Method for transduction beamforming of reconfigurable intelligent reflecting surface and laminated intelligent metasurface

Abstract

The application belongs to the technical field of communication and perception integration, and particularly relates to a sensing beam forming method for reconfigurable intelligent reflecting surface and laminated intelligent metasurface. Θ The specific process of the method is as follows: taking the deployment position vector of the RIS, the reflection phase shift diagonal matrix of the RIS and the phase shift diagonal matrix of the first layer of the SIM as joint optimization variables, constructing a joint optimization model with multi-user and rate maximization as the target while meeting the target sensing accuracy constraint; taking the RIS deployment area constraint, the RIS unit phase shift constraint and the SIM layer super atom phase shift constraint as conditions; establishing the inverse relationship between the two-dimensional CRB and the target direction beam pattern gain, and equivalently converting the original CRB constraint into the beam pattern gain constraint to obtain a new optimization problem; for the new optimization problem, the joint optimization variables are decomposed into three optimization problems and solved to obtain the locally optimal RIS deployment position, SIM phase shift matrix and RIS phase shift matrix.

Description

Technical Field

[0001] This invention belongs to the field of communication and sensing integration technology, specifically relating to a method for synesthetic beamforming of a reconfigurable smart reflective surface and a stacked smart metasurface. Background Technology

[0002] Overview of Integrated Sensing and Communication (ISAC) Technology: With the continuous development of research on Sixth Generation (6G) mobile communication, future wireless networks not only need to meet the requirements of high-speed and low-latency communication, but also need to have high-precision environmental perception, target localization, and target tracking capabilities. ISAC technology, through deep integration of spectrum resources, hardware platforms, and waveform design, achieves coordinated optimization of communication and sensing functions within the same system, significantly improving spectrum and hardware utilization. Therefore, it is considered one of the key technologies for 6G wireless networks.

[0003] To further improve the performance of ISAC systems, reconfigurable smart surface technologies have received widespread attention in recent years. On the one hand, with the continuous increase in antenna array size, traditional all-digital beamforming, while offering high waveform design flexibility, requires a large number of radio frequency (RF) links, resulting in high hardware complexity, power consumption, and cost. To address this issue, hybrid beamforming has been proposed as a more cost-effective and energy-efficient approach, but its constant mode constraint also limits the freedom of beam design to some extent.

[0004] On the other hand, Reconfigurable Intelligent Surfaces (RIS), as an electromagnetic control structure composed of a large number of low-cost passive units, can achieve programmable reflected beamforming by adjusting the phase of each reflecting unit, thereby improving wireless link quality under low power consumption conditions. Most existing RISs adopt a single-layer structure, which limits their ability to control electromagnetic waves, thus constraining the potential for system performance improvement. To enhance the freedom of electromagnetic wave control, Stacked Intelligent Metasurfaces (SIMs) have been proposed. SIMs, through a multi-layered cascaded transmissive metasurface structure, can control propagating electromagnetic waves layer by layer, enabling more precise beamforming and signal processing directly in the wave domain, and possessing stronger beam control capabilities compared to traditional single-layer RISs.

[0005] The existing technical solutions that are closest to this invention mainly include the following two categories.

[0006] The first type of existing scheme is an ISAC system based on RIS (Receptor-Assisted Component Analysis). This type of scheme typically deploys a RIS between the base station (BS) and the communication user or sensing target. By establishing cascaded channel models from BS to RIS, RIS to the user, and RIS to the target, it jointly optimizes the active beamforming of the BS and the passive reflection phase shift of the RIS to improve user access speed, extend coverage, and enhance sensing performance in the target direction. A typical implementation of this type of scheme involves constructing a multi-user signal-to-interference-plus-noise ratio (SINR) or rate maximization problem, under the conditions of satisfying transmit power constraints, RIS unit phase constraints, and sensing performance constraints. The transmit beam and RIS phase shift matrices are then iteratively solved using methods such as Alternating Optimization (AO).

[0007] The second type of existing scheme is based on SIM-assisted ISAC systems. This type of scheme typically integrates multiple SIMs at the BS end. Each layer of the SIM consists of multiple programmable superatoms, which can apply independent transmission phase shifts to electromagnetic waves passing through that layer, thereby directly completing beamforming in the electromagnetic domain. Existing research has focused on SIM-assisted multiple-input single-output (MISO) systems, holographic multiple-input multiple-output (MIMO) systems, and downlink multi-user ISAC systems. Typically, this involves jointly optimizing the BS transmit power and the SIM phase shift matrix to improve spectral efficiency or user sum rate under sensing beammap constraints. The implementation method generally involves first establishing an inter-SIM layer transmission model, a communication channel model, and a target echo model; then constructing an optimization problem with the sum rate maximization objective and sensing beammap or Cramer-Rao Bound (CRB) constraints as limitations; and finally solving the problem using algorithms such as AO and Gradient Ascent (GA).

[0008] However, most existing SIM-assisted ISAC schemes are purely transmissive structures. When the line-of-sight (LoS) link between the BS and the communication user or sensing target is obstructed by obstacles such as buildings and trees, system performance degrades significantly. To overcome this problem, some research has proposed introducing a Reference Indicator (RIS) in addition to the SIM, constructing a virtual LoS link through the RIS to bypass obstacles and enhance communication and sensing performance. In such schemes, cascaded propagation models are typically established simultaneously for SIM to RIS, RIS to user, and RIS to target. The wave domain beamforming of the SIM, the reflection beamforming of the RIS, and the deployment location of the RIS are jointly optimized to improve user numbers and data rates while meeting the two-dimensional Direction of Arrival (DoA) estimation accuracy constraints.

[0009] Although the aforementioned existing technologies have been able to improve the communication and sensing performance of the ISAC system to some extent, the following problems still exist: First, the pure SIM transmission structure is prone to significant degradation of link performance in occlusion scenarios; second, the RIS auxiliary link has a "double fading" effect, and its performance is highly sensitive to the RIS deployment location; third, when considering SIM phase shift, RIS phase shift, and RIS location optimization at the same time, the coupling between the communication target and the sensing target is severe, resulting in high solution complexity and difficulty in engineering implementation.

[0010] The closest existing technical solutions to this invention mainly include SIM-based sensing systems and RIS-assisted sensing systems that further introduce RIS on top of SIM. Although the above solutions can improve the communication performance and sensing capabilities of the system to a certain extent, they still have the following shortcomings.

