a constant; if not satisfied, it is executed by the ISAC base station beam vector optimization module, and if satisfied, it jumps and is executed by the output module;

[0157] ISAC base station beam vector optimization module: taking the mean square error MSE (n) obtained by the judgment module as an input parameter, executing the ISAC base station beam vector optimization method, and outputting an M×L-dimensional matrix X * whose elements are all complex numbers; where, M and L are natural numbers, representing the number of rows and columns of the matrix respectively, and the superscript * represents the optimal value of X;

[0158] RIS phase shift matrix amplitude optimization module: taking X * obtained by the ISAC base station beam vector optimization module as an input parameter, executing the RIS phase shift matrix amplitude optimization method, and outputting the transmission phase shift matrix amplitude and the reflection phase shift matrix amplitude

[0159] RIS Transmission and Reflection Phase Shift Matrix Phase Optimization Module: Using the transmission phase shift matrix amplitude and the reflection phase shift matrix amplitude obtained by the RIS phase shift matrix amplitude optimization module as input parameters, execute the RIS transmission and reflection phase shift matrix phase optimization method, and output an N×N transmission matrix and a reflection matrix, both of whose elements are complex numbers. Here, N is the number of reflection-transmission units of the RIS, representing the number of rows and columns of the matrix. and the reflection phase shift matrix amplitude as input parameters, execute the RIS transmission and reflection phase shift matrix phase optimization method, output an N c ×N c dimensional transmission matrix and reflection matrix where N c is the number of reflection-transmission units of the RIS, representing the number of rows and columns of the matrix;

[0160] Current Mean Square Error Estimation Module: Using the obtained X, [parameters not clearly defined in the original], and [parameters not clearly defined in the original] as input parameters, calculate the estimated mean square error MSE of the user information symbols of the current system, let n = n + 1, and jump to the judgment module for execution; * , and as input parameters, calculate the estimated mean square error MSE of the user information symbols of the current system, let n = n + 1, and jump to the judgment module for execution; (n) , let n = n + 1, and jump to the judgment module for execution;

[0161] Output Module: Using the optimal value of the estimated mean square error of the user information symbols obtained by the judgment module as the output result.

[0162] For other contents of this embodiment, reference can be made to the above method embodiment.

[0163] The present invention also discloses an electronic device, including:

[0164] a processor;

[0165] a memory for storing a program, which, when called and executed by the processor, causes the processor to execute the above method or system.

[0166] The present invention can minimize the estimated mean square error of the user information symbols of the system and ensure the quality of user communication services, achieving an optimal compromise between user communication and target perception in the ISAC system.

[0167] Although the embodiments of the present invention have been clearly described. However, for those skilled in the art, without departing from the principle and spirit of the method of the present invention, various changes, modifications, substitutions, and variations can be made to these embodiments. The scope of the present invention is defined by the appended claims and their equivalents, and still belongs to the scope of the method of the present invention and is still regarded as the protection scope of the present invention.

Claims

1. The MSE minimization beamforming method for user information symbols of the STAR-RIS assisted ISAC system, characterized in that It includes the following steps: S1: The ISAC base station sends a precoding signal to the STAR-RIS; S2: The communication user and the sensing target respectively receive the precoding signals in step S1 as input parameters, estimate the MSE based on the information symbols received by the user, define the MSE between the received symbol and the desired symbol, and calculate the estimated MSE of the information symbols received by the user (n) ; where, MSE (n) represents the mean square error calculated in the nth calculation; S3: Determine the MSE obtained in step S2 (n) whether it satisfies |MSE (n) - MSE (n-1) | ≤ ε, where the initial value of the mean square error MSE (0) = 0, and ε is a constant; if not satisfied, then execute step S4, if satisfied, then jump to and execute step S8; S4: Use the mean squared error MSE obtained in step S3 (n) as the input parameter, execute the ISAC base station beam vector optimization method, and output an M×L-dimensional matrix X whose elements are all complex numbers * ; where M and L are natural numbers, representing the number of rows and columns of the matrix respectively, and the superscript * represents the optimal value of X; S5: Take the X obtained in step S4 * , as the input parameter, execute the RIS phase shift matrix amplitude optimization method, and output the transmission phase shift matrix amplitude with all elements being real numbers and the reflection phase shift matrix amplitude where the superscript * represents and the optimal values of; S6: Take the amplitude of the transmission phase shift matrix obtained in step S5 and the amplitude of the reflection phase shift matrix as input parameters, execute the RIS transmission and reflection phase shift matrix phase optimization method, and output an N c ×N c -dimensional transmission matrix and reflection matrix where N c is the number of reflection-transmission units of the RIS, representing the number of rows and columns of the matrix, and the superscript * represents and optimal values; S7: Take the X obtained in step S4 * , the obtained in step S5, and the obtained in step S6 as input parameters, and calculate the estimated mean square error MSE of the user information symbol of the current system (n) , let n = n + 1, and jump to step S3; S8: Estimate the optimal value of the mean square error of the information symbols received by the user obtained in step S3 as the output result.

