Physical layer secure transmission method based on time modulation reconfigurable surface assistance

Abstract

The invention discloses a physical layer secure transmission method based on time modulation reconfigurable surface assistance, and belongs to the technical field of physical layer security, a TMA-RIS-assisted secure communication system is constructed, and the TMA-RIS-assisted secure communication system comprises a single-antenna base station, a single-antenna legal user, a single-antenna eavesdropper and a time modulation technology-based RIS model; a base station of a single antenna transmits a signal to a legal user of the single antenna, an eavesdropper of the single antenna eavesdrops the transmitted information, a direct link between the base station of the single antenna and the legal user of the single antenna is blocked, and a communication link is established through an RIS model based on the time modulation technology. The amplitude-phase joint regulation and control characteristic of the TMA-RIS based on the time modulation reconfigurable intelligent surface is further researched, so that the beam forming precision of the discrete phase RIS is improved, and the physical layer safety performance of the system is enhanced.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of physical layer security, and particularly relates to a physical layer security transmission method based on time modulation reconfigurable surface assistance. BACKGROUND

[0002] Reconfigurable intelligent surface (RIS) can dynamically adjust the wireless channel and is widely used in wireless physical layer security communication technology. RIS can use passive beamforming to enhance the channel gain of legitimate users while weakening the channel gain of eavesdroppers, thereby realizing physical layer security. However, in order to achieve the above goal, RIS needs to be able to adjust the amplitude and phase of its elements with high precision. In actual systems, due to the cost and hardware complexity of the control unit, RIS elements usually only support discrete phase shift configuration. However, discrete phase shift limits the beamforming capability of RIS. Therefore, extending the feasible region of amplitude and phase joint optimization of RIS by using time modulation technology to improve the security performance of the system is still a key problem that needs further research.

[0003] Due to the openness of the wireless channel, information is extremely vulnerable to illegal eavesdropping during transmission. Traditional security technologies based on cryptography face the potential risk of being cracked with the development of emerging computing technologies such as quantum computers. Therefore, physical layer security technology, as a supplement to traditional encryption methods, has received widespread attention in recent years. Its main technologies include beamforming and artificial noise, etc. In actual wireless propagation environment, the direct link between the base station and the legitimate user may be blocked by buildings or other obstacles, resulting in a decline in channel quality or even the inability to establish an effective connection. To address this problem, reconfigurable intelligent surface (RIS) has become a research hotspot in the field of physical layer security in recent years due to its ability to reconstruct the signal propagation environment.

[0004] RIS is usually composed of a large number of passive reflecting elements, each of which can independently apply a specific phase shift to the incident signal. By adjusting the phase shift parameters of RIS, RIS can reconstruct the wireless propagation environment and improve the signal transmission quality. Most research based on RIS assumes that RIS has the ability of continuous phase shift. However, due to the cost and hardware complexity of the control unit, RIS elements in actual systems usually only support discrete phase shift settings. Discrete phase shift RIS has the problem of limited beamforming capability.

[0005] Given the characteristics of time modulation single radio frequency chain, the introduction of time modulation technology into RIS to enhance the beamforming capability has attracted attention in the academic community. Research on time modulation technology in RIS has made some progress, but its research in the field of physical layer security communication still needs further exploration and analysis. SUMMARY

[0006] Therefore, the present application aims to provide a time modulation based reconfigurable surface assisted physical layer security transmission method, which introduces time modulation technology under the condition of actual RIS discrete phase shift limitation to improve the amplitude and phase control ability of RIS elements on reflected signals and the accuracy of beamforming.

[0007] To achieve the above-mentioned purpose, the present application provides the following technical solutions: A time modulation based reconfigurable surface assisted physical layer security transmission method, a TMA-RIS assisted security communication system is constructed, the TMA-RIS assisted security communication system includes a single antenna base station, a single antenna legitimate user, a single antenna eavesdropper and a RIS model based on time modulation technology. The single antenna base station transmits signals to the single antenna legitimate user, the single antenna eavesdropper eavesdrops on the transmitted information, the direct link between the single antenna base station and the single antenna legitimate user is blocked, and a communication link is established through the RIS model based on time modulation technology.

