A flexible intelligent metasurface sensing and communication integrated beam and morphology combined optimization method

Abstract

The application discloses a flexible intelligent metasurface sensing and communication integrated beam and form combined optimization method, comprising the following steps: based on a beamforming matrix and an antenna deformation parameter, a joint objective function is constructed by a weighted sum of a communication target function and a sensing target function; fixing the antenna deformation parameter, the joint objective function is processed by inequality transformation to obtain a first convex upper bound function about the beamforming matrix, and the beamforming matrix is updated based on the first convex upper bound function and a power constraint; based on the updated beamforming matrix, the joint objective function is processed by inequality transformation to obtain a second convex upper bound function about the antenna deformation parameter, and the antenna deformation parameter is updated based on the second convex upper bound function and an antenna position constraint; based on the alternately iterated and updated beamforming matrix and antenna deformation parameter, the joint optimization result is obtained until the joint objective function value meets a convergence condition.

Description

Technical Field

[0001] This invention belongs to the field of integrated communication and sensing technology assisted by intelligent metasurfaces, and particularly relates to a method for joint optimization of beam and morphology of integrated sensing beam on flexible intelligent metasurfaces. Background Technology

[0002] With the large-scale deployment of fifth-generation mobile communication technology (5G) and the pre-research and development of sixth-generation mobile communication technology (6G), wireless communication networks are evolving towards higher spectral efficiency, lower latency, and massive connectivity. In this process, Integrated Communication and Sensing (ISAC) technology has become one of the core research directions. It significantly improves spectrum utilization efficiency by sharing spectrum resources and signal waveforms on a unified hardware platform, simultaneously achieving high-speed data transmission and high-precision environmental sensing. Flexible intelligent metasurfaces (FIMs), as a novel array architecture composed of a large number of mobile antenna elements, can dynamically adjust the spatial position of antenna elements according to channel environment and service requirements, achieving flexible control of the electromagnetic beam. Introducing FIMs into ISAC systems, utilizing their highly flexible morphological adjustment capabilities, provides a hardware foundation for simultaneously meeting the dual requirements of multi-user service quality and sensing spatial resolution.

[0003] However, existing technologies still face the following challenges: First, communication and sensing performance are difficult to optimize jointly. Existing methods often only focus on one aspect and lack an effective mechanism to allocate weights as needed to synergistically improve both performances. Second, the system computational complexity is too high, especially when it involves the joint control of multi-user beamforming and antenna morphology. Traditional algorithms need to solve large-scale non-convex problems, resulting in a large number of iterations and long processing delays, making it difficult to adapt to the real-time response requirements in dynamically changing environments. Third, the fairness of user service quality is difficult to guarantee. Some methods focus on maximizing the total system rate and tend to over-allocate power to users with good channel conditions, making it difficult to effectively guarantee the service quality of users with weak channels.

[0004] Therefore, this invention proposes a flexible intelligent metasurface integrated beam and morphology joint optimization method. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a flexible intelligent metasurface integrated beam and morphology joint optimization method to solve the problems existing in the prior art.

[0006] To achieve the above objectives, this invention provides a flexible intelligent metasurface integrated beam and morphology joint optimization method, comprising: S1: Based on the beamforming matrix and antenna deformation parameters, a joint objective function is constructed by weighted summation of the communication objective function and the sensing objective function; wherein, the communication objective function is obtained based on the user rate, and the sensing objective function is obtained based on the beam pattern of the target area; S2: Fix the antenna deformation parameters, process the joint objective function using inequality transformation to obtain a first convex upper bound function for the beamforming matrix, and update the beamforming matrix based on the first convex upper bound function and the power constraint. S3: Based on the updated beamforming matrix, the joint objective function is processed by inequality transformation to obtain a second convex upper bound function for the antenna deformation parameters, and the antenna deformation parameters are updated based on the second convex upper bound function and the antenna position constraint. S4: Based on the beamforming matrix and antenna deformation parameters updated by alternating iterations, repeat S2-S3 until the joint objective function value satisfies the convergence condition, and obtain the joint optimization result.

[0007] Optionally, the process of constructing a joint objective function based on the beamforming matrix and antenna deformation parameters, which is a weighted sum of the communication objective function and the sensing objective function, includes: Based on the channel information and beamforming matrix of each user, the rate of each user is obtained, and the rate of each user is subjected to soft max-min rate fairness regularization to obtain the communication objective function; Based on the deviation between the beammap of the target region and the desired beammap, a two-dimensional grid point beammap fitting function containing energy concentration bands and energy suppression bands is constructed to obtain the sensing target function; Based on preset communication weights and perception weights, the communication objective function and the perception objective function are weighted and summed to obtain the joint objective function.

