Star-ris position optimization method and device based on mm framework

Abstract

The embodiment of the application provides a STAR-RIS position optimization method and device based on an MM framework, a position related term coefficient set is constructed through a channel matrix and a user angle parameter, a convex optimization solving model is formed by combining a gradient vector and a Hessian matrix norm to respectively construct a concave lower bound and a convex upper bound replacement function, and the final element position configuration is issued to a driving mechanism to complete closed-loop deployment adjustment through iterative convergence judgment, effectively solving the deficiencies of traditional technologies in position related term modeling, non-convex replacement function construction and iterative convergence configuration, and providing technical support for intelligent optimization and adaptive space deployment of a movable element position of a STAR-RIS assisted communication system.

Description

Technical Field

[0001] This application relates to the field of data processing, specifically to a STAR-RIS position optimization method and apparatus based on the MM framework. Background Technology

[0002] Existing STAR-RIS (Simultaneously Transmitting and Reflecting RIS; RIS: reconfigurable intelligent surface) location optimization methods have significant shortcomings. Traditional systems perform poorly in channel information acquisition and location-related term modeling. They typically treat intelligent metasurface elements as fixed deployments and lack the ability to obtain the channel matrix from the base station to the movable intelligent metasurface element from the channel estimation unit, calculate the path difference function of each element by combining the user's azimuth and elevation parameters, and expand the effective channel magnitude squared to obtain the set of location-related term coefficients. This results in insufficient fine-grained modeling capability of the contribution of element spatial location to channel gain, making it difficult to provide an accurate basis for subsequent location optimization.

[0003] Furthermore, existing technologies face bottlenecks in constructing substitution functions for non-convex trigonometric function terms and in convex optimization modeling. Most systems lack the ability to extract non-convex trigonometric function terms from the set of position-related coefficients using the MM framework (Majorization-Minimization), calculate the gradient vector and Hessian matrix norm at the current iteration point, and construct quadratic concave lower bound substitution functions and quadratic convex upper bound substitution functions, respectively. This prevents the efficient substitution of the concave lower bound substitution function into the signal power term and the convex upper bound substitution function into the interference power term to form a solvable convex optimization model. Consequently, this affects the solvability and optimization quality of joint optimization of component positions in scenarios where users in both the STAR-RIS reflection and transmission regions are simultaneously serving each other.

[0004] Existing systems have technical shortcomings in iterative convergence control and component position configuration distribution. They lack a complete closed-loop optimization execution mechanism that synchronously updates fractional programming parameters with the optimal component position coordinates output by the solver, compares them with preset convergence threshold conditions to determine iteration termination, and distributes the final component position configuration to the component drive mechanism for spatial deployment adjustment. This affects the adaptive position adjustment capability of the movable component intelligent metasurface in dynamic channel scenarios and the system capacity gain. Solving these problems is of great significance for improving the intelligence level of position optimization in the STAR-RIS assisted communication system. Summary of the Invention

[0005] To address the problems in the existing technology, this application provides a STAR-RIS position optimization method and apparatus based on the MM framework, which can effectively solve the shortcomings of traditional technologies in position-related term modeling, non-convex substitution function construction and iterative convergence configuration distribution, and provides technical support for intelligent optimization and adaptive spatial deployment of movable components in STAR-RIS assisted communication systems.

[0006] To solve at least one of the above problems, this application provides the following technical solution: Firstly, this application provides a STAR-RIS position optimization method based on the MM framework, including: The channel matrix from the base station to the smart metasurface of the movable element is obtained from the channel estimation unit. The azimuth and elevation parameters of the users in the reflection area and the transmission area relative to the smart metasurface of the movable element are obtained from the user positioning unit. Based on the channel matrix and the azimuth and elevation parameters, the path difference function of each element with respect to the base station direction and the user direction is calculated to obtain the path difference function set. The path difference function set is used to expand the square of the effective channel magnitude of each user to obtain the location correlation coefficient set. For the element to be optimized, non-convex trigonometric function terms are extracted from the set of position-related coefficients. The gradient vector and Hessian matrix norm of the non-convex trigonometric function terms at the current iteration point are calculated to obtain a gradient parameter set. The gradient parameter set is used to construct a quadratic concave lower bound substitution function and a quadratic convex upper bound substitution function. The quadratic concave lower bound substitution function is substituted into the signal power term and the quadratic convex upper bound substitution function is substituted into the interference power term to form a convex optimization solution model. The optimal position coordinates of the component are obtained by calling the optimization solver on the convex optimization solution model. The optimal position coordinates of the component are written into the position configuration and the fractional programming parameters are updated. The fractional programming parameters are compared with the preset convergence threshold condition. When the preset convergence threshold condition is met, the final component position configuration is sent to the component driving mechanism of the movable component intelligent metasurface to adjust the component spatial deployment.

[0007] Furthermore, it also includes: reading the line-of-sight component estimate and the non-line-of-sight component estimate from the base station to the smart metasurface of the movable element from the channel estimation unit; performing a weighted synthesis of the line-of-sight component estimate and the non-line-of-sight component estimate based on a preset Rice factor to obtain a channel matrix; and decomposing the channel matrix according to the element index to obtain the channel column vector corresponding to each element and writing it into the channel parameter buffer. The spatial coordinates of users in the reflection and transmission areas are read from the user positioning unit. Based on the reference origin coordinates of the intelligent metasurface of the movable element and the spatial coordinates, direction vector calculation is performed to obtain the direction vector of each user. The direction vector of each user is projected onto the horizontal and vertical planes to calculate the azimuth and elevation angles respectively to obtain the azimuth and elevation angle parameters. The azimuth and elevation angle parameters are associated and stored with the channel column vector in the channel parameter buffer.

[0008] Furthermore, it also includes: calculating the path difference function of each element with respect to the base station direction based on the position coordinates of each element and the azimuth and elevation angle of the base station; calculating the path difference function of each element with respect to the user direction based on the position coordinates of each element and the azimuth and elevation angle of the user; and organizing the path difference function of each element with respect to the base station direction and the path difference function of each element with respect to the user direction into a path difference function set. Based on the path difference function set, the squared effective channel magnitude of each user is expanded into a summation of cascaded link autocorrelation terms and cross terms. The complex exponential product coefficients of each element pair are extracted from the cascaded link autocorrelation terms to obtain double summation coefficients. The complex exponential coefficients of each element are extracted from the cross terms to obtain single summation coefficients. The double summation coefficients and the single summation coefficients are combined to obtain a set of location correlation coefficients.

[0009] Furthermore, it also includes: selecting double summation coefficients and single summation coefficients related to the index of the element to be optimized from the set of position-related coefficients, and expanding the complex exponential terms in the double summation coefficients and the single summation coefficients into a linear combination of cosine function terms and sine function terms using Euler's formula to obtain non-convex trigonometric function terms; The gradient vector is obtained by taking the first-order partial derivative of the non-convex trigonometric function terms based on the position coordinates of the element to be optimized. The Hessian matrix is ​​obtained by taking the second-order partial derivative of the non-convex trigonometric function terms based on the position coordinates of the element to be optimized. The Frobenius norm is calculated on the Hessian matrix to obtain the quadratic coefficients. The gradient vector and the quadratic coefficients are then organized into a gradient parameter set.

[0010] Furthermore, it also includes: reading the gradient vector and quadratic coefficient from the gradient parameter set; constructing a quadratic concave lower bound substitution function based on the inner product of the current iteration point function value and the gradient vector and the position increment vector minus half of the product of the quadratic coefficient and the square of the magnitude of the position increment vector; and constructing a quadratic convex upper bound substitution function based on the inner product of the current iteration point function value and the gradient vector and the position increment vector plus half of the product of the quadratic coefficient and the square of the magnitude of the position increment vector. The quadratic concave lower bound substitution function is substituted into the position-related part of each user signal power term to form a signal power concave function expression. The quadratic convex upper bound substitution function is substituted into the position-related part of each user interference power term to form an interference power convex function expression. Based on the signal power concave function expression and the interference power convex function expression, a convex form of the signal-to-interference-plus-noise ratio (SINR) constraint is constructed. The convex form of the SINR constraint is combined with the component region boundary constraint and the component spacing linearization constraint to form a convex optimization solution model.