2. The method for minimizing the MSE of the user information symbols in the STAR-RIS assisted ISAC system according to claim 1, wherein In step S4, the optimization method for the beam vector X of the ISAC base station is as follows: The ISAC system includes a base station with a positive integer M number of antennas, K single-antenna communication users, T detection targets, a STAR-RIS with a positive integer N number of reflection-transmission units c and a positive integer N number of sensing units s ; and an obstacle that blocks the line of sight between the communication users and the sensing targets and the base station. Among them, the sets of communication users and sensing targets are respectively expressed as: The communication channel coefficient matrix is expressed as follows: is an N×M-dimensional matrix with all elements being complex numbers, representing the channel coefficient matrix from the ISAC base station to the STAR-RIS; is an N×1-dimensional vector with all elements being complex numbers, representing the channel from the STAR-RIS to the k-th communication user; among them, the phase shift transmission matrix of the STAR-RIS and the reflection matrix are defined as where ρ i,n ∈[0,1] and θ i,n ∈[0,2π] respectively represent the amplitude and phase shift response of the n-th element, and satisfy diag(·) represents a diagonal matrix; after L time slots, in the STAR-RIS-assisted non-line-of-sight ISAC system, the ISAC base station sends s k symbols that reach the communication user through the transmission of the RIS, and the received signal at the communication user is expressed as: Among them, is a K×L-dimensional matrix with all elements being complex numbers; is an N c ×K-dimensional matrix, representing the joint channel from the RIS to the communication user, and F H is the conjugate transpose of F; is a K×M-dimensional matrix with all elements being complex numbers, representing the joint channel from the ISAC base station to K users over L frame time slots; is the RIS phase shift transmission matrix; is the precoding signal matrix transmitted by the ISAC base station; is a K×L-dimensional matrix with all elements being complex numbers, representing the additive noise received by the communication user that follows a Gaussian distribution; the symbol to be received by the communication user is Then Y is re-expressed as: where S is a K×L-dimensional matrix with all elements being complex numbers; the second term represents multi-user interference, and the total power of MUI is: Among them, is the Frobenius norm operation; the signal-to-interference-plus-noise ratio of the k-th user per frame is expressed as: where h k denotes the k-th row of H, s k,j denotes the symbol at the k-th row and j-th column, E(·) denotes the expected value of the independent variable with respect to j, is a constant and is the variance of the complex additive white Gaussian noise at user k; the total rate calculation formula is The MSE is defined as: where, y l is the l-th column of Y, denotes the 2-norm calculation; for the target sensing part, a RIS with N s sensing units is utilized to estimate the directions of arrival of T targets located at different angles , t = 1, ..., T; then after L time slots, the signals received by the N s sensing units are expressed as: where, α t represents the reflection coefficient of the t-th target, is an N c ×1 vector with all elements being complex numbers, representing the RIS reflection element steering vector; λ is a positive integer representing the normalized element spacing; is an N s ×1 vector with all elements being complex numbers, representing the RIS sensing element steering vector; is an N s ×L matrix with all elements being complex numbers, representing additive white Gaussian noise with zero mean and covariance matrix R N ; the estimated Cramér-Rao bound CRB of the azimuth angle and the direction determination of other targets are as follows: where Tr(·) is the trace operation of a matrix, denotes the derivative of denotes the derivative of, b i and a i respectively denote and the i-th entry of; the azimuth angle the estimated CRB of is less than the threshold Γ t , and the relationship is expressed as follows: The problem of minimizing the estimated mean square error MSE of the user information symbols is modeled as: where x m,l represents the entry at the (m, l) - th position in X, P t is the maximum transmit power of the ISAC base station, M is a positive integer; C1 is the constant - modulus constraint of the ISAC waveform; C2 and C3 are the phase constraints of the RIS phase - shift matrix during transmission and reflection; C4 is the constraint for the direction - of - arrival estimation of the sensing target. Define η t = 1 / (2|α t | 2 Γ t ) represents a very small real number; C5 is the amplitude constraint of the RIS phase - shift matrix during transmission and reflection; C6 and C7 are the same - amplitude representations of the RIS phase - shift matrix; Fix optimize X to complete the constant - modulus design of the ISAC waveform. Therefore, the problem is reformulated as: where C1 and C4 are the constraints in equation (9); Vectorize X into Therefore, the mean square error of the information symbol estimation and the constraint C4 are respectively reformulated as: wherein, is the Kronecker product operation, vec(·) is vectorization, Re{·} is the operation of taking the real part of a complex number, and (·) H is the conjugate transpose of a matrix, denotes definition; introducing an auxiliary variable μ = [μ1,..., μ T , the constraint C4 is re-expressed as: where μ is a T×1-dimensional array with all elements being positive real numbers; According to equation (13), equation (10) is reformulated as: where C1 is the constraint condition of equation (10), and C4 is the constraint condition for simplified solution in equation (10); The penalty function method is introduced, and the specific expression is: Among them, the penalty coefficient υ t satisfies υ in each iteration t > 0; therefore, in each iteration, is used to update υ t ; under the condition of determining x, μ t is expressed as: μ t = max[x H Φ t x - η t , 0] (16) where max[·] represents taking the maximum value in the set; According to equation (15), equation (14) is reformulated as: Among them, where x is optimized on the ML-dimensional complex circle; define as the feasible region of the problem, that is Let be a point on, then the tangent space of is denoted as where ⊙ represents the Hadamard product; the Riemannian gradient is expressed as: Among them, is the projection towards the tangent space; is the Euclidean gradient of the objective function and the expression is: where the expression of ζ'(x) is: According to the Riemannian steepest descent algorithm for iterative update, the descent direction of the nth iteration is selected as the negative counterpart of the Riemannian gradient, so the update of x at the (n + 1)th iteration is: where δ n is the step size; represents a retraction operation that is used to map points in the tangent space to the manifold; for a spherical ball, the retraction operation is expressed as: Solving equation (22) gives the optimal beam vector $\mathbf{X}$ of the ISAC base station * .