[0008] Optionally, the expression for the communication objective function is: In the formula, For channel information, Let be the beamforming matrix for user k. For rate fairness regularization parameters, To represent noise interference other than user k information, y is the antenna deformation parameter, and d is the beamforming matrix. This is the objective function for communication.

[0009] Optionally, the expression for the perception target function is: In the formula, To perceive the target function, yes Grid points on the top express area, express area, express Quantity, express middle Quantity, It is an energy concentration zone. This is the energy suppression zone.

[0010] Optionally, the process of updating the beamforming matrix includes: Based on the beamforming matrix obtained in the previous iteration, a fractional quadratic transformation is applied to the communication objective function to obtain a tight convex upper bound of the communication objective function with respect to the beamforming matrix. Based on the beamforming matrix obtained in the previous iteration, a first-order expansion is applied to the sensing objective function to obtain a compact convex upper bound of the sensing objective function with respect to the beamforming matrix. Based on preset communication weights and perception weights, the tight convex upper bound of the communication objective function with respect to the beamforming matrix and the tight convex upper bound of the perception objective function with respect to the beamforming matrix are weighted and summed to obtain the first convex upper bound function. The first convex upper bound function is solved, and the solution is projected onto the feasible region that satisfies the power constraint to obtain the updated beamforming matrix.

[0011] Optionally, the process of applying a fractional quadratic transformation to the communication objective function based on the beamforming matrix obtained in the previous iteration to obtain the compact convex upper bound of the communication objective function with respect to the beamforming matrix includes: Based on the beamforming matrix obtained in the previous iteration, the signal term and interference plus noise term for each user are calculated to obtain the first ratio term. The first ratio term in the communication objective function is processed by fractional quadratic transformation to obtain a quadratic surrogate function with respect to the beamforming matrix; The quadratic surrogate function is compacted at the beamforming matrix obtained in the previous iteration to obtain the compact convex upper bound of the communication objective function with respect to the beamforming matrix.

[0012] Optionally, the process of applying a first-order expansion to the sensing objective function based on the beamforming matrix obtained in the previous iteration to obtain the compact convex upper bound of the sensing objective function with respect to the beamforming matrix includes: Based on the beamforming matrix obtained in the previous iteration, the function value of the square root term in the sensing target function at the current iteration point is calculated to obtain the first constant term; The square root term is expanded in first order at the current iteration point to obtain a linear approximation term for the beamforming matrix; Based on the first constant term and the linear approximation term, a tight convex upper bound for the sensing objective function with respect to the beamforming matrix is ​​constructed.

[0013] Optionally, the process of updating the antenna deformation parameters includes: Based on the updated beamforming matrix and the antenna deformation parameters obtained in the previous iteration, a fractional quadratic transformation and eigenvalue upper bound approximation are applied to the communication objective function to obtain a tight convex upper bound of the communication objective function with respect to the antenna deformation parameters. Based on the updated beamforming matrix and the antenna deformation parameters obtained in the previous iteration, a first-order expansion and eigenvalue upper bound approximation are applied to the sensing objective function to obtain a tight convex upper bound of the sensing objective function with respect to the antenna deformation parameters. Based on preset communication weights and sensing weights, the tight convex upper bound of the communication objective function with respect to the antenna deformation parameters and the tight convex upper bound of the sensing objective function with respect to the antenna deformation parameters are weighted and summed, and the nonlinear terms in the steering vector are approximated by a second-order expansion to obtain the second convex upper bound function in quadratic form. The second convex upper bound function is solved, and the solution is projected onto the feasible region that satisfies the antenna position constraint to obtain the updated antenna deformation parameters.

[0014] Optionally, the process of applying a fractional quadratic transform and eigenvalue upper bound approximation to the communication objective function to obtain the compact convex upper bound of the communication objective function with respect to the antenna deformation parameters includes: Based on the updated beamforming matrix and the antenna deformation parameters obtained in the previous iteration, a fractional quadratic transformation is applied to the communication objective function to obtain the first intermediate function. For the quadratic matrix involving the antenna deformation parameters in the first intermediate function, calculate the largest eigenvalue of the quadratic matrix, and construct a linear upper bound for the quadratic term based on the product of the largest eigenvalue and the square of the magnitude of the antenna deformation parameter vector, thereby obtaining the tight convex upper bound of the communication objective function with respect to the antenna deformation parameters.

[0015] Optionally, the process of applying a first-order expansion and eigenvalue upper bound approximation to the sensing target function to obtain the compact convex upper bound of the sensing target function with respect to the antenna deformation parameters includes: Based on the updated beamforming matrix and the antenna deformation parameters obtained in the previous iteration, the square root term in the sensing objective function is expanded in first order to obtain the second intermediate function. For the quadratic matrix involving the antenna steering vector in the second intermediate function, calculate the maximum eigenvalue of the quadratic matrix, and construct a linear upper bound based on the maximum eigenvalue to obtain the tight convex upper bound of the sensing target function with respect to the antenna deformation parameter.

