Energy-efficient beamforming design method for ris-assisted secure isac system

Abstract

The present application relates to a RIS-assisted secure ISAC system energy efficiency maximization beamforming design method, belonging to the technical field of communication and perception integration. A RIS-assisted secure ISAC system model is constructed, a communication model and a perception model of the system are constructed, a joint optimization problem with the goal of system energy efficiency maximization is established, and an AO framework and related optimization algorithms are used to solve the joint optimization problem. The present application has the advantage of first realizing system energy efficiency maximization under the constraints of user communication service quality, security rate and perception accuracy in the RIS-assisted ISAC system, and significantly overcoming the trade-off problem between energy efficiency and security performance in traditional systems. Simulation results show that the proposed scheme can achieve 1.6-2.2 times energy efficiency improvement compared to the system without RIS, and effectively suppress the received signal-to-interference-and-noise ratio of the eavesdropper, providing a feasible technical approach for the design of secure, efficient and integrated communication and perception systems in 6G networks.

Description

Technical Field

[0001] This invention belongs to the field of Integrated Sensing and Communication (ISAC) technology, specifically relating to a joint beamforming and reflection design method for achieving secure communication, high-precision sensing, and high-energy-efficiency transmission in an ISAC system assisted by a Reconfigurable Intelligent Surface (RIS). Background Technology

[0002] With the evolution of 6G mobile communication network technology, increasingly stringent requirements are being placed on spectrum resource utilization and data transmission performance. Currently, the frequency bands used by communication and radar systems are constantly expanding, leading to greater overlap. To meet the dual demands of high-quality wireless connectivity and high-precision environmental perception for emerging applications such as UAV swarm control and autonomous driving, the integration of communication and radar sensing functions has become crucial. Against this backdrop, Integrated Sensing and Communication (ISAC) technology has emerged. By sharing hardware and spectrum resources, it enables the coordinated operation of communication and sensing functions and is widely considered one of the most promising key enabling technologies for 6G networks.

[0003] However, the development of ISAC systems still faces multiple challenges. First, due to their use of open spectrum and broadcast transmission, the system inherently carries information security risks and is vulnerable to attacks by malicious eavesdroppers. Second, there is an inherent trade-off between spectrum efficiency and energy consumption, and security enhancement measures, such as emitting artificial noise (AN), often further exacerbate power consumption, making optimizing system energy efficiency while ensuring security a critical challenge. Furthermore, in practical deployments, complex wireless environments often lead to obstruction or severe fading of the direct link between base stations and users, limiting communication and sensing performance.

[0004] To address the aforementioned propagation problems, Reconfigurable Intelligent Surface (RIS) technology has garnered significant attention in recent years. RIS is a planar array composed of numerous low-cost, programmable reflective elements that can dynamically adjust the electromagnetic properties of each element through an intelligent controller, thereby reshaping the wireless propagation environment. Introducing RIS into ISAC systems can not only effectively alleviate non-line-of-sight transmission problems but also enhance the signal of legitimate users through intelligent beam steering, while suppressing the reception quality of eavesdroppers, thus improving system performance and enhancing physical layer security.

[0005] While existing research has explored the application of RIS in ISAC systems, or considered security enhancement or energy efficiency optimization separately, there is still a lack of research on introducing AN to enhance security in RIS-assisted ISAC systems, and on jointly optimizing beamforming, artificial noise, and RIS reflection phase to maximize system energy efficiency (EE) within this framework. Current solutions fail to systematically achieve global synergistic optimization of communication, sensing, security, and energy efficiency under multiple stringent constraints, including ensuring user service quality, communication security and confidentiality rates, and radar sensing accuracy. Summary of the Invention

[0006] This invention provides a beamforming design method for maximizing energy efficiency in a RIS-assisted secure ISAC system, addressing the shortcomings of existing RIS-assisted ISAC systems in the coordinated optimization of security, energy efficiency, and sensing performance. The aim is to maximize the overall system energy efficiency within a limited system power budget by jointly optimizing the base station's transmit beamforming matrix, the covariance matrix of artificial noise, and the RIS's reflection phase matrix, while ensuring the quality of service for legitimate users, meeting the confidentiality rate security threshold, and achieving a predetermined target sensing accuracy.

[0007] The technical solution adopted by this invention includes the following steps:

[0008] Step 1: Construct a RIS-assisted secure ISAC system model:

[0009] Step 2: Construct the system's communication and perception models:

[0010] In the communication model described, the total signal transmitted by the base station Represented as:

[0011]

[0012] Among them, the communication signals transmitted by the base station are used It is indicated that its beamforming matrix is ​​represented by express, ,make ,in Representing the Beamforming vectors for each user Represents its conjugate transpose, rank , The AN vector represents the artificial noise emitted by the base station to interfere with eavesdroppers. The covariance matrix of the artificial noise AN is represented by the reflection phase matrix of RIS, which is defined as follows: ,in ,in It is a natural constant. It is the imaginary unit, phase. Let the modulus , Representing RIS Unit, assuming base station to RIS, the first The equivalent channels for each legitimate user and eavesdropper are respectively: , , It means that among them Representing the first Individual users, eavesdroppers, and base stations, from RIS to the 1st The equivalent channels for a legitimate user and an eavesdropper are represented as follows: , , Representing RIS, the signal transmitted by the base station travels through a direct link. Reaching the At a legitimate user location, or after being reflected by RIS, the data is ultimately received by the user. The comprehensive equivalent channel is: Then the first The signal received by each user is represented as follows:

[0013]

[0014] in For the received noise at the user end, according to the received signal model given in equation (2), the user... The signal-to-interference-plus-noise ratio (SINR) is expressed as:

[0015]

[0016] in, Representing the Beamforming vectors for each user The reachability and rate of the system are expressed as:

[0017]

[0018] in, On behalf of users The achievable rate, similarly, let the eavesdropper's comprehensive equivalent channel be: The signal received by the eavesdropper is represented as:

[0019]

[0020] in For the received noise at the eavesdropper's end, according to the received signal model given in equation (5), the eavesdropper eavesdrops on the user. The SINR is:

[0021]

[0022] Then the eavesdropper eavesdrops on the user The achievable rate of a signal is expressed as:

[0023]

[0024] Therefore, users The confidentiality rate is written as:

[0025]

[0026] here ;

[0027] In the aforementioned sensing model, the base station receives... Parameter estimation is performed on the target echo signal in each time slot, and the threshold value of CRB at the target is used as the sensing constraint variable of the system:

[0028]

[0029] in, Let the transmitted signal covariance matrix be... From the perspective of representing the goal, Represents the upper bound of CRB;

[0030] Step 3: Establish a joint optimization problem with the goal of maximizing system energy efficiency:

[0031] The energy efficiency is defined as the ratio of the system's achievable sum rate to its total power consumption.

[0032]

[0033] in, Represents the efficiency of the power amplifier. Represents the base station's transmit power consumption. To determine the static circuit power consumption, an optimization problem is established, and the beamforming matrix is ​​jointly optimized. Artificial noise covariance matrix and RIS reflection matrix To maximize energy efficiency And satisfy the total transmit power constraint, the minimum SINR constraint for each user, the minimum security rate constraint for each user, the sensing CRB constraint, and the RIS unit mode constraint.