[0008] As a further preferred embodiment of the present application, the RIS model based on time modulation technology expands the feasible region of RIS phase shift through time modulation technology, which dynamically controls each element of RIS to generate a periodic modulation sequence through the rapid switching of high-speed radio frequency switches; Let the period of time modulation be , the modulation sequence is expressed as follows: (2) Wherein, j is the imaginary unit, represents the natural constant, respectively represent the starting time when the element switches to the corresponding phase; , wherein represents the number of bits used to indicate the phase offset order ; is expanded into a Fourier series as follows: (3) Wherein, represents the modulation frequency, is the Fourier coefficient of the th harmonic; The amplitude and phase weighting of the incident signal by the th element of RIS is expressed as follows: (4) Wherein, and represent the normalized on-time; ​Through time modulation, the amplitude and phase control of the array elements is extended from discrete points on the complex plane to a continuous convex set, and its feasible region is... express.

[0009] As a further preferred embodiment of the present invention, let the number of array elements of RIS be... Channel vector from base station to RIS As shown below: in, Indicates the base station to the Channel coefficients of each RIS array element; Assuming the channel from the base station to the RIS is a direct link, then It is expressed as follows: in, This represents the path loss per unit distance. Represents the fading coefficient. Indicates the distance from the base station to the RIS; Indicates wavelength, where Indicates the center frequency. , and These represent the first RIS. The three-dimensional coordinate vectors of the first array element and the first array element. The normalized unit vector from the base station to the RIS is calculated as follows: in Represents the center coordinate vector of RIS. This represents the coordinate vector of the base station.

[0010] As a further preferred embodiment of the present invention, the legitimate user receives the signal. The calculation is expressed as follows: in Indicates sending a signal. Denotes the magnitude-phase weighting matrix of RIS, where Indicates the first The amplitude and phase weighting coefficients of each TMA-RIS array element. This represents the Gaussian white noise received by the user. This represents the channel vector from the base station to the RIS. This represents the channel vector from the RIS to the legitimate user.

[0011] As a further preferred embodiment of the present invention, the signal-to-noise ratio received by a legitimate user is expressed as follows: in Defined as transmission power; Assuming the transmitted signal follows a Gaussian distribution, the transmission rate of a legitimate user is expressed as follows: The eavesdropper's transmission rate is expressed as follows: in This represents the channel vector from RIS to the eavesdropper. The noise power received by the eavesdropping device is represented by: The system's secure rate is defined as: As a further preferred embodiment of the present invention, in order to improve the security rate of the system, the following problem is addressed: Introducing variables , It can be rewritten as: in ; The optimization objective formula (13) is rewritten as: Will The vertices are arranged in a counterclockwise direction as follows ,in Define the edge vector connecting adjacent vertices as The outer normal vector of each edge is represented as For each edge feasible region Require any point Located inside this edge, i.e., satisfying Constraints Expand as The constraints of the linear inequalities, namely After merging the constraints of all edges into a matrix form, the final feasible region of the constraints is obtained as follows: The optimization objective formula (15) is rewritten as follows: in .

[0012] As a further preferred embodiment of the present invention, the definition is... For the first The optimal solution for the next iteration is obtained, and a surrogate function is constructed based on this solution. Using the Lagrange multiplier method, the first multiplier is defined as... The non-negative Lagrange multipliers at the next update iteration are ,in, To constrain the first The Lagrange multipliers of each array element are represented as Represented as constraint number Lagrange multipliers of the boundary; the problem is further described as: Where the Lagrange function Represented as: right The gradient is calculated as follows: in Indicates in The Hessian matrix at that location, Defined as a constraint matrix, denoted as In order to solve (18) The optimal solution is to let To obtain the updated iteration direction for: Let the first The approximate matrix of the second-order Hessian inverse in the next iteration is: The iteration direction is then represented as: in The update formula is calculated as follows: in The update expression for the variable is: in express The update step size is used to synchronously update the Lagrange multipliers, and the calculation formula is as follows: in This represents the update step size of the Lagrange multipliers. express The One element; Through variables By alternating updates with Lagrange multipliers, an optimized solution for the amplitude-phase weighting coefficients of each array element is obtained.

[0013] As a further preferred embodiment of the present invention, the timing design principle of prioritizing the minimum number of switching operations is adopted. When the optimal solution is located at the boundary of the feasible region, the weighting coefficient is represented by a linear combination of two vertices. When the optimal solution is located inside the feasible region, according to the Calaciodorli theorem, the weighting coefficient is represented by a linear combination of three phases. Given the weighting coefficients, the corresponding turn-on timing can be deduced.

