A joint beamforming and power optimization method for STAR-RIS covert communication

Abstract

This invention discloses a joint beamforming and power optimization method for STAR-RIS covert communication, belonging to the fields of wireless communication and physical layer security technology. First, the invention dynamically switches based on spatial location information to redirect the power budget originally allocated to the transmission module to the reflection channel, thereby physically blocking energy leakage paths and achieving full energy recovery. Then, using Pinsker's inequality and Kullback-Leibler divergence, the covertness requirement is transformed into a convex threshold constraint, and a multi-dimensional variable deeply coupled non-convex joint optimization model is constructed with the goal of maximizing the covert transmission rate. Finally, an alternating optimization algorithm is used to decouple and solve the model. This invention, by constructing a deeply coupled system of scene-aware dynamic switching, full energy recovery mechanism, and one-dimensional search algorithm, effectively improves the covert transmission rate in cross-side scenarios, significantly reduces the computational overhead of large-scale intelligent reflectors, and has good engineering deployment feasibility.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication and physical layer security technology, specifically relating to a joint beamforming and power optimization method for STAR-RIS covert communication. Background Technology

[0002] With the development of 6G (6th Generation Mobile Communication Technology), achieving ubiquitous coverage and ultra-high reliability has become a fundamental goal of future network architecture. However, the inherent openness and broadcast nature of wireless channels make physical layer transmission highly susceptible to security risks such as illegal monitoring or deliberate interference. In highly sensitive scenarios such as military operations or tactical intelligence, even the mere detectability of a signal's presence can trigger location attacks or complex traffic analysis. Therefore, "covert communication," as a new paradigm for achieving "presence security," aims to hide the presence of legitimate signals within background noise, preventing vigilant illegal monitoring ends from reliably distinguishing signals from pure thermal noise, thereby ensuring a low probability of detection for sensitive data.

[0003] Traditional covert communication schemes primarily rely on power control or artificial noise (AN), but their performance is fundamentally limited by the "square root law," meaning the cumulative number of covertly transmitted bits is only proportional to the square root of channel resource utilization, causing the communication rate to asymptotically decay to zero as the code length increases. Furthermore, in complex wireless environments with severe congestion and coverage blind spots, transmitters are often forced to drastically reduce their transmission power to avoid detection, leading to a sharp drop in the signal-to-noise ratio at legitimate receivers and even link interruption. To overcome this physical limitation, reconfigurable intelligent surfaces (RIS) with the ability to actively reshape the spatial electromagnetic environment have been introduced. However, the inherent "half-space" reflection characteristic of traditional RIS introduces a fatal topological flaw: legitimate receivers located in the transmission area behind the RIS are in a coverage dead zone and cannot receive service.

[0004] To address the topological limitations of traditional RIS (Radio Router Surface) systems, the Simultaneously Transmitting and Reflecting Reconfigurable Intelligent Surface (STAR-RIS) emerged, enabling simultaneous signal transmission and reflection for 360° full-space coverage. However, with the increasing complexity of network topologies, existing STAR-RIS protocols have revealed new critical security vulnerabilities in covert scenarios: when legitimate receivers and illegitimate monitoring devices are located on different sides of the STAR-RIS, traditional static protocols inevitably lead to severe energy leakage problems.

[0005] Specifically, existing research suffers from three main limitations: First, there is a serious risk of energy leakage. Most existing solutions are based on a simplified symmetric topology assumption that both the legitimate receiver and the illegitimate monitoring end are located on the same side, ignoring the inherent energy leakage backdoor induced by static protocols in cross-side scenarios. Once the illegitimate monitoring end is located in the transmission coverage area, traditional solutions can only blindly reduce the total transmission power of the transmitter to prevent this. This results in both legitimate and leaked signals being weakened indiscriminately, making it impossible for the legitimate receiver to communicate normally, and the system is trapped in a dead end where "concealment is impossible to communicate, and communication is impossible to conceal." Second, the active shutdown capability of STAR-RIS has not been fully explored and utilized to achieve energy accumulation. The total internal reflection of traditional RIS is derived from static physical constraints, while STAR-RIS can achieve deep integration of topology decisions and physical resources. However, existing technologies treat the transmission coefficient as a fixed deployment parameter, lacking dynamic perception and response capabilities to network geometry. They fail to consider it as a "recoverable energy resource," missing the boundary-optimal strategy of actively shutting down transmission modules and channeling the saved power to legitimate reflection channels, thus failing to translate energy-saving constraints into effective interference suppression capabilities. Finally, they lack theoretical performance limits under ideal geometric conditions. Existing robust design techniques mainly focus on worst-case approximate numerical optimization under imperfect Channel State Information (CSI), failing to provide accurate theoretical benchmarks and performance boundaries for the allocation of hidden resources in practical systems.

[0006] In summary, in order to fully unleash the potential of STAR-RIS in all-space covert communication, it is necessary to break away from the traditional passive defense paradigm that relies solely on power suppression. A physical layer active defense strategy that is sensitive to network geometry is urgently needed. Therefore, this invention proposes a joint beamforming and power optimization method for STAR-RIS covert communication, which fundamentally blocks energy leakage paths and approaches the theoretical limit of system communication rate under strict covert constraints. Summary of the Invention

[0007] The purpose of this invention is to provide a joint beamforming and power optimization method for STAR-RIS covert communication, which can effectively overcome the technical defects of existing solutions, such as energy leakage caused by static protocols in cross-side communication topologies and the sharp decline in the performance of legitimate links caused by traditional global power suppression.