3. The MSE minimization beamforming method for user information symbols of the STAR-RIS assisted ISAC system according to claim 2, characterized in that, In step S5, the optimization method for the amplitude of the RIS phase shift matrix is implemented by the following steps: S5.1: Equation (9) is reformulated as: where C4, C5, C6, and C7 are all the constraint conditions in equation (10); S5.2: Transform and into vector forms and respectively. Therefore, the minimum mean square error of the information symbol estimated by the user and the constraint C4 in Equation (24) are reformulated as follows: Among them, Tr(·) represents the trace operation of a matrix, ⊙ represents the Hadamard product operation, (·) T represents the transpose of a matrix, (·) H represents the conjugate transpose of a matrix, e * represents the conjugate of e; define C = FF H ,D = GXX H G H ,E = GXS H F H and S5.3: According to equations (25) and (26), the minimum mean square error of the estimated information symbols and the constraint C4 in equation (29) are respectively reformulated as: S5.4: In equations (27) and (28), define and Then equation (24) can be reformulated as: Among them, C4 is the objective function and constraint condition obtained by simplifying formula (24), and C5 is the constraint condition of formula (24); S5.5: Equation (29) can be solved using the KKT conditions; first, find the Lagrangian function of equation (29), which is expressed as: Among them, is the Lagrange multiplier; then the KKT conditions are written as: Among them, represents the Lagrangian function for taking the partial derivative; S5.6: Analyze Equation (31). When and hold, When and hold, where min{·} represents taking the minimum value in the set. In summary, we obtain which is expressed as follows: S5.7: According to and equation (32), obtain 4. The MSE minimization beamforming method for user information symbols of the STAR-RIS assisted ISAC system according to claim 3, characterized in that, In step S6, the optimization method for the phase of the RIS transmission and reflection phase shift matrix is implemented by the following steps: S6.1: According to equations (27) and (28), the problem is reformulated as follows: where the objective function in equation (33) is the objective function obtained by simplifying and solving equation (27), and C2 and C6 are the constraint conditions in equation (9); the objective function in equation (34) is a newly defined auxiliary variable, and C3, C4, and C7 are the constraint conditions in equation (9); S6.2: The only constraint of Equation (33) is the constant modulus constraint C2; Optimize on the N c dimensional complex circle; Define as the feasible region of the problem, that is Let be a point on, then The tangent space of is expressed as: where Re{·} represents the operation of taking the real part of a complex number, and ⊙ represents the Hadamard product operation, denotes the conjugate of; S6.3: Obtain the Riemannian gradient of the objective function by projecting the Euclidean gradient, which is expressed as follows: ​ Among them, is the projection towards the tangent space, is the objective function of the Euclidean gradient, which is expressed as follows: S6.4: Update iteratively according to the Riemann steepest descent algorithm. The descent direction at the n-th iteration is chosen as the negative counterpart of the Riemann gradient. Therefore, the update at the (n + 1)-th iteration is: Among them, δ n is the step size, represents a retraction operation, which is used to map points in the tangent space to the manifold ; S6.5: Solve Equation (38) and C6 to obtain the phase of the optimal RIS transmission phase shift matrix S6.6: In formula (34), C4 is a non-convex constraint. Let Then According to the successive linearization