Method for improving security performance of satellite RSMA system based on BD-RIS assistance

Abstract

The application relates to a method for improving the security performance of a satellite RSMA system based on BD-RIS assistance. The method comprises the following steps: according to the concatenated channel coefficients of a satellite to a legal user and an illegal node, decomposing to-be-transmitted information into a public stream and a private stream by using RSMA technology, calculating the receiving signal-to-noise ratio of both parties, and then obtaining the communication rate of the public stream and the private stream of the legal user and the eavesdropping rate of an eavesdropper. A target function is constructed by using the rates, a preset loss function is combined, and a BD-RIS reflection coefficient and satellite transmission beam forming vector optimization model is established. A double-cycle PDD algorithm is adopted for solving, the problem is split by using a BCD method, non-convexity is processed by using SCA, the symmetric unit constraint of the reflection coefficient matrix is first relaxed and then projected, and the optimized vector and matrix are obtained. The system security transmission rate is calculated by using the method, and the security performance is enhanced.

Description

Technical Field

[0001] This application relates to the field of wireless communication technology, and in particular to a method for improving the security performance of a BD-RIS assisted satellite RSMA system. Background Technology

[0002] In recent years, with the rapid development of wireless communication technology, satellite communication has become a core component of future sixth-generation (6G) networks, driving the transformation of global communication infrastructure towards an integrated air-space-ground-sea framework. As a fundamental pillar of this integrated network, satellite communication, with its seamless coverage, ultra-high capacity, and ultra-low latency, can achieve Tbps-level data rates, Kbps / Hz-level spectral efficiency, and millisecond-level latency. These transformative capabilities fill the gaps in traditional terrestrial infrastructure coverage in remote areas, marine environments, and the aviation sector, facilitating the realization of barrier-free global communication.

[0003] However, the broadcast nature of wireless transmission exposes satellite communications to serious security vulnerabilities, potentially allowing malicious eavesdroppers to intercept private data. While traditional encryption mechanisms currently offer some level of security, their reliance on computational complexity makes them increasingly vulnerable to the exponential growth of computing power. Against this backdrop, physical layer security has emerged as a groundbreaking paradigm based on information theory. It leverages the inherent randomness, diversity, and dynamic nature of wireless channels to achieve unconditional security. Unlike encryption methods, physical layer security does not depend on computational complexity and remains robust even against adversaries with unlimited processing power, thus becoming a crucial means of achieving information-theoretical security (a level of protection unattainable by traditional encryption methods).

[0004] While physical layer security offers a new path to secure satellite communications, its practical deployment faces challenges posed by the unique propagation characteristics of satellite channels. Satellite communications must cope with atmospheric attenuation and weather-induced fading, factors that introduce unpredictable path losses and deteriorate channel conditions. Furthermore, the wide coverage of satellites often leads to overlap between the channel coverage areas of legitimate users and eavesdroppers, resulting in high spatial correlation and weakening the effectiveness of traditional physical layer security technologies that rely on channel differences to enhance security, such as artificial noise and beamforming. The lack of efficient technical solutions to suppress the communication performance of unauthorized nodes makes it difficult to meet the security requirements of satellite communications in complex scenarios. Summary of the Invention

[0005] Therefore, it is necessary to provide a method for improving the security performance of the BD-RIS-assisted satellite RSMA system, which can effectively suppress the communication performance of illegal nodes and improve the security performance of the system, in order to address the above-mentioned technical problems.

[0006] A method for improving the security performance of a BD-RIS-assisted satellite RSMA system is provided. The method is applied to a BD-RIS-assisted satellite RSMA system, which includes a satellite transmitting node with multiple antennas, a BD-RIS equipped with multiple reflective elements, a legitimate user receiving node with a direct link that is blocked, and an illegal receiving node with multiple potential eavesdroppers.

[0007] Based on the concatenated channel coefficients from the satellite transmitting node to the legitimate user receiving node and the illegitimate receiving node, RSMA technology is used to decompose the information to be transmitted into a public stream and a private stream, and the received signal-to-noise ratio at the legitimate user and the eavesdropper is calculated. The public stream communication rate and private stream communication rate of the legitimate user and the eavesdropper's eavesdropping rate on the public stream data and the legitimate user are calculated using the received signal-to-noise ratio at the legitimate user and the eavesdropper.

[0008] An objective function is constructed using the public and private communication rates of legitimate users and the eavesdropping rate of eavesdroppers on public data and legitimate users. Based on the objective function and a pre-set loss function, an optimization model of BD-RIS reflection coefficient and satellite transmission beamforming vector is constructed.