[0008] To achieve the above objectives, the technical solution adopted by this invention is: a joint beamforming and power optimization method for STAR-RIS covert communication, comprising the following steps: Step S1: Acquire the geometric topology information of the communication system and perform scene-aware dynamic switching: acquire the real-time spatial location information of the transmitting end, the legitimate receiving end, the illegitimate monitoring end, and STAR-RIS in the communication system; determine whether the illegitimate monitoring end is located in the transmission coverage area of ​​STAR-RIS and whether the legitimate receiving end is located in the reflection coverage area of ​​STAR-RIS based on the spatial location information; when the determination result is yes, generate a mode switching command to switch the STAR-RIS from the dual working mode that allows simultaneous transmission and reflection to the full aperture reflection working mode; Step S2: Constructing the transmission signal vector and establishing concealment constraints: Constructing the transmission signal vector at the transmitting end, the transmission signal vector is composed of an information signal carrying target information and an artificial noise signal used to cover the information signal. Based on the detection error probability of the illegal monitoring end, using the Pinsker inequality and Kullback-Leibler divergence, the concealment requirement of the system is transformed into a calculable convex threshold constraint on the signal-to-noise ratio received by the illegal monitoring end. Step S3: Construct a multidimensional variable deep-coupled non-convex optimization problem: With the goal of maximizing the covert transmission rate of the legitimate receiver, under the conditions of satisfying the convex threshold constraint, the total transmit power constraint of the transmitter, and the STAR-RIS reflection phase unit mode constraint, construct a multidimensional variable deep-coupled non-convex optimization problem that includes information transmit power, active beamforming vector, artificial noise precoding matrix, and STAR-RIS reflection phase shift matrix. Step S4: Decoupling and solving the non-convex optimization problem: The non-convex optimization problem is decoupled using an alternating optimization algorithm, and the three sub-problems are solved iteratively until the system's covert transmission rate reaches the convergence condition.

[0009] Furthermore, the specific steps of step S1 include: Step S11: The system detects the spatial location of communication nodes in real time and obtains the quasi-static Rayleigh fading channel state information of each link; Step S12: When the STAR-RIS covert communication system detects that the illegal monitoring end is located in the STAR-RIS transmission coverage area and the legitimate receiving end is located in the reflection coverage area, the system determines that there is a high energy leakage risk in the current communication topology. In response to this determination, the system triggers an active security reconfiguration decision, generates a mode switching command, and forces the STAR-RIS to switch from the dual working mode that allows simultaneous transmission and reflection to the full aperture reflection working mode, that is, the controller forces the transmission amplitude of all units to be zero. Step S13: According to the law of conservation of energy, the electromagnetic energy budget originally allocated to the transmission region is completely recovered and aggregated into the reflection channel, so that the reflection amplitude reaches the theoretical maximum value, i.e. .

[0010] Furthermore, the specific process of transforming the system's concealment requirement into a calculable convex threshold constraint regarding the signal-to-noise ratio received by the illegal monitoring terminal in step S2 includes: Using the Pinsker inequality principle, a theoretical lower bound relationship between the total detection error probability and the Kullback-Leibler divergence is established, and the original concealment constraints are derived by combining them with the system's fundamental concealment constraints: In the formula, This represents the Kullback-Leibler divergence of the observed distribution under two physical assumptions. Let be an arbitrarily small positive constant; where the two physical assumptions include the transmitter not transmitting a signal and the transmitter transmitting a signal; Based on the probability density function of the signal received by the illegal monitoring terminal under two physical assumptions, the Kullback-Leibler divergence is expanded and simplified to obtain the convex threshold constraint condition for the signal-to-noise ratio received by the illegal monitoring terminal: Among them, the ratio of the effective signal received by the illegal monitoring terminal to the total power of artificial noise and the background noise power. The expression is: In the formula, This represents the variance of the received signal at the illegal monitoring end while the transmitting end is transmitting a signal; This represents the variance of the received signal at the illegal monitoring end when the transmitting end is not sending a signal; Indicates the information transmission power. This indicates the direct channel from the sending end to the illegal monitoring end. Indicates satisfaction The active beamforming vector, The variance of the background additive white Gaussian noise at the illegal monitoring end is represented as follows: This is the artificial noise precoding matrix.

[0011] Furthermore, the non-convex optimization problem with deep coupling of multidimensional variables in step S3 is expressed as: In the formula, This represents the received signal-to-interference-plus-noise ratio (SIR) at the legitimate receiver, Bob. Indicates the power of artificial noise emission. This represents the upper limit of the total transmit power of the legal transmitter. For the first Phase shift angle of each reflecting unit.

[0012] Furthermore, the first subproblem of the non-convex optimization problem is the joint optimization subproblem of direct information transmission power and active beamforming. The solution process includes: fixing the artificial noise precoding matrix and the phase shift matrix, using the Cauchy-Schwarz inequality to determine the optimal active beamforming direction to achieve maximum ratio transmission, and using the Dinkelbach method to transform the fractional objective function into a subtraction form. The optimal information transmission power is calculated through one-step iteration to achieve joint optimization of information transmission power and active beamforming vector.

[0013] Furthermore, the second subproblem of the nonconvex optimization problem is the artificial noise precoding matrix optimization subproblem. Its solution process includes: fixing the updated information transmission power, active beamforming vector and phase shift matrix, minimizing the artificial noise interference at the legitimate receiver as the objective, using semi-positive definite relaxation techniques to remove the rank constraint, and transforming the nonconvex artificial noise precoding optimization problem into a convex semi-positive definite programming problem, so as to solve for the optimal artificial noise precoding matrix.

[0014] Furthermore, the third subproblem of the nonconvex optimization problem is the STAR-RIS reflection phase shift matrix optimization subproblem. Its solution process includes: fixing all updated variables in the first two subproblems, analytically decoupling the interference terms in the objective function through complex modulus expansion, transforming the multivariate coupled phase shift optimization problem into a single-variable fractional function about the phase of a single STAR-RIS unit, then performing a one-dimensional search on a preset discrete phase set, updating the optimal phase shift of each STAR-RIS unit one by one, and finally executing the converged resource allocation strategy.

[0015] The beneficial effects of the above technical solution are as follows: 1. This invention can effectively block energy leakage paths and improve the security of cross-side communication. Specifically, this invention uses a geometry-topology-driven STAR-RIS full-aperture reflection mode reconstruction. Based on the real-time spatial location information of the legitimate receiver and the illegitimate monitoring end, it dynamically determines the cross-side scenario and triggers mode switching, forcibly switching STAR-RIS from dual-operation mode to total reflection mode. This physically cuts off the energy leakage path to the illegitimate monitoring end on the transmission side, effectively enhancing the defense dimension and security performance in cross-side communication scenarios.

[0016] 2. This invention can alleviate the limitations of covertness constraints and overcome the shortcomings of traditional rate saturation. Specifically, this invention introduces artificial noise as a dynamic power buffer mechanism through joint resource allocation of artificial noise precoding and active beamforming, effectively removing the limitation of signal transmission power imposed by strict covertness constraints and improving the problem of transmission rate saturation in traditional covert communication schemes.