[0011] First, most existing SIM-assisted ISAC solutions employ a purely transmissive structure, whose beamforming and propagation adaptability are easily limited by actual obstruction environments. When the LoS between the BS and the communication user or sensing target is blocked by buildings, trees, or other obstacles, system performance will significantly degrade. This indicates that relying solely on the transmissive characteristics of the SIM makes it difficult to simultaneously guarantee stable communication coverage and sensing accuracy in complex propagation scenarios.

[0012] Secondly, while introducing RIS (Resonance Induction System) into a SIM system can bypass obstructions by constructing a virtual Loss of Position (LoS) link, the RIS-assisted link typically suffers from a "double fading" effect. This means the signal experiences more severe end-to-end power attenuation during cascade propagation, thus weakening the overall gain of communication and sensing. Furthermore, the RIS's auxiliary effect is highly sensitive to its deployment location; different installation locations significantly impact cascaded channel quality, target-direction echo gain, and multi-user interference distribution. Therefore, existing solutions struggle to fully leverage the advantages of RIS-SIM collaboration when the RIS location is not effectively optimized.

[0013] Furthermore, in multi-user ISAC scenarios, the system not only needs to improve the number of users and the rate of operation, but also needs to meet the target perception accuracy constraints. Existing research typically uses the CRB (Center for Recognition) based on two-dimensional angle of arrival (DoA) estimation to characterize perception performance. However, there is a strong non-convex coupling relationship between the CRB and the SIM phase shift, RIS phase shift, and RIS deployment location, which makes it difficult to solve the original joint optimization problem, resulting in high computational complexity and making it difficult to directly apply to engineering implementation. Especially when simultaneously optimizing SIM wave domain beamforming, RIS reflection beamforming, and RIS location, this coupling relationship is further aggravated, causing existing methods to suffer from poor solvability, convergence difficulties, and high global optimization challenges.

[0014] Therefore, existing technologies urgently need to address the following technical issues: how to construct a syn-sensory beamforming method that can simultaneously utilize the SIM wave domain modulation capability and the RIS reflection enhancement capability in scenarios with obstruction and complex propagation loss; how to incorporate the RIS deployment location into the system joint design while overcoming the dual fading effects of the RIS link to improve communication link quality and target sensing performance; and how to reduce the difficulty of solving the joint optimization problem of SIM phase shift, RIS phase shift, and RIS location while satisfying CRB sensing constraints, thereby achieving an efficient, feasible, and high-performance beamforming design for multi-user ISAC systems. Summary of the Invention

[0015] The purpose of this invention is to propose a perceptual beamforming method for RIS and SIM to solve the problems of performance degradation in occlusion scenarios, double fading of RIS-assisted links and sensitivity to deployment location, and the difficulty in directly solving the high coupling between sensing accuracy constraints and beamforming variables.

[0016] The technical solution to the problem of this invention is as follows:

[0017] A method for sensing beamforming using RIS and SIM, applicable to a multi-user communication and sensing integrated ISAC system comprising a base station (BS), a reconfigurable intelligent reflector (RIS), and a SIM. The system consists of a single-antenna communication user and a sensing target, where the BS is equipped with a stacked intelligent metasurface SIM, which is composed of L layers of cascaded metasurfaces, each layer containing N superatoms; the RIS contains Mr reflective units; the specific process of this method is as follows: Step 1: Using the RIS deployment location vector The reflection phase shift diagonal matrix of RIS Θ and SIM The phase shift diagonal matrix of the layer is used as the joint optimization variable to construct a joint optimization model with the goal of maximizing multi-user and rate while satisfying the target perception accuracy constraint; at the same time, it is based on the constraints of RIS deployment area, RIS unit phase shift constraint and SIM layer superatomic phase shift constraint. Step 2: Establish the inverse relationship between the two-dimensional CRB and the beammap gain of the target direction, and transform the original CRB constraint into an equivalent beammap gain constraint to obtain a new optimization problem; Step 3: For the new optimization problem obtained in Step 2, the joint optimization variables are decomposed into three optimization problems, specifically: 1. Optimize the RIS deployment position under the condition of fixed SIM phase shift matrix and RIS phase shift matrix, to obtain the RIS position optimization subproblem; 2. Optimize the phase shift matrix of each layer of SIM under the condition of fixed RIS deployment position and RIS phase shift matrix, to obtain the SIM phase shift optimization subproblem; 3. Optimize the RIS reflection phase shift matrix under the condition of fixed RIS deployment position and SIM phase shift matrix, to obtain the RIS phase shift optimization subproblem. Step 4: Solve the three sub-problems separately to obtain the locally optimal RIS deployment location, SIM phase shift matrix, and RIS phase shift matrix.

[0018] Optionally, the joint optimization model and constraints in step one of this invention are as follows:

[0019] In the formula, Represents the deployment location vector of the RIS; Θ This represents the reflection phase shift diagonal matrix of RIS; Indicates SIM number The phase shift diagonal matrix of the layer; Indicates the first Signal-to-Interference-plus-Noise Ratio (SINR) for communication users; Represents the trace of the CRB matrix for the two-dimensional DoA estimation of the target; This represents the upper bound of the CRB corresponding to the target perception accuracy; This indicates the two-dimensional feasible region that RIS allows for deployment; Represents the set of RIS reflection units; Represents the set of superatoms in each SIM layer; Represents the SIM layer index set. Subscript The value can be 1- , Subscript The value can be 1- Since there is a strong coupling relationship between the RIS position, RIS phase shift and SIM phase shift, and all of them are constrained by the unit modulus, the original problem is a highly nonconvex optimization problem.

[0020] Optionally, the present invention transforms the original CRB constraint into an equivalent beammap gain constraint as follows: Will" "Transformed into "Target direction beammap gain not lower than threshold" The equivalent constraint of "" leads to a new optimization problem:

[0021] In the formula, Indicates the target link loss; Indicates the direction of the target The RIS array response vector at that location; This indicates a cascaded channel from SIM to RIS; Represents the covariance matrix of the transmitted waveform; This represents the beammap gain threshold for the target direction. This transformation converts the previously difficult-to-solve CRB accuracy constraint into a more engineering-feasible beammap gain threshold constraint.

[0022] Optionally, the RIS location optimization subproblem described in this invention employs a continuous convex approximation method. By performing a first-order Taylor expansion on the large-scale path loss correlation term and beammap gain term, the original non-convex location optimization problem is transformed into a convex subproblem for iterative solution. When the objective function gain of two consecutive iterations is lower than a preset threshold, the iteration stops, and the locally optimal deployment location of the RIS is output. .

[0023] Optionally, the SIM phase shift optimization subproblem described in this invention employs a gradient ascent algorithm based on a penalty function. The sensing beammap gain constraint is incorporated into the objective function through a penalty term to iteratively update the phase shift of each SIM superatom layer. The iteration stops when the objective function gain of two consecutive iterations falls below a preset threshold, and the optimized SIM phase shift matrix is ​​output. .