[0034] Step 4: Solve the joint optimization problem using the AO framework and related optimization algorithms:

[0035] The joint optimization problem is solved iteratively using the AO framework. In each iteration, the fractional objective function is first transformed into a subtractive form using the Dinkelbach method, and auxiliary variables are introduced. The reachable rate expression is then processed using Lagrange dual transformation and quadratic transformation. Then, the original problem is decomposed into three subproblems concerning the beamforming matrix, the artificial noise covariance matrix, and the RIS reflection matrix, and convex optimization is performed using SDR and Schur complement techniques, respectively.

[0036] The RIS-assisted secure ISAC system model constructed in step 1 of this invention is as follows:

[0037] Build a equipped A base station (BS) with one transmit and receive antenna, simultaneously serving as... A single-antenna user is provided with service, and a point target is detected. The antennas are arranged in a uniform linear array ULA with half-wavelength spacing, and the RIS is composed of... Composed of passive reflective elements, the system is deployed near the user to reconstruct the wireless propagation environment and enhance secure communication. The system introduces artificial noise (AN) at the base station (BS) to actively interfere with potential eavesdroppers. It assumes perfect channel state information (CSI) and adopts a shared deployment, with all antennas used for both communication and sensing simultaneously.

[0038] The joint optimization model established in step 3 of this invention is expressed as follows:

[0039] Under the constraints of total base station transmission power, minimum SINR for each user, minimum security rate for each user, perceived CRB, and RIS unity modulus, a joint optimization model is established for the base station beamforming matrix, AN covariance matrix, and RIS reflection coefficient matrix, with the goal of maximizing system EE:

[0040]

[0041] Among them, constraints 1 indicates the power budget constraint of the base station. This represents the maximum allowable power consumption of the base station, a constraint. 2. To ensure the communication quality of each user, the SINR of each user must be maintained at a predefined signal-to-noise ratio threshold. Above, constraints 3 is a constraint to ensure system security, requiring the confidentiality rate to be greater than a certain threshold. ,constraint 4. The magnitude and phase constraints of each RIS unit are specified. To ensure the performance of target estimation, a predefined parameter is set. As the upper limit of CRB, and in CRB constraints are given in section 5. 6. The covariance matrix of artificial noise must be a positive semi-definite matrix. This model uniformly considers communication rate, sensing accuracy, physical layer security and energy consumption, and maximizes the overall energy efficiency of the system through joint optimization.

[0042] The steps in step 4 of this invention, which use the AO algorithm to solve for the base station beamforming matrix, AN covariance matrix, and RIS reflection phase matrix, are as follows:

[0043] 1) Algorithm preprocessing: Transform the objective function into a confidentiality rate constraint;

[0044] Using the AO framework, joint optimization is achieved by iteratively solving three sub-problems. , and First, the Dinkelbach method is used to process the fractional form of the energy efficiency objective function. Introducing auxiliary variables This transforms the original maximization problem into an equivalent maximization problem. ,in Here is the expression for total power consumption; next, it represents the achievable processing speed. Fractional SINR within logarithmic terms, introducing auxiliary variables Thus, the reach and rate The equivalent rewrite is as follows:

[0045]

[0046] The optimal value is: Subsequently, the third term of equation (12) has a nonconvex fraction problem, so an auxiliary variable is introduced. And by applying a quadratic transformation, it is converted into a representation of... and Combinations of quadratic forms and linear terms:

[0047]

[0048] in The representative takes the real part. represent conjugate, The optimal value is:

[0049]

[0050] get and Then, by omitting the constant term, the optimization objective is simplified to:

[0051]

[0052] For non-convex confidentiality constraints Introducing auxiliary variables and define , The confidentiality constraint is transformed into:

[0053]

[0054] Based on the above simplification, problem (11) is equivalently restated as follows:

[0055]

[0056] 2) Fixed and ,optimization ;

[0057] exist Optimization while keeping variables constant First, we address the perceived CRB constraints. The expression is written as:

[0058]

[0059] in, Define constants ,constraint( 5) Rewritten as:

[0060]

[0061] make And by utilizing Schur complementarity, equation (19) is equivalent to the following form:

[0062]

[0063] in, At this time, targeting and Equation (20) is convex, and the objective and constraints are rewritten as:

[0064]

[0065] Note the constraints. 1) All of the above Irrelevant items were included middle;

[0066] In (21), due to the optimization variables Its column vector The simultaneous existence of these factors makes the solution process quite complex. To simplify the expression and unify the variable forms, we utilize... This column vector combination relationship will transform the original problem into a series of vector combinations. All optimizations are converted into optimizations of each column. The optimization, firstly, involves constraints ( 1) Rewritten as:

[0067]

[0068] This constraint applies to It is a convex constraint, constraint ( 2) Rewritten as:

[0069]

[0070] in, For the objective function in (21), it can be rewritten as:

[0071]

[0072] in: , For confidentiality constraints ( 3) Rewritten as:

[0073]

[0074] in: For constraints ( 4),

[0075] make And by The above equation becomes:

[0076]

[0077] Due to constraints (23)(25)(26) regarding Since both are non-convex, the original quadratic optimization problem is transformed into an equivalent positive semidefinite programming problem. To achieve this, an extended vector is introduced. ,use Combining the linear and quadratic terms in the objective function, equation (24) can be written as:

[0078]

[0079] in: Constraint (22) can be written in the following equivalent form:

[0080]

[0081] Constraint (23) can be transformed into:

[0082]

[0083] in: ,make Constraint (25) is rewritten as:

[0084]

[0085] Based on this, auxiliary variables are introduced: And by utilizing the properties of the matrix trace, equation (27) becomes:

[0086]

[0087] Similarly, constraint (28) is reformulated as:

[0088]

[0089] Constraints (29) and (30) are rearranged as follows:

[0090]

[0091]

[0092] make Rearranging equation (26) yields:

[0093]

[0094] in: ,because Therefore, constraints are introduced:

[0095]

[0096] Due to the presence of the rank-1 constraint, the above optimization problem remains non-convex. Using a positive semidefinite relaxation method to remove the rank-1 constraint, the problem is transformed into a standard positive semidefinite programming problem, which can be efficiently solved using CVX. The optimization problem and constraints are then rearranged as follows:

[0097]

[0098] If you obtain If the rank-1 constraint is not satisfied, eigenvalue decomposition can be performed, and the vector corresponding to the largest eigenvalue can be taken as an approximate solution to obtain the optimal beamforming vector. Optimal beamforming vector Represented as

[0099]

[0100] in, ;

[0101] 3) Fix and ,optimization ;

[0102] exist With all variables remaining constant, the optimization problem (17) simplifies to:

[0103]

[0104] For power constraints ( 1) Transform it into the following form:

[0105]

[0106] in, For user QoS constraints ( 2) Organize it as follows:

[0107]

[0108] in: Regarding the confidentiality rate constraint (16), following the processing method of formula (41), we can rearrange and obtain:

[0109]

[0110] in: Similarly, for constraints Simplified to:

[0111]

[0112] in: The optimization objectives and constraints are rearranged to obtain:

[0113]

[0114] At this time, in response to Problem (44) is convex and can be solved using tools such as CVX;

[0115] 4) Fix and ,optimization .