[0017] 3. This invention reduces the computational complexity of the algorithm and enhances the feasibility of system engineering. Specifically, this invention employs an alternating optimization framework, achieving analytical decoupling through complex modulus expansion. It decomposes the multivariable coupled phase shift optimization problem into a univariate fractional function concerning the phase of a single STAR-RIS unit. Subsequently, a one-dimensional search is performed on a preset set of discrete phases, updating the optimal phase shift of each unit sequentially. This keeps the phase optimization complexity at a level that increases linearly with the number of reflective units, effectively reducing the computational overhead of large-scale intelligent surface systems and demonstrating good engineering deployment feasibility and technical scalability. Attached Figure Description

[0018] Figure 1 A schematic diagram of the geometric topology and physical channel model of a STAR-RIS covert communication system provided in an embodiment of the present invention; Figure 2 This is a curve showing the convergence performance of the covert transmission rate of the alternating optimization algorithm in this embodiment of the invention. Figure 3 This is a graph showing the relationship between the system's covert transmission rate and maximum transmission power in an embodiment of the present invention. Figure 4 This is a graph showing the relationship between the system's covert transmission rate and the covert constraint threshold in an embodiment of the present invention. Figure 5 This is a graph showing the relationship between the system's covert transmission rate and the number of STAR-RIS reflection units in an embodiment of the present invention. Figure 6 This is a graph showing the relationship between the system's covert transmission rate and the number of transmitting antennas in an embodiment of the present invention. Figure 7 This is a graph showing the relationship between the system's covert transmission rate and the noise power of the legitimate receiver in an embodiment of the present invention. Detailed Implementation

[0019] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0020] It should be noted that, unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0021] like Figure 1 As shown, the physical topology model of the STAR-RIS covert communication system mainly includes four communication nodes: equipped with Alice, the transmitter with a single antenna; Bob, the legitimate receiver equipped with a single antenna; Willie, the illegitimate monitoring receiver equipped with a single antenna; and other devices deployed in space equipped with… A reconfigurable smart surface with one reflective unit. In the channel environment of this system topology, there is an objectively direct communication link between the transmitter Alice and the legitimate receiver Bob, as shown in the figure. The path shown in the figure, and Alice's signal can also reach Bob via STAR-RIS reflection, i.e., in the figure. The path shown creates a combined "direct + reflection" equivalent channel at the legitimate receiving end; similarly, a direct monitoring link also exists between the illegitimate monitoring ends Willie and Alice, as shown in the diagram. The path is shown. It is particularly important to emphasize that when this system detects an illegal monitoring terminal located within the STAR-RIS transmission coverage area and whether the legitimate receiving terminal is located within the STAR-RIS reflection coverage area, the system will trigger an active security reconfiguration decision, generating a mode switching command. This will force STAR-RIS to switch from a dual-mode operation allowing simultaneous transmission and reflection to a full-aperture reflection mode, completely severing the original cascaded leakage link from Alice to Willie via STAR-RIS at the physical level. This embodiment assumes Alice is aware of global channel state information to explore the theoretical upper limit of system performance under this geometric topology. Based on the above physical topology and channel environment, this embodiment proposes a joint beamforming and power optimization method for STAR-RIS covert communication, the specific steps of which are as follows: Step S1: Obtain the geometric topology information of the communication system and perform scene-aware dynamic switching: Obtain the real-time spatial location information of the transmitting end, the legitimate receiving end, the illegitimate monitoring end, and STAR-RIS in the communication system; Determine whether the illegitimate monitoring end is located in the transmission coverage area of ​​STAR-RIS and whether the legitimate receiving end is located in the reflection coverage area of ​​STAR-RIS based on the spatial location information; When the determination result is yes, generate a mode switching command to switch STAR-RIS from the dual working mode that allows simultaneous transmission and reflection to the full aperture reflection working mode, that is, force the transmission amplitude of all units of STAR-RIS to zero to physically block the energy leakage path to the transmission coverage area, and set the reflection amplitude of all units to the maximum value based on the principle of energy conservation, so that the power budget originally allocated to the transmission module is completely redirected to the reflection channel.

[0022] Step S2: Constructing the transmission signal vector and establishing concealment constraints: Constructing a transmission signal vector at the transmitting end, the transmission signal vector is composed of an information signal carrying target information and an artificial noise signal used to cover the information signal. Based on the detection error probability of the illegal monitoring end, using the Pinsker inequality and Kullback-Leibler divergence, the concealment requirement of the system is transformed into a calculable convex threshold constraint regarding the signal-to-noise ratio received by the illegal monitoring end.

[0023] Step S3: Construct a multidimensional variable deeply coupled non-convex optimization problem: With the goal of maximizing the covert transmission rate of the legitimate receiver, under the conditions of satisfying the convex threshold constraint, the total transmit power constraint of the transmitter, and the STAR-RIS reflection phase unit mode constraint, construct a multidimensional variable deeply coupled non-convex optimization problem that includes information transmit power, active beamforming vector, artificial noise precoding matrix, and STAR-RIS reflection phase shift matrix.

[0024] Step S4: Decoupling and solving the non-convex optimization problem: The non-convex optimization problem is decoupled using an alternating optimization algorithm, and the three sub-problems are solved iteratively until the system's covert transmission rate reaches the convergence condition.

[0025] The steps of this invention will be described in detail below: Step S1: Obtain the geometric topology information of the STAR-RIS covert communication system and perform dynamic switching for scene awareness.

[0026] Step S11: The STAR-RIS covert communication system detects the spatial location of communication nodes in real time and obtains the quasi-static Rayleigh fading channel state information of each link. Specifically, this includes the direct channel from the transmitter Alice to the legitimate receiver Bob. The direct channel from Alice (the sending end) to Willie (the illegal monitoring end) The channel from Alice to STAR-RIS and the reflection channel from STAR-RIS to Bob Meanwhile, the various reflection units in the STAR-RIS covert communication system ( The reflection amplitude coefficient With transmission amplitude coefficient Strictly adhere to the energy conservation coupling constraint, that is .

[0027] Step S12: When the STAR-RIS covert communication system detects that the illegal monitoring terminal Willie is located in the STAR-RIS's transmission coverage area and the legitimate receiving terminal Bob is located in the reflection coverage area, the system determines that the current communication topology has a high risk of energy leakage. In response to this determination, the system triggers an active security reconfiguration decision, generates a mode switching command, and forcibly switches STAR-RIS from a dual-mode operation that allows simultaneous transmission and reflection to a full-aperture reflection mode, thereby physically cutting off the energy leakage path to the transmission coverage area. Specifically, the controller forcibly sets the transmission amplitude of all units to zero, i.e. .