[0016] Compared with the prior art, the present invention has the following advantages and technical effects: This invention constructs a joint objective function that weights and sums communication and sensing, and employs an alternating iterative optimization framework. This transforms the original large-scale non-convex programming problem into a convex upper bound function of the beamforming matrix and antenna deformation parameters, significantly reducing computational complexity and avoiding the extensive iterations and processing delays caused by directly solving non-convex problems in traditional methods. This allows for rapid response to dynamic environmental changes. Simultaneously, the communication objective function is constructed based on user rate fairness, ensuring fair service quality for all users under different channel conditions and avoiding uneven resource allocation. By pre-setting communication and sensing weights, flexible on-demand allocation of communication and sensing performance is achieved, overcoming the limitation of existing technologies that can only focus on a single objective. Simulation results show that this invention, while ensuring user service quality, can form a highly directional sensing beammap that closely matches the target area, exhibiting excellent integrated communication and sensing performance. Attached Figure Description

[0017] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of the integrated sensing algorithm according to an embodiment of the present invention; Figure 2 This is a schematic diagram illustrating the convergence of the algorithm in an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the pure communication performance of the algorithm in an embodiment of the present invention, wherein (a) represents the achievable minimum user rate varying with a fixed number of users. Variation, (b) is the minimum achievable user rate at a fixed transmit power. The following changes; Figure 4 The beam that can be achieved by the algorithm in this embodiment of the invention. Figure 1 ; Figure 5 The beam that can be achieved by the algorithm in this embodiment of the invention. Figure 2 ; Figure 6 This is a schematic diagram illustrating the communication performance of an embodiment of the present invention, wherein (a) is the algorithm. A schematic diagram of communication performance under changing conditions, (b) is... A diagram illustrating communication performance under changing conditions. Detailed Implementation

[0018] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0019] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0020] Existing technologies address user service quality (or perceived beamforming) issues through various mathematical methods, thereby supporting a better user experience in different wireless communication environments. However, analysis from the perspectives of system complexity, user service quality, and future applications reveals the following technical challenges: In terms of system complexity: due to their high computational complexity (Technology 2 involves multiple decision variables and quadratic convex constraints, while Technology 3 is a high-order mathematical problem, which is more difficult to solve), technology 2 and 3 will become very challenging when processing and analyzing large amounts of data, especially in large-scale network environments. The huge amount of data will place extremely high demands on analysis and simulation, making it almost impossible to react quickly to data changes.

[0021] From the perspective of user service quality: Technology 1 struggles to guarantee service quality for all users simultaneously. Because its objective function maximizes the sum rate of all users, it easily allocates base station power to users with better channel conditions, resulting in users with relatively poor channel conditions receiving very little or no power, leading to zero data rate for some users. Technology 3, by solving a fourth-order problem to obtain a two-dimensional beammap, can only detect targets in a specific direction and is insufficient for focusing on a precise location.

[0022] In terms of subsequent applications: Technology 1 focuses on the total throughput of all users and can maximize the utilization of power, but it is not friendly to users with poor channel conditions; Technology 2 can ensure the rate fairness of all users, thereby guaranteeing user QoS, but it takes a long time and has limited support for environments that require real-time adjustment; Technology 3 can provide two-dimensional beammaps, but once the environment becomes more complex, its mathematical problems are difficult to solve, and it is difficult to provide effective support for large-scale network problems.

[0023] Furthermore, current integrated sensing algorithms mainly suffer from the following problems: they cannot simultaneously guarantee communication and sensing performance: they can only adjust the other performance while guaranteeing one performance, and cannot customize the weights; they cannot achieve fast dynamic updates: updating data takes a long time, and the answer can only be obtained by solving complex non-convex problems.

[0024] Based on the analysis of the prior art, the main problems addressed by this invention are: reducing system complexity by proposing an efficient algorithm architecture to address the high computational demands of large-scale data processing and complex environments, thereby reducing computational load, improving data processing speed, and ensuring real-time performance; optimizing user service quality by dynamically adjusting the collaborative optimization mechanism of communication and sensing to ensure fair service quality for all users under different channel conditions and avoid uneven resource allocation; enhancing dynamic update capabilities by providing an efficient dynamic update algorithm that can respond quickly to data changes, avoiding time delays in existing technologies and ensuring the system can adapt to environmental changes in real time; and achieving dual optimization of communication and sensing by simultaneously optimizing communication and sensing performance through a custom weighting mechanism, overcoming the limitations of existing technologies that can only focus on a single objective.