[0024] Optionally, the RIS phase shift optimization subproblem described in this invention is solved using the SCA-ECA algorithm based on continuous convex approximation and element-wise coordinate ascent. During the solution process, each RIS reflection unit is treated as an independent coordinate block. In each update, only the phase of one unit is adjusted, while the phases of other units remain unchanged. This process continues until all units have completed one round of updates, at which point the RIS phase shift matrix has completed one round of updates. When the objective function gain of two consecutive iterations falls below a preset threshold, the iteration stops, and the optimized RIS phase shift matrix is ​​output. .

[0025] Beneficial effects: In complex propagation scenarios with occlusion, by introducing RIS into a SIM-assisted ISAC system and further optimizing its deployment location, a virtual line-of-sight link can be established, enhancing the system's spatial degrees of freedom and sensory coordination capabilities. This effectively alleviates the performance degradation problem of the pure SIM transmission architecture under occlusion conditions. Furthermore, by transforming the CRB accuracy constraint of the two-dimensional DoA estimation into a target direction beammap gain threshold constraint, the problem avoids directly handling highly non-convex sensing accuracy conditions, significantly improving the solvability and engineering feasibility. Moreover, by embedding RIS location optimization, SIM phase shift optimization, and RIS phase shift optimization into a unified AO framework for joint solution, both high-performance SGE can achieve better phase alignment, and low-complexity DGAS can reduce computational burden. Simulation results show that compared to the baseline scheme using only SIM, introducing RIS under the same sensing constraints can bring about approximately 1.5 times the sum rate gain. Simultaneously, RIS location optimization can further improve performance compared to the fixed-position RIS scheme, indicating that this invention has good practical value and promising prospects in multi-user sensory scenarios. Attached Figure Description

[0026] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 The curves showing the influence of the sum rate on the number of SIM layers in the DGAS algorithm.

[0028] Figure 2 The curves showing the influence of the sum rate on the number of SIM layers in the SGE algorithm.

[0029] Figure 3 The curves showing the effect of DGAS algorithm on the sum rate and the number of RIS.

[0030] Figure 4 The effect curve of SGE algorithm on sum rate and number of RIS.

[0031] Figure 5 The curves showing the effect of the summation rate on the number of iterations.

[0032] Figure 6 This is a flowchart of the present invention. Detailed Implementation

[0033] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0034] It should be noted that, in the absence of conflict, the following embodiments and features can be combined with each other; and, based on the embodiments of this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0035] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0036] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments, which is a method for inductive beamforming of reconstructable intelligent reflective surface RIS and stacked intelligent metasurface SIM.

[0037] This invention aims to address multi-user ISAC scenarios, revealing the communication-sensing coupling mechanism under the synergistic effect of SIM and RIS under conditions of obstruction and complex propagation loss. It analyzes the evolution of communication performance under sensing accuracy constraints and constructs an implementable joint optimization framework. This invention synergistically integrates the multi-layer electromagnetic wave domain modulation capability of SIM with the positional deployment freedom and reflection beamforming capability of RIS. While meeting the target two-dimensional DoA sensing accuracy, it maximizes multi-user downlink speed and achieves a synergistic improvement in communication and sensing performance. The specific process is as follows: Step 1: Using the RIS deployment location vector The reflection phase shift diagonal matrix of RIS Θ and SIM The phase shift diagonal matrix of the layer is used as the joint optimization variable to construct a joint optimization model with the goal of maximizing multi-user and rate while satisfying the target perception accuracy constraint; at the same time, it is based on the constraints of RIS deployment area, RIS unit phase shift constraint and SIM layer superatomic phase shift constraint. Step 2: Establish the inverse relationship between the two-dimensional CRB and the beammap gain of the target direction, and transform the original CRB constraint into an equivalent beammap gain constraint to obtain a new optimization problem; Step 3: For the new optimization problem obtained in Step 2, the joint optimization variables are decomposed into three optimization problems, specifically: First, under the condition of fixing the SIM phase shift matrix and the RIS phase shift matrix, optimize the RIS deployment position to obtain the RIS position optimization subproblem; Second, under the condition of fixing the RIS deployment position and the RIS phase shift matrix, optimize the phase shift matrix of each layer of SIM to obtain the SIM phase shift optimization subproblem; Third, under the condition of fixing the RIS deployment position and the phase shift matrix of each layer of SIM, optimize the RIS reflection phase shift matrix to obtain the RIS phase shift optimization subproblem. Step 4: Solve the three sub-problems separately to obtain the locally optimal RIS deployment location, SIM phase shift matrix, and RIS phase shift matrix.

[0038] This embodiment establishes a SIM-RIS-assisted ISAC system model and communication and sensing performance indicators; it derives the relationship between the CRB estimated in two-dimensional DoA and the beammap gain in the target direction, transforming the CRB constraint, which is difficult to process directly, into a beammap gain constraint that is easier to optimize; it adopts the AO framework to iteratively update the RIS deployment location, the phase shift of each layer of SIM, and the RIS phase shift, forming a high-performance SGE implementation and a low-complexity DGAS implementation. The core problem addressed by this embodiment is to jointly optimize the SIM phase shift, RIS phase shift, and RIS deployment location under CRB constraints to maximize users and data rate.

[0039] like Figure 5 As shown, the specific implementation steps are as follows: Step 1: This invention considers a system consisting of a base station (BS), a SIM, and a RIS. An ISAC system consisting of a single-antenna communication user and a sensing target. BS configuration. The antenna is arranged in a uniform linear array (ULA) configuration. The SIM is mounted on the BS side and located at... Plane. SIM is composed of Composed of layers of metasurfaces, each layer is modeled as having A uniform planar array (UPA) of superatoms, wherein, and These represent the number of superatoms in the horizontal and vertical directions, respectively. The SIM integrates an intelligent control unit that can precisely and independently adjust the transmission phase shift of each superatom in each layer. Because the direct link from the BS to the user and target is obstructed, an additional RIS is deployed in the scene to construct a virtual line-of-sight link and simultaneously serve communication and sensing functions.

[0040] For ease of description, the SIM layer index set is defined as follows: Each layer of superatomic assembly is The user set is . No. Layer The transmission phase shift of a superatom is expressed as: ,in Therefore, the first The phase shift diagonal matrix of the layer SIM is written as

[0041] remember For the first layer to the first The inter-layer propagation matrix of the layer. When At that time, according to the Rayleigh-Sommerfeld diffraction theory, the interlayer... From the first superatom to the... The propagation coefficient of each superatom is related to the propagation distance, interlayer spacing, and wavelength, thus allowing the construction of the propagation matrix between layers. Furthermore, the overall transmission matrix of the SIM can be expressed as...