[0028] Step S13: According to the law of conservation of energy, the electromagnetic energy budget originally allocated to the transmission coverage area is completely recovered and aggregated into the reflection channel, forcing the reflection amplitude to reach its theoretical maximum value, i.e. In this full-aperture reflection mode, the phase shift matrix of STAR-RIS is simplified to a unit-mode diagonal matrix containing only passive reflection phase shifts. ,in, For the first Phase shift angle of each reflecting unit.

[0029] Step S2: Construct the transmitted signal vector and establish concealment constraints.

[0030] Step S21: Construct a model of the transmitting end signal and the legitimate receiving end channel.

[0031] The transmitted signal vector generated by Alice It is composed of the superposition of the data stream carrying target information and the artificial noise vector of the cover signal, and its expression is: (1) in, Symbols representing normalized target information; To meet Active beamforming vector; Information transmission power; These are independent and identically distributed Gaussian artificial noise vectors. The precoding matrix is ​​an artificial noise matrix; and the total transmit power of the STAR-RIS covert communication system is limited by... , This represents the upper limit of Alice's total transmission power.

[0032] After joint transmission via the direct path and the STAR-RIS reflection path, the composite received signal at Bob's end... Represented as: (2) in, The background at the Bob end is additive white Gaussian noise.

[0033] Step S22: Construct the illegal monitoring terminal channel model.

[0034] Since step S1 has completely blocked the cascading leakage link to the transmission coverage area, Willie's received signal is dominated by the direct link. No signal is transmitted at the transmitting end (assuming...). ) and sending signals (assuming Willie's received signal under the two physical states of ) They are represented as follows: (3) in, The background noise at Willie is additive white Gaussian noise.

[0035] exist Under these conditions, the variance of the received signal Its probability density function for: (4) exist Under these conditions, the variance of the received signal Its probability density function for: (5) S23: In order to quantify the signal detection capability of the illegal monitoring terminal Willie, its detection process is modeled as a binary hypothesis testing decision process.

[0036] Specifically, the definition Willie concluded that Alice did not send a signal and supported the hypothesis. Decision-making; definition Willie concluded that Alice was sending a signal and supported the hypothesis. The decision.

[0037] Under this binary decision-making framework, the detection process of the illegal monitoring terminal Willie will face two types of detection errors: false alarm probability, i.e., Alice did not actually send a signal (assuming...). (This is true) but Willie incorrectly determined the probability that it sent a signal, denoted as... The probability of a missed detection, i.e., whether Alice actually sent a signal (assuming...). (This is true) but Willie incorrectly determined the probability that it did not send a signal, denoted as... Under the assumption of equal prior probabilities, Willie's total detection error probability... It is the sum of the two error probabilities mentioned above, that is .

[0038] The core requirement of covert communication lies in severely limiting Willie's ability to reliably distinguish transmission activities, thereby ensuring that its total detection error probability is not lower than a theoretical lower bound threshold close to 1. This fundamental covert constraint is defined as: (6) in, ( ) is an arbitrarily small positive constant used to characterize the preset concealment level required by the system.

[0039] S24: According to Pinsker's inequality theorem, the total detection error probability Kullback-Leibler divergence of observed distributions under two physical assumptions There exists a theoretical lower bound relationship between them, and the derivation of the relational inequality is as follows: (7) The Kullback-Leibler divergence is defined in the continuous domain as: .

[0040] Combined with the system's basic concealment constraints Covert communication requires that the above Kullback-Leibler divergence must satisfy more stringent mathematical boundaries, that is, the original covertness constraint is derived as follows: (8) Step S25: Derivation of Kullback-Leibler divergence expectation and establishment of convex threshold constraint.

[0041] The Kullback-Leibler divergence of the signal received at the Willie end, under two physical assumptions, is defined as follows: Expanding the expected value, we get: (9) in, yes arrive The Kullback-Leibler divergence.

[0042] make ,in, Substituting, we get (10) The requirement for concealment is that Willie's detection performance is close to random guessing, i.e. ( (It is an arbitrarily small constant). Where, Willie's false alarm probability is... (Misjudging as having communication when there is no communication) and the probability of missed detection are: (Misjudging no communication when there is communication). According to Pinsker's inequality in information theory, when When the above conditions are met, the calculable convex threshold constraint regarding the signal-to-noise ratio received by the illegal monitoring end in this invention is: (11) Step S3: Construct a non-convex optimization problem with deep coupling of multidimensional variables.

[0043] Step S31: Construct the received signal-to-interference-plus-noise ratio and objective function for the legitimate receiver.

[0044] Taking into account both the direct communication link from Alice to Bob and the cascaded reconstruction path via STAR-RIS reflection, the received signal-to-interference-plus-noise ratio at the legitimate receiver, Bob, is... The mathematical analytical expression is defined as follows: (12) Accordingly, the maximum achievable covert transmission rate of the legitimate receiver Bob within a given time slot is the objective function of the system. , represented as: (13) Step S32: Determine the final control objective of the system and construct a joint optimization model.

[0045] The ultimate control objective of the system is to maximize the covert transmission rate of the legitimate link while satisfying the concealment constraint. This involves considering the physical and hardware limitations of all parties involved in the system and constructing a mechanism for controlling information transmission power. Active beamforming vector Artificial noise precoding matrix and STAR-RIS passive phase shift matrix The joint optimization model, i.e., a nonconvex optimization problem with deep coupling of multidimensional variables, is specifically expressed as follows: (14) in, This indicates the power emitted by artificial noise.

[0046] Step S33: Analyze the non-convex characteristics and solution difficulties of the non-convex optimization problem with deep coupling of multidimensional variables.

[0047] The multivariate joint optimization model constructed above is subject to several complex physical constraints: among them, the logarithmic fractional implicitness constraint, the artificial noise power constraint including trace operation, and the unit mode constraint of the STAR-RIS reflection unit all exhibit highly non-convex characteristics.

[0048] In addition, four core optimization variables ( There is a deep product coupling between the denominator and numerator in the signal-to-interference-plus-noise ratio (SIR) formula. Mathematically, this problem belongs to the category of non-convex optimization problems that are nondeterministic and polynomial-hard, and cannot be solved directly by standard convex optimization solvers (such as CVX). Therefore, technically, this leads to the need for an alternating optimization algorithm and a step-by-step analytical decoupling strategy in the subsequent step S4.