[0025] To address the aforementioned issues, this invention proposes a sensing-communication integrated algorithm for flexible smart metasurfaces, aiming to overcome the limitations of traditional sensing-communication integrated algorithms. By iteratively optimizing the beamforming matrix and deformation parameters (i.e., antenna position), this invention can simultaneously achieve good communication and sensing performance. Communication performance is reflected in user QoS, i.e., a good minimum user rate and a sum rate, while sensing performance is reflected in the three-dimensional beammap. This invention significantly reduces system complexity through mathematical methods. For large-scale data processing and complex environments, it uses an efficient iterative update algorithm to improve data processing capabilities and avoid many problems existing in current technologies. Furthermore, by customizing weights, it can simultaneously optimize communication and sensing performance, overcoming the limitation of existing technologies that can only focus on a single objective. S1: Based on the beamforming matrix and antenna deformation parameters, construct a joint objective function that is a weighted sum of the communication objective function and the sensing objective function; wherein, the communication objective function is obtained based on the user rate, and the sensing objective function is obtained based on the target region beammap; S2: Fix the antenna deformation parameters, process the joint objective function using inequality transformation to obtain a first convex upper bound function with respect to the beamforming matrix, and update the beamforming matrix based on the first convex upper bound function and power constraints; S3: Based on the updated beamforming matrix, process the joint objective function using inequality transformation to obtain a second convex upper bound function with respect to the antenna deformation parameters, and update the antenna deformation parameters based on the second convex upper bound function and antenna position constraints; S4: Based on the alternately iteratively updated beamforming matrix and antenna deformation parameters, repeat S2-S3 until the value of the joint objective function satisfies the convergence condition, and obtain the joint optimization result.

[0026] The inequalities involved in this embodiment are as follows: If function In the domain Above point Satisfying Then the function is called a function. The immediate lower bound at that point, and vice versa.

[0027] The following inequalities apply to all , and , Established, there are: (A.1) like Then the following inequality applies to all , and , have: (A.2) Through expressions ,in It is a convex function, and It is a concave quadratic function, for all , as well as The following inequalities all hold: (A.3) For a positive semidefinite matrix and and matrix variables of appropriate dimensions. ,function It is a convex function such that the following inequality applies to all and Both are true: (A.4) For all and The following inequality can be derived from the convexity of the Frobenius norm: (A.5) In this embodiment, many variables in the formula are intermediate variables, used only to facilitate formula derivation and have no parameter meaning. The general interpretation of the parameters that do have parameter meaning is as follows: All variables with a superscript number in the upper right corner... The meaning of all represents the first The variables obtained from the next iteration. All variables have a lower right corner. (i.e., Cummunication) is a variable used when deriving the communication function, indicated by the underscore in the lower right corner. The variables in "(Sensing)" are those used in deriving the sensing function. The numbers 1 or 2 in the lower right corner are only for distinguishing steps and are not related to the variables themselves. The meaning of "k" or "n" in the lower right corner is: "k" represents the variable for user k, and "n" represents the variable for antenna n.

[0028] like Figure 1 As shown, this embodiment provides a flexible intelligent metasurface integrated beam and morphology joint optimization method, including the following steps: Step 1: Constructing the objective function of the synesthesia integration algorithm.

[0029] Due to numerous problems with existing technologies, the objective functions of existing algorithms are not suitable for use in the integrated sensing of FIM and are difficult to port. Therefore, the joint objective function of this invention is derived from the communication objective function. Perception objective function and communication weight Perceived weights Together constitute, that is Its constraints consist of power constraints and antenna position constraints. Communication objective function The main objective function used is the soft max-min algorithm, and the newly defined perceptual function is also employed. They are combined. Among them, the communication weight... and perceived weights It can adjust itself, thereby dynamically adjusting the required communication and sensing performance. The communication objective function... for: in For channel information, Let be the beamforming matrix for user k. For rate fairness regularization parameters, This refers to noise interference other than user k information.

[0030] And the perception function for: in yes Grid points on the top as well as They represent and The area; and Then it means and middle Quantity, It is an energy concentration zone. This is the energy suppression zone.

[0031] Furthermore, The objective function for Gaussian white noise communication The derivation process is as follows: Since the formula for calculating user speed is: To simplify the processing of this formula, we consider it equivalent to the following problem: This problem is equivalent to: This problem is equivalent to: Because when When A is sufficiently small and A is sufficiently large, there exists a matrix. Therefore, the above formula is equivalent to the following formula: Substituting the transformed expression into the natural logarithm function, we obtain the following form: because because In a specific scenario, this is a definite value, so in this invention, we only need to consider the first term in the above equation, thereby obtaining the objective function: in, This refers to noise interference other than the user k information. Therefore, the objective function is... It is strongly correlated with the communication target.

[0032] Step 2: Reduce the objective function by updating the beamforming matrix.