[0116] exist Assuming the variables remain constant, let: ,in , The optimization objective in (17) can be simplified to:

[0117]

[0118] Define a diagonal matrix: , Base station to user The equivalent channel is written as: The equivalent channel from the base station to the eavesdropper is written as: ;set up , , , Therefore, according to the above formula, we get: Similarly, let , , , ,but: Then, for equation (45), the expected signal term can be rewritten as:

[0119]

[0120] For the interference terms, expand and simplify them as follows:

[0121]

[0122] For artificial noise The term, when expanded in quadratic form, yields:

[0123]

[0124] in , , ,make: , , The optimization objective (45) is re-expressed as:

[0125]

[0126] in: , ,make , For all Summation, and removing the summation from the summation. Irrelevant constant terms, we get:

[0127]

[0128] Regarding the user SINR constraint in problem (17) 2), due to , After cross-multiplication and rearranging, we get:

[0129]

[0130] Similarly, the confidentiality rate constraint is handled in the same way as the user SINR constraint. In the confidentiality rate constraint (16), for This term can be transformed into a form similar to equation (51):

[0131]

[0132] for This item means: , , , , , Organize it as follows:

[0133]

[0134] Because the above objective function and constraint terms already exist The linear terms also have The quadratic term is transformed as follows: Let , , ,because:

[0135]

[0136] The optimization objective (50) can be written in the form of a linear trace:

[0137]

[0138] The SINR constraint (51) is also written in the form of a linear trace, let:

[0139]

[0140] Then equation (51) is transformed into:

[0141]

[0142] Similarly, regarding the confidentiality rate constraint, let:

[0143]

[0144] The confidentiality constraints (52) and (53) can be expressed as linear trace inequalities:

[0145]

[0146] For the unit modulus constraint, it can be transformed into:

[0147]

[0148] All about The optimization problem is rewritten as:

[0149]

[0150] For the optimization problem (61), removing the rank-1 constraint results in a standard SDP problem, which can be solved using CVX. Once the optimal solution is obtained... Recovery is achieved through eigenvalue decomposition or Gaussian randomization. Thus, the RIS emission matrix is ​​obtained. .

[0151] The beneficial effects of this invention are:

[0152] 1. Significantly Improved System Energy Efficiency and Enhanced Communication Security: Addressing the challenge of balancing energy efficiency and security performance in ISAC systems, this invention, for the first time, unifies the modeling of maximizing system energy efficiency with physical layer security rate and sensing accuracy constraints based on Cramer-Rao bounds within a RIS-assisted ISAC framework. By jointly optimizing base station active beamforming, artificial noise covariance, and RIS passive reflection phase, the proposed scheme achieves optimal system resource allocation while strictly meeting user service quality, security rate, and sensing accuracy requirements. Simulation results show that compared to traditional schemes without RIS, the proposed joint optimization design improves system energy efficiency by 1.6 to 2.2 times, while effectively suppressing the eavesdropper signal-to-interference-plus-noise ratio to an extremely low negative value, fundamentally enhancing the system's secure transmission capabilities.

[0153] 2. Achieving Global Co-optimization of Communication, Sensing, Security, and Energy Efficiency under Multiple Strict Constraints: Existing research mostly optimizes single performance indicators of ISAC systems, such as rate, sensing error, or security capacity, lacking system-level co-design under multiple objectives and constraints. This invention constructs a complete optimization problem model including total power, user SINR, security rate, sensing CRB, and RIS unit modulus constraints, and innovatively proposes an efficient alternating optimization solution framework. This framework uses the Dinkelbach method, Lagrange multiplication, and quadratic transformation to handle fractional objectives and logarithmic terms, and utilizes semidefinite relaxation and Schur complement techniques to handle non-convex constraints, successfully decomposing the complex original problem into three efficiently solvable convex subproblems, achieving global performance balance and significant improvement under multiple coupled constraints.

[0154] 3. The proposed alternative optimization algorithm is efficient and robust: The solution algorithm based on the alternating optimization framework proposed in this invention ensures monotonic convergence of the target energy efficiency by iteratively updating the beamforming matrix, artificial noise covariance matrix, and RIS phase matrix. The algorithm fully utilizes the efficiency of the Dinkelbach method in handling fractional programming, the flexibility of quadratic transformation decoupling problems, and the universality of semidefinite relaxation combined with Schur complement in handling complex constraints. Numerical simulations verify that the algorithm can converge quickly and stably under different numbers of RIS units, different user SINR thresholds, and different power budgets. In addition, the system energy efficiency increases significantly with the increase of the number of RIS units, proving that introducing RIS to provide additional spatial degrees of freedom is an effective way to overcome the system performance bottleneck, and providing reliable algorithmic support for the design of high-efficiency, high-security, and high-precision multifunctional integrated systems in future 6G networks. Attached Figure Description

[0155] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0156] Figure 2 This is a model diagram of the RIS-assisted safety ISAC system in this invention;

[0157] Figure 3 This is a flowchart of the alternating optimization algorithm in this invention;

[0158] Figure 4 This is a schematic diagram illustrating the energy efficiency convergence of the algorithm proposed in this invention;

[0159] Figure 5 This is a schematic diagram illustrating the reachability and rate convergence of the algorithm proposed in this invention;

[0160] Figure 6 This is a schematic diagram illustrating the convergence of the algorithm proposed in this invention for the perceptual CRB constraint;

[0161] Figure 7 This invention relates to the number of RIS elements. A schematic diagram of the SINR of the eavesdropper when the SINR is 16;

[0162] Figure 8 This invention relates to the number of RIS elements. A diagram illustrating the confidentiality rate of each user when =16;

[0163] Figure 9 This invention relates to the number of RIS elements. And a comparison chart of system energy efficiency under different user SINR thresholds. Detailed Implementation

[0164] The present invention will be further described in detail below with reference to the accompanying drawings and specific examples. It should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0165] See Figure 1 It includes the following steps:

[0166] Step 1: Construct a RIS-assisted secure ISAC system model:

[0167] Build a equipped A base station (BS) with one transmit and receive antenna, simultaneously serving as... A single-antenna user is provided with service, and a point target is detected. The antennas are arranged in a uniform linear array (ULA) with half-wavelength spacing. Furthermore, the RIS consists of... Composed of passive reflective elements, the system is deployed near the user to reconstruct the wireless propagation environment and enhance secure communication. Artificial noise (AN) is introduced at the base station (BS) to actively interfere with potential eavesdroppers. Assuming perfect Channel State Information (CSI), the system adopts a shared deployment, with all antennas used for communication and sensing simultaneously.

[0168] The RIS (Reflector System) is a passive reflector composed of numerous low-cost, programmable reflector elements. It can dynamically adjust the phase shift of each reflector element via an intelligent controller, thereby reshaping the wireless propagation environment. This invention utilizes the RIS to provide enhanced signal paths for legitimate users, while actively degrading the eavesdropper's channel through beamforming and AN (Anchor Array) co-design. This significantly improves the physical layer security and overall energy efficiency of the system without consuming additional RF chain power.