[0049] Step S4: Decoupling and solving the non-convex optimization problem.

[0050] By decoupling the non-convex optimization problem, three sub-problems are obtained: the joint optimization sub-problem of information transmission power and active beamforming, the optimization sub-problem of artificial noise precoding matrix, and the optimization sub-problem of STAR-RIS reflection phase shift matrix.

[0051] (I) Joint Optimization Subproblem of Information Transmission Power and Active Beamforming Define an equivalent composite channel, which is the superposition of the direct link from Alice to Bob and the channel via the STAR-RIS reflection link. .

[0052] definition ,because and Fixed, therefore Let be a constant. Then the first subproblem of the nonconvex optimization problem can be transformed into: (15) Due to the fractional function ( ),maximize Equivalent to finding the maximum parameter , making existence satisfy Therefore, for the first subproblem, the goal of this step is to find a... , making satisfy .

[0053] Specifically, initialization Through the first The second iteration solves the problem. To obtain the optimal solution ,renew until ( For precision, such as 10 -4 ),at this time .

[0054] For fixed Then it is necessary to obtain the objective function. The maximum value. According to the Cauchy-Schwarz inequality, we get... (16) in, And if and only if and The equality holds if the directions are the same, that is... ( (This is the power gain of the equivalent channel). The first subproblem can then be transformed into: (17) For fixed Substitute Then, the objective function can be transformed into .

[0055] Configure the channel to be non-blocking, i.e. Then it is not difficult to deduce that the objective function changes with... Monotonically increasing, therefore optimal Take the maximum value. That is, to make full use of the total power budget. and Substitute into Dinkelbach update formula have to, (18) Therefore, if we set After the first iteration In the second iteration, substitute calculate We can obtain, (19) therefore The iteration terminates. Therefore... It converges after one iteration.

[0056] (ii) Subproblem of optimizing the artificial noise precoding matrix The core of the second sub-problem is fixing the STAR-RIS phase shift matrix. Information power and beamforming vector Under these conditions, the artificial noise (AN) precoding matrix is ​​optimized. The goal is to minimize the interference of AN on Bob, while simultaneously satisfying the concealment constraint on Willie and the power constraint of AN. Furthermore, the power of AN at Bob's location is... As can be seen from the first subproblem... and .

[0057] Define the equivalent channel of AN at Bob as The information signal leakage power at Willie is (because ); Equivalent channel of AN at Willie The objective function is the interference power of AN at Bob. Perform minimization.

[0058] The second subproblem can then be transformed into: (20) make The concealment constraint can be transformed into: (twenty one) To simplify the differentiation, let ( , , ), then for Differentiation yields (twenty two) By taking the derivative, we can see that The first derivative of is always non-negative (and positive in most cases), therefore It is about It is a strictly monotonically increasing function.

[0059] This means that the interference power of AN on Willie The larger, The larger the value, the easier it is for Willie to detect the presence of the signal. Therefore, it exists. Make The constraints are simplified to The second subproblem can then be transformed into: (twenty three) make ,satisfy and , Let be the AN flow number, usually taken as 1 to reduce complexity. Then, according to the properties of the trace, , , .

[0060] The second subproblem can then be transformed into: (twenty four) Therefore, the second subproblem is transformed into a convex semidefinite programming problem, which can be solved using convex optimization tools such as CVX. Its optimal solution satisfies the following condition, namely the Karush-Kuhn-Tucker (KKT) condition: the existence of Lagrange multipliers. (AN power constraint) and (Hidden constraints) make Simultaneously satisfying the complementary relaxation condition and .

[0061] If the constraint is not tight, the corresponding multiplier is 0, that is, the corresponding Lagrange function is: (25) Since the rank constraint is removed after relaxation, the solution obtained is... The rank may be greater than It needs to be restored to the original variable. .

[0062] Therefore, it can be divided into two situations: if ,Right now ,but (Single-flow AN) directly satisfies the rank constraint of the original problem, requires no approximation, and is the ideal form of the optimal solution; if Then it is necessary to approximate the recovery using the Gaussian randomization method. Eigenvalue decomposition yields ,in, It is an eigenvector. Take the front The eigenvectors corresponding to the largest eigenvalues and eigenvalues ,structure ,at this time The original constraints are approximately satisfied.

[0063] Given that this invention assumes AN to be a single flow, simulation observations show that the vast majority of optimal solutions... satisfy No approximation is needed. This applies to a very small number of cases. In this case, after recovery using the Gaussian randomization method, a scaling factor will be introduced. right Feasibility checks and adjustments are performed until all constraints are strictly satisfied. This guarantee mechanism ensures the physical feasibility of the recovered solution and strictly maintains the hidden constraints, resulting in negligible speed performance loss, making it a primary measure to ensure system security. Therefore, the optimal solution can be obtained. The corresponding AN precoding matrix It satisfies the requirement of minimizing the AN interference at Bob's location and strictly satisfying the AN power constraint and Willie's concealment constraint.

[0064] (III) STAR-RIS reflection phase shift matrix optimization subproblem The goal of the third subproblem is to optimize the phase shift matrix. To maximize Bob's received SINR while satisfying the physical constraints of STAR-RIS, i.e., the phase shift modulus value is 1.

[0065] Define the equivalent channels at Bob as follows: Then the third subproblem can be transformed into: (26) in, ,make (constant, and) (Irrelevant), the signal vector from Alice to STAR-RIS is denoted as The channel vector from STAR-RIS to Bob is denoted as We can obtain, Similarly, we can conclude that ,make (Constant), the AN vector from Alice to STAR-RIS is denoted as .

[0066] Assuming fixed Only optimization .make , , , Then the objective function can be transformed into: (27) Using the properties of the modulus of a complex number as well as , It is a fixed value, that is , These are constants, and for the sake of convenience in formula derivation, they can be temporarily ignored when performing complex modulo operations on the grouped denominators. To ensure correct results, adding these fixed values ​​after the derivation will guarantee the correct values. Therefore, (28) (29) make , All are complex constants. Therefore, the objective function can also be written as: (30) To maximize , need to maximize, Minimize. According to the properties of complex numbers, for the unit complex number... and constant , The maximum value is If and only if ,Right now Similarly, we can conclude that... The minimum value is If and only if ,Right now However, a balance needs to be struck to achieve the optimal result. Therefore, for univariate optimization problems on the unit circle, a one-dimensional search (1D Search) method is used to solve them. The optimal value is determined to ensure that the global optimal solution is obtained within the search precision. feasible domain Uniform discretization Each point defines the search set. ,in, These are the preset discretization accuracy parameters.