[0033] Since the currently constructed problem is a large-scale non-convex programming problem, and there is currently no known computational method, it is necessary to use appropriate mathematical methods to process the objective function, transforming it into a tractable convex problem, and then iteratively reducing the beamforming matrix to continuously decrease the objective function. Because the objective function is derived from the communication objective function... and perception function Composition, in which This is the beamforming matrix obtained from the previous iteration. The two objective functions will be processed and transformed separately below.

[0034] Step 2.1: Based on the beamforming matrix obtained in the previous iteration, apply a fractional quadratic transformation to the communication objective function to obtain a compact convex upper bound of the communication objective function with respect to the beamforming matrix. That is, fix the antenna deformation parameters. By applying inequality (A.2) and Then we can obtain the following about the communication objective function. The tight upper boundary: In the formula, Add a noise term to the interference. For the signal term, the first ratio term is... .

[0035] Specifically, a fractional quadratic transformation is used to process the first ratio term in the communication objective function to obtain a quadratic surrogate function with respect to the beamforming matrix. , , as well as .

[0036] The quadratic surrogate function is compacted at the beamforming matrix obtained in the previous iteration to obtain the compact convex upper bound of the communication objective function with respect to the beamforming matrix.

[0037] Since its tightly convex upper bound is a convex function of the beamforming matrix, the optimal solution for each iteration can be found by the bisection method, thereby searching for the optimal beamforming matrix.

[0038] Step 2.2: Based on the beamforming matrix obtained in the previous iteration, expand the sensing objective function to obtain a compact convex upper bound of the sensing objective function with respect to the beamforming matrix. That is, fix... Due to the square root term It is a convex function, applied by using inequality (A.5) and ,in, Let V be the transpose of the guide vector v, and V be the matrix formed by arranging the guide vectors according to the number of paths L. Then the perception target function can be obtained. The tight upper boundary: in , as well as .

[0039] Based on the beamforming matrix obtained in the previous iteration, the function value of the square root term in the sensing objective function at the current iteration point is calculated to obtain the first constant term. The square root term is expanded in first order at the current iteration point to obtain a linear approximation term for the beamforming matrix. Based on the first constant term and the linear approximation term, a tight convex upper bound for the sensing objective function with respect to the beamforming matrix is ​​constructed.

[0040] Since its tightly convex upper bound is also a convex function for the beamforming matrix, the optimal solution for each iteration can be found by the bisection method, thereby searching for the optimal beamforming matrix.

[0041] Step 2.3: Based on preset communication weights and sensing weights, perform a weighted summation of the tightly convex upper bound of the communication objective function with respect to the beamforming matrix and the tightly convex upper bound of the sensing objective function with respect to the beamforming matrix to obtain the first convex upper bound function. Solve the first convex upper bound function and project the solution onto the feasible region that satisfies the power constraint to obtain the updated beamforming matrix.

[0042] Since the upper bound of the objective function has been found, and the required communication weights have been set... and perceived weights The optimized beamforming matrix is ​​obtained by mapping its beamforming matrix onto points that satisfy the power constraints.

[0043] Step 3: Reduce the objective function by updating the deformation parameters.

[0044] Updating the deformation parameters alters the channel between the base station and the user, improving the user's QoS by improving channel conditions. Simultaneously, changing the deformation parameters can also modify the antenna's steering vector, thereby improving beam pattern quality. Similarly, by using mathematical methods to process the objective function, transforming it into a tractable convex problem, and then iteratively reducing the deformation parameters, the objective function is continuously improved. Since the objective function is derived from the communication objective function... and perception function Composition, in which These are the deformation parameters obtained from the previous iteration. The two objective functions will be processed and transformed separately below.

[0045] Step 3.1: Based on the updated beamforming matrix and the antenna deformation parameters obtained in the previous iteration, apply a fractional quadratic transformation and eigenvalue upper bound approximation to the communication objective function to obtain the tight convex upper bound of the communication objective function with respect to the antenna deformation parameters.

[0046] That is, based on the updated beamforming matrix and the antenna deformation parameters obtained in the previous iteration, a fractional quadratic transformation is applied to the communication objective function to obtain the first intermediate function. Since the beamforming matrix has already been updated in step 2, it is fixed. By applying inequality (A.2) and The following communication objective function is obtained. The tight upper boundary: The quadratic matrix involving the antenna deformation parameters in the first intermediate function and The maximum eigenvalue of the quadratic matrix is ​​calculated, and based on the product of the maximum eigenvalue and the square of the magnitude of the antenna deformation parameter vector, a linear upper bound for the quadratic term is constructed, thus obtaining a tight convex upper bound for the communication objective function with respect to the antenna deformation parameter.

[0047] in , , as well as .

[0048] Regarding the third item Using inequality (A.4), we can obtain: in ,as well as .

[0049] Next, the objective function is transformed using inequality (A.3): The intermediate variable is , as well as .in For the guide vector, the formula contains as well as .