[0042] The above modeling shows that the present invention achieves beam control in the electromagnetic wave domain through a multi-layer cascaded transmission structure.

[0043] RIS is It consists of several reflective units, employing a unit mode reflection model with adjustable phase and fixed amplitude. Its reflection phase shift matrix can be expressed as:

[0044] in, Let the position of BS be... The RIS position is , No. The location of each user is The target location is The location of the RIS is restricted to a given feasible deployment area, i.e. , The BS transmission signal is denoted as... It satisfies zero mean and unit covariance. Except In addition to the communication stream, this invention further introduces an independent sensing stream to increase the degrees of freedom in beam design; therefore, the total number of streams is taken as... The transmit signal of the SIM output layer is represented as: ,in, The power allocation diagonal matrix is ​​given by the corresponding transmit covariance matrix: .

[0045] The SIM to RIS link uses the Rician fading model, and the RIS to user link is denoted as... . No. The received signal for each user consists of the desired communication term, multi-user interference term, perceived flow leakage term, and noise term, and its corresponding signal-to-interference-plus-noise ratio (SINR) is denoted as . The achievable speed for users is .

[0046] On the perception side, assuming the target is located in the far field of the RIS, a point target model is adopted. The RIS steering vector is written as:

[0047]

[0048]

[0049] in, and Let these represent the target's elevation and azimuth angles, respectively. Consider... The first snapshot, the... The echo signal of a snapshot can be represented at the BS end as:

[0050] in, This characterizes the combined effect of round-trip propagation loss and the target's radar cross section (RCS). By stacking and quantizing multiple snapshot echoes, a Fisher Information Matrix (FIM) can be established. Then, the CRB of the target's two-dimensional DoA estimate can be obtained using the Schur Complement.

[0051] in, Therefore, the present invention constructs the following joint optimization problem:

[0052] in, The target is the upper bound of the CRB. Deploy a feasible region for RIS. Due to the high coupling between RIS location, RIS phase shift, and SIM phase shift, and the fact that they are all constrained by unity modulus, the original problem is a highly nonconvex optimization problem.

[0053] Step 2: Establish the inverse relationship between the 2D CRB and the target direction beammap gain, and reconstruct the original problem into a beammap-constrained problem. Specifically: Since the CRB constraints in the original problem are related to... , Θ and Exhibiting high non-convexity, it is difficult to process directly. Therefore, this invention reconstructs the FIM block matrix and introduces the Schur complement matrix to establish an analyzable lower bound for the CRB matrix trace. The paper presents the following key conclusion: when the beam pattern gain in the target direction is sufficiently large, the trace of the CRB matrix is ​​approximately inversely proportional to the beam pattern gain in that direction, i.e.

[0054] in, Indicates the direction of the target Beam pattern gain at the location, It is the target's pitch angle. It is the azimuth angle. More specifically, the target direction beammap gain is defined as... , in, The target link path loss. Based on this approximate inverse relationship, this invention transforms the original CRB constraint " "Transformed into "Target direction beammap gain not lower than threshold" The equivalent constraint of "" is used to rewrite the original problem as

[0055] Through this reconstruction, the present invention avoids directly solving highly complex CRB constraints, thereby improving the tractability of the problem.

[0056] Step 3: Using the AO framework, the reconstructed problem is decomposed into three iteratively solved subproblems. For the reconstructed problem (P2), this invention uses the AO framework to solve it, decomposing the original problem into three subproblems, which are iterated alternately in the outer loop. The three subproblems are: RIS deployment location optimization, SIM phase shift optimization, and RIS phase shift optimization. For the high-performance implementation, RIS location optimization uses SCA, SIM phase shift optimization uses GA optimization based on a penalty term, and RIS phase shift optimization uses SCA combined with element-wise coordinate ascent (SCA-ECA). For the low-complexity implementation, the SCA optimization for RIS location is retained, and the RIS phase shift optimization is replaced with GA updates, thus forming the DGAS algorithm combining double gradient ascent and SCA.

[0057] Step 4: Solve the three sub-problems separately to obtain the locally optimal RIS deployment location, SIM phase shift matrix, and RIS phase shift matrix.

[0058] 4.1: For the RIS deployment location subproblem, a continuous convex approximation algorithm is used for solution, specifically: (1) The phase shift matrices of each layer of the fixed SIM and the phase shift matrices of the RIS Θ Then, the original problem (P2) can be reduced to a problem only concerning the RIS deployment location. The optimization problem, namely

[0059] Among them, changed to This represents the two-dimensional feasible deployment region of RIS. This represents the large-scale path loss of the target-aware link. Since changes in the RIS's location primarily affect the propagation distances of the BS–RIS, RIS–user, and RIS–target links, this subproblem focuses on location-dependent large-scale fading terms.

[0060] (2) In order to explicitly separate the influence of the RIS position on the objective function and constraints of the subproblem, the beamforming term independent of the RIS position is incorporated into a constant, and the first term is defined as follows: The effective signal items and interference items for each user are as follows:

[0061] And introduce slack variables , Indicates RIS to the 1st The large-scale path loss of the equivalent cascaded link for each user. Therefore, the first... The signal-to-interference-plus-noise ratio (SIR) for an individual user can be rewritten as:

[0062] Similarly, for perception constraints, all terms except the target path loss are incorporated into a constant:

[0063] and define Then the beam pattern gain in the target direction can be written as: After the above transformation, the non-convexity in the RIS position optimization subproblem mainly focuses on... and right and On the non-linear dependence.

[0064] (3) Due to the user rate function:

[0065] about Since it is a non-convex form, at the current iteration point Perform a first-order Taylor expansion on it and construct its linear lower bound. We can then obtain the... The lower bound of the user rate is: .

[0066] Therefore, each term in the original objective function, representing the user rate, can be defined by its linear lower bound. This replaces the original non-convex objective function, thereby making it lower bounded.

[0067] (4) For the beammap gain term in the perception constraint Regarding It is also a non-convex function. Therefore, at the current iteration point... Performing a first-order Taylor expansion at the given location, we obtain its linear lower bound as follows: Therefore, the original constraint It can be derived from its approximate form Replacement, thereby transforming perceptual constraints into information about Linear constraints.