[0169] Step 2: Construct the system's communication and perception models:

[0170] In the communication model described, the total signal transmitted by the base station Represented as:

[0171]

[0172] Among them, the communication signals transmitted by the base station are used It is indicated that its beamforming matrix is ​​represented by express, ,make ,in Representing the Beamforming vectors for each user Represents its conjugate transpose, rank , The AN vector represents the artificial noise emitted by the base station to interfere with eavesdroppers. The covariance matrix of the artificial noise AN is represented by the reflection phase matrix of RIS, which is defined as follows: ,in ,in It is a natural constant. It is the imaginary unit, phase. Let the modulus , Representing RIS Unit, assuming base station to RIS, the first The equivalent channels for each legitimate user and eavesdropper are respectively: , , It means that among them Representing the first Individual users, eavesdroppers, and base stations, from RIS to the 1st The equivalent channels for a legitimate user and an eavesdropper are represented as follows: , , Representing RIS, the signal transmitted by the base station is transmitted via a direct link. Reaching the At a legitimate user's location, data can also be received by the user after being reflected by RIS. Let's say the user... The comprehensive equivalent channel is: Then the first The signal received by each user is represented as follows:

[0173]

[0174] in For the received noise at the user end, according to the received signal model given in equation (2), the user... The signal-to-interference-plus-noise ratio (SINR) is expressed as:

[0175]

[0176] in, Representing the Beamforming vectors for each user The reachability and rate of the system are expressed as:

[0177]

[0178] Similarly: Let the eavesdropper's comprehensive equivalent channel be: The signal received by the eavesdropper is represented as:

[0179]

[0180] in For the received noise at the eavesdropper's end, according to the received signal model given in equation (5), the eavesdropper eavesdrops on the user. The SINR is:

[0181]

[0182] Then the eavesdropper eavesdrops on the user The achievable rate of a signal is expressed as:

[0183]

[0184] Therefore, users The confidentiality rate is written as:

[0185]

[0186] here ;

[0187] In the aforementioned sensing model, the base station receives... Parameter estimation is performed on the target echo signal in each time slot, and the threshold value of CRB at the target is used as the sensing constraint variable of the system:

[0188]

[0189] in, Let the transmitted signal covariance matrix be... From the perspective of representing the goal, Represents the upper bound of CRB;

[0190] Step 3: Establish a joint optimization problem with the goal of maximizing system energy efficiency:

[0191] The energy efficiency is defined as the ratio of the system's achievable sum rate to its total power consumption.

[0192]

[0193] in, Represents the efficiency of the power amplifier. Represents the base station's transmit power consumption. To determine the static circuit power consumption, an optimization problem is established, and the beamforming matrix is ​​jointly optimized. Artificial noise covariance matrix and RIS reflection matrix To maximize energy efficiency To satisfy constraints on total transmit power, minimum SINR for each user, minimum security rate for each user, perceived CRB, and RIS unit modulus, a joint optimization model is established for the base station beamforming matrix, AN covariance matrix, and RIS reflection coefficient matrix, with the goal of maximizing system EE, under the constraints of total base station transmit power, minimum SINR for each user, minimum security rate for each user, perceived CRB, and RIS unit modulus.

[0194]

[0195] Among them, constraints 1 indicates the power budget constraint of the base station. This represents the maximum allowable power consumption of the base station, a constraint. 2. To ensure the communication quality of each user, the SINR of each user must be maintained at a predefined signal-to-noise ratio threshold. Above, constraints 3 is a constraint to ensure system security, requiring the confidentiality rate to be greater than a certain threshold. ,constraint 4. The magnitude and phase constraints of each RIS unit are specified. To ensure the performance of target estimation, a predefined parameter is set. As the upper limit of CRB, and in CRB constraints are given in section 5. 6. The covariance matrix of artificial noise must be a positive semi-definite matrix. This model uniformly considers communication rate, sensing accuracy, physical layer security and energy consumption, and maximizes the overall energy efficiency of the system through joint optimization.

[0196] Step 4: Solve the joint optimization problem using the AO framework and related optimization algorithms:

[0197] First, the Dinkelbach method is used to transform the fractional objective function into a reducing form, and auxiliary variables are introduced to handle the reachable rate expression using Lagrange dual transformation and quadratic transformation. Then, the AO framework is used to decompose the original problem into... , and The three subproblems are solved iteratively.

[0198] The Dinkelbach method is a classic fractional programming technique, first proposed in 1967, and widely used to solve energy efficiency fractional optimization problems in communication systems. Its core idea is to introduce auxiliary variables to transform the original fractional maximization problem into a parameterized subtraction form, and then iteratively update these parameters to approximate the optimal solution. The advantage of this method is that it can transform complex fractional programming into a series of more manageable subproblems, and it typically exhibits superlinear convergence speed.

[0199] Lagrange dual transform and quadratic transform are efficient processing tools developed in recent years for non-convex problems involving logarithmic rates and fractional signal-to-interference-plus-noise ratio (SINR) in communication and signal processing. The Lagrange dual transform decouples the logarithmic term in the objective function from its internal fractional terms by introducing auxiliary variables; the quadratic transform further processes the remaining fractional structure after the transformation, converting it into a combination of quadratic forms and linear terms with respect to the optimization variables. The core idea of ​​these two transforms is to transform the non-convex composite function structure into a series of separable and easily processed subproblems by introducing appropriate auxiliary variables, thus laying the foundation for subsequent convex approximations or direct optimization.

[0200] Semidefinite relaxation (SDR) is a powerful tool for solving nonconvex optimization problems with quadratic constraints. Its core idea is to transform the nonconvex quadratic equality or inequality constraints in the original problem into linear constraints with respect to this SDR matrix and a nonconvex rank-1 constraint by raising the original optimization variable vector to a positive semidefinite matrix. By temporarily ignoring this rank-1 constraint, the problem is transformed into a standard, efficiently solvable semidefinite programming (SDP) problem. Schur complement is a key tool for handling linear matrix inequalities (LMIs). It can equivalently transform certain complex nonlinear matrix inequalities into a larger-dimensional LMI, thus facilitating unified processing within the SDP framework.

[0201] This invention is the first to systematically combine the Dinkelbach method, Lagrange duality, quadratic transformation, and SDR and Schur complement techniques. Through an alternating optimization framework, it collaboratively optimizes the base station active beamforming matrix, AN covariance matrix, and RIS reflection phase matrix. This achieves maximum global energy efficiency for a RIS-assisted secure ISAC system while strictly satisfying multiple constraints related to communication service quality, physical layer security, and sensing accuracy. The specific process of the submitted alternating optimization algorithm is as follows:

[0202] 1) Algorithm preprocessing: Transform the objective function into a confidentiality rate constraint;

[0203] Using the AO framework, joint optimization is achieved by iteratively solving three sub-problems. , and First, the Dinkelbach method is used to process the fractional form of the energy efficiency objective function. Introducing auxiliary variables This transforms the original maximization problem into an equivalent maximization problem. ,in Here is the expression for total power consumption; next, it represents the achievable processing speed. Fractional SINR within logarithmic terms, introducing auxiliary variables Thus, the reach and rate The equivalent rewrite is as follows:

[0204]

[0205] The optimal value is: Subsequently, the third term of equation (12) has a nonconvex fraction problem, so an auxiliary variable is introduced. And by applying a quadratic transformation, it is converted into a representation of... and Combinations of quadratic forms and linear terms:

[0206]

[0207] in The representative takes the real part. represent conjugate, The optimal value is:

[0208]

[0209] get and Then, by omitting the constant term, the optimization objective is simplified to:

[0210]

[0211] For non-convex confidentiality constraints Introducing auxiliary variables and define , The confidentiality constraint is transformed into:

[0212]

[0213] Based on the above simplification, problem (11) is equivalently restated as follows:

[0214]

[0215] 2) Fixed and ,optimization ;

[0216] exist Optimization while keeping variables constant First, we address the perceived CRB constraints. The expression is written as:

[0217]

[0218] in, Define constants ,constraint( 5) Rewritten as:

[0219]

[0220] make And by utilizing Schur complementarity, equation (19) is equivalent to the following form:

[0221]

[0222] in, At this time, targeting and Equation (20) is convex, and the objective and constraints are rewritten as:

[0223]

[0224] Note the constraints. 1) All of the above Irrelevant items were included middle;

[0225] In (21), due to the optimization variables Its column vector The simultaneous existence of these factors makes the solution process quite complex. To simplify the expression and unify the variable forms, we utilize... This column vector combination relationship will transform the original problem into a series of vector combinations. All optimizations are converted into optimizations of each column. The optimization, firstly, involves constraints ( 1) Rewritten as:

[0226]

[0227] This constraint applies to It is a convex constraint, constraint ( 2) Rewritten as:

[0228]

[0229] in, For the objective function in (21), it can be rewritten as:

[0230]

[0231] in: , For confidentiality constraints ( 3) Rewritten as:

[0232]

[0233] in: For constraints ( 4),

[0234] make And by The above equation becomes:

[0235]

[0236] Due to constraints (23)(25)(26) regarding Since all problems are non-convex, they remain difficult to handle. To overcome this difficulty, the original quadratic optimization problem is transformed into an equivalent positive semidefinite programming problem. To achieve this, an extended vector is introduced. ,use Combining the linear and quadratic terms in the objective function, equation (24) can be written as:

[0237]

[0238] in: Constraint (22) can be written in the following equivalent form:

[0239]

[0240] Constraint (23) can be transformed into:

[0241]

[0242] in: ,make Constraint (25) is rewritten as:

[0243]

[0244] Based on this, auxiliary variables are introduced: And by utilizing the properties of the matrix trace, equation (27) becomes:

[0245]

[0246] Similarly, constraint (28) is reformulated as:

[0247]

[0248] Constraints (29) and (30) are rearranged as follows:

[0249]

[0250]

[0251] make Rearranging equation (26) yields:

[0252]

[0253] in: ,because Therefore, constraints are introduced:

[0254]

[0255] Due to the presence of the rank-1 constraint, the above optimization problem remains non-convex. To overcome this challenge, a semidefinite relaxation method is employed. Specifically, by removing the rank-1 constraint, the problem is transformed into a standard semidefinite programming problem, which can be efficiently solved using CVX. The optimization problem and constraints are then rearranged as follows:

[0256]

[0257] If you obtain If the rank-1 constraint is not satisfied, eigenvalue decomposition can be performed, and the vector corresponding to the largest eigenvalue can be taken as an approximate solution to obtain the optimal beamforming vector. Optimal beamforming vector Represented as

[0258]

[0259] in, ;

[0260] 3) Fix and ,optimization ;

[0261] exist With all variables remaining constant, the optimization problem (17) simplifies to:

[0262]

[0263] For power constraints ( 1) Transform it into the following form:

[0264]

[0265] in, For user QoS constraints ( 2) Organize it as follows:

[0266]

[0267] in: Regarding the confidentiality rate constraint (16), following the processing method of formula (41), we can rearrange and obtain:

[0268]

[0269] in: Similarly, for constraints Simplified to:

[0270]

[0271] in: The optimization objectives and constraints are rearranged to obtain:

[0272]

[0273] At this time, in response to Problem (44) is convex and can be solved using tools such as CVX;

[0274] 4) Fix and ,optimization .

[0275] exist Assuming the variables remain constant, let: ,in , The optimization objective in (17) can be simplified to:

[0276]

[0277] Define a diagonal matrix: , Base station to user The equivalent channel is written as: The equivalent channel from the base station to the eavesdropper is written as: ;set up , , , Therefore, according to the above formula, we get: Similarly, let , , , ,but: Then, for equation (45), the expected signal term can be rewritten as:

[0278]

[0279] For the interference terms, expand and simplify them as follows:

[0280]

[0281] For artificial noise The term, when expanded in quadratic form, yields:

[0282]

[0283] in , , ,make: , , The optimization objective (45) is re-expressed as:

[0284]

[0285] in: , ,make , For all Summation, and removing the summation from the summation. Irrelevant constant terms, we get:

[0286]

[0287] Regarding the user SINR constraint in problem (17) 2), due to , After cross-multiplication and rearranging, we get:

[0288]

[0289] Similarly, the confidentiality rate constraint is handled in the same way as the user SINR constraint. In the confidentiality rate constraint (16), for This term can be transformed into a form similar to equation (51):

[0290]

[0291] for This item means: , , , , , Organize it as follows:

[0292]

[0293] Because the above objective function and constraint terms already exist The linear terms also have To better handle the quadratic term, we perform the following transformation: Let , , ,because:

[0294]

[0295] The optimization objective (50) can be written in the form of a linear trace:

[0296]

[0297] The SINR constraint (51) is also written in the form of a linear trace, let:

[0298]

[0299] Then equation (51) is transformed into:

[0300]

[0301] Similarly, regarding the confidentiality rate constraint, let:

[0302]

[0303] The confidentiality constraints (52) and (53) can be expressed as linear trace inequalities:

[0304]

[0305] For the unit modulus constraint, it can be transformed into:

[0306]

[0307] All about The optimization problem is rewritten as:

[0308]

[0309] For the optimization problem (61), removing the rank-1 constraint results in a standard SDP problem, which can be solved using CVX. Once the optimal solution is obtained... Recovery is achieved through eigenvalue decomposition or Gaussian randomization. Thus, the RIS emission matrix is ​​obtained. .

[0310] In summary, by combining the Alternating Optimization (AO) algorithm, the Dinkelbach algorithm, the Lagrange dual algorithm, the quadratic transformation algorithm, the semidefinite relaxation (SDR) algorithm, and the Schur complement algorithm, the optimal system utility under general conditions can be obtained.

[0311] The technical effects of the present invention will be further explained in detail below with reference to simulation experiments:

[0312] The effectiveness of the present invention is verified by comparing the proposed solution with existing solutions in terms of energy efficiency, confidentiality rate, and user SINR.

[0313] 1. Simulation parameter settings.