[0050] Final form have: This is the first intermediate function, and thus the communication objective function. We obtain its compact convex upper bound. Since its compact convex upper bound is a convex function with respect to the deformation parameter, we can find the optimal solution for each iteration using the bisection method, thereby searching for the optimal deformation parameter.

[0051] Step 3.2: Based on the updated beamforming matrix and the antenna deformation parameters obtained in the previous iteration, apply a first-order expansion and eigenvalue upper bound approximation to the sensing objective function to obtain a compact convex upper bound of the sensing objective function with respect to the antenna deformation parameters, i.e., a fixed upper bound. ,because In variables The above is a convex function, which is applied to the following variables using inequality (A.5): You can obtain: In the above formula Defined as: Therefore, based on the updated beamforming matrix and the antenna deformation parameters obtained in the previous iteration, the square root term in the sensing objective function is expanded in first order to obtain the second intermediate function. Perception objective function It becomes: For the quadratic matrix involving the antenna steering vector in the second intermediate function, calculate the largest eigenvalue of the quadratic matrix, and construct a linear upper bound based on the largest eigenvalue to obtain the compact convex upper bound of the sensing target function with respect to the antenna deformation parameter. That is, transform the above equation according to inequality (A.4): in Therefore, the perception objective function It becomes: in Transform using inequality (A.3): in , as well as .

[0052] Therefore, the perception objective function It becomes: in Mode For the guide vector, the formula contains as well as The intermediate variable is defined as follows: In the formula, The pitch angle, This is the azimuth angle. The target function is thus perceived. By obtaining its compact convex upper bound, the problem can be solved by using the bisection method to find the optimal solution for each iteration, thereby searching for the optimal deformation parameters.

[0053] Step 3.3: Based on the preset communication weights and sensing weights, perform a weighted summation of the tight convex upper bound of the communication objective function with respect to the antenna deformation parameters and the tight convex upper bound of the sensing objective function with respect to the antenna deformation parameters, and perform a second-order expansion approximation on the nonlinear terms in the steering vector to obtain the second convex upper bound function in quadratic form; solve the second convex upper bound function and project the solution to the feasible region that satisfies the antenna position constraints to obtain the updated antenna deformation parameters.

[0054] Since the upper bound of the objective function has been found, and the required communication weights have been set... and perceived weights Channel conditions can be improved by changing deformation parameters, and beam pattern quality can be enhanced by changing the antenna's steering vector.

[0055] By repeating steps 2 and 3, the corresponding beamforming matrix and deformation parameters are iterated continuously. Each iteration yields a beamforming matrix and deformation parameters that reduce the objective function. This process is repeated multiple times until a convergence condition is met. Specifically, the convergence condition is that the change in the objective function is less than a set threshold, meaning the absolute value of the objective function in the current iteration compared to the previous iteration, divided by the previous objective function value, is less than 10^-3. .

[0056] Step 4: Verify the effectiveness of the method through simulation.

[0057] The UMi-Street Canyon line-of-sight (LOS) scenario is adopted as specified in the 3GPP TR 38.901 standard. K=10 users are randomly deployed within a ring-shaped area centered on the base station with an inner radius of 500 meters and an outer radius of 700 meters. The base station is located at (0,0,10) meters, and the user's assumed height is 1.5 meters. A ray-traced channel is used (this can be omitted if appropriate; it is not the focus here). Unless otherwise specified, the following default parameters are used: Noise density carrier frequency The required beam pattern has a power concentration band of 28 GHz and a bandwidth of 100 MHz. With inhibition band Set as as well as .

[0058] Step 4.1: Verify the convergence of the present invention.

[0059] like Figure 2 As shown, the objective function decreases rapidly in the first 5 iterations, then tends to level off, and after 25 iterations, the algorithm makes the objective function meet the convergence condition.

[0060] Step 4.2: Check the communication weight Perceived weights The communication performance that can be achieved at that time, such as Figure 3 As shown, Figure 3 It demonstrates the minimum user rate achieved through soft maximization of minimum user rate optimization. Figure 3 (a) shows the achievable minimum user rate with a fixed number of users. Change; and Figure 3 (b) in the above can achieve the minimum user rate at a fixed transmit power. The following changes show that the algorithm can guarantee the user's QoS quality under various circumstances.

[0061] Step 4.3: Check the communication weight Perceived weights The perceptual performance that can be achieved at that time, such as Figure 4 As shown, Figure 4 The beam pattern that the algorithm can achieve shows that the peaks of the beam pattern have extremely strong directionality, and the main beam is perfectly aligned with the target direction.