[0011] Furthermore, it also includes: assembling the objective function coefficients, constraint coefficient matrices, and constant vectors of the convex optimization solution model into a standard optimization problem data structure, and calling the optimization solver to perform interior point method on the standard optimization problem data structure to obtain the optimal position coordinates of the components and the values ​​of auxiliary variables; Write the optimal position coordinates of the element into the coordinate storage area of ​​the corresponding element index in the position configuration. Based on the optimal position coordinates of the element, recalculate the signal power and interference plus noise power of each user to obtain the power calculation result. Write the ratio of signal power to interference plus noise power in the power calculation result into the parameter storage area as the update value of the fractional programming parameter.

[0012] Furthermore, it also includes: reading the current round fractional programming parameters and the previous round fractional programming parameters from the parameter storage area, calculating the difference between the current round fractional programming parameters and the previous round fractional programming parameters and obtaining the relative change to obtain the parameter change, and comparing the parameter change with the preset convergence threshold condition to obtain the convergence determination result. When the convergence determination result is non-convergence, the current component position configuration is used as the initial position for the next iteration and the component traversal optimization process is returned. When the convergence determination result is convergence, the coordinates of each component are read from the position configuration to obtain the final component position configuration. The final component position configuration is encapsulated as a control command and sent to the component driving mechanism of the movable component intelligent metasurface through the control signaling interface to adjust the component space deployment.

[0013] Secondly, this application provides a STAR-RIS position optimization device based on the MM framework, comprising: The location calculation module is used to obtain the channel matrix from the channel estimation unit to the smart metasurface of the movable element, obtain the azimuth and elevation parameters of the user in the reflection area and the user in the transmission area relative to the smart metasurface of the movable element from the user positioning unit, calculate the path difference function of each element with respect to the direction of the base station and the direction of the user based on the channel matrix and the azimuth and elevation parameters, and obtain a set of path difference functions. The set of path difference functions is used to expand the square of the effective channel magnitude of each user to obtain a set of location correlation coefficients. The model building module is used to extract non-convex trigonometric function terms from the set of position-related coefficients for the element to be optimized, calculate the gradient vector and Hessian matrix norm of the non-convex trigonometric function terms at the current iteration point to obtain a gradient parameter set, use the gradient parameter set to construct a quadratic concave lower bound substitution function and a quadratic convex upper bound substitution function, substitute the quadratic concave lower bound substitution function into the signal power term and substitute the quadratic convex upper bound substitution function into the interference power term to form a convex optimization solution model; The position optimization module is used to call the optimization solver to solve the convex optimization solution model to obtain the optimal position coordinates of the component, write the optimal position coordinates of the component into the position configuration and update the fractional programming parameters, compare the fractional programming parameters with the preset convergence threshold condition, and when the preset convergence threshold condition is met, send the final component position configuration to the component driving mechanism of the movable component intelligent metasurface to adjust the component spatial deployment.

[0014] Thirdly, this application provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the STAR-RIS position optimization method based on the MM framework.

[0015] Fourthly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the STAR-RIS position optimization method based on the MM framework.

[0016] Fifthly, this application provides a computer program product, including a computer program / instructions that, when executed by a processor, implement the steps of the STAR-RIS location optimization method based on the MM framework.

[0017] As can be seen from the above technical solution, this application provides a STAR-RIS position optimization method and device based on the MM framework. It constructs a set of position-related term coefficients by using the channel matrix and user angle parameters, and constructs a convex optimization solution model by combining the gradient vector and Hessian matrix norm to form a quadratic concave lower bound and convex upper bound substitution function. The final component position configuration is then sent to the drive mechanism to complete the closed-loop deployment adjustment through iterative convergence judgment. This effectively solves the shortcomings of traditional technologies in terms of position-related term modeling, non-convex substitution function construction, and iterative convergence configuration sending, and provides technical support for the intelligent optimization and adaptive spatial deployment of movable component positions in the STAR-RIS assisted communication system. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart illustrating the STAR-RIS position optimization method based on the MM framework in an embodiment of this application. Figure 2 This is a structural diagram of the STAR-RIS position optimization device based on the MM framework in the embodiments of this application. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0021] The acquisition, storage, use, and processing of data in this application comply with relevant laws and regulations.

[0022] In view of the problems existing in the prior art, this application provides a STAR-RIS position optimization method and device based on the MM framework. The method constructs a set of position-related coefficients by using the channel matrix and user angle parameters, and constructs a convex optimization solution model by combining the gradient vector and Hessian matrix norm to form a quadratic concave lower bound and convex upper bound substitution function. The final component position configuration is then sent to the drive mechanism to complete the closed-loop deployment adjustment through iterative convergence judgment. This method effectively solves the shortcomings of traditional technologies in terms of position-related term modeling, non-convex substitution function construction, and iterative convergence configuration sending, and provides technical support for the intelligent optimization and adaptive spatial deployment of movable components in the STAR-RIS assisted communication system.

[0023] To effectively address the shortcomings of traditional techniques in areas such as location-related term modeling, non-convex substitution function construction, and iterative convergence configuration deployment, and to provide technical support for intelligent optimization and adaptive spatial deployment of movable components in STAR-RIS assisted communication systems, this application provides an embodiment of a STAR-RIS location optimization method based on the MM framework. See [link to embodiment]. Figure 1 The STAR-RIS position optimization method based on the MM framework specifically includes the following: Step S101: Obtain the channel matrix from the base station to the smart metasurface of the movable element from the channel estimation unit; obtain the azimuth and elevation parameters of the user in the reflection area and the user in the transmission area relative to the smart metasurface of the movable element from the user positioning unit; calculate the path difference function of each element with respect to the base station direction and the user direction based on the channel matrix and the azimuth and elevation parameters to obtain the path difference function set; use the path difference function set to expand the square of the effective channel magnitude of each user to obtain the location correlation coefficient set. In this embodiment, the line-of-sight (LAS) component estimates and non-LAS component estimates from the base station to the smart metasurface of the movable element are read from the channel estimation unit. The LAS component estimates characterize the channel response when there is a direct propagation path between the base station antenna array and each element, while the non-LAS component estimates characterize the multipath channel response reaching each element after reflection from surrounding scatterers. A weighted synthesis of the LAS and non-LAS component estimates is performed based on a preset Rice factor, which reflects the relative intensity ratio of LAS propagation to scatter propagation. The weighted synthesis process multiplies the LAS component estimates by the Rice factor normalization weights and adds them to the complementary weighted components of the non-LAS component estimates to obtain the channel matrix.

[0024] The channel matrix is ​​decomposed column-wise according to the element index. The decomposition process sequentially extracts the column vectors corresponding to the first to last elements in the matrix. The dimension of each channel column vector is equal to the number of base station antennas, representing the complex channel gain from each base station antenna to that element. In this embodiment, the channel column vectors corresponding to each element are written to the channel parameter buffer. During writing, the element index is used as the storage address identifier, facilitating subsequent retrieval and calling by index during path difference function calculation.

[0025] After the aforementioned channel parameters are written, this embodiment reads the spatial coordinates of the user in the reflection area and the user in the transmission area from the user positioning unit. These spatial coordinates are represented in a three-dimensional Cartesian coordinate system. Direction vector calculation is performed based on the reference origin coordinates of the intelligent metasurface of the movable element and the spatial coordinates. The calculation process subtracts the reference origin coordinates from the user coordinates to obtain the direction vector pointing to the user. In this embodiment, each user direction vector is projected onto a horizontal plane and a vertical plane, respectively. The angle between the horizontal projection vector and the positive direction of the reference axis is the azimuth angle, and the angle between the direction vector and the horizontal plane is the elevation angle, thus obtaining the azimuth and elevation angle parameters. These azimuth and elevation angle parameters are associated with the channel column vectors in the channel parameter buffer, stored according to user and element indices.

[0026] Accordingly, this embodiment calculates the path difference function of each component with respect to the base station direction based on the position coordinates of each component and the base station azimuth and elevation angles. The path difference function represents the difference in propagation distance of a signal from the base station direction to the position of a component relative to the reference origin. The calculation process adds the product of the component's horizontal coordinate with the sine of the base station azimuth and the cosine of the base station elevation angle, and the product of the component's vertical coordinate with the sine of the base station elevation angle. This embodiment uses the same method to calculate the path difference function of each component with respect to the user direction based on the position coordinates of each component and the user azimuth and elevation angles, and organizes the path difference functions of each component with respect to the base station direction and the path difference functions of each component with respect to the user direction into a path difference function set.

[0027] After the path difference function set is constructed, this embodiment expands the squared effective channel magnitude of each user into a summation of cascaded link autocorrelation terms and cross terms based on the path difference function set. The cascaded link autocorrelation term is the expansion result of the product of the cascaded channel component via the movable element intelligent metasurface and its own conjugate, including the complex exponential product structure of each element pair. The cross term is the expansion result of the cross product of the cascaded channel component and the direct channel component, including the individual complex exponential structure of each element.