[0067] In specific implementation, precise settings This setting enables a phase shift search accuracy of 0.5 degrees. This ensures the extremely high accuracy of the local optimal solution and effectively avoids the performance loss caused by coarse-grained discretization. Next, all discrete phases are traversed. Calculate the corresponding Therefore, we can conclude that ,use replace The first of the matrix diagonal elements Next From 1 to The solution is obtained by calculating the system's covert transmission rate before and after the update. If the absolute value of the difference between the objective function values ​​of two adjacent iterations is less than the preset system convergence accuracy, then the joint optimization algorithm is determined to have reached convergence and the iteration is terminated. in, This is the minimum value, which is set to 10 in this embodiment. -3 And each iteration maximizes the current The corresponding SINR is monotonically non-decreasing and has an upper bound, so the algorithm will inevitably converge to a local optimum. Therefore, we can finally obtain... .

[0068] Furthermore, iteratively solving each subproblem can continuously improve the objective function. Specifically, with a fixed artificial noise precoding matrix... With phase shift matrix In this case, the first subproblem directly maximizes the objective function, i.e., the signal-to-interference-plus-noise ratio (SIR) at the legitimate receiver. Therefore, the updated value must satisfy... At a fixed information transmission power Active beamforming vector and At that time, the second subproblem indirectly improves performance by minimizing artificial noise interference to Bob, the legitimate receiver. Therefore, the updated It will not decrease. (In a fixed position) , and At that time, the third subproblem was to adjust the phase shift to maximize the received signal at Bob's location, ensuring... The objective value is monotonically increasing. The strictly non-decreasing nature of the objective value in the iterative steps inherently guarantees the monotonic evolution of the result sequence. Given that the transmitter power is limited by… The channel gain amplitude is bounded and the positive noise power ( From this, we can deduce that: (31) Obviously, There exists an upper bound. According to the monotonically convergent theorem in mathematical analysis, a monotonically non-decreasing sequence with an upper bound must converge to a certain limit. Because the sequence generated by the algorithm of this invention... It satisfies both the conditions of "monotonically non-decreasing" and "with an upper bound", so theoretically it is strictly guaranteed that it can converge to a local optimum.

[0069] In the specific solution process, firstly, the artificial noise precoding matrix and phase shift matrix are fixed, and the optimal active beamforming direction is determined using the Cauchy-Schwarz inequality to achieve maximum ratio transmission (MRT). The Dinkelbach method is then used to transform the fractional objective function into a subtraction form, and the optimal information transmission power is calculated through a one-step iterative solution. Secondly, the updated information transmission power, active beamforming vector, and phase shift matrix are fixed, and the goal is to minimize artificial noise interference at the legitimate receiver. Semidefinite relaxation (SDR) techniques are used to remove the rank constraint, transforming the non-convex artificial noise precoding optimization problem into a convex semidefinite programming problem. The programmable phase shift optimization (SDP) problem is solved to find the optimal artificial noise precoding matrix. Finally, all other updated variables are fixed, and the interference terms in the objective function are analytically decoupled through complex modulus expansion. The multivariate coupled phase shift optimization problem is transformed into a univariate fractional function of the phase of a single STAR-RIS unit. Then, a one-dimensional search is performed on the preset discrete phase set to update the optimal phase shift of each STAR-RIS unit one by one, and finally, the converged resource allocation strategy is executed.

[0070] This embodiment provides a detailed analysis of the computational complexity of the alternating optimization algorithm. It is assumed that Alice, STAR-RIS, and the artificial noise generator are each configured with... Root antenna, Each reflective unit and The computational complexity analysis of the beams is divided into three independent sub-problems.

[0071] First, the core of the first sub-problem lies in calculating the effective channel. .because yes ( )and ( The product of ), and the diagonal matrix only needs to be multiplied by ). Multiplying corresponding rows has a time complexity of O(n log n). Subsequently, yes ( (vector) and ( The product of matrices. Due to subsequent... and The optimization involves low-order terms, and the total complexity of this subproblem is determined to be... .

[0072] Secondly, the objective function of the second subproblem is to minimize ,in, for Vector, and for Matrix. Expanding this quadratic term yields... ,in, for Matrix, generating The complexity. Then with The multiplication operation produces The complexity is . Therefore, the total complexity is . .

[0073] Finally, in the third subproblem, the optimal phase shift value of each reflecting unit depends on a single The equivalent channel components of the unit need to be calculated. .in, represent The OK( ), and beamforming vector ( The computational complexity of the dot product is . Therefore, calculate sequentially. The computational complexity of one STAR-RIS unit is .

[0074] Furthermore, since the interference terms introduced by the artificial noise path have the same computational order, the overall complexity order remains unchanged. This phase optimization process employs a unit-by-unit iterative optimization strategy with successive coordinate descent. Specifically, for Each of the STAR-RIS units, in A high-precision one-dimensional search is performed on discrete candidate phase points. Since the optimal phase shift of a single element is coupled with the phase shifts of other elements, this sequential update process typically requires a small number of inner iterations to ensure the convergence of the phase matrix. In practice, the number of inner iterations is... This is sufficient to satisfy the convergence requirement. In summary, the total computational complexity of the third subproblem is expressed as: .

[0075] In summary, the overall complexity of each alternating iteration is mainly dominated by the SDP solver and the iterative phase search, i.e.: (32) consider The outermost iteration has a total algorithm complexity of O(n). Although the number of discrete points in a one-dimensional search (e.g.) The number of global iterations required is relatively large. Smaller (approximately 20 times) and inner iterations Very few.

[0076] This method successfully achieves phase optimization accuracy (through high precision). A reasonable trade-off between computational efficiency and overall complexity is achieved, ensuring that the overall complexity is acceptable in practical deployments. The analytical results of the complexity analysis highlight the practical feasibility of the algorithm: at a fixed search resolution... With inner iteration At that time, the computational overhead is relative to the number of STAR-RIS units. exhibiting linear expansion Meanwhile, this linearity effectively avoids the curse of exponential dimensionality typical of exhaustive search, ensuring strong scalability in large-scale hardware deployments. Furthermore, by deriving the analytical solution for decoupling interference terms, the optimization process is simplified to unit-by-unit iterations involving only basic algebraic operations. This avoidance of inverting high-order matrices highlights the framework's extremely hardware-friendly properties for parallel processing. Finally, the parameters... Its flexibility provides a trade-off for dynamic design, enabling the system to strike a balance between near-optimal throughput and the stringent latency requirements of real-time 6G resource scheduling.