[0062] Step 4.4: As Figure 5 As shown, the test is performed when the communication weight Perceived weights The sensing performance achievable under change, the ISAC algorithm in , The sensing performance achievable at that time shows that although the energy of the main beam is relatively lower than that of pure sensing (i.e., , While it declined somewhat (at certain times), it still maintained a good directional trend. And... Fixed, and When changes occur, the target function is perceived. And it changes accordingly, when Perception objective function The initial value was 0.0105, but when it changed to 110 and 130, the perception objective function... The values ​​are 0.0102 and 0.0099 respectively, meaning that the perception performance increases with... It grows bigger and gets better.

[0063] Step 4.5: Check the communication weight Perceived weights The communication performance that can be achieved when changes occur, such as Figure 6 As shown, Figure 6 (a) in the diagram illustrates the communication weight. Fixed as 1 Figure 6 (b) in the diagram illustrates the perceptual weights. Under changing conditions, the minimum user rate and total rate achieved. With... With the increase of perceptual weights, both the minimum user rate and the total rate decreased; however, the algorithm exhibited excellent communication performance under all perceptual weight settings.

[0064] Based on the above technical solution, the present invention has the following technical advantages: (1) Lower system complexity: This invention proposes an efficient algorithm architecture that transforms the original non-convex optimization problem into a convex problem through complex mathematical methods. These convex problems can be solved by using closed-form solutions, thereby avoiding the use of CVX in MATLAB to solve large-scale non-convex problems, greatly reducing the amount of computation and improving the speed of data processing.

[0065] (2) Optimize user service quality: By dynamically adjusting the collaborative optimization mechanism of communication and sensing, and iterating the beamforming matrix and deformation parameters alternately, the computational load is greatly reduced compared to existing methods, ensuring fair service quality for all users under different channel conditions and avoiding uneven resource allocation.

[0066] (3) Custom weighting mechanism: By custom weighting mechanism, communication and perception performance can be optimized at the same time, overcoming the limitation of existing technologies that can only focus on a single target.

[0067] Furthermore, in step 1, the highly effective objective function proposed in this invention is used to construct a computational framework, thereby achieving comprehensive protection of communication and sensing performance. This not only guarantees the QoS of all users but also increases the total throughput of all users.

[0068] Furthermore, in step 2, the present invention uses a unique mathematical method to transform the original large-scale non-convex programming problem into a convex optimization problem and several corresponding subproblems, thereby making the problem easier to solve and greatly reducing the amount of computation.

[0069] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A flexible intelligent metasurface integrated beam and morphology joint optimization method, characterized in that, Includes the following steps: S1: Based on the beamforming matrix and antenna deformation parameters, a joint objective function is constructed by weighted summation of the communication objective function and the sensing objective function; wherein, the communication objective function is obtained based on the user rate, and the sensing objective function is obtained based on the beam pattern of the target area; S2: Fix the antenna deformation parameters, process the joint objective function using inequality transformation to obtain a first convex upper bound function for the beamforming matrix, and update the beamforming matrix based on the first convex upper bound function and the power constraint. S3: Based on the updated beamforming matrix, the joint objective function is processed by inequality transformation to obtain a second convex upper bound function for the antenna deformation parameters, and the antenna deformation parameters are updated based on the second convex upper bound function and the antenna position constraint. S4: Based on the beamforming matrix and antenna deformation parameters updated by alternating iterations, repeat S2-S3 until the joint objective function value satisfies the convergence condition, and obtain the joint optimization result.

2. The flexible intelligent metasurface integrated beam and morphology co-optimization method according to claim 1, characterized in that, The process of constructing a joint objective function based on the beamforming matrix and antenna deformation parameters, which is a weighted sum of the communication objective function and the sensing objective function, includes: Based on the channel information and beamforming matrix of each user, the rate of each user is obtained, and the rate fairness regularization of each user rate is applied to the softmax-min rate to obtain the communication objective function. Based on the deviation between the beammap of the target region and the desired beammap, a two-dimensional grid point beammap fitting function containing energy concentration bands and energy suppression bands is constructed to obtain the sensing target function; Based on preset communication weights and perception weights, the communication objective function and the perception objective function are weighted and summed to obtain the joint objective function.

3. The flexible intelligent metasurface integrated beam and morphology co-optimization method according to claim 2, characterized in that, The expression for the communication objective function is: In the formula, For channel information, Let be the beamforming matrix for user k. For rate fairness regularization parameters, The noise interference is excluding user k information, where y is the antenna deformation parameter and d is the beamforming matrix. This is the objective function for communication.

4. The flexible intelligent metasurface integrated beam and morphology co-optimization method according to claim 3, characterized in that, The expression for the perception target function is: In the formula, To perceive the target function, yes Grid points on the top express area, express area, express Quantity, express middle Quantity, It is an energy concentration zone. This is the energy suppression zone.