[0028] In this embodiment, the complex exponential product coefficients of each element pair are extracted from the cascaded link autocorrelation term to obtain double summation coefficients, where the index of the double summation coefficient corresponds to the combination of the first and second elements. The complex exponential coefficients of each element are extracted from the cross term to obtain single summation coefficients, where the index of the single summation coefficient corresponds to a single element. The double summation coefficients and the single summation coefficients are merged to obtain a set of position-related term coefficients. This set of position-related term coefficients is written to the decomposition result cache for subsequent steps, S102, to retrieve and call when extracting non-convex trigonometric function terms related to the index of the element to be optimized.

[0029] Step S102: For the element to be optimized, extract non-convex trigonometric function terms from the set of position-related coefficients, calculate the gradient vector and Hessian matrix norm of the non-convex trigonometric function terms at the current iteration point to obtain a gradient parameter set, use the gradient parameter set to construct a quadratic concave lower bound substitution function and a quadratic convex upper bound substitution function, substitute the quadratic concave lower bound substitution function into the signal power term and substitute the quadratic convex upper bound substitution function into the interference power term to form a convex optimization solution model; In this embodiment, the set of location-related coefficients written to the decomposition result buffer in step S101 is used to filter double-summation coefficients and single-summation coefficients related to the index of the element to be optimized. The filtering process traverses the index pairs of the double-summation coefficients, retaining coefficients whose first or second element index is equal to the index of the element to be optimized, and simultaneously extracting coefficients whose index is equal to the index of the element to be optimized from the single-summation coefficients. The filtered coefficients contain a location-related structure expressed in complex exponential form, where the exponent part of the complex exponent is a linear combination of the path difference function of the element to be optimized with respect to the base station direction and the path difference function with respect to the user direction.

[0030] After the extraction of the screening coefficients, this embodiment expands the complex exponent terms in the double summation coefficients and the single summation coefficients into a linear combination of cosine and sine function terms using Euler's formula. In the expansion process, the real part of the complex exponent is represented as a cosine function, and the imaginary part as a sine function. The independent variables of both the cosine and sine functions are linear combinations of path difference functions. This embodiment merges the expanded cosine and sine function terms with the same independent variable structure. The merged expression constitutes a non-convex trigonometric function term. The non-convexity of the non-convex trigonometric function term stems from the non-linear dependence of the trigonometric functions on the component position coordinates.

[0031] Accordingly, this embodiment obtains the gradient vector by calculating the first-order partial derivatives of the non-convex trigonometric function terms with respect to the position coordinates of the element to be optimized. The gradient vector contains two components: the first component is the partial derivative of the non-convex trigonometric function terms with respect to the horizontal coordinates of the element, and the second component is the partial derivative of the non-convex trigonometric function terms with respect to the vertical coordinates of the element. For the cosine function term, its partial derivative with respect to the position coordinates is the product of the negative sine function and the path difference function with respect to the position coordinates. For the sine function term, its partial derivative with respect to the position coordinates is the product of the cosine function and the path difference function with respect to the position coordinates. The partial derivative of the path difference function with respect to the horizontal coordinates of the element is the difference between the products of the azimuth sine and the elevation cosine, and its partial derivative with respect to the vertical coordinates of the element is the difference between the elevation sine and the vertical coordinates.

[0032] After the gradient vector is calculated, this embodiment obtains the Hessian matrix by calculating the second-order partial derivatives of the non-convex trigonometric function terms with respect to the position coordinates of the element to be optimized. The Hessian matrix is ​​a second-order symmetric matrix, with diagonal elements representing the second-order partial derivatives of the non-convex trigonometric function terms with respect to the horizontal and vertical coordinates, respectively, and off-diagonal elements representing mixed second-order partial derivatives. This embodiment calculates the Frobenius norm of the Hessian matrix to obtain the quadratic coefficients, where the Frobenius norm is the square root of the sum of the squares of the elements of the Hessian matrix. The gradient vector and the quadratic coefficients are organized into a gradient parameter set, which is then written into the gradient parameter buffer.

[0033] Based on the aforementioned gradient parameter set, this embodiment reads the gradient vector and quadratic term coefficients from the gradient parameter buffer to construct the substitution function. The expression for the quadratic concave lower bound substitution function is: V(w) = h(w0) + d^T (w - w0) - (r / 2) ||w - w0||^2, Where h(w0) represents the function value of the non-convex trigonometric function term at the current iteration point w0, d represents the gradient vector, w represents the position vector of the element to be optimized, r represents the coefficient of the quadratic term, and ||w - w0||^2 represents the squared magnitude of the position increment vector. The quadratic concave lower bound substitution function V(w) is not greater than the original function value throughout the entire domain and is tangent to the original function at the current iteration point. The construction method of the quadratic convex upper bound substitution function is similar to that of the quadratic concave lower bound substitution function, except that the negative sign is changed to a positive sign to make the quadratic term positive, so that it is not less than the original function value throughout the entire domain.

[0034] In this embodiment, the quadratic concave lower bound substitution function is substituted into the position-related part of each user signal power term to form a signal power concave function expression, and the quadratic convex upper bound substitution function is substituted into the position-related part of each user interference power term to form an interference power convex function expression. Based on the signal power concave function expression and the interference power convex function expression, a convex form of the signal-to-interference-plus-noise ratio (SIR) constraint is constructed. The convex SIR constraint is expressed as the difference between the signal power concave function and the product of the fractional programming parameter and the interference power convex function, which is not less than the auxiliary variable. In this embodiment, the convex form of the SIR constraint is combined with the component region boundary constraint and the component spacing linearization constraint to form a convex optimization solution model. The component region boundary constraint is expressed as the upper and lower limits of the component's horizontal and vertical coordinates, and the component spacing linearization constraint is obtained by performing a first-order Taylor expansion of the original modulus constraint at the current iteration point. The convex optimization solution model is written into the optimization problem cache for subsequent step S103 to call the optimization solver for solution.

[0035] Step S103: Call the optimization solver to solve the convex optimization model to obtain the optimal position coordinates of the element, write the optimal position coordinates of the element into the position configuration and update the fractional programming parameters, compare the fractional programming parameters with the preset convergence threshold condition, and when the preset convergence threshold condition is met, send the final element position configuration to the element driving mechanism of the movable element intelligent metasurface to adjust the element spatial deployment.

[0036] In this embodiment, the objective function coefficients, constraint coefficient matrix, and constant vector are read from the convex optimization solution model written into the optimization problem buffer in step S102. The objective function coefficients include weighted coefficients of each user auxiliary variable, and the constraint coefficient matrix includes linear and quadratic coefficients corresponding to the convex form of the signal-to-interference-plus-noise ratio constraint, the upper and lower limits of the position coordinates corresponding to the element region boundary constraint, and the first-order expansion coefficients corresponding to the linearization constraint of the element spacing. This embodiment assembles the objective function coefficients, the constraint coefficient matrix, and the constant vector into a standard optimization problem data structure, which conforms to the input format specification of a convex quadratic programming problem.

[0037] After the standard optimization problem data structure is assembled, this embodiment calls the optimization solver to perform an interior-point method solution on the standard optimization problem data structure. The interior-point method constructs a central path within the feasible region and gradually approaches the optimal solution along the path. Each iteration solves Newton's equations to obtain the search direction and step size, terminating when the duality gap is less than a preset accuracy threshold. The optimization solver outputs the optimal position coordinates of the element and the values ​​of auxiliary variables. The optimal position coordinates of the element include the horizontal and vertical coordinate components of the element to be optimized.

[0038] Accordingly, in this embodiment, the optimal location coordinates of the component are written into the coordinate storage area of ​​the corresponding component index in the location configuration. The writing process uses the component index as the storage address to locate the target storage unit and overwrites the original coordinate values. After the optimal location coordinates of the component are written, this embodiment recalculates the signal power and interference plus noise power of each user based on the updated location configuration. The signal power calculation process multiplies the square of the effective channel magnitude of each user by the square of the corresponding beamforming vector magnitude. The interference plus noise power calculation process accumulates the interference power terms from other users and adds them to the noise power to obtain the power calculation result.