[0077] To further verify the effectiveness and beneficial effects of the joint optimization algorithm proposed in this invention, this embodiment provides specific system simulation parameter settings and performance verification results. In the simulation evaluation, the system adopts a two-stage channel processing strategy: the first stage adopts a fully normalized channel gain strategy, that is, the gain of each link is set to 1.0, which aims to eliminate the interference of environmental factors such as large-scale path loss, thereby isolating and verifying the convergence efficiency of the algorithm itself and its ability to mine coherent beamforming gain under an ideal mathematical model; the second stage introduces an asymmetric hybrid gain setting, setting the direct link gain to 1.0 and the STAR-RIS cascaded link attenuation penalty to 0.5, to simulate the inherent physical path loss in actual two-hop links, and to test the algorithm's ability to compensate for attenuation using spatial degrees of freedom under power-constrained and channel fading conditions.

[0078] In a specific embodiment, the core default parameters of the system are configured as follows: the number of antennas of the transmitting end Alice. The number of reflective units in STAR-RIS Artificial noise precoded stream number Maximum total transmission power dBm, the background noise power of both the legitimate receiver and the illegitimate monitoring end is -60dBm, concealment constraint threshold. Number of discrete points in one-dimensional search .

[0079] To highlight the necessity of multi-dimensional resource joint optimization in this invention, four benchmark comparison schemes were designed in the simulation: benchmark scheme 1 (BM1, without STAR-RIS assistance), benchmark scheme 2 (BM2, without artificial noise, i.e. ), Reference scheme 3 (BM3, fixed STAR-RIS phase shift) and reference scheme 4 (BM4, fixed artificial noise precoding).

[0080] Combination Figure 2 The convergence performance curve of the algorithm shows that, dBm and Under representative settings, the alternating optimization algorithm proposed in this invention exhibits explosive performance growth within the initial 5 iterations. Its covert transmission rate achieves approximately 90% steady-state performance improvement and stably converges to the theoretical performance upper limit of approximately 40 bps / Hz within 10 iterations. This smooth and oscillating steady-state convergence trajectory not only verifies the efficiency of the Dinkelbach method in decoupling complex non-convex fractional objectives but also numerically confirms the high compactness of the SDR solver, demonstrating that the algorithm can effectively avoid local traps in non-convex spaces and achieve stable convergence to high-quality local optima.

[0081] Combination Figure 3 and Figure 4 It can be seen that this invention has successfully achieved a fundamental transformation in the system's physical operating mechanism. For example... Figure 3 As shown, the baseline scheme 2, lacking artificial noise buffering, stagnates at a low transmission rate of 14.5 bps / Hz across a wide power range of 10 dBm to 40 dBm. This exposes the rigid power constraint imposed by the stealth constraint in traditional protocols: to avoid exposure, the transmitter is forced to discard most of its available power budget. In contrast, the present invention uses artificial noise as a key dynamic power buffer, successfully breaking the physical power constraint imposed by stealth by precisely injecting interference into the illegal subspace to raise its detection threshold. Under full power conditions, the present invention achieves a performance gain of up to 176% compared to BM2, demonstrating that the system has successfully transitioned from a "stealth-constrained" state to a "power-constrained" state. Meanwhile, as... Figure 4 As shown, when the concealment threshold When the threshold is tightened from 0.30 to 0.05, the concealment rate of the present invention remains locked at a high level and exhibits saturation characteristics, successfully achieving effective decoupling between the performance upper limit and the security threshold, demonstrating extremely strong security robustness.

[0082] Combination Figure 5 and Figure 6 This further reveals the significant advantages of the present invention in terms of spatial degree of freedom gain and resource adaptation. For example... Figure 5 As shown, even with a sparse array of only 5 reflective units, the proposed solution still achieves a high initial concealment rate of 38 bps / Hz. This demonstrates that the instantaneous depth synergy between active precoding and passive phase shift can greatly compensate for the limitations of hardware scale. With the increase in [specific parameters], the performance growth rate slowed down and stabilized around 40 bps / Hz, reflecting that after the algorithm fully released the spatial degrees of freedom, the system quickly reached the physical upper limit determined by the transmit power budget. For example... Figure 6 As shown, increasing the number of transmitting antennas This invention enables the projection of artificial noise onto a wider null space to suppress unauthorized monitoring and protect legitimate signals. However, the fixed phase-shift reference scheme 3 (BM3) has limitations. The severe performance degradation revealed the fatal cost of mismatch between expanding the transmit dimension and static relay configuration: an unoptimized STAR-RIS degenerates into an uncontrollable scatterer, randomly reflecting enhanced artificial noise as severe self-interference, forcing the system to drastically reduce information power to salvage the receiver's signal-to-interference-plus-noise ratio. This invention, through instantaneous joint optimization, ensures that the additional hardware degrees of freedom are fully converted into constructive gains, preventing catastrophic performance loss.

[0083] Finally combined Figure 7 The survivability of this system against severe environmental fluctuations was evaluated. As the background noise power of the legitimate receiver Bob increased, all schemes experienced monotonic rate decay due to signal-to-noise ratio degradation. However, the scheme of this invention maintained the highest covert transmission rate throughout the entire noise degradation range, demonstrating excellent environmental adaptability. Observing the attenuation slope, it can be seen that the baseline scheme lacking artificial noise is extremely sensitive to background noise and exhibits a sharp performance collapse, indicating that traditional architectures lack the resilience to reallocate resources to combat environmental erosion under stringent covert constraints. This invention, through the synergy of artificial noise and spatial modulation, not only effectively weakens the detection capability of illegal monitoring terminals but also anchors the performance baseline for legitimate transmission, ensuring the system's high survivability and robustness in extremely harsh electromagnetic environments.

[0084] In summary, the joint beamforming and power optimization method for STAR-RIS covert communication proposed in this invention has the characteristics of high covert security, effective breakthrough of traditional power blocking bottlenecks, low computational complexity, and strong engineering feasibility.