5. The flexible intelligent metasurface integrated beam and morphology co-optimization method according to claim 1, characterized in that, The process of updating the beamforming matrix includes: Based on the beamforming matrix obtained in the previous iteration, a fractional quadratic transformation is applied to the communication objective function to obtain a tight convex upper bound of the communication objective function with respect to the beamforming matrix. Based on the beamforming matrix obtained in the previous iteration, a first-order expansion is applied to the sensing objective function to obtain a compact convex upper bound of the sensing objective function with respect to the beamforming matrix. Based on preset communication weights and perception weights, the tight convex upper bound of the communication objective function with respect to the beamforming matrix and the tight convex upper bound of the perception objective function with respect to the beamforming matrix are weighted and summed to obtain the first convex upper bound function. The first convex upper bound function is solved, and the solution is projected onto the feasible region that satisfies the power constraint to obtain the updated beamforming matrix.

6. The flexible intelligent metasurface integrated beam and morphology co-optimization method according to claim 5, characterized in that, Based on the beamforming matrix obtained in the previous iteration, the process of applying a fractional quadratic transformation to the communication objective function to obtain the compact convex upper bound of the communication objective function with respect to the beamforming matrix includes: Based on the beamforming matrix obtained in the previous iteration, the signal term and interference plus noise term for each user are calculated to obtain the first ratio term. The first ratio term in the communication objective function is processed by fractional quadratic transformation to obtain a quadratic surrogate function with respect to the beamforming matrix; The quadratic surrogate function is compacted at the beamforming matrix obtained in the previous iteration to obtain the compact convex upper bound of the communication objective function with respect to the beamforming matrix.

7. The flexible intelligent metasurface integrated beam and morphology co-optimization method according to claim 5, characterized in that, Based on the beamforming matrix obtained in the previous iteration, the process of applying a first-order expansion to the sensing objective function to obtain the compact convex upper bound of the sensing objective function with respect to the beamforming matrix includes: Based on the beamforming matrix obtained in the previous iteration, the function value of the square root term in the sensing target function at the current iteration point is calculated to obtain the first constant term; The square root term is expanded in first order at the current iteration point to obtain a linear approximation term for the beamforming matrix; Based on the first constant term and the linear approximation term, a tight convex upper bound for the sensing objective function with respect to the beamforming matrix is ​​constructed.

8. The flexible intelligent metasurface integrated beam and morphology co-optimization method according to claim 1, characterized in that, The process of updating the antenna deformation parameters includes: Based on the updated beamforming matrix and the antenna deformation parameters obtained in the previous iteration, a fractional quadratic transformation and eigenvalue upper bound approximation are applied to the communication objective function to obtain a tight convex upper bound of the communication objective function with respect to the antenna deformation parameters. Based on the updated beamforming matrix and the antenna deformation parameters obtained in the previous iteration, a first-order expansion and eigenvalue upper bound approximation are applied to the sensing objective function to obtain a tight convex upper bound of the sensing objective function with respect to the antenna deformation parameters. Based on preset communication weights and sensing weights, the tight convex upper bound of the communication objective function with respect to the antenna deformation parameters and the tight convex upper bound of the sensing objective function with respect to the antenna deformation parameters are weighted and summed, and the nonlinear terms in the steering vector are approximated by a second-order expansion to obtain the second convex upper bound function in quadratic form. The second convex upper bound function is solved, and the solution is projected onto the feasible region that satisfies the antenna position constraint to obtain the updated antenna deformation parameters.

9. The flexible intelligent metasurface integrated beam and morphology co-optimization method according to claim 8, characterized in that, The process of applying a fractional quadratic transform and eigenvalue upper bound approximation to the communication objective function to obtain the compact convex upper bound of the communication objective function with respect to the antenna deformation parameter includes: Based on the updated beamforming matrix and the antenna deformation parameters obtained in the previous iteration, a fractional quadratic transformation is applied to the communication objective function to obtain the first intermediate function. For the quadratic matrix involving the antenna deformation parameters in the first intermediate function, calculate the largest eigenvalue of the quadratic matrix, and construct a linear upper bound for the quadratic term based on the product of the largest eigenvalue and the square of the magnitude of the antenna deformation parameter vector, thereby obtaining the tight convex upper bound of the communication objective function with respect to the antenna deformation parameters.

10. The flexible intelligent metasurface integrated beam and morphology co-optimization method according to claim 8, characterized in that, The process of applying a first-order expansion and eigenvalue upper bound approximation to the sensing target function to obtain the compact convex upper bound of the sensing target function with respect to the antenna deformation parameters includes: Based on the updated beamforming matrix and the antenna deformation parameters obtained in the previous iteration, the square root term in the sensing objective function is expanded in first order to obtain the second intermediate function. For the quadratic matrix involving the antenna steering vector in the second intermediate function, calculate the maximum eigenvalue of the quadratic matrix, and construct a linear upper bound based on the maximum eigenvalue to obtain the tight convex upper bound of the sensing target function with respect to the antenna deformation parameter.

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