[0009] The dual-loop PDD algorithm is used to solve the optimization model of BD-RIS reflection coefficient and satellite transmission beamforming vector. Using the BCD method, the joint optimization problem is decomposed into two sub-problems: satellite transmission beamforming vector design and BD-RIS reflection coefficient matrix optimization. The symmetric unitary constraint on the BD-RIS reflection coefficient matrix is ​​first relaxed and optimized by SCA to handle non-convexity, and then symmetric unitary projection is performed to satisfy the original constraint, so as to obtain the optimized satellite transmission beamforming vector and BD-RIS reflection coefficient matrix.

[0010] The system's security performance is enhanced by calculating the system's secure transmission rate based on the optimized satellite transmission beamforming vector and the BD-RIS reflection coefficient matrix.

[0011] The aforementioned method for improving the security performance of a BD-RIS-assisted satellite RSMA system involves using RSMA technology to split the information to be transmitted into a public stream and a private stream, and designing corresponding beamforming precoding matrices. Simultaneously, based on the CSI between the satellite and legitimate users and eavesdroppers, a Multi-Factor Optimization (MMF) problem is constructed with the objective of maximizing the worst-case security rate for legitimate users. This optimization problem sets multiple constraints, including user service quality requirements, symmetric unitary constraints on the BD-RIS reflection coefficient matrix, satellite transmit power limits, eavesdropper channel uncertainty range, and public rate constraints, ensuring that the optimization process aligns with the needs of actual communication scenarios. To address the complex non-convex nature of this optimization problem, a PDD algorithm with a dual-loop architecture is adopted as the core solution scheme. The inner loop uses the Block Coordinate Descent (BCD) method to decompose the joint optimization task into two sub-problems: satellite transmit beamforming vector design and BD-RIS reflection coefficient matrix optimization. Furthermore, the SCA algorithm is used to transform the original non-convex problem into a tractable convex optimization form. To address the challenge of directly solving the BD-RIS symmetric unitary constraints, this paper first relaxes them into convex constraints and incorporates them into the optimization process. After the problem is solved, a symmetric unitary projection operation is used to ensure that the BD-RIS reflection coefficient matrix satisfies the original constraints. Finally, using the optimized satellite transmit beamforming vector and the BD-RIS reflection coefficient matrix, in-depth calculations and analyses are performed on the system's secure transmission rate. Simulation experiments show that this application significantly enhances the system's security performance while effectively guaranteeing the communication rate, effectively resisting potential eavesdropping threats. It provides a practical technical path for achieving secure and efficient satellite communication in complex environments, fully verifying the effectiveness and reliability of this optimization scheme in practical applications. Attached Figure Description

[0012] Figure 1 This is a block diagram of a satellite RSMA system with BD-RIS total scattering matrix control in one embodiment;

[0013] Figure 2 This is a flowchart illustrating a method for improving the security performance of a BD-RIS-assisted satellite RSMA system in one embodiment. Detailed Implementation

[0014] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0015] The security performance enhancement method for the BD-RIS assisted satellite RSMA system provided in this application can be applied to, for example... Figure 1The satellite RSMA system with BD-RIS total scattering matrix control shown includes a satellite transmitting node with multiple antennas, a BD-RIS equipped with multiple reflector units, a legitimate user receiving node with a direct link obstructed, and multiple illegal receiving nodes for potential eavesdroppers.

[0016] In one embodiment, such as Figure 2 As shown, a method for improving the security performance of a BD-RIS-assisted satellite RSMA system is provided, including the following:

[0017] Step 202: Based on the concatenated channel coefficients from the satellite transmitting node to the legitimate user receiving node and the illegitimate receiving node, RSMA technology is used to decompose the information to be transmitted into a public stream and a private stream, and the received signal-to-noise ratio at the legitimate user and the eavesdropper is calculated; the received signal-to-noise ratio at the legitimate user and the eavesdropper is used to calculate the public stream communication rate and the private stream communication rate of the legitimate user, as well as the eavesdropper's eavesdropping rate on the public stream data and the legitimate user.

[0018] The satellite transmission signal was obtained as follows:

[0019] ;

[0020] in, This represents the satellite transmission beamforming matrix. Represents the transmit beamforming vector of the public signal. The transmit beamforming vector representing the private signal. Symbols representing signals transmitted by satellites.

[0021] Assuming the direct links between the satellite and legitimate users and eavesdroppers are blocked, therefore the first... The first legitimate user and the The received signal of an eavesdropper can be represented as:

[0022] ;

[0023] ;

[0024] in, This represents the reflection coefficient matrix of BD-RIS. and Indicates BD-RIS to the 1st The user and the The channel vector of an eavesdropper This represents the channel matrix from the satellite to BD-RIS. and Indicates the first The user and the The noise at the eavesdropper's location is additive white Gaussian noise, assuming the noise power at the legitimate user's location and the eavesdropper's location are equal, i.e. , J / K represents the Boltzmann constant. Indicates the noise bandwidth. Indicates ambient temperature.