[0068] (5) Even after the above processing, constraints still exist. The constraint is nonconvex. To further transform this constraint into a tractable form, auxiliary variables are introduced. and ,in , , and let the first Each auxiliary variable corresponds to the perceived target distance, i.e. .in, This represents the distance between BS and RIS. Indicates RIS and the first The distance between users This represents the distance between the RIS and the target. This allows the inverse path loss constraint to be uniformly written as: , in, and These represent the path loss exponents of the BS–RIS link and the RIS–user or RIS–target link, respectively. Indicates the carrier wavelength.

[0069] (6) Due to the function It is still a non-convex function, therefore at the current iteration point Performing a first-order Taylor expansion on the given surface yields a linear approximation: , ,

[0070] Therefore, constraints The following linear lower bound can be used as an alternative:

[0071] After this step, the non-convex constraint originally caused by the coupling of geometric distance and path loss is transformed into a constraint concerning... , and Linear constraints.

[0072] (7) In summary, the RIS deployment location optimization subproblem can be reconstructed into a class of convex optimization problems, namely . The above problem can be solved efficiently using convex optimization tools such as CVX. In the algorithm implementation, the RIS positions are first initialized. Auxiliary variables , and Then, in each iteration, the objective function and constraints are linearized to the first order around the current iteration point, and the corresponding convex subproblem is solved. Finally, the RIS position and each auxiliary variable are updated. The iteration stops when the gain of the objective function in two consecutive iterations falls below a preset threshold, and the locally optimal deployment position of the RIS is output. .

[0073] 4.2: For the SIM phase shifter problem, a gradient ascent algorithm based on a penalty function is used for solution, specifically as follows: (1) In a fixed RIS deployment location ( ) and RIS phase shift matrix ( When ), the original problem ((P2)) can be degenerated into a problem concerning only the phase shift matrices of each layer of SIM ( The optimization problem is as follows: To avoid directly handling the non-convex coupling caused by the sensing beammap gain constraint, this constraint is incorporated into the objective function, constructing an optimization problem with a penalty term:

[0074] in, >0 is a penalty factor used to balance maximizing users and rates with meeting the target direction beammap gain constraint; This represents a perception constraint penalty term, applied when the beammap gain in the target direction is not lower than a threshold. hour, =0, otherwise the penalty term is activated.

[0075] (2) Since the objective function includes both the communication part and the sensing part, therefore for the first... Layer Superatomic phase shift When finding the partial derivative, the gradient can be decomposed into two parts, namely

[0076] in, This represents the communication target item corresponding to the rate. This represents the penalty term introduced by the sensing beammap gain constraint.

[0077] (3) For the communication part, the first definition is... The expected signal power term of the user and the first Road signal to the first The interference power items caused by each user are as follows:

[0078] in, Indicates the relationship with the first The equivalent excitation vector corresponding to the data stream. and These represent the large-scale path loss of the corresponding links. and These are the power allocation coefficients for the corresponding streams. Then the communication objective function is related to... The partial derivative can be written as

[0079] This equation shows that the effect of SIM phase shift on user rate can be decomposed into two parts: "enhancing desired signal term" and "suppressing multi-user interference term".

[0080] (4) In order to further explicitly write out and The expression introduces an auxiliary matrix. and , respectively defined as

[0081]

[0082] remember For matrix The OK, For matrix The Column, then there are ， , in, This indicates the operation of taking the imaginary part. The above results show that the first... Layer The phase shift of a single superatom will affect both the communication signal and the interference signal through its forward and backward propagation links in the overall SIM cascaded transmission matrix.

[0083] (5) For the sensing part, since the penalty term essentially corresponds to the target direction beammap gain constraint, its relation to The partial derivative can be written as , Among them, the upper limit of summation This represents the total number of communication and sensing flows. This formula reflects the influence mechanism of the phase shift of each SIM layer on the echo gain in the target direction. That is, by adjusting the transmission phase of each superatom layer, the equivalent radiation field in the target direction is enhanced, thereby meeting the sensing beammap gain threshold requirement.

[0084] (6) To improve numerical stability and prevent excessive gradients in one dimension from causing oscillations in the update process, the gradients of all SIM phase shift variables are normalized, i.e. in, This represents the maximum absolute value among all current gradient components. This normalization step ensures that gradient updates across different layers and superatoms are on a relatively uniform numerical scale.

[0085] (7) After gradient normalization, the SIM phase shift is updated using the gradient ascent method based on Armijo backtracking search, i.e.

[0086] in, The step size parameter is adaptively determined by Armijo backtracking search. This update method improves the algorithm's convergence stability and implementation efficiency while ensuring the objective function remains monotonically constant.

[0087] (8) In summary, the specific implementation process of SIM phase shift optimization is as follows: First, initialize the SIM phase shift matrices of each layer. Then, in each iteration, based on the current RIS position... and RIS phase shift matrix The gradients of the communication and sensing parts are calculated; then the gradients are normalized, and the step size is determined using Armijo line search to synchronously update the phase shifts of all superatoms; when the objective function gain of two adjacent iterations is lower than a preset threshold, the iteration stops, and the optimized SIM phase shift matrix is ​​output.

[0088] This completes the optimized design of the transmission phase shift of each layer of the SIM under the conditions of fixed RIS deployment location and RIS phase shift.

[0089] 4.3: For the RIS phase shifter problem, the SCA-ECA algorithm based on continuous convex approximation and element-wise coordinate ascent is used for solution, specifically: (1) In a fixed RIS deployment location Phase shift matrices of each layer of SIM Then, the original problem (P2) can be degenerated into a problem concerning only the RIS phase shift matrix. The optimization problem is as follows. To avoid the strong non-convex coupling caused by directly handling the target direction beammap gain constraint, this constraint is incorporated into the objective function, constructing an optimization problem with a penalty term:

[0090] in, >0 is a penalty factor used to balance the maximization of sum rate with the target direction beammap gain constraint; As a perception constraint penalty term, when the target direction beammap gain is not lower than a threshold hour, =0, otherwise the penalty term is activated.

[0091] (2) Due to the sum rate term in the objective function with respect to the RIS phase shift matrix It presents a non-convex logarithmic form, therefore, the first... The rate term for each user is rewritten as the difference between two logarithmic functions, i.e.

[0092] ， 。

[0093] (3) At the t-th iteration point At this point, a first-order Taylor expansion is performed on the above logarithmic function to construct a representation of... A tractable approximate objective function. Specifically, define...

[0094] Here, the symbol "(:)" denotes the Frobenius inner product of matrices. Therefore, for... and In respectively The area unfolds, with

[0095] Therefore, the linearized sum rate approximation objective function can be obtained: .

[0096] After this step, the original non-convex rate function is replaced with a locally linear approximation near the current iteration point.