[0039] After the power calculation result is obtained, this embodiment writes the ratio of signal power to interference plus noise power in the power calculation result into the parameter storage area as the updated value of the fractional programming parameter. The update of the fractional programming parameter follows the parameter iteration rule in fractional programming theory, and the updated parameter value reflects the actual signal-to-interference-plus-noise ratio level of each user under the current location configuration. This embodiment reads the fractional programming parameters of the current round and the fractional programming parameters of the previous round from the parameter storage area, calculates the difference between the fractional programming parameters of the current round and the fractional programming parameters of the previous round, and obtains the parameter change by calculating the relative change. The parameter change is defined as the ratio of the absolute value of the difference to the parameter value of the previous round.

[0040] In this embodiment, the parameter changes are numerically compared with a preset convergence threshold to obtain a convergence determination result. When the parameter changes for all users are less than the preset convergence threshold, the convergence determination result is set to a converged state. When the parameter changes for any user are not less than the preset convergence threshold, the convergence determination result is set to a non-converged state. The preset convergence threshold is configured according to the system's requirements for optimization accuracy and latency; the smaller the threshold, the more stringent the convergence determination.

[0041] When the convergence determination result is non-convergence, this embodiment uses the current component position configuration as the initial position for the next iteration, updates the index of the component to be optimized to the next component, and returns to the component traversal optimization process of step S102. After all components have been traversed, the next outer iteration is entered, and the component traversal and sub-problem solving process is repeated until the convergence condition is met. When the convergence determination result is convergence, this embodiment reads the coordinates of each component from the position configuration to obtain the final component position configuration, encapsulates the final component position configuration into a control command, and sends it to the component driving mechanism of the movable component intelligent metasurface through the control signaling interface. After receiving the control command, the component driving mechanism drives each component to complete the physical position adjustment to achieve dynamic reconfiguration of the component space deployment.

[0042] As can be seen from the above description, the STAR-RIS position optimization method based on the MM framework provided in this application can construct a set of position-related coefficients through the channel matrix and user angle parameters, and construct a convex optimization solution model by combining the gradient vector and Hessian matrix norm to form a quadratic concave lower bound and convex upper bound substitution function, respectively. The final component position configuration is then sent to the drive mechanism to complete the closed-loop deployment adjustment through iterative convergence judgment. This effectively solves the shortcomings of traditional technologies in position-related term modeling, non-convex substitution function construction, and iterative convergence configuration sending, and provides technical support for the intelligent optimization and adaptive spatial deployment of movable component positions in the STAR-RIS assisted communication system.

[0043] In one embodiment of the STAR-RIS position optimization method based on the MM framework of this application, it may further include the following: Step S201: Read the line-of-sight component estimate and the non-line-of-sight component estimate from the base station to the smart metasurface of the mobile element from the channel estimation unit. Perform weighted synthesis on the line-of-sight component estimate and the non-line-of-sight component estimate based on the preset Rice factor to obtain the channel matrix. Decompose the channel matrix according to the element index to obtain the channel column vector corresponding to each element and write it into the channel parameter buffer. Step S202: Read the spatial position coordinates of the user in the reflection area and the user in the transmission area from the user positioning unit. Calculate the direction vector of each user based on the reference origin coordinates of the intelligent metasurface of the movable element and the spatial position coordinates. Project the direction vector of each user onto the horizontal and vertical planes respectively to calculate the azimuth and elevation angles to obtain the azimuth and elevation angle parameters. Associate and store the azimuth and elevation angle parameters with the channel column vector in the channel parameter buffer.

[0044] In this embodiment, the line-of-sight (LAS) component estimates and non-LAS component estimates from the base station to the smart metasurface of the movable element are read from the channel estimation unit. The LAS component estimates are obtained by the channel estimation unit through pilot signal measurement and least squares estimation, representing the complex channel response of the direct propagation path between the base station antenna array and each element. The non-LAS component estimates are obtained by the channel estimation unit through joint estimation of statistical channel model and instantaneous measurement values, representing the multipath channel response reaching each element after scattering from surrounding buildings and obstacles, with each element following a zero-mean complex Gaussian distribution.

[0045] After the line-of-sight component estimates and non-line-of-sight component estimates are read, this embodiment performs a weighted synthesis of the line-of-sight component estimates and non-line-of-sight component estimates based on a preset Rice factor. The preset Rice factor represents the relative power ratio of the line-of-sight propagation component and the scattering propagation component, and is determined by the electromagnetic propagation characteristics of the system deployment environment. The weighted synthesis process multiplies the line-of-sight component estimates by a Rice factor normalization weight, which is calculated as the square root of the ratio of the Rice factor plus one. The non-line-of-sight component estimates are multiplied by a complementary normalization weight, which is calculated as the square root of the ratio of one to the sum of the Rice factor plus one. The two weighted results are added to obtain the channel matrix. The number of rows in the channel matrix equals the total number of elements in the movable element smart metasurface, and the number of columns equals the number of base station antennas.

[0046] Accordingly, this embodiment decomposes the channel matrix by element index to obtain the channel column vector corresponding to each element. The decomposition process sequentially extracts the row vectors corresponding to the first to last elements in the channel matrix. The dimension of each channel column vector is equal to the number of base station antennas, and the m-th element in the vector represents the complex channel gain from the m-th base station antenna to that element. In this embodiment, the channel column vector corresponding to each element is written into the channel parameter buffer. During writing, the element index is used as the storage address identifier to establish an index mapping relationship. The channel parameter buffer is used for reading and calling during the associated storage process in step S202.

[0047] After the aforementioned channel column vector is written into the channel parameter buffer, this embodiment reads the spatial coordinates of users in the reflection and transmission regions from the user positioning unit. These spatial coordinates are represented using a three-dimensional Cartesian coordinate system, with the origin set at the geometric center of the plane containing the intelligent metasurface of the movable element. Users in the reflection region are located in the reflection half-space of the intelligent metasurface of the movable element, and users in the transmission region are located in the transmission half-space of the intelligent metasurface of the movable element. The spatial coordinates of both types of users are determined by the user positioning unit using a combination of angle-of-arrival estimation and ranging methods.

[0048] Based on the reference origin coordinates of the intelligent metasurface of the movable element and the spatial position coordinates, this embodiment performs direction vector calculation to obtain the direction vectors of each user. The direction vector calculation process involves subtracting the reference origin coordinates from the user's spatial position coordinates to obtain a three-dimensional vector pointing to that user. Then, the three-dimensional vector is normalized to obtain a unit direction vector. In this embodiment, the direction vectors of each user are projected onto the horizontal and vertical planes respectively to calculate the azimuth and elevation angles. During the horizontal plane projection process, the horizontal component of the direction vector is extracted and its angle with the positive direction of the reference axis is calculated to obtain the azimuth angle. During the vertical plane projection process, the angle between the direction vector and the horizontal plane is calculated to obtain the elevation angle, thereby obtaining the azimuth and elevation angle parameters.

[0049] After the azimuth and elevation parameters are calculated, this embodiment associates and stores these parameters with the channel column vectors in the channel parameter buffer. The association storage process establishes a dual index structure of user index and element index, with each user's corresponding azimuth and elevation parameters forming an association record with the channel column vectors of all elements. The association storage result is written into a channel angle association table, which is used in subsequent step S301 to retrieve and call data based on the user index and element index when calculating the path difference function of each element with respect to the base station direction and the user direction.

[0050] In one embodiment of the STAR-RIS position optimization method based on the MM framework of this application, it may further include the following: Step S301: Calculate the path difference function of each element with respect to the base station direction based on the position coordinates of each element, the azimuth angle of the base station, and the elevation angle of the base station; calculate the path difference function of each element with respect to the user direction based on the position coordinates of each element, the azimuth angle of the user, and the elevation angle of the user; organize the path difference functions of each element with respect to the base station direction and the path difference functions of each element with respect to the user direction into a path difference function set. Step S302: Based on the path difference function set, expand the square of the effective channel magnitude of each user into a summation of cascaded link autocorrelation terms and cross terms. Extract the complex exponential product coefficients of each element pair from the cascaded link autocorrelation terms to obtain double summation coefficients. Extract the complex exponential coefficients of each element from the cross terms to obtain single summation coefficients. Combine the double summation coefficients and the single summation coefficients to obtain a set of location correlation coefficients.

[0051] In this embodiment, the base station azimuth and elevation parameters are read from the channel angle association table written in step S202, and the current position coordinates of each component are read from the position configuration storage area. Based on the position coordinates of each component and the base station azimuth and elevation, the path difference function of each component with respect to the base station direction is calculated. The path difference function represents the difference in the propagation distance of a signal from the base station direction to the position of a certain component relative to the reference origin. The calculation process obtains the first component by multiplying the horizontal coordinate of the component by the sine of the base station azimuth and the cosine of the base station elevation, and obtains the second component by multiplying the vertical coordinate of the component by the sine of the base station elevation. The first component and the second component are added to obtain the path difference function value of the component with respect to the base station direction.