[0314] In a simulated RIS-assisted ISAC system, the base station is considered to be equipped with a certain number of antennas. A ULA array with an antenna spacing of 8 is configured, where the antenna spacing is half a wavelength and the base station is placed at (0,0,10). The RIS is placed at (50,0,10), and the reflector is configured as follows: =16. For radar target estimation, the target angle is... =80°, frame length The setting is 16. Additionally, the base station serves 3 downlink users, with a maximum transmit power of 16. Set to 40dBm, power amplifier efficiency =0.7, static-dynamic power component Set to 25 dBm. Users and eavesdroppers are randomly distributed within a circular area centered at (40,0,0) with a radius of 10. Unless otherwise specified, the noise variance at the user, eavesdropper, and target locations is set. = = =-50dBm. For simplicity, set the signal-to-interference-plus-noise ratio (SIR) threshold for all users. =3dB, security threshold Set to 0.5 bits / s / Hz. All communication channels are modeled as Rician channels, which can be represented as:

[0315]

[0316] Among them, path loss is used This indicates that the Rician factor is used... express, and These are respectively the direction of launch and receiving direction Related guide vectors. It follows a Rayleigh distribution with zero mean and unit variance. Furthermore, the sensing channel is modeled as a steering vector associated with the target direction.

[0317] 2. Simulation content and result analysis.

[0318] Figure 4 The number of fixed base station antennas is shown. At the same time, the number of different RIS reflective elements The dynamic changes in energy efficiency compared to the baseline without RIS during alternating optimization iterations are analyzed. Overall, all configurations with RIS exhibit significant convergence behavior during the AO iteration process: EE rapidly increases in the first 20 AO iterations, continues to rise between 20 and 30 iterations, and gradually enters a stable range after 30 iterations. This indicates that the AO algorithm and the Dinkelbach algorithm can effectively optimize the base station transmit beamforming matrix. Artificial noise matrix and RIS reflection matrix The energy efficiency of the RIS gradually approaches the optimal solution; while the energy efficiency (EE) of the No-RIS baseline remains at a low level, eventually stabilizing at 7.6 bits / J / Hz, verifying the core role of RIS in improving energy efficiency. The number of reflective elements in the RIS... In terms of impact, energy efficiency follows The increase of shows a monotonically increasing trend: The final EE value is the highest, close to 17 bits / J / Hz; Secondly, EE is approximately 14 bits / J / Hz; and The efficiency values ​​stabilized at approximately 13 bits / J / Hz and 12.5 bits / J / Hz, respectively. The core reason for this efficiency gap lies in the increased spatial phase modulation freedom resulting from the increased number of RIS reflector units, ultimately driving the improvement in energy efficiency. Compared to the No-RIS baseline, the configuration with RIS achieved an energy efficiency improvement of approximately 1.6 to 2.2 times. Furthermore, the "No optimization" curve in the figure represents the system energy efficiency without beamforming and RIS phase optimization. Its value remained constant and at the lowest level throughout the iteration process, further highlighting the importance of optimization algorithms in unlocking the potential of RIS and improving system performance.

[0319] Figure 5 The convergence processes of system sums and rates under different RIS configurations and a baseline without RIS were compared, intuitively demonstrating the enhancing effect of RIS on system transmission capacity. The sums and rates of all configurations exhibited an evolution trajectory of "rapid surge – slow decline – eventual stabilization," profoundly revealing the dynamic trade-off between rate and power under the goal of maximizing energy efficiency. Specifically, in the early stages of iteration, the Dinkelbach auxiliary variable... The beamforming and artificial noise resources are actively utilized to rapidly increase the beam rate and speed, as optimization objectives tend to prioritize increasing the rate. This drives the beam rate to its peak value. As iterations continue... Increasing or decreasing power consumption contributes more significantly to energy efficiency. Therefore, the algorithm actively reduces power consumption while meeting user constraints such as SINR, security rate, and sensing accuracy. and The intensity of the voltage causes the sum and rate to drop from their peaks, eventually converging to a balance point that balances speed and power consumption. For example... The speed peaks around 10 iterations, reaching approximately 17 bits / s / Hz, then gradually decreases and stabilizes at 9.1 bits / s / Hz after 40 iterations. The No-RIS system, however, experiences a brief initial spike followed by a drop to approximately 5.6 bits / s / Hz. Therefore, this "rise then fall" pattern directly reflects the dynamic trade-off between speed and power consumption in maximizing EE. Comparing the RIS-enabled and non-RIS-unenabled versions, the RIS-enabled version shows a 30%-60% improvement in sumR compared to the non-RIS system, providing support for the RIS-assisted ISAC system to improve overall speed.

[0320] Figure 6The figure illustrates the evolution of the system's sensing accuracy constraint feasibility with the number of alternating optimization iterations under different numbers of RIS reflector units and NO-RIS conditions. The vertical axis represents the minimum eigenvalue of the linear matrix inequality corresponding to CRB. The non-negativity of the curves indicates that the perception constraints are feasible, and the horizontal axis represents the number of AO iterations. Overall, all curves show a rapid decline followed by a gradual stabilization at a level slightly above zero, indicating that the algorithm can gradually coordinate communication and perception resources during the iteration process, enabling the system to gradually converge from the initial region of relaxed perception constraints to an optimal equilibrium point close to the constraint boundaries. Towards the later stages of iteration, all curves converge to stable values ​​close to zero but always positive, indicating that the CRB constraints are strictly satisfied throughout the process, and the algorithm ultimately pushes the system to the critical boundary of perception performance requirements, achieving maximum energy efficiency while satisfying perception accuracy.

[0321] Figure 7 Showing The trend of the signal-to-interference-plus-noise ratio (SINR) of the eavesdropper when eavesdropping on different users at a value of 16, along with the algorithm iterations, intuitively reflects the system's performance in terms of physical layer security. As shown in the figure, all three curves eventually converge to a low negative value, indicating that the quality of the eavesdropping channel is effectively suppressed. The blue curve represents the SINR of the eavesdropper eavesdropping on user 1's information, which stabilizes at around -5 dB after 30 iterations. This value means that the useful signal power received by the eavesdropper is only 31.6% of its total interference and noise power, making it unable to effectively resolve information. This indicates that although the resource allocation strategy in the early stages of the algorithm may have temporarily worsened the security performance of user 1, the system successfully enhanced the protection of the link for this user through subsequent synergistic optimization of the transmit beamforming matrix, artificial noise covariance matrix, and RIS phase. Similarly, the SINR of eavesdropping on user 2 shows the same trend and eventually stabilizes at a lower level of around -8 dB, showing that the algorithm has a more significant effect on suppressing eavesdropping on user 2. For user 3, its corresponding eavesdropping SINR shows the most ideal decreasing trend, rapidly dropping from the initial -2 dB to below -12 dB and remaining stable. This value corresponds to a signal power that accounts for only 6.3% of the interference noise power, indicating that user 3's communication confidentiality is guaranteed at the highest level. Overall, the simulation results fully verify the effectiveness of the proposed algorithm. Through a multi-dimensional collaborative design of transmit beamforming, RIS intelligent reflection, and artificial noise injection, the algorithm can proactively and differentially degrade the eavesdropper's receiving environment while satisfying multi-user communication quality and system energy efficiency, ultimately achieving multi-objective optimization of "security-energy efficiency-rate," providing a reliable basis for the physical layer security design of practical systems.