[0085] Finally, it should be noted that any parts of this invention not described in detail are prior art. Those skilled in the art will understand that the above descriptions are merely preferred embodiments of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A joint beamforming and power optimization method for STAR-RIS covert communication, characterized in that, Includes the following steps: Step S1: Obtain the geometric topology information of the communication system and perform dynamic switching for scene awareness: Obtain the real-time spatial location information of the transmitting end, legitimate receiving end, illegitimate monitoring end, and STAR-RIS in the communication system; Based on the spatial location information, it is determined whether the illegal monitoring terminal is located in the transmission coverage area of ​​STAR-RIS and whether the legitimate receiving terminal is located in the reflection coverage area of ​​STAR-RIS; When the determination result is yes, a mode switching command is generated to switch the STAR-RIS from the dual working mode that allows simultaneous transmission and reflection to the full aperture reflection working mode. Step S2: Constructing the transmission signal vector and establishing concealment constraints: Constructing the transmission signal vector at the transmitting end, the transmission signal vector is composed of an information signal carrying target information and an artificial noise signal used to cover the information signal. Based on the detection error probability of the illegal monitoring end, using the Pinsker inequality and Kullback-Leibler divergence, the concealment requirement of the system is transformed into a calculable convex threshold constraint on the signal-to-noise ratio received by the illegal monitoring end. Step S3: Construct a multidimensional variable deep-coupled non-convex optimization problem: With the goal of maximizing the covert transmission rate of the legitimate receiver, under the conditions of satisfying the convex threshold constraint, the total transmit power constraint of the transmitter, and the STAR-RIS reflection phase unit mode constraint, construct a multidimensional variable deep-coupled non-convex optimization problem that includes information transmit power, active beamforming vector, artificial noise precoding matrix, and STAR-RIS reflection phase shift matrix. Step S4: Decoupling and solving the non-convex optimization problem: The non-convex optimization problem is decoupled using an alternating optimization algorithm, and the three sub-problems are solved iteratively until the system's covert transmission rate reaches the convergence condition.

2. The joint beamforming and power optimization method for STAR-RIS covert communication according to claim 1, characterized in that, The specific steps of step S1 include: Step S11: The system detects the spatial location of communication nodes in real time and obtains the quasi-static Rayleigh fading channel state information of each link; Step S12: When the STAR-RIS covert communication system detects that the illegal monitoring end is located in the STAR-RIS transmission coverage area and the legitimate receiving end is located in the reflection coverage area, the system determines that there is a high energy leakage risk in the current communication topology. In response to this determination, the system triggers an active security reconfiguration decision, generates a mode switching command, and forces the STAR-RIS to switch from the dual working mode that allows simultaneous transmission and reflection to the full aperture reflection working mode, that is, the controller forces the transmission amplitude of all units to be zero. Step S13: According to the law of conservation of energy, the electromagnetic energy budget originally allocated to the transmission region is completely recovered and aggregated into the reflection channel, so that the reflection amplitude reaches the theoretical maximum value, i.e. .

3. The joint beamforming and power optimization method for STAR-RIS covert communication according to claim 1, characterized in that, The specific process of transforming the system's concealment requirement into a calculable convex threshold constraint regarding the signal-to-noise ratio received by the illegal monitoring terminal in step S2 includes: Using the Pinsker inequality principle, a theoretical lower bound relationship between the total detection error probability and the Kullback-Leibler divergence is established, and the original concealment constraints are derived by combining them with the system's fundamental concealment constraints: In the formula, This represents the Kullback-Leibler divergence of the observed distribution under two physical assumptions. Let be an arbitrarily small positive constant; where the two physical assumptions include the transmitter not transmitting a signal and the transmitter transmitting a signal; Based on the probability density function of the signal received by the illegal monitoring terminal under two physical assumptions, the Kullback-Leibler divergence is expanded and simplified to obtain the convex threshold constraint condition for the signal-to-noise ratio received by the illegal monitoring terminal: Among them, the ratio of the effective signal received by the illegal monitoring terminal to the total power of artificial noise and the background noise power. The expression is: In the formula, This represents the variance of the received signal at the illegal monitoring end while the transmitting end is transmitting a signal; This represents the variance of the received signal at the illegal monitoring end when the transmitting end is not sending a signal; Indicates the information transmission power. This indicates the direct channel from the sending end to the illegal monitoring end. Indicates satisfaction The active beamforming vector, The variance of the background additive white Gaussian noise at the illegal monitoring end is represented as follows: This is the artificial noise precoding matrix.

4. The joint beamforming and power optimization method for STAR-RIS covert communication according to claim 1, characterized in that, The nonconvex optimization problem with deep coupling of multidimensional variables in step S3 is expressed as follows: In the formula, This represents the received signal-to-interference-plus-noise ratio (SIR) at the legitimate receiver, Bob. Indicates the power of artificial noise emission. This represents the upper limit of the total transmit power of the legal transmitter. For the first Phase shift angle of each reflecting unit.

5. The joint beamforming and power optimization method for STAR-RIS covert communication according to claim 1, characterized in that, The first subproblem of the nonconvex optimization problem is the joint optimization of direct information transmission power and active beamforming. The solution process includes: fixing the artificial noise precoding matrix and the phase shift matrix, using the Cauchy-Schwarz inequality to determine the optimal active beamforming direction to achieve maximum transmission ratio, and using the Dinkelbach method to transform the fractional objective function into a subtraction form. The optimal information transmission power is then calculated through one-step iteration to achieve joint optimization of information transmission power and active beamforming vector.

6. The joint beamforming and power optimization method for STAR-RIS covert communication according to claim 1, characterized in that, The second subproblem of the nonconvex optimization problem is the artificial noise precoding matrix optimization subproblem. Its solution process includes: fixing the updated information transmission power, active beamforming vector and phase shift matrix, minimizing artificial noise interference at the legitimate receiver as the objective, using positive semidefinite relaxation techniques to remove rank constraints, and transforming the nonconvex artificial noise precoding optimization problem into a convex positive semidefinite programming problem to solve for the optimal artificial noise precoding matrix.

7. The joint beamforming and power optimization method for STAR-RIS covert communication according to claim 1, characterized in that, The third subproblem of the nonconvex optimization problem is the STAR-RIS reflection phase shift matrix optimization subproblem. Its solution process includes: fixing all updated variables in the first two subproblems, decoupling the interference terms in the objective function analytically through complex modulus expansion, transforming the multivariate coupled phase shift optimization problem into a single variable fractional function about the phase of a single STAR-RIS unit, then performing a one-dimensional search on a preset discrete phase set, updating the optimal phase shift of each STAR-RIS unit one by one, and finally executing the converged resource allocation strategy.

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