[0052] After the path difference function of each element with respect to the base station direction is calculated, this embodiment calculates the path difference function of each element with respect to the user direction based on the position coordinates of each element and the user azimuth and elevation angles. Calculations are performed separately for users in the reflection and transmission areas, retrieving the corresponding azimuth and elevation parameters from the channel angle association table according to the user index. The calculation process involves multiplying the element's horizontal coordinate with the sine of the user azimuth and the cosine of the user elevation angle to obtain the first component, and multiplying the element's vertical coordinate with the sine of the user elevation angle to obtain the second component. The first component and the second component are added to obtain the path difference function value of the element with respect to the user direction.

[0053] Accordingly, this embodiment organizes the path difference functions of each element with respect to the base station direction and the path difference functions of each element with respect to the user direction into a path difference function set. The path difference function set is organized using a three-dimensional index structure: the first dimension corresponds to the element number, the second dimension distinguishes between the base station direction and the user direction, and the third dimension corresponds to the user number. The path difference function set is written into a path difference buffer for retrieval and calling by index when expanding the square of the effective channel modulus of each user in step S302.

[0054] After the aforementioned path difference function set is written into the path difference buffer, this embodiment expands the squared effective channel magnitude of each user into a summation of cascaded link autocorrelation terms and cross-terms based on the path difference function set. For users in the reflection area, the effective channel includes cascaded link components via the smart metasurface of the movable element and direct link components from the base station to the user. The squared effective channel magnitude expansion includes three categories: cascaded link autocorrelation terms, cross-terms of cascaded links and direct links, and direct link autocorrelation terms. For users in the transmission area, the effective channel only includes cascaded link components, and the squared effective channel magnitude expansion includes only cascaded link autocorrelation terms.

[0055] This embodiment extracts the complex exponential product coefficients of each element pair from the cascaded link autocorrelation term to obtain double summation coefficients. The cascaded link autocorrelation term is expanded into a double summation form according to the element index, with the summation variables corresponding to the first element index and the second element index, respectively. Each summation term contains the product of two complex exponential functions. The exponential part of the complex exponential function is formed by a linear combination of the path difference function with respect to the base station direction and the path difference function with respect to the user direction for the corresponding element in the path difference function set. This embodiment extracts the complex exponential product coefficients corresponding to each element pair. The complex exponential product coefficients contain the product of the outer product matrix element of the reflection coefficient and the correlation coefficient of the beamforming vector, and are organized by element pair index to form double summation coefficients.

[0056] After the double summation coefficients are extracted, this embodiment extracts the complex exponential coefficients of each element from the cross terms to obtain single summation coefficients. The cross terms are expanded into single summation form according to element index, and each summation term contains the product of a single complex exponential function and the direct channel correlation coefficient. The exponential part of the complex exponential function is formed by a linear combination of the path difference function of the corresponding element in the path difference function set with respect to the base station direction and the path difference function with respect to the user direction. This embodiment extracts the complex exponential coefficients corresponding to each element, which contain the product of the reflection coefficient vector elements, the direct channel vector elements, and the beamforming vector elements, and organizes them according to element index to form single summation coefficients.

[0057] In this embodiment, the double summation coefficients and the single summation coefficients are merged to obtain a set of position-related coefficients. The merging process establishes a unified index structure; the double summation coefficients are stored by element pair index, and the single summation coefficients are stored by unit element index. The two types of coefficients are distinguished by coefficient type identifiers. The set of position-related coefficients is written to the decomposition result cache for subsequent steps, such as S401, to retrieve and call the coefficients based on element index and coefficient type when extracting non-convex trigonometric function terms for the element to be optimized.

[0058] In one embodiment of the STAR-RIS position optimization method based on the MM framework of this application, it may further include the following: Step S401: Select double summation coefficients and single summation coefficients related to the index of the element to be optimized from the set of position-related coefficients. Expand the complex exponential terms in the double summation coefficients and single summation coefficients into a linear combination of cosine function terms and sine function terms using Euler's formula to obtain non-convex trigonometric function terms. Step S402: Obtain the gradient vector by calculating the first-order partial derivative of the non-convex trigonometric function terms based on the position coordinates of the element to be optimized; obtain the Hessian matrix by calculating the second-order partial derivative of the non-convex trigonometric function terms based on the position coordinates of the element to be optimized; calculate the Frobenius norm of the Hessian matrix to obtain the quadratic coefficients; and organize the gradient vector and the quadratic coefficients into a gradient parameter set.

[0059] In this embodiment, the set of position-related coefficients written to the decomposition result cache in step S302 is used to filter double-summation coefficients and single-summation coefficients related to the index of the element to be optimized. The filtering process traverses the element pair indices of the double-summation coefficients, retaining coefficients where the first element index or the second element index is equal to the index of the element to be optimized, and simultaneously extracting coefficients where the element index is equal to the index of the element to be optimized from the single-summation coefficients. The filtered coefficients contain position-related structures expressed in complex exponential form, and the coefficients corresponding to the remaining elements are treated as constants in the current unit optimization process.

[0060] After the extraction of the filtering coefficients, this embodiment expands the complex exponent terms in the double summation coefficients and the single summation coefficients into a linear combination of cosine and sine function terms using Euler's formula. In the expansion process, the real part of the complex exponent is represented as a cosine function, and the imaginary part as a sine function. The independent variables of both the cosine and sine functions are linear combinations of the path difference function of the element to be optimized with respect to the base station direction and the path difference function with respect to the user direction. This embodiment merges the expanded trigonometric function terms according to their independent variable structure. The merged expression constitutes a non-convex trigonometric function term, which is written into the trigonometric function buffer for use in step S402 when calculating the gradient vector and Hessian matrix.

[0061] Based on the non-convex trigonometric function terms written to the trigonometric function buffer in step S401 above, this embodiment calculates the first-order partial derivatives of the position coordinates of the element to be optimized to obtain the gradient vector. The gradient vector contains two components: the first component is the partial derivative of the non-convex trigonometric function term with respect to the horizontal coordinate of the element, and the second component is the partial derivative of the non-convex trigonometric function term with respect to the vertical coordinate of the element. The calculation process for the partial derivative of the cosine function term involves multiplying the negative sine function with respect to the path difference function with respect to the position coordinates, and the calculation process for the partial derivative of the sine function term involves multiplying the cosine function with respect to the path difference function with respect to the position coordinates. The sum of these partial derivatives forms the corresponding components of the gradient vector.

[0062] After the gradient vector calculation is completed, this embodiment obtains the Hessian matrix by calculating the second-order partial derivatives of the non-convex trigonometric function terms with respect to the position coordinates of the element to be optimized. The Hessian matrix is ​​a second-order symmetric matrix. The elements in the first row and first column are the second-order partial derivatives of the non-convex trigonometric function terms with respect to the horizontal coordinate, the elements in the second row and second column are the second-order partial derivatives of the non-convex trigonometric function terms with respect to the vertical coordinate, and the off-diagonal elements are the mixed second-order partial derivatives of the horizontal and vertical coordinates. The calculation of the second-order partial derivatives involves the product of the second derivative of the trigonometric function and the square of the partial derivative of the path difference function.

[0063] Accordingly, this embodiment calculates the Frobenius norm of the Hessian matrix to obtain the quadratic coefficients. The Frobenius norm is calculated as the square root of the sum of the squares of the four elements of the Hessian matrix, and the quadratic coefficients are used to control the curvature of the quadratic term of the substitution function to ensure the global bound property. In this embodiment, the gradient vector and the quadratic coefficients are organized into a gradient parameter set, which is written into the gradient parameter buffer for subsequent steps S501 to read and call when constructing the quadratic concave lower bound substitution function and the quadratic convex upper bound substitution function.

[0064] In one embodiment of the STAR-RIS position optimization method based on the MM framework of this application, it may further include the following: Step S501: Read the gradient vector and quadratic coefficient from the gradient parameter set. Construct a quadratic concave lower bound substitution function based on the inner product of the current iteration point function value and the gradient vector and the position increment vector minus half of the product of the quadratic coefficient and the square of the magnitude of the position increment vector. Construct a quadratic convex upper bound substitution function based on the inner product of the current iteration point function value and the gradient vector and the position increment vector plus half of the product of the quadratic coefficient and the square of the magnitude of the position increment vector. Step S502: Substitute the quadratic concave lower bound substitution function into the position-related part of each user signal power term to form a signal power concave function expression; substitute the quadratic convex upper bound substitution function into the position-related part of each user interference power term to form an interference power convex function expression; construct a convex form of the signal-to-interference-plus-noise ratio (SINR) constraint based on the signal power concave function expression and the interference power convex function expression; combine the convex form of the SINR constraint with the component region boundary constraint and the component spacing linearization constraint to form a convex optimization solution model.