[0097] (4) For the perception constraint penalty term Similarly, at the current iteration point Performing a first-order Taylor expansion at that point, we have

[0098] The gradient of the penalty term can be written as: ， The gradient expression shows that the phase of each RIS reflection unit has an explicit effect on the beam pattern gain in the target direction. Therefore, the echo gain in the target direction can be improved by gradually adjusting the phase shift of each RIS unit.

[0099] (5) After the above linearization process, the original RIS phase shift optimization problem can be reconstructed into the following approximate subproblem:

[0100] Although the problem has been approximated by continuous convexity, due to... Still constrained by the unit modulus, direct overall optimization remains quite difficult.

[0101] (6) To this end, the element-wise coordinate ascending method is further adopted to optimize each reflection unit of the RIS one by one.

[0102] First, the RIS phase shift matrix is ​​randomly initialized. A discrete angle search grid is defined for each RIS reflection unit.

[0103] in, This indicates the number of grid points in the phase search.

[0104] Then, for the first Each RIS reflection unit performs a one-dimensional angle search: while fixing the rest ( Under the condition that the phase shift of each element remains unchanged, traverse the angle mesh. Calculate the objective function value for each candidate phase, and select the phase value that maximizes the current objective.

[0105] The above process is performed sequentially for each RIS unit until all units have completed one round of updates.

[0106] Compared with the traditional block coordinate ascent method, this method applies to the entire RIS phase shift matrix. Unlike treating each RIS reflection unit as a single, unified variable, this invention employs an element-wise coordinate ascending algorithm. Each RIS reflection unit is treated as an independent coordinate block, and only the phase of one unit is adjusted during each update, while the phases of other units remain unchanged. This allows for more precise adjustment of the objective function and reduces the computational difficulty associated with a one-time global optimization. After one round of element-wise search, the RIS phase shift matrix is ​​updated as follows:

[0107] The embodiments are further illustrated by Matlab simulations to demonstrate the inductive beamforming method of the present invention for RIS and SIM.

[0108] 1) Simulation system parameter settings To verify the effectiveness of the proposed RIS-SIM integrated beamforming method, a SIM-RIS-assisted multi-user communication and sensing simulation scenario was constructed. The carrier frequency was set to 28 GHz. The spacing between each superatomic layer of the SIM was set to... The unit area is taken as The base station's total transmit power is set to 18 dBm, and the antenna gain is set to 5 dBi. Free space path loss parameters are set to... = 60 dB, where the path loss index of the BS-RIS link is taken as =2.0, the path loss exponent of RIS to the user and target links is taken as 2.0. The power of the additive white Gaussian noise is set to... 104 dBm. The system is set to [number missing]. There is one single-antenna communication user and one sensing target. The base station location is set to (0,0,22) m, and the target location is set to (5,5,18) m. The location of each user is set to (10k, 10k, 0) m, where =1,2,3,4. The deployable area of ​​the RIS is set to... , Unless otherwise specified, the default number of base station antennas is [number to be filled in]. Number of superatoms per SIM layer The number of RIS reflection units is taken =100. All simulation results were obtained by averaging 200 independent Monte Carlo experiments. Perceptual constraints were determined using the target direction beammap gain threshold. Characterization, in which Indicates no perceptual constraint. and These represent different perception thresholds.

[0109] Results Analysis To verify the effectiveness of the proposed RIS and SIM inductive beamforming method, simulation analysis was conducted from three aspects: the number of SIM layers, the number of RIS units, and the algorithm's iterative convergence behavior. The simulation results mainly examine the sum rate performance of the improved SGE algorithm and the low-complexity DGAS algorithm under different sensing constraints, different system sizes, and different RIS deployment strategies, and further compare the performance differences between RIS location optimization and fixed deployment.

[0110] Figure 1 Curves showing the system and rate performance as a function of the number of SIM layers under the DGAS algorithm are presented. It can be seen that as the number of SIM layers increases... With the increase of the number of SIM layers, the system and rate initially increase rapidly, then gradually saturate, indicating that increasing the number of SIM layers effectively improves the degrees of freedom in electromagnetic wave domain control, thereby enhancing the system's sensing and coordination capabilities. However, when the number of layers increases to a certain extent, the gain brought by the additional layers gradually weakens. This shows that increasing the number of SIM layers has a significant promoting effect on performance improvement, but not an unlimited increase will bring the same benefits. Further observation from the results under different sensing constraints reveals that when the target direction beammap gain threshold increases, the system and rate decrease. This is because stricter sensing constraints allocate more beam degrees of freedom to target sensing, thus compressing the space for communication performance improvement. Meanwhile, the DGAS curve with RIS location optimization is consistently higher than the corresponding curve with fixed RIS location, indicating that RIS deployment location optimization can significantly improve the quality of cascaded links and enhance the overall system performance. Compared with a random phase-shifted baseline, the proposed DGAS algorithm... The proposed joint optimization method can achieve a performance improvement of approximately 25 times, demonstrating that it can effectively leverage the performance advantages of SIM and RIS co-design.

[0111] Figure 2 Curves showing the system and rate variations with the number of SIM layers under the SGE algorithm are presented. Their overall trend is similar to... Figure 1The results are largely consistent: as the number of SIM layers increases, the sum rate initially grows rapidly before gradually entering a saturation range. This indicates that regardless of whether a high-performance or low-complexity algorithm is used, the spatial-wave domain degree of freedom expansion brought about by increasing the number of SIM layers can effectively improve system performance. Compared to DGAS, SGE consistently achieves a higher sum rate under the same system configuration. This is because SGE employs a more refined continuous convex approximation and element-wise coordinate ascent mechanism in RIS phase shift optimization, resulting in better phase alignment. The figure also shows that, under the same sensing constraints, the system performance after introducing RIS achieves a sum rate gain of up to approximately 1.5 times compared to the traditional reference scheme using only SIM. This demonstrates that the introduction of RIS effectively mitigates performance losses caused by occlusion and significantly enhances communication and sensing link quality by constructing virtual line-of-sight links. Furthermore, RIS location optimization still brings further performance improvements compared to fixed deployment, further validating the importance of location optimization in this system. Regarding the impact of the sensing threshold, as the constraints increase from no sensing restrictions to a more stringent threshold, the sum rate shows a significant decreasing trend, reflecting the inherent trade-off between communication performance and sensing performance.