[0025] However, in real-world communication environments, obtaining a perfect CSI from a passive eavesdropper is extremely difficult. To improve the system's robustness, a bounded error model is employed here. To perform modeling, that is:

[0026] ;

[0027] in, This represents the estimated channel vector. Indicates the estimation error. It is a constant greater than zero.

[0028] The received signal-to-noise ratio (SNR) at the legitimate user and the eavesdropper can be calculated based on the channel coefficients from the satellite to the legitimate user and the eavesdropper. After receiving the signal, each user first decodes the public rate, treating all private stream signals as interference during the decoding process. Then, the user... After eliminating the public stream signal and decoding the private stream signal, the signal-to-noise ratio (SNR) of the public data stream and the SNR of the private data stream can be obtained as follows:

[0029] ;

[0030] ;

[0031] in, This indicates the calculation of the square of the modulus. Therefore, it can be used to calculate the user's... The public stream communication rate and the private stream communication rate are and To ensure that all legitimate users can decode public stream data, the public stream data that all users can implement should satisfy the following conditions: The sum of the public flow rates of all users equals ,Right now Therefore, users The total communication rate is .

[0032] Because all eavesdroppers employ a maximum ratio merging strategy to enhance their eavesdropping capabilities, the... The eavesdropper accessed public streaming data and the first The signal-to-noise ratio of eavesdropping on a user's private stream data can be expressed as:

[0033] ;

[0034] ;

[0035] No. The eavesdropper accessed public streaming data and the first The eavesdropping rate of an individual user can be expressed as: and Finally, we can obtain the first... The expression for the secure transmission rate for a single user:

[0036] ;

[0037] in, Indicates the first The shared flow rate allocation coefficient for each user and satisfying the following conditions: , Indicates output A value larger than 0.

[0038] Step 204: Construct an objective function using the public and private flow communication rates of legitimate users and the eavesdropping rate of the eavesdropper on the public flow data and legitimate users. Based on the objective function and the pre-set loss function, construct an optimization model of BD-RIS reflection coefficient and satellite transmission beamforming vector.

[0039] Employing the MMF strategy to maximize The minimum secure transmission rate among all users is used as the objective function:

[0040] ;

[0041] Where constraint C1 represents The service quality requirements for each user, C2 ensures that all users can decode correctly. C3 ensures that the eavesdropper cannot decode correctly. C4 represents the satellite's transmit power constraint, C5 ensures that the public rate of each legitimate user is greater than or equal to 0, C6 represents the symmetric unitary constraint of the BD-RIS reflection coefficient matrix, and C7 represents the uncertainty constraint of the eavesdropper CSI. The complete expression is as follows:

[0042] ;

[0043] in, , This application considers the worst-case channel estimation error. It maximizes the numerator of the eavesdropper's received signal-to-noise ratio and minimizes its denominator, letting... We can obtain:

[0044] ;

[0045] ;

[0046] After introducing channel error, the first The secure transmission rate for a single user can be expressed as follows:

[0047] .

[0048] Step 206: The dual-loop PDD algorithm is used to solve the optimization model of BD-RIS reflection coefficient and satellite transmission beamforming vector. Using the BCD method, the joint optimization problem is decomposed into two sub-problems: satellite transmission beamforming vector design and BD-RIS reflection coefficient matrix optimization. The symmetric unitary constraint on the BD-RIS reflection coefficient matrix is ​​first relaxed and optimized by SCA to handle non-convexity, and then symmetric unitary projection is performed to satisfy the original constraint, so as to obtain the optimized satellite transmission beamforming vector and BD-RIS reflection coefficient matrix.

[0049] By introducing auxiliary variables , , The problem of solving the BD-RIS reflection coefficient and satellite transmitted beamforming vector optimization model is transformed into the following optimization problem:

[0050] ;

[0051] C17 is obtained by relaxing constraint C6. Finally, solving this optimization problem yields the result. It is also necessary to perform a symmetric unitary projection to map it into a symmetric unitary matrix.

[0052] To effectively handle the optimization problem P2, a PDD framework with a double-loop structure is adopted. First, a penalty factor is introduced. This allows us to construct an augmented Lagrange problem from the original optimization problem. To construct the Lagrange problem, we introduce auxiliary variables. Come on This is converted into an equality constraint, i.e., Substituting this equality constraint as a penalty term into the objective function, we get:

[0053] ;

[0054] Among them, the penalty factor , It is a dual variable.

[0055] In the double-loop iterative structure of the PDD framework, the inner loop focuses on solving the augmented Lagrange problem, while the outer loop is responsible for updating the dual variable and the penalty factor. To address the coupling characteristics of the optimization variables in the inner loop, the BCD algorithm is used to decompose the augmented Lagrange problem into two independent sub-problem modules, which are then processed separately. and The solution is then performed. In each internal iteration, variable decoupling is achieved by alternately fixing one module and optimizing another, forming a closed-loop iterative solution process. This approach ensures step-by-