[0065] In this embodiment, the gradient vector and quadratic coefficients are read from the gradient parameter set written into the gradient parameter buffer in step S402, and the function values ​​of the non-convex trigonometric functions at the current iteration point are read from the trigonometric function buffer. The current iteration point is the position coordinate of the element to be optimized at the beginning of this iteration, and the function value is calculated by substituting the coordinates of the current iteration point into the non-convex trigonometric function term. In this embodiment, the position increment vector is defined as the difference between the position vector to be optimized and the position vector of the current iteration point, and the two components of the position increment vector represent the position adjustment amount in the horizontal and vertical directions, respectively.

[0066] After the gradient vector and quadratic coefficients are read, this embodiment constructs a quadratic concave lower bound substitution function based on the inner product of the current iteration point function value and the gradient vector and the position increment vector, minus half the product of the quadratic coefficient and the square of the magnitude of the position increment vector. The expression of the quadratic concave lower bound substitution function is: L(q) = f(q0) + e^T (q - q0) - (s / 2) ||q - q0||^2, Where f(q0) represents the function value of the non-convex trigonometric function term at the current iteration point q0, e represents the gradient vector, q represents the position vector of the element to be optimized, s represents the coefficient of the quadratic term, and ||q - q0||^2 represents the squared magnitude of the position increment vector. The quadratic concave lower bound substitution function L(q) is not greater than the value of the original non-convex trigonometric function term throughout the entire domain and is tangent to the original function at the current iteration point.

[0067] Accordingly, this embodiment constructs a quadratic convex upper bound substitution function based on the inner product of the current iteration point function value, the gradient vector, and the position increment vector, plus half the product of the quadratic term coefficient and the square of the magnitude of the position increment vector. The construction process of the quadratic convex upper bound substitution function is similar to that of the quadratic concave lower bound substitution function, except that the sign of the quadratic term is positive, making the entire function exhibit convex properties. The quadratic convex upper bound substitution function is not less than the value of the original non-convex trigonometric function term throughout its domain and is tangent to the original function at the current iteration point. In this embodiment, the coefficients of the quadratic concave lower bound substitution function and the quadratic convex upper bound substitution function are written into the substitution function coefficient buffer for reading and calling in step S502.

[0068] After the aforementioned substitution function coefficients are written into the substitution function coefficient buffer, this embodiment substitutes the quadratic concave lower bound substitution function into the position-related part of each user signal power term to form a signal power concave function expression. During the substitution process, the non-convex trigonometric function terms related to the position of the element to be optimized in the signal power term are replaced with the corresponding quadratic concave lower bound substitution function, while the constant terms unrelated to the position of the element to be optimized remain unchanged. The signal power concave function expression is the sum of a concave quadratic function about the position vector of the element to be optimized and a constant, preserving the concave function property for maximization.

[0069] In this embodiment, the quadratic convex upper bound substitution function is substituted into the position-related part of each user interference power term to form a convex function expression for the interference power. During the substitution process, non-convex trigonometric function terms related to the position of the element to be optimized in the interference power term are replaced with the corresponding quadratic convex upper bound substitution function, while constant terms unrelated to the position of the element to be optimized remain unchanged. The convex function expression for the interference power is the sum of a convex quadratic function about the position vector of the element to be optimized and a constant, and is used as an upper bound estimate of the interference power for constraint construction.

[0070] Based on the concave signal power function expression and the convex interference power function expression, this embodiment constructs a convex form of the signal-to-interference-plus-noise ratio (SIR) constraint. The convex SIR constraint is expressed as the difference between the concave signal power function expression and the product of the fractional programming parameters and the convex interference power function expression, where the difference is not less than the auxiliary variable. The fractional programming parameters are read from the parameter storage area. This embodiment combines the convex form of the SIR constraint with the component region boundary constraint and the component spacing linearization constraint to form a convex optimization solution model. The component region boundary constraint is expressed as an inequality where the horizontal and vertical coordinates of the component to be optimized lie within a preset square region. The component spacing linearization constraint is obtained by performing a first-order Taylor expansion of the distance magnitude constraint between the component to be optimized and other components at the current iteration point. The convex optimization solution model is written into the optimization problem cache area for subsequent steps S601 to call the optimization solver.

[0071] In one embodiment of the STAR-RIS position optimization method based on the MM framework of this application, it may further include the following: Step S601: Assemble the objective function coefficients, constraint coefficient matrices, and constant vectors of the convex optimization solution model into a standard optimization problem data structure, and call the optimization solver to perform the interior point method on the standard optimization problem data structure to obtain the optimal position coordinates of the components and the values ​​of the auxiliary variables; Step S602: Write the optimal position coordinates of the element into the coordinate storage area of ​​the corresponding element index in the position configuration. Based on the optimal position coordinates of the element, recalculate the signal power and interference plus noise power of each user to obtain the power calculation result. Write the ratio of signal power to interference plus noise power in the power calculation result into the parameter storage area as the update value of the fractional programming parameter.

[0072] In this embodiment, the objective function coefficients, constraint coefficient matrices, and constant vector are read from the convex optimization solution model written into the optimization problem buffer in step S502. The objective function coefficients include weighted coefficients for each user auxiliary variable, determined by the system's preset user priority weights. The constraint coefficient matrix includes quadratic and linear coefficients corresponding to the convex form of the signal-to-interference-plus-noise ratio constraint, upper and lower limit coefficients of the position coordinates corresponding to the component region boundary constraint, and first-order Taylor expansion coefficients corresponding to the linearization constraint of the component spacing. The constant vector includes the right-hand side constants of each constraint.

[0073] After the objective function coefficients, constraint coefficient matrices, and constant vectors are read, this embodiment assembles the data into a standard optimization problem data structure. The assembly process follows the standard input format for convex quadratic programming problems. The objective function is represented by a quadratic form matrix and a linear form vector; the equality constraints are represented by a coefficient matrix and a constant vector; and the inequality constraints are also represented by a coefficient matrix and a constant vector. The variable dimension of the standard optimization problem data structure includes the two-dimensional position coordinates of the element to be optimized and the auxiliary variables corresponding to each user.

[0074] Accordingly, this embodiment calls the optimization solver to perform an interior-point method solution on the standard optimization problem data structure. The interior-point method constructs a barrier function within the feasible region and gradually approximates the optimal solution along the central path. In each iteration, it calculates the Newton direction and step size parameters, updating the original and dual variables until the duality gap is less than a preset accuracy threshold. After solving, the optimization solver outputs the optimal position coordinates of the element and the values ​​of auxiliary variables. The optimal position coordinates of the element include the optimal horizontal and vertical coordinate values ​​of the element to be optimized.

[0075] After the optimal position coordinates of the component and the values ​​of the auxiliary variables are output, this embodiment writes the optimal position coordinates of the component into the coordinate storage area of ​​the corresponding component index in the position configuration. During the writing process, the target storage unit is located using the index of the component to be optimized as the storage address, and the optimal values ​​of the horizontal and vertical coordinates are used to overwrite the original coordinate values. The position configuration is updated immediately after the component optimization is completed, so that subsequent component optimizations can calculate the path difference function and channel response based on the latest position configuration.

[0076] Based on the optimal location coordinates of the components, this embodiment recalculates the signal power and interference plus noise power of each user to obtain the power calculation result. The signal power calculation process recalculates the square of the effective channel magnitude of each user based on the updated location configuration, and multiplies the square of the effective channel magnitude by the square of the corresponding beamforming vector magnitude to obtain the signal power value. The interference plus noise power calculation process recalculates the interference power items from other users according to the updated location configuration, accumulates them, and then adds them to the receiver noise power to obtain the interference plus noise power value.

[0077] In this embodiment, the ratio of signal power to interference plus noise power in the power calculation result is written into the parameter storage area as the updated value of the fractional programming parameters. The update process calculates the ratio of signal power to interference plus noise power for each user separately and writes the ratio into the parameter storage unit corresponding to the user index in the parameter storage area. The update of the fractional programming parameters follows the Tinkelbach parameter iteration rule in fractional programming theory. The updated parameter values ​​reflect the actual signal-to-interference-plus-noise ratio (SNR) level of each user under the current location configuration, and are read and called by subsequent steps S701 when performing convergence determination and iterative control.