[0112] Figure 3 Curves showing the system performance and speed as a function of the number of RIS units under the DGAS algorithm are presented. It can be seen that as the number of RIS units increases... With the increase of [number], the system and overall speed show a monotonically increasing trend, indicating that increasing the number of RIS reflector units can effectively improve the energy focusing capability in the target direction and the effective signal strength on the user side, thereby improving the system's communication efficiency and sensing capability. However, when [number] reflector units increase, the system's overall speed and speed show a monotonically increasing trend, indicating that increasing the number of RIS reflector units can effectively improve the energy focusing capability in the target direction and the effective signal strength on the user side, thereby improving the system's communication efficiency and sensing capability. As the number of RIS units increases to a higher level, the slope of the curve gradually decreases, indicating that the performance improvement brought about by increasing the number of RIS units exhibits diminishing marginal returns. This means that system design should not simply pursue a larger RIS scale, but should comprehensively consider hardware complexity, deployment costs, and performance gains. Results from different SIM scales also show that when the number of superatoms per layer of the SIM is large, the overall system performance and speed are higher, indicating that SIM and RIS have a significant synergistic benefit in improving system performance. Meanwhile, the RIS location optimization curve is consistently higher than the corresponding curve without location optimization, indicating that optimizing the RIS deployment location remains an important means of improving performance for the DGAS algorithm. At that time, the proposed DGAS algorithm achieved a sum rate approximately 20 times that of the random phase-shifted baseline, further demonstrating that even with a low-complexity design, the joint optimization strategy can still bring significant performance gains.

[0113] Figure 4 Curves showing the system performance and speed as a function of the number of RIS units under the SGE algorithm are presented.Figure 3 Similarly, as the number of RIS units increases, the sum rate increases significantly, but the rate of increase gradually slows down, reflecting the typical saturation characteristics brought about by RIS scaling. Compared to DGAS, SGE exhibits a higher sum rate under all RIS unit number configurations, indicating its superior advantage in phase shift optimization accuracy and local phase coordination capability. Especially at larger RIS scales, SGE can more fully utilize the array gain and geometric gain brought by the reflection units, thereby achieving better system performance. Furthermore, under the same configuration, the SGE curve using RIS position optimization always lies above the baseline of fixed RIS deployment and random phase shift, indicating that the improved performance joint optimization method still has a stable advantage in scenarios with increased RIS number. At that time, the sum rate obtained by the proposed SGE algorithm was about 21.5 times that of the random phase shift scheme, indicating that by jointly optimizing the SIM phase shift, RIS phase shift and RIS deployment location, the sensory collaboration potential of the system can be significantly released.

[0114] Figure 5 Curves depicting the system sum and rate as a function of iterations are presented to illustrate the convergence behavior of the proposed algorithm. It can be seen that both SGE and DGAS, under different SIM layer configurations, can rapidly improve the sum and rate within a relatively small number of iterations, and then gradually converge to a stable value, indicating that the proposed alternative optimization framework has good convergence performance and feasibility. As the number of SIM layers increases, the final convergence sum and rate level of the algorithm also increases accordingly, which is consistent with the previous... Figure 1 and Figure 2 The observed trends are consistent, further validating the positive effect of increasing the number of SIM layers on improving system performance. Meanwhile, for any given number of layers, the final convergence value of SGE is consistently higher than that of DGAS, indicating that while the high-performance algorithm has higher computational complexity, it can obtain better local optima; while DGAS, although slightly sacrificing final performance, still maintains a faster convergence speed and lower implementation complexity, demonstrating a good performance-complexity trade-off.

[0115] Based on the simulation results above, it can be concluded that: the proposed SIM and RIS inductive beamforming methods can significantly improve the system performance and speed while satisfying the perception constraints; increasing the number of SIM layers and RIS units both help improve system performance, but their benefits gradually saturate at larger scales; optimizing the RIS deployment location can bring stable additional gains under different algorithms and system scales; SGE has better performance, while DGAS achieves significant performance improvement while maintaining lower complexity, thus both are suitable for practical scenarios with different performance and complexity requirements.

[0116] Compared with existing technologies, the RIS and SIM inductive beamforming method proposed in this application has at least the following technical advantages: (1) This application effectively solves the problem of significant performance degradation of existing SIM solutions in obstructed scenarios by introducing RIS into a SIM-assisted sensing system and further incorporating the deployment location of RIS into joint optimization. Existing SIM solutions mainly rely on transmission links to achieve beam control. When there is obstruction between the base station and the user or target, the system link quality will deteriorate significantly, leading to a decrease in communication rate and a deterioration in sensing performance. This application adds RIS to the SIM and provides an additional reflection enhancement path for obstructed scenarios by constructing a virtual line-of-sight propagation link. At the same time, this application does not just introduce RIS, but further uses its deployment location as an optimization variable and designs it in a unified manner with SIM phase shift and RIS phase shift. Since the geometric position of RIS directly affects the path loss of cascaded links, the echo gain in the target direction, and the received signal strength on the user side, position optimization can place the reflection link in a more favorable propagation area, thereby effectively improving the quality of cascaded channels. In other words, the technical effect of this application does not simply come from adding a reflective surface, but from the synergistic design of "structural introduction + position optimization + phase joint control", thus it can more effectively improve communication and sensing performance in obstructed environments than existing solutions.

[0117] (2) This application effectively solves the problem that the perception accuracy constraint in the existing joint optimization model is difficult to handle directly by converting the Cramer-Rao bound constraint of the two-dimensional angle of arrival estimation into the target direction beammap gain constraint, and improves the engineering feasibility of the solution. In the prior art, perception performance is usually characterized by the accuracy of the two-dimensional angle of arrival estimation, and this accuracy constraint is generally represented by the Cramer-Rao bound. Since the Cramer-Rao bound is strongly coupled with variables such as transmit covariance, SIM phase shift, RIS phase shift and RIS position, directly using it as the optimization constraint will lead to a highly non-convex problem that is difficult to solve. To address this problem, this application first analyzes the intrinsic relationship between the Cramer-Rao bound of the two-dimensional angle of arrival estimation and the target direction beammap gain, establishes the inverse correspondence between the two in the high beammap gain region, and then transforms the Cramer-Rao bound constraint, which was originally difficult to solve directly, into the constraint form of "target direction beammap gain is not lower than the threshold". In this way, the perception constraint is transformed from an abstract parameter estimation accuracy condition into a more intuitive and easier-to-handle beam control condition. Its technical advantages are: on the one hand, it reduces the difficulty of solving joint optimization problems, and on the other hand, it makes the setting of the perception threshold more in line with the parameter configuration habits in engineering applications, thus taking into account both theoretical rigor and implementation feasibility.