method, rewrite C4 as: wherein, is the result of the previous iteration; according to Equation (39), Equation (34) is transformed as follows: where C3 is the constraint condition of equation (34), and C4 is the constraint condition obtained by simplifying and solving C4 in equation (34); S6.7: Solve that the solution of equation (40) is a linear problem, and solve it through a convex optimization solver to obtain According to C7 in equation (34), obtain the phase of the optimal RIS reflection phase shift matrix 5. The MSE-minimized beamforming system for user information symbols of the STAR-RIS-aided ISAC system, which is used to perform the method according to any one of claims 1-4, is characterized in that It includes the following modules: Precoding signal transmission module: used for the base station to transmit a precoding signal to the STAR-RIS; Mean Square Error Estimation Module: Taking the precoded signals respectively received by the communication user and the sensing target as input parameters, defining the MSE of the received symbol and the desired symbol according to the estimated MSE of the user information symbol, and calculating the estimated MSE of the user information symbol (n) ; where, MSE (n) represents the mean square error obtained in the nth calculation; Judgment module: Judge the MSE obtained by the mean square error estimation module (n) whether it satisfies |MSE (n) - MSE (n-1) | ≤ ε, where the initial value of the mean square error MSE (0) = 0, ε is a constant; if not satisfied, it is executed by the ISAC base station beam vector optimization module, if satisfied, it jumps and is executed by the output module; ISAC base station beam vector optimization module: taking the mean square error MSE obtained by the judgment module (n) as the input parameter, executing the ISAC base station beam vector optimization method, and outputting an M×L-dimensional matrix X with all elements being complex numbers * ; where M and L are natural numbers, representing the number of rows and columns of the matrix respectively, and the superscript * represents the optimal value of X; RIS Phase Shift Matrix Amplitude Optimization Module: Take the X obtained by the ISAC base station beam vector optimization module * , as input parameters, execute the RIS phase shift matrix amplitude optimization method, and output the transmission phase shift matrix amplitude with all elements being real numbers and the reflection phase shift matrix amplitude RIS Transmission and Reflection Phase Shift Matrix Phase Optimization Module: The transmission phase shift matrix amplitude obtained by the RIS phase shift matrix amplitude optimization module and the reflection phase shift matrix amplitude are used as input parameters to execute the RIS transmission and reflection phase shift matrix phase optimization method, and an N c ×N c dimensional transmission matrix and a reflection matrix are output. Among them, N c is the number of reflection-transmission units of the RIS, representing the number of rows and columns of the matrix; Current mean square error estimation module: Take the obtained X * , and as input parameters, and calculate the estimated mean square error MSE (n) of the user information symbol of the current system. Let n = n + 1, and jump to the judgment module for execution; Output module: Based on the optimal value of the estimated mean square error of the user information symbols obtained by the judgment module as the output result.

6. An electronic device, characterized in that, It includes: Processor; Memory, used to store programs. When the program is called and executed by the processor, the processor executes the method described in any one of claims 1-4 or the system described in claim 5.

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