[0322] Figure 8 This demonstrates the secure communication performance of the EE-maximized system from the user's perspective, providing the achievable rate for each user. eavesdropper eavesdropping rate And the confidentiality rate corresponding to each user The red dashed line in the diagram represents the pre-set confidentiality threshold. =0.5 bits / s / Hz, used to visually assess the compliance of communication security. Looking at the relative height of the bars, User 1 has the highest achievable rate, approximately 3.5 bits / s / Hz, while its corresponding eavesdropping rate is successfully suppressed to only about 0.4 bits / s / Hz, thus achieving a confidentiality rate far exceeding... User 2 has the lowest achievable rate, approximately 1.7 bits / s / Hz, but its eavesdropping rate is also the lowest, around 0.2 bits / s / Hz, thus its confidentiality rate also meets the constraints. This collectively demonstrates that the proposed algorithm, while achieving the target rate allocation and meeting the basic communication needs of each user, can effectively weaken the information interception capability of the eavesdropping channel through beamforming and artificial noise, ultimately achieving a good synergy and balance between system efficiency and communication security.

[0323] Figure 9 This demonstrates that, under different user SINR threshold constraints, the system energy efficiency varies with the number of RIS units. The relationship between changes in the SINR threshold, the absence of a RIS benchmark, and the lack of optimization solutions. Overall, as the user's SINR threshold... With the increase in SINR, system energy efficiency decreases across all configurations. This is because higher SINR requirements force the system to allocate more power to meet communication quality demands, thus reducing energy utilization efficiency. Specifically, in RIS-assisted configurations, system energy efficiency increases with the number of RIS units. It increases monotonically with the increase of . For example, when When =3, the corresponding Its energy efficiency is approximately 12.8 bits / J / Hz, while Energy efficiency improved to approximately 15 bits / J / Hz. This phenomenon stems from the spatial degree-of-freedom gain provided by the increased number of RIS units. Compared to the baseline without RIS, all RIS-assisted configurations exhibited significant energy efficiency gains, with some configurations achieving approximately 2 to 3 times performance improvement. This further validates the crucial role of RIS in enhancing system energy efficiency and supporting high-quality-of-service communication. Systems without RIS, relying solely on direct links with significant path losses, must significantly increase transmit power to cope with stringent SINR constraints, leading to a rapid deterioration in energy efficiency as the SINR threshold increases. Furthermore, the "no optimization" curve in the figure consistently maintains the lowest energy efficiency level and hardly changes with the SINR threshold.

[0324] In summary, the simulation results show that: Figure 4The study revealed that the system energy efficiency increases monotonically with the increase of the number of RIS units, verifying the convergence of the proposed algorithm and the core role of RIS in overcoming the energy efficiency bottleneck. Figure 5 It demonstrates the dynamic trade-off between system speed and power consumption under the goal of maximizing EE, showing that the algorithm achieves an effective balance between speed and power consumption. Figure 6 This confirms that the algorithm can strictly meet the sensing accuracy constraints and pushes the system to the CRB boundary to achieve optimal energy efficiency; Figure 7 It has been demonstrated that joint optimization can differentiate and effectively suppress SINR from eavesdroppers, thus ensuring physical layer security. Figure 8 This indicates that the confidentiality rate of all users far exceeds the preset threshold, and the system provides sufficient security margin while meeting communication quality requirements; Figure 9 This demonstrates that under stricter user SINR requirements, RIS can significantly mitigate the decline in energy efficiency by providing spatial degrees of freedom, showcasing its ability to support high-quality-of-service communication.

Claims

1. A beamforming design method for maximizing energy efficiency in a RIS-assisted safe ISAC system, characterized in that, Includes the following steps: Step 1: Construct a RIS-assisted secure ISAC system model: Step 2: Construct the system's communication and perception models: In the communication model described, the total signal transmitted by the base station Represented as: ； Among them, the communication signals transmitted by the base station are used It is indicated that its beamforming matrix is ​​represented by express, ,make ,in Representing the Beamforming vectors for each user Represents its conjugate transpose, rank , The AN vector represents the artificial noise emitted by the base station to interfere with eavesdroppers. The covariance matrix of the artificial noise AN is represented by the reflection phase matrix of RIS, which is defined as follows: ,in ,in It is a natural constant. It is the imaginary unit, phase. Let the modulus , Representing RIS Unit, assuming base station to RIS, the first The equivalent channels for each legitimate user and eavesdropper are respectively: , , It means that among them Representing the first Individual users, eavesdroppers, and base stations, from RIS to the 1st The equivalent channels for a legitimate user and an eavesdropper are represented as follows: , , Representing RIS, the signal transmitted by the base station travels through a direct link. Reaching the At a legitimate user location, or after being reflected by RIS, the data is ultimately received by the user. The comprehensive equivalent channel is: Then the first The signal received by each user is represented as follows: ； in For the received noise at the user end, according to the received signal model given in equation (2), the user The signal-to-interference-plus-noise ratio (SINR) is expressed as: ； in, Representing the Beamforming vectors for each user The reachability and rate of the system are expressed as: ； in, On behalf of users The achievable rate, similarly, let the eavesdropper's comprehensive equivalent channel be: The signal received by the eavesdropper is represented as: ； in For the received noise at the eavesdropper's end, according to the received signal model given in equation (5), the eavesdropper eavesdrops on the user. The SINR is: ； Then the eavesdropper eavesdrops on the user The achievable rate of a signal is expressed as: ； Therefore, users The confidentiality rate is written as: ； here ; In the aforementioned sensing model, the base station receives... Parameter estimation is performed on the target echo signal in each time slot, and the threshold value of CRB at the target is used as the sensing constraint variable of the system: ； in, The transmitted signal covariance matrix, From the perspective of representing the goal, Represents the upper bound of CRB; Step 3: Establish a joint optimization problem with the goal of maximizing system energy efficiency: The energy efficiency is defined as the ratio of the system's achievable sum rate to its total power consumption. ； in, Represents the efficiency of the power amplifier. Represents the base station's transmit power consumption. To determine the static circuit power consumption, an optimization problem is established, and the beamforming matrix is ​​jointly optimized. Artificial noise covariance matrix and RIS reflection matrix To maximize energy efficiency And satisfy the total transmit power constraint, the minimum SINR constraint for each user, the minimum security rate constraint for each user, the sensing CRB constraint, and the RIS unit mode constraint. Step 4: Solve the joint optimization problem using the AO framework and related optimization algorithms: The joint optimization problem is solved iteratively using the AO framework. In each iteration, the fractional objective function is first transformed into a subtractive form using the Dinkelbach method, and auxiliary variables are introduced. The reachable rate expression is then processed using the Lagrange dual transformation and the quadratic transformation. Then, the original problem is decomposed into three subproblems concerning the beamforming matrix, the artificial noise covariance matrix, and the RIS reflection matrix, and convex optimization is performed using SDR and Schur complement techniques, respectively.

2. The beamforming design method for maximizing energy efficiency in a RIS-assisted safe ISAC system according to claim 1, characterized in that: The RIS-assisted secure ISAC system model constructed in step 1 is as follows: Build a equipped A base station (BS) with one transmit and receive antenna, simultaneously serving as... A single-antenna user is provided with service, and a point target is detected. The antennas are arranged in a uniform linear array ULA with half-wavelength spacing, and the RIS is composed of... Composed of passive reflective elements, the system is deployed near the user to reconstruct the wireless propagation environment and enhance secure communication. Artificial noise (AN) is introduced at the base station (BS) to actively interfere with potential eavesdroppers. Assuming perfect channel state information (CSI), the system adopts a shared deployment, with all antennas used for both communication and sensing simultaneously.