[0078] In one embodiment of the STAR-RIS position optimization method based on the MM framework of this application, it may further include the following: Step S701: Read the current round fractional programming parameters and the previous round fractional programming parameters from the parameter storage area, calculate the difference between the current round fractional programming parameters and the previous round fractional programming parameters, and obtain the relative change to get the parameter change. Compare the parameter change with the preset convergence threshold condition to obtain the convergence determination result. Step S702: When the convergence determination result is non-convergence, the current component position configuration is used as the initial position for the next iteration and the component traversal optimization process is returned. When the convergence determination result is convergence, the coordinates of each component are read from the position configuration to obtain the final component position configuration. The final component position configuration is encapsulated into a control command and sent to the component driving mechanism of the movable component intelligent metasurface through the control signaling interface to adjust the component space deployment.

[0079] In this embodiment, the fractional programming parameters for the current round and the previous round are read from the fractional programming parameters written into the parameter storage area in step S602. The current round fractional programming parameters are the calculated results of the ratio of each user signal power to interference plus noise power at the end of the current outer layer iteration, and the previous round fractional programming parameters are the corresponding parameter values ​​stored at the end of the previous outer layer iteration. The parameter storage area uses a double buffering mechanism to store parameter values ​​for two adjacent rounds, and is distinguished by round identifier during reading.

[0080] After the parameters for the current round of fractional programming and the parameters for the previous round are read, this embodiment calculates the difference between the parameters for the current round and the parameters for the previous round and obtains the relative change to get the parameter change. The difference calculation process is performed separately for each user, subtracting the parameter value of the previous round from the parameter value of the current round to obtain the absolute difference. The relative change calculation process divides the absolute difference by the parameter value of the previous round to obtain the parameter change for each user. When the parameter value of the previous round is close to zero, the absolute difference is used as the change index to avoid numerical overflow.

[0081] Accordingly, this embodiment compares the parameter changes with a preset convergence threshold to obtain a convergence determination result. The comparison process iterates through the parameter changes for all users. When the parameter changes for all users are less than the preset convergence threshold, the convergence determination result is set to a converged state. When the parameter changes for any user are not less than the preset convergence threshold, the convergence determination result is set to a non-converged state. The preset convergence threshold is specified by system configuration parameters; a smaller threshold requires higher convergence accuracy.

[0082] When the convergence determination result is non-convergence, this embodiment configures the current element position as the initial position for the next iteration and returns to the element traversal optimization process. During the return execution process, the outer iteration round counter is incremented, the index of the element to be optimized is reset to the first element, and starting from step S401, the processes of selecting coefficients, calculating gradients, constructing substitution functions, and solving convex optimization subproblems are sequentially performed on each element. After all elements have been traversed, the convergence determination in step S701 is executed again, and this process is repeated until the convergence condition is met.

[0083] When the convergence determination result indicates convergence, this embodiment reads the coordinates of each element from the location configuration to obtain the final element location configuration. The reading process extracts the horizontal and vertical coordinate values ​​of each element sequentially from the coordinate storage area according to the element index, organizing all element coordinates into a location configuration data structure. The final element location configuration represents the optimal spatial deployment scheme of each element in the two-dimensional plane after the algorithm converges.

[0084] In this embodiment, the final component location configuration is encapsulated as a control command and sent to the component driving mechanism of the movable component smart metasurface via a control signaling interface. During the encapsulation process, a command header field and a component quantity field are added to the front of the final component location configuration according to the control signaling protocol format, and a check field is added to the back to ensure transmission integrity. After receiving the control command, the component driving mechanism parses the target coordinates of each component and drives the mechanical execution unit to move each component from its current physical position to the target position, completing the dynamic adjustment of the component spatial deployment of the movable component smart metasurface.

[0085] To effectively address the shortcomings of traditional technologies in areas such as location-related term modeling, non-convex substitution function construction, and iterative convergence configuration distribution, and to provide technical support for the intelligent optimization and adaptive spatial deployment of movable components in STAR-RIS assisted communication systems, this application provides an embodiment of a STAR-RIS location optimization device based on the MM framework for implementing all or part of the aforementioned STAR-RIS location optimization method based on the MM framework. See [link to embodiment]. Figure 2The STAR-RIS position optimization device based on the MM framework specifically includes the following components: The location calculation module 10 is used to obtain the channel matrix from the base station to the smart metasurface of the movable element from the channel estimation unit, obtain the azimuth and elevation parameters of the user in the reflection area and the user in the transmission area relative to the smart metasurface of the movable element from the user positioning unit, calculate the path difference function of each element with respect to the base station direction and the user direction based on the channel matrix and the azimuth and elevation parameters to obtain a set of path difference functions, and use the set of path difference functions to expand the square of the effective channel magnitude of each user to obtain a set of location correlation coefficients. The model building module 20 is used to extract non-convex trigonometric function terms from the set of position-related coefficients for the element to be optimized, calculate the gradient vector and Hessian matrix norm of the non-convex trigonometric function terms at the current iteration point to obtain a gradient parameter set, use the gradient parameter set to construct a quadratic concave lower bound substitution function and a quadratic convex upper bound substitution function, substitute the quadratic concave lower bound substitution function into the signal power term and substitute the quadratic convex upper bound substitution function into the interference power term to form a convex optimization solution model; The position optimization module 30 is used to call the optimization solver to solve the convex optimization solution model to obtain the optimal position coordinates of the element, write the optimal position coordinates of the element into the position configuration and update the fractional programming parameters, compare the fractional programming parameters with the preset convergence threshold condition, and when the preset convergence threshold condition is met, send the final element position configuration to the element driving mechanism of the movable element intelligent metasurface to adjust the element spatial deployment.

[0086] As can be seen from the above description, the STAR-RIS position optimization device based on the MM framework provided in this application can construct a set of position-related coefficients through the channel matrix and user angle parameters, and construct a convex optimization solution model by combining the gradient vector and Hessian matrix norm to form a quadratic concave lower bound and convex upper bound substitution function respectively. Through iterative convergence judgment, the final component position configuration is sent to the driving mechanism to complete the closed-loop deployment adjustment. This effectively solves the shortcomings of traditional technologies in position-related term modeling, non-convex substitution function construction and iterative convergence configuration sending, and provides technical support for the intelligent optimization and adaptive spatial deployment of movable component positions in the STAR-RIS assisted communication system.

[0087] This invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the STAR-RIS location optimization method based on the MM framework.

[0088] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned STAR-RIS location optimization method based on the MM framework.

[0089] This invention also provides a computer program product, which includes a computer program that, when executed by a processor, implements the above-described STAR-RIS location optimization method based on the MM framework.

[0090] In this embodiment of the invention, a set of position-related coefficients is constructed by using the channel matrix and user angle parameters. By combining the gradient vector and the Hessian matrix norm, a convex optimization solution model is formed by constructing a quadratic concave lower bound and a convex upper bound substitution function. The final component position configuration is then sent to the drive mechanism through iterative convergence judgment to complete the closed-loop deployment adjustment. This effectively solves the shortcomings of traditional technologies in terms of position-related term modeling, non-convex substitution function construction, and iterative convergence configuration sending. It provides technical support for the intelligent optimization and adaptive spatial deployment of movable component positions in the STAR-RIS assisted communication system.

[0091] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0092] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0093] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0094] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0095] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A STAR-RIS position optimization method based on the MM framework, characterized in that, The method includes: The channel matrix from the base station to the smart metasurface of the movable element is obtained from the channel estimation unit. The azimuth and elevation parameters of the users in the reflection area and the transmission area relative to the smart metasurface of the movable element are obtained from the user positioning unit. Based on the channel matrix and the azimuth and elevation parameters, the path difference function of each element with respect to the base station direction and the user direction is calculated to obtain the path difference function set. The path difference function set is used to expand the square of the effective channel magnitude of each user to obtain the location correlation coefficient set. For the element to be optimized, non-convex trigonometric function terms are extracted from the set of position-related coefficients. The gradient vector and Hessian matrix norm of the non-convex trigonometric function terms at the current iteration point are calculated to obtain a gradient parameter set. The gradient parameter set is used to construct a quadratic concave lower bound substitution function and a quadratic convex upper bound substitution function. The quadratic concave lower bound substitution function is substituted into the signal power term and the quadratic convex upper bound substitution function is substituted into the interference power term to form a convex optimization solution model. The optimal position coordinates of the component are obtained by calling the optimization solver on the convex optimization solution model. The optimal position coordinates of the component are written into the position configuration and the fractional programming parameters are updated. The fractional programming parameters are compared with the preset convergence threshold condition. When the preset convergence threshold condition is met, the final component position configuration is sent to the component driving mechanism of the movable component intelligent metasurface to adjust the component spatial deployment.