[0014] The beneficial effects of this invention are as follows: This invention introduces time modulation technology under the practical discrete phase shift constraint of RIS (Resonance Array Components) to improve the amplitude and phase control capability of RIS elements on reflected signals and the accuracy of beamforming. It further investigates the amplitude and phase joint control characteristics based on Time Modulation Reconfigurable Smart Surface (TMA-RIS) to improve the beamforming accuracy of discrete-phase RIS, thereby enhancing the physical layer security performance of the system. Furthermore, considering the coupling between time modulation timing parameters, direct optimization would lead to high computational complexity. This invention proposes an inverse optimization strategy to effectively avoid the high complexity problem caused by direct timing optimization, achieving efficient and feasible timing design for TMA-RIS. This invention aims to optimize the system's security rate. Compared with traditional discrete RIS, this invention not only effectively improves the system's security rate but also enhances stability under different eavesdropping directions.

[0015] Other advantages, objectives, and features of the invention will be set forth in the following description and will be apparent to those skilled in the art in some respects, or may be learned by practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0016] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration: Figure 1 This is a model diagram of the TMA-RIS-assisted secure communication system of the present invention; Figure 2 This is a schematic diagram of the feasible region for amplitude-phase continuity of the TMA-RIS of the present invention; Figure 3 This is a diagram showing the relationship between the security rate and the eavesdropping angle under the 1-bit phase configuration of this invention. Figure 4 This is a diagram showing the relationship between the security rate and the eavesdropping angle under the 2-bit phase configuration of this invention. Figure 5 This is a graph showing the relationship between the security rate of this invention and the size of the RIS array; Figure 6 This is a graph showing the relationship between the safety rate and transmission power of this invention. Detailed Implementation

[0017] like Figures 1-6 As shown, this invention belongs to the field of physical layer security, specifically involving extending the phase shift feasible domain of discrete reconfigurable smart surfaces through time modulation technology, thereby improving beamforming accuracy and enhancing system security rate and transmission stability.

[0018] This invention proposes a method for secure transmission based on a time-modulated array reconfigurable smart surface-assisted beamforming (RIS). This method significantly improves beamforming accuracy by introducing time modulation technology to extend the feasible region of amplitude-phase joint optimization of the RIS. Compared with traditional discrete-phase RIS, this invention not only improves the system's security performance but also enhances the stability of transmission in different directions.

[0019] 1. For example Figure 1 As shown, we consider a TMA-RIS-assisted secure communication system. Specifically, the system involves a single-antenna base station transmitting signals to a single-antenna user, while a single-antenna eavesdropper attempts to intercept the transmitted information. Due to obstructions, the direct communication path between the base station and the user equipment is blocked; therefore, we employ a time-modulated RIS to establish a stable communication link for the user. Assuming that the RIS, the legitimate user, and the eavesdropper are all located in the far field, a plane wave approximation model can be used.

[0020] 2. RIS model based on time modulation technology: In practice, due to hardware limitations, RIS typically employs a discrete phase design. The discrete phase is set within the range [0, 2π). A uniform quantization level, specifically given as... (1) in Indicates the number of phase offset levels The number of bits. To improve beamforming performance and overcome the accuracy limitations of discrete phase design, this invention introduces time modulation technology to extend the feasible domain of RIS phase shift. Time modulation technology dynamically controls each element of the RIS through rapid switching of a high-speed RF switch, causing it to generate a periodic modulation sequence. Therefore, when a signal is incident on the RIS, this technology is equivalent to applying periodic timing modulation to the signal. Assuming the period of time modulation is... Then the modulation sequence can be defined as (2) in j is the imaginary unit. Represents the natural constant. , These represent the start times when the array elements switch to their corresponding phases. Given the periodicity of the modulation timing, It can be expanded into a Fourier series, represented as (3) in Indicates the modulation frequency. For the first The Fourier coefficients of the second harmonic. Clearly, time modulation will inevitably generate an infinite number of harmonics. However, harmonic aliasing can be avoided when the modulation frequency is greater than the signal bandwidth. Under this condition, the fourth harmonic of the RIS... The amplitude and phase weighting of each element with respect to the incident signal can be characterized by the coefficients of the fundamental wave. (4) in and This represents the normalized on-time. For example... Figure 2 As shown, due to time modulation, the amplitude and phase control of the array elements is extended from discrete points on the complex plane to a continuous convex set, and its feasible region is expressed as... express.