3. The beamforming design method for maximizing energy efficiency in a RIS-assisted safe ISAC system according to claim 1, characterized in that, The joint optimization model established in step 3 is expressed as follows: Under the constraints of total base station transmission power, minimum SINR for each user, minimum security rate for each user, perceived CRB, and RIS unity modulus, a joint optimization model is established for the base station beamforming matrix, AN covariance matrix, and RIS reflection coefficient matrix, with the goal of maximizing system EE: ； Among them, constraints 1 indicates the power budget constraint of the base station. This represents the maximum allowable power consumption of the base station, a constraint.

2. To ensure the communication quality of each user, the SINR of each user must be maintained at a predefined signal-to-noise ratio threshold. Above, constraints 3 is a constraint to ensure system security, requiring the confidentiality rate to be greater than a certain threshold. ,constraint 4. The magnitude and phase constraints of each RIS unit are specified. To ensure the performance of target estimation, a predefined parameter is set. As the upper limit of CRB, and in CRB constraints are given in section 5.

6. The covariance matrix of artificial noise must be a positive semi-definite matrix. This model uniformly considers communication rate, sensing accuracy, physical layer security and energy consumption, and maximizes the overall energy efficiency of the system through joint optimization.

4. The beamforming design method for maximizing energy efficiency in a RIS-assisted safe ISAC system according to claim 1, characterized in that: The steps in step 4, which use the AO algorithm to solve for the base station beamforming matrix, AN covariance matrix, and RIS reflection phase matrix, are as follows: 1) Algorithm preprocessing: Transform the objective function into a confidentiality rate constraint; Using the AO framework, joint optimization is achieved by iteratively solving three sub-problems. , and First, the Dinkelbach method is used to process the fractional form of the energy efficiency objective function. Introducing auxiliary variables This transforms the original maximization problem into an equivalent maximization problem. ,in Here is the expression for total power consumption; next, it represents the achievable processing speed. Fractional SINR within logarithmic terms, introducing auxiliary variables Thus, the reach and rate The equivalent rewrite is as follows: ； The optimal value is: Subsequently, the third term of equation (12) has a nonconvex fraction problem, so an auxiliary variable is introduced. And by applying a quadratic transformation, it is converted into a representation of... and Combinations of quadratic forms and linear terms: ； in The representative takes the real part. represent conjugate, The optimal value is: ； get and Then, by omitting the constant term, the optimization objective is simplified to: ； For non-convex confidentiality constraints Introducing auxiliary variables and define , The confidentiality constraint is transformed into: ； Based on the above simplification, problem (11) is equivalently restated as follows: ； 2) Fixed and ,optimization ; exist Optimization while keeping variables constant First, we address the perceived CRB constraints. The expression is written as: ； in, Define constants ,constraint( 5) Rewritten as: ； make And by utilizing Schur complementarity, equation (19) is equivalent to the following form: ； in, At this time, targeting and Equation (20) is convex, and the objective and constraints are rewritten as: ； Note the constraints. 1) All of the above Irrelevant items were included middle; In (21), due to the optimization variables Its column vector The simultaneous existence of these factors makes the solution process quite complex. To simplify the expression and unify the variable forms, we utilize... This column vector combination relationship will transform the original problem into a series of vector combinations. All optimizations are converted into optimizations of each column. The optimization, firstly, involves constraints ( 1) Rewritten as: ； This constraint applies to It is a convex constraint, constraint ( 2) Rewritten as: ； in, For the objective function in (21), it can be rewritten as: ； in: , For confidentiality constraints ( 3) Rewritten as: ； in: For constraints ( 4), make And by The above equation becomes: ； Due to constraints (23)(25)(26) regarding Since both are non-convex, the original quadratic optimization problem is transformed into an equivalent positive semidefinite programming problem. To achieve this, an extended vector is introduced. ,use Combining the linear and quadratic terms in the objective function, equation (24) can be written as: ； in: Constraint (22) can be written in the following equivalent form: ； Constraint (23) can be transformed into: ； in: ,make Constraint (25) is rewritten as: ； Based on this, auxiliary variables are introduced: And by utilizing the properties of the matrix trace, equation (27) becomes: ； Similarly, constraint (28) is reformulated as: ； Constraints (29) and (30) are rearranged as follows: ； ； make Rearranging equation (26) yields: ； in: ,because Therefore, constraints are introduced: ； Due to the presence of the rank-1 constraint, the above optimization problem remains non-convex. Using a positive semidefinite relaxation method to remove the rank-1 constraint, the problem is transformed into a standard positive semidefinite programming problem, which can be efficiently solved using CVX. The optimization problem and constraints are then rearranged as follows: ； If you obtain If the rank-1 constraint is not satisfied, eigenvalue decomposition can be performed, and the vector corresponding to the largest eigenvalue can be taken as an approximate solution to obtain the optimal beamforming vector. Optimal beamforming vector Represented as ； in, ; 3) Fix and ,optimization ; exist With all variables remaining constant, the optimization problem (17) simplifies to: ； For power constraints ( 1) Transform it into the following form: ； in, For user QoS constraints ( 2) Organize it as follows: ； in: Regarding the confidentiality rate constraint (16), following the processing method of formula (41), we can rearrange and obtain: ； in: Similarly, for constraints Simplified to: ； in: The optimization objectives and constraints are rearranged to obtain: ； At this time, in response to Problem (44) is convex and can be solved using tools such as CVX; 4) Fix and ,optimization ; exist Assuming the variables remain constant, let: ,in , The optimization objective in (17) can be simplified to: ； Define a diagonal matrix: , Base station to user The equivalent channel is written as: The equivalent channel from the base station to the eavesdropper is written as: ;set up , , , Therefore, according to the above formula, we get: Similarly, let , , , ,but: Then, for equation (45), the expected signal term can be rewritten as: ； For the interference terms, expand and simplify them as follows: ； For artificial noise The term, when expanded in quadratic form, yields: ； in , , ,make: , , The optimization objective (45) is re-expressed as: ； in: , ,make , For all Summation, and removing the summation with respect to the summation. Irrelevant constant terms, we get: ； Regarding the user SINR constraint in problem (17) 2), due to , After cross-multiplication and rearranging, we get: ； Similarly, the confidentiality rate constraint is handled in the same way as the user SINR constraint. In the confidentiality rate constraint (16), for This term can be transformed into a form similar to equation (51): ； for This item means: , , , , , Organize it as follows: ； Because the above objective function and constraint terms already exist The linear terms also have The quadratic term is transformed as follows: Let , , ,because: ； The optimization objective (50) can be written in the form of a linear trace: ； The SINR constraint (51) is also written in the form of a linear trace, let: ； Then equation (51) is transformed into: ； Similarly, regarding the confidentiality rate constraint, let: ； The confidentiality constraints (52) and (53) can be expressed as linear trace inequalities: ； For the unit modulus constraint, it can be transformed into: ； All about The optimization problem is rewritten as: ； For the optimization problem (61), removing the rank-1 constraint results in a standard SDP problem, which can be solved using CVX. Once the optimal solution is obtained... Recovery is achieved through eigenvalue decomposition or Gaussian randomization. Thus, the RIS emission matrix is ​​obtained. .

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