2. The STAR-RIS position optimization method based on the MM framework according to claim 1, characterized in that, The process of obtaining the channel matrix from the base station to the smart metasurface of the movable element from the channel estimation unit, and obtaining the azimuth and elevation parameters of the users in the reflection and transmission regions relative to the smart metasurface of the movable element from the user positioning unit, includes: The line-of-sight component estimate and the non-line-of-sight component estimate are read from the channel estimation unit from the base station to the intelligent metasurface of the movable element. The line-of-sight component estimate and the non-line-of-sight component estimate are weighted and synthesized based on the preset Rice factor to obtain the channel matrix. The channel matrix is ​​decomposed according to the element index to obtain the channel column vector corresponding to each element and written into the channel parameter buffer. The spatial coordinates of users in the reflection and transmission areas are read from the user positioning unit. Based on the reference origin coordinates of the intelligent metasurface of the movable element and the spatial coordinates, direction vector calculation is performed to obtain the direction vector of each user. The direction vector of each user is projected onto the horizontal and vertical planes to calculate the azimuth and elevation angles respectively to obtain the azimuth and elevation angle parameters. The azimuth and elevation angle parameters are associated and stored with the channel column vector in the channel parameter buffer.

3. The STAR-RIS position optimization method based on the MM framework according to claim 1, characterized in that, The path difference function set is obtained by calculating the path difference function of each element with respect to the base station direction and the user direction based on the channel matrix, the azimuth angle, and the elevation angle parameters. This path difference function set is then used to expand the square of the effective channel magnitude of each user to obtain a set of location-related coefficients, including: The path difference function of each component with respect to the base station direction is calculated based on the position coordinates of each component, the azimuth angle of the base station, and the elevation angle of the base station. The path difference function of each component with respect to the user direction is calculated based on the position coordinates of each component, the azimuth angle of the user, and the elevation angle of the user. The path difference functions of each component with respect to the base station direction and the path difference functions of each component with respect to the user direction are organized into a path difference function set. Based on the path difference function set, the squared effective channel magnitude of each user is expanded into a summation of cascaded link autocorrelation terms and cross terms. The complex exponential product coefficients of each element pair are extracted from the cascaded link autocorrelation terms to obtain double summation coefficients. The complex exponential coefficients of each element are extracted from the cross terms to obtain single summation coefficients. The double summation coefficients and the single summation coefficients are combined to obtain a set of location correlation coefficients.

4. The STAR-RIS position optimization method based on the MM framework according to claim 1, characterized in that, The step of extracting non-convex trigonometric function terms from the set of position-related coefficients for the element to be optimized, and calculating the gradient vector and Hessian matrix norm of the non-convex trigonometric function terms at the current iteration point to obtain the gradient parameter set includes: From the set of position-related coefficients, select double summation coefficients and single summation coefficients related to the index of the element to be optimized. Expand the complex exponential terms in the double summation coefficients and single summation coefficients into a linear combination of cosine function terms and sine function terms using Euler's formula to obtain non-convex trigonometric function terms. The gradient vector is obtained by taking the first-order partial derivative of the non-convex trigonometric function terms based on the position coordinates of the element to be optimized. The Hessian matrix is ​​obtained by taking the second-order partial derivative of the non-convex trigonometric function terms based on the position coordinates of the element to be optimized. The Frobenius norm is calculated on the Hessian matrix to obtain the quadratic coefficients. The gradient vector and the quadratic coefficients are then organized into a gradient parameter set.

5. The STAR-RIS position optimization method based on the MM framework according to claim 1, characterized in that, The step of using the gradient parameter set to construct a quadratic concave lower bound substitution function and a quadratic convex upper bound substitution function, substituting the quadratic concave lower bound substitution function into the signal power term, and substituting the quadratic convex upper bound substitution function into the interference power term to form a convex optimization solution model includes: Read the gradient vector and quadratic coefficient from the gradient parameter set. Construct a quadratic concave lower bound substitution function based on the inner product of the current iteration point function value and the gradient vector and the position increment vector minus half of the product of the quadratic coefficient and the square of the magnitude of the position increment vector. Construct a quadratic convex upper bound substitution function based on the inner product of the current iteration point function value and the gradient vector and the position increment vector plus half of the product of the quadratic coefficient and the square of the magnitude of the position increment vector. The quadratic concave lower bound substitution function is substituted into the position-related part of each user signal power term to form a signal power concave function expression. The quadratic convex upper bound substitution function is substituted into the position-related part of each user interference power term to form an interference power convex function expression. Based on the signal power concave function expression and the interference power convex function expression, a convex form of the signal-to-interference-plus-noise ratio (SINR) constraint is constructed. The convex form of the SINR constraint is combined with the component region boundary constraint and the component spacing linearization constraint to form a convex optimization solution model.

6. The STAR-RIS position optimization method based on the MM framework according to claim 1, characterized in that, The process of calling the optimization solver to solve the convex optimization model to obtain the optimal position coordinates of the component, writing the optimal position coordinates of the component into the position configuration, and updating the fractional programming parameters includes: The objective function coefficients, constraint coefficient matrices, and constant vectors of the convex optimization solution model are assembled into a standard optimization problem data structure. The optimization solver is then called to perform the interior point method on the standard optimization problem data structure to obtain the optimal position coordinates of the components and the values ​​of the auxiliary variables. Write the optimal position coordinates of the element into the coordinate storage area of ​​the corresponding element index in the position configuration. Based on the optimal position coordinates of the element, recalculate the signal power and interference plus noise power of each user to obtain the power calculation result. Write the ratio of signal power to interference plus noise power in the power calculation result into the parameter storage area as the update value of the fractional programming parameter.

7. The STAR-RIS position optimization method based on the MM framework according to claim 1, characterized in that, The step of comparing the fractional programming parameters with a preset convergence threshold condition, and then, when the preset convergence threshold condition is met, sending the final component position configuration to the component driving mechanism of the movable component intelligent metasurface to adjust the component spatial deployment, includes: Read the current round fractional programming parameters and the previous round fractional programming parameters from the parameter storage area, calculate the difference between the current round fractional programming parameters and the previous round fractional programming parameters, and obtain the relative change to get the parameter change. Compare the parameter change with the preset convergence threshold condition to obtain the convergence determination result. When the convergence determination result is non-convergence, the current component position configuration is used as the initial position for the next iteration and the component traversal optimization process is returned. When the convergence determination result is convergence, the coordinates of each component are read from the position configuration to obtain the final component position configuration. The final component position configuration is encapsulated as a control command and sent to the component driving mechanism of the movable component intelligent metasurface through the control signaling interface to adjust the component space deployment.

8. A STAR-RIS position optimization device based on the MM framework, characterized in that, The device includes: The location calculation module is used to obtain the channel matrix from the channel estimation unit to the smart metasurface of the movable element, obtain the azimuth and elevation parameters of the user in the reflection area and the user in the transmission area relative to the smart metasurface of the movable element from the user positioning unit, calculate the path difference function of each element with respect to the direction of the base station and the direction of the user based on the channel matrix and the azimuth and elevation parameters, and obtain a set of path difference functions. The set of path difference functions is used to expand the square of the effective channel magnitude of each user to obtain a set of location correlation coefficients. The model building module is used to extract non-convex trigonometric function terms from the set of position-related coefficients for the element to be optimized, calculate the gradient vector and Hessian matrix norm of the non-convex trigonometric function terms at the current iteration point to obtain a gradient parameter set, use the gradient parameter set to construct a quadratic concave lower bound substitution function and a quadratic convex upper bound substitution function, substitute the quadratic concave lower bound substitution function into the signal power term and substitute the quadratic convex upper bound substitution function into the interference power term to form a convex optimization solution model; The position optimization module is used to call the optimization solver to solve the convex optimization solution model to obtain the optimal position coordinates of the component, write the optimal position coordinates of the component into the position configuration and update the fractional programming parameters, compare the fractional programming parameters with the preset convergence threshold condition, and when the preset convergence threshold condition is met, send the final component position configuration to the component driving mechanism of the movable component intelligent metasurface to adjust the component spatial deployment.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the STAR-RIS position optimization method based on the MM framework as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the STAR-RIS position optimization method based on the MM framework as described in any one of claims 1 to 7.

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