[0021] 2. Received signal model based on TMA-RIS: Assume the number of elements in the RIS is Therefore, the channel vector from the base station to the RIS Defined as (5) in Indicates the base station to the The channel coefficients of each RIS element. Assuming the channel from the base station to the RIS is a direct link, then... It can be given as (6) in, This represents the path loss per unit distance. Represents the fading coefficient. This indicates the distance from the base station to the RIS. Indicates wavelength, where Indicates the center frequency. .also, and They represent the first, second, and third RIS, respectively. The three-dimensional coordinate vectors of the first array element and the first array element. The normalized unit vector from the base station to the RIS can be calculated as follows: (7) in Represents the center coordinate vector of RIS. This represents the coordinate vector of the base station. Similarly, the channel vector from the RIS to the legitimate user. It can also be represented accordingly. Therefore, the received signal model can be calculated as follows: (8) in This indicates that a signal has been sent. Denotes the magnitude-phase weighting matrix of RIS, where Indicates the first Amplitude and phase shift weighting of each TMA-RIS array element. This represents the Gaussian white noise received by the user. Similarly, the eavesdropper's received signal... It can also be expressed in a similar way.

[0022] 3. Security Rate Performance Analysis: During the process of the base station sending signals to the user, the signal can be eavesdropped on by an eavesdropper. Therefore, it is necessary to further analyze the security rate of the system to form a target problem for optimization, thereby improving the communication security of the system. According to formula (8), the signal-to-noise ratio received by the user can be written as: (9) in Defined as transmission power. Assuming the transmitted signal follows a Gaussian distribution, the user's transmission rate can be written as... (10) Similarly, the eavesdropper's transmission rate can be written as (11) in This represents the channel vector from the RIS to the eavesdropper. This represents the noise power received by the eavesdropping device. Therefore, the system's secure rate can be defined as... (12) 4. Optimize the problem description: As mentioned above, the RIS's control capability over the channel depends not only on its discrete phase shift control but also on the time modulation. It can be observed that directly optimizing the time modulation sequence requires simultaneously determining the parameters. and This poses a significant challenge to direct optimization methods. Therefore, this invention employs a reverse optimization strategy, using direct optimization of the weighting coefficients to deduce the optimal modulation sequence. To improve the system's secure speed, we establish the following problem... (13) 5. Quasi-Newton optimization algorithm based on rank-1 correction: To facilitate optimized calculations, we introduce variables. ,So It can be further written as (14) in , Therefore, the optimization objective (13) can be rewritten as follows: (15) To represent the feasible region of the constraints, we will The vertices are arranged in a counterclockwise direction as follows ,in , Define the edge vector connecting adjacent vertices as... Then the outer normal vector of each edge can be represented as For each edge Feasible domain requirements Require any point It must be located inside the edge, that is, satisfying... Then the constraints It can be expanded into M The constraints of the linear inequalities, namely (16) Therefore, by merging the constraints of all edges into a matrix form, we can obtain the final feasible region of the constraints. Then (15) can be further expressed as (17) in , .

[0023] Clearly, this optimization problem is a non-convex problem.

[0024] To solve this problem This paper proposes a quasi-Newton optimization algorithm based on rank-1 correction. The core of this algorithm is to construct a convex surrogate function in each iteration to approximate the original objective function. Specifically, it defines... For the first k The optimal solution for the next iteration is obtained, and a surrogate function is constructed based on this solution. Meanwhile, to handle constraints, we employ the Lagrange multiplier method, defining the first multiplier as... k The non-negative Lagrange multipliers at the next update iteration are .in, To constrain the first The Lagrange multipliers of each array element are represented as , Represented as constraint number m Lagrange multipliers of the boundary. Based on this, the problem is further described as follows: (18) Where the Lagrange function It can be represented as (19) Furthermore, right We can obtain the gradient. (20) in Defined as a constraint matrix, denoted as (twenty one) In order to solve (18) The optimal solution is to let This allows us to obtain updated iteration directions. for (twenty two) Since accurately calculating the second-order Hessian matrix of the objective function in each iteration introduces high computational complexity, this scheme adopts a quasi-Newton method based on rank-1 correction to efficiently approximate the Hessian matrix through iterative updates, thereby simplifying the calculation process. Let the th... The approximate matrix of the second-order Hessian inverse in the next iteration is: Then the iteration direction can be expressed as (twenty three) in The update formula is calculated as follows: (twenty four) in Based on this, the update expression for the variable is: (25) in express The update step size. To effectively handle the constraints in the problem, the Lagrange multipliers need to be updated synchronously, and the calculation formula is: (26) in This represents the update step size of the Lagrange multipliers. express The m Each element.