[0118] (3) This application constructs a block-based solution framework based on alternating optimization to iteratively optimize the RIS position, SIM phase shift, and RIS phase shift respectively, which can ensure performance improvement while taking into account algorithm convergence and implementation complexity. Since the optimization variables in this application include both continuous spatial position variables and multiple unit modulus phase variables, if the overall solution is directly applied, the computational complexity is high and it is difficult to guarantee stable convergence. Therefore, this application decomposes the original joint optimization problem into RIS position optimization subproblems, SIM phase shift optimization subproblems, and RIS phase shift optimization subproblems, and processes them with appropriate solution methods. Among them, the position subproblem uses the continuous convex approximation method to gradually linearize the non-convex terms related to path loss and geometric distance, thereby achieving iterative solution; the SIM phase shift subproblem introduces a penalty term and uses the gradient ascent method to update the transmission phase shift of each layer, so that the communication target and the sensing target can be coordinated and optimized under a unified objective function; the RIS phase shift subproblem uses a combination of continuous convex approximation and element-wise coordinate ascent to gradually update the phase of each reflection unit, thereby improving the phase matching accuracy. It is precisely because this application adopts this technical approach of "block modeling, step-by-step solution, and alternating iteration" that the entire scheme can achieve both high summation rate and good perceptual performance, while maintaining good convergence and feasibility. Furthermore, this application can choose between high-performance and low-complexity implementations according to actual needs, thus offering greater flexibility and applicability compared to existing technologies.

[0119] (4) This application not only improves the system's communication performance but also achieves more stable synergistic gain while satisfying perception constraints, resulting in better system scalability. From a technical perspective, SIM provides multi-layered wave domain modulation degrees of freedom, RIS provides environmental reflection enhancement degrees of freedom, and RIS position optimization further provides spatial geometric degrees of freedom. This application integrates these three types of degrees of freedom into the same synergistic design framework, enabling the system to simultaneously perform synergistic optimization in the spatial domain, propagation domain, and beam domain. Therefore, as the number of RIS units increases, the system can make fuller use of the new hardware resources, transforming them into higher user and rate performance and better target direction energy focusing effect. This demonstrates that this application not only achieves performance advantages at the current system scale but also maintains continuous gain capability as the system scale expands, thus possessing significant engineering promotion value.

[0120] In summary, the above are merely preferred 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 method for sensing beamforming of RIS and SIM, applicable to a multi-user communication and sensing integrated ISAC system comprising a base station (BS), a reconfigurable intelligent reflector (RIS), and a SIM. The system comprises a single-antenna communication user and a sensing target, wherein the BS is equipped with a stacked intelligent metasurface SIM, the SIM being composed of L layers of cascaded metasurfaces, each layer containing N superatoms; the RIS contains Mr reflective units; its characteristic is... The specific process of this method is as follows: Step 1: Using the RIS deployment location vector The reflection phase shift diagonal matrix of RIS Θ and SIM The phase shift diagonal matrix of the layer is used as the joint optimization variable to construct a joint optimization model with the goal of maximizing multi-user and rate while satisfying the target perception accuracy constraint; at the same time, it is based on the constraints of RIS deployment area, RIS unit phase shift constraint and SIM layer superatomic phase shift constraint. Step 2: Establish the inverse relationship between the two-dimensional CRB and the beammap gain of the target direction, and transform the original CRB constraint into an equivalent beammap gain constraint to obtain a new optimization problem; Step 3: For the new optimization problem obtained in Step 2, the joint optimization variables are decomposed into three optimization problems, specifically:

1. Optimize the RIS deployment position under the condition of fixed SIM phase shift matrix and RIS phase shift matrix, to obtain the RIS position optimization subproblem; 2. Optimize the phase shift matrix of each layer of SIM under the condition of fixed RIS deployment position and RIS phase shift matrix, to obtain the SIM phase shift optimization subproblem; 3. Optimize the RIS reflection phase shift matrix under the condition of fixed RIS deployment position and SIM phase shift matrix, to obtain the RIS phase shift optimization subproblem. Step 4: Solve the three sub-problems separately to obtain the locally optimal RIS deployment location, SIM phase shift matrix, and RIS phase shift matrix.

2. The RIS and SIM inductive beamforming method according to claim 1, characterized in that, The joint optimization model and constraints in step one are as follows: In the formula, Represents the deployment location vector of the RIS; Θ This represents the reflection phase shift diagonal matrix of RIS; Indicates SIM number The phase shift diagonal matrix of the layer; Indicates the first The signal-to-interference-to-noise ratio of communication users; Represents the trace of the CRB matrix for the two-dimensional DoA estimation of the target; This represents the upper bound of the CRB corresponding to the target perception accuracy; This indicates the two-dimensional feasible region that RIS allows for deployment; Represents the set of RIS reflection units; Represents the set of superatoms in each SIM layer; Represents the SIM layer index set. Subscript The value can be 1- , Subscript The value can be 1- .

3. The RIS and SIM inductive beamforming method according to claim 2, characterized in that, The process of converting the original CRB constraint into an equivalent beammap gain constraint is as follows: Will" "Converted to "Target direction beam pattern gain not lower than threshold" The equivalent constraint of "" leads to a new optimization problem: In the formula, Indicates the target link loss; Indicates the direction of the target The RIS array response vector at that location; This indicates a cascaded channel from SIM to RIS; Represents the covariance matrix of the transmitted waveform; The beam pattern gain threshold represents the target direction.

4. The RIS and SIM inductive beamforming method according to claim 3, characterized in that, The RIS location optimization subproblem employs a continuous convex approximation method. By performing a first-order Taylor expansion on the large-scale path loss and beammap gain terms, the original non-convex location optimization problem is transformed into a convex subproblem for iterative solution. Iteration stops when the objective function gain of two consecutive iterations falls below a preset threshold, and the locally optimal deployment location of the RIS is output. .

5. The RIS and SIM inductive beamforming method according to claim 3, characterized in that, The SIM phase shift optimization subproblem employs a gradient ascent algorithm based on a penalty function. The sensing beammap gain constraint is incorporated into the objective function through a penalty term to iteratively update the phase shift of each SIM superatom layer. Iteration stops when the objective function gain of two consecutive iterations falls below a preset threshold, and the optimized SIM phase shift matrix is ​​output. .

6. The RIS and SIM inductive beamforming method according to claim 3, characterized in that, The RIS phase shift optimization subproblem is solved using the SCA-ECA algorithm based on continuous convex approximation and element-wise coordinate ascent. During the solution process, each RIS reflection unit is treated as an independent coordinate block. In each update, only the phase of one unit is adjusted, while the phases of other units remain unchanged. This process continues until all units have completed one round of updates, at which point the RIS phase shift matrix has completed one round of updates. Iteration stops when the objective function gain falls below a preset threshold between two consecutive iterations, and the optimized RIS phase shift matrix is ​​output. .

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