[0025] In summary, through variables By employing alternating updates of Lagrange multipliers, this scheme implements a computationally efficient analytical optimization algorithm to obtain the optimized solution for the amplitude and phase weighting coefficients of each array element. Building upon this, to further reduce system complexity and control overhead, this invention adopts a timing design principle prioritizing the minimum number of switching operations. Specifically, when the optimized solution lies on the feasible region boundary, the weighting coefficients can be represented by a linear combination of two vertices; while when the optimized solution lies within the feasible region, according to Calaciodori's theorem, the weighting coefficients can be represented by a linear combination of three phases. Therefore, given the weighting coefficients, the corresponding conduction timing can be deduced, resulting in a complete timing control scheme. This design improves the accuracy of RIS beamforming while achieving efficient and feasible time modulation timing control, providing an effective implementation scheme for physical layer secure transmission based on TMA-RIS.

[0026] This invention aims to optimize system security rate. Compared to traditional discrete RIS schemes, this invention not only effectively improves system security rate but also enhances stability under different eavesdropping directions. The simulation uses a genetic algorithm (GA) to optimize the discrete RIS scheme and compares this invention with discrete RIS schemes and continuous-phase RIS schemes.

[0027] To demonstrate that the proposed solution maintains stable security performance even when the eavesdropper is positioned in different eavesdropping directions. Figure 3 and Figure 4 The security rate relative to the eavesdropping position was simulated under both 1-bit and 2-bit RIS schemes. The figures clearly show that the TMA-RIS scheme significantly improves the stability of the system's security performance. Specifically, the traditional discrete RIS scheme suffers from limited beamforming accuracy due to phase quantization errors, resulting in significant fluctuations in security performance when the eavesdropping angle changes dynamically. In contrast, TMA-RIS significantly improves beamforming accuracy by expanding the feasible optimization domain, thus significantly enhancing the stability of the system's security performance. Furthermore, compared to the 1-bit scheme, the system using the 2-bit TMA-RIS architecture exhibits a significantly higher security rate. This performance improvement is mainly due to the wider amplitude and phase joint optimization feasible domain provided by 2-bit TMA-RIS, enabling more precise beam control. Therefore, the 2-bit phase shifter configuration scheme will be used in subsequent simulations.

[0028] To further evaluate the safety performance of the present invention, Figure 5 The proposed TMA-RIS scheme is compared with discrete RIS schemes and continuous phase modulation schemes. The figure shows the curves of the safe rate versus the RIS element size using a 2-bit phase configuration, where the RIS size is... ,in The column number is indicated. Experimental results show that the proposed scheme significantly improves system security performance compared to discrete RIS design schemes, and its performance approaches that of continuous phase modulation schemes.

[0029] Figure 6 The figure illustrates the change in system safety rate relative to transmit power. It shows that, compared to discrete RIS designs, the proposed solution effectively improves safety performance and approaches the performance level of an ideal continuous-phase RIS solution. Specifically, under the same safety rate requirement, the TMA-RIS-based solution reduces transmit power by approximately 4 dB compared to discrete RIS solutions; and compared to continuous-phase RIS solutions, the transmit power difference can be controlled within 1 dB.

[0030] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made to it in form and detail without departing from the scope defined by the claims of the present invention.

Claims

1. A time modulation based reconfigurable surface assisted physical layer security transmission method, characterized in that: a TMA-RIS assisted secure communication system is constructed, which includes a single-antenna base station, a single-antenna legitimate user, a single-antenna eavesdropper and a RIS model based on time modulation technology; the single-antenna base station transmits signals to the single-antenna legitimate user, the single-antenna eavesdropper eavesdrops the transmitted information, the direct link between the single-antenna base station and the single-antenna legitimate user is blocked, and a communication link is established through the RIS model based on time modulation technology. 2.The time-modulation based reconfigurable surface-aided physical layer security transmission method of claim 1, wherein: The RIS model based on the time modulation technology expands the feasible region of the phase shift of the RIS through the time modulation technology, which dynamically controls each element of the RIS to generate a periodic modulation sequence through the rapid switching of a high-speed radio frequency switch; the period of the time modulation is , and the modulation sequence is as follows: (2) wherein, j is an imaginary unit, represents a natural constant, respectively represent the starting time when the array element switches to the corresponding phase; wherein represents the number of bits for indicating the phase offset level . Will Expanded into a Fourier series, it is represented as follows: (3) wherein denotes the modulation frequency, is the Fourier coefficient of the harmonic; RIS's The amplitude and phase weighting of each array element with respect to the incident signal is represented by the coefficients of the fundamental wave as follows: (4) wherein and is expressed as normalized on-time; By time modulation, the amplitude and phase control of the array elements is extended from discrete points in the complex plane to a convex set with continuous amplitude and phase, whose feasible region is denoted by . 3.The time modulation based reconfigurable surface assisted physical layer security transmission method according to claim 2, characterized in that: Let the number of elements of the RIS be The channel vector of the base station to the RIS is as follows: ​ wherein, denotes a channel coefficient of the base station to the j-th RIS element; denotes a channel coefficient of the base station to the j-th RIS element; Let the channel from the base station to the RIS be a direct link, then is represented as follows: wherein denotes the path loss per unit distance, denotes the fading coefficient, denotes the distance from the base station to the RIS; denotes the wavelength, wherein denotes the center frequency, , and denote the three-dimensional coordinate vectors of the first antenna element and the first antenna element of the RIS, respectively, denotes the normalized unit vector from the base station to the RIS, calculated as follows: wherein denotes the center coordinate vector of the RIS, denotes the coordinate vector of the base station.

4. The method of claim 3, wherein the time-based modulation is based on a time-division multiplexing (TDM) scheme. Legal user receives signal The computational representation of this is as follows: wherein represents a transmit signal, represents an amplitude and phase weighting matrix of the RIS, wherein represents an amplitude and phase weighting coefficient of the th TMA-RIS element, represents a Gaussian white noise received by the user, represents a channel vector from the base station to the RIS, represents a channel vector from the RIS to the legitimate user.

5. The method of claim 4, wherein the time-based modulation is based on a time-division multiplexing (TDM) scheme. the signal-to-noise ratio of the legitimate user is represented as follows: wherein defined as the transmit power; assuming that the transmitted signal obeys Gaussian distribution, the transmission rate of the legitimate user is represented as follows: the transmission rate of the eavesdropper is represented as follows: wherein denotes the channel vector from the RIS to the eavesdropper, denotes the noise power received at the eavesdropper; the security rate of the system is defined as: 。 6. A physical layer secure transmission method based on time-modulated reconfigurable surface assistance according to claim 5, characterized in that: in order to improve the security rate of the system, the following problem is established: Introducing variables , Rewritten as: wherein ; the optimization objective formula (13) is rewritten as: The vertices of the convex hull of are arranged in counterclockwise direction as , where , the edge vector connecting adjacent vertices is defined as , the outward normal vector of each edge is represented as , for each edge , the feasible region requires that any point lies on the inside of the edge, i.e. satisfies ; the constraint condition expands to linear inequality constraints, i.e. After combining the constraints of all edges into matrix form, the final feasible region of the constraints is ; and the optimization objective formula (15) is rewritten as follows: wherein .

7. The method of claim 6, wherein the time-based modulation is a time-based modulation of a reconfigurable surface. Definitions For the first iteration, the optimization solution is set to and based on this, the proxy function is constructed for ; Using the Lagrange multiplier method, the first multiplier is defined as... The non-negative Lagrange multipliers at the next update iteration are: ,in, To constrain the first The Lagrange multipliers of each array element are represented as Represented as constraint number Lagrange multipliers of the boundary; the problem is further described as: where the Lagrangian function is expressed as: to Gradient, as follows: wherein denotes the Hessian matrix at is defined as the constraint matrix, denoted as​ To solve the optimal solution of (18), let , we get the updated iteration direction as: ​ Let the approximation matrix of the inverse Hessian matrix of the second order in the kth iteration be , then the iteration direction is represented as: ​ wherein The update formula for is calculated as: wherein , the update expression of the variable is: wherein represents the update step of the Lagrange multiplier, the update of the synchronous update, the calculation formula is: wherein denotes the update step of the Lagrange multiplier, denotes the first element of By the variable The optimization solution of the amplitude and phase weighting coefficient of each array element is obtained by the alternative update of the Lagrange multiplier. 8.The time-modulation based reconfigurable surface-aided physical layer security transmission method of claim 7, wherein: a minimum switching number priority timing design principle is adopted, when the optimization solution is located on the boundary of the feasible region, the weighted coefficient is represented by a linear combination of two vertices; when the optimization solution is located inside the feasible region, according to the Karatsuba theorem, the weighted coefficient is represented by a linear combination of three phases, and the corresponding conduction timing is back calculated in the case of known weighted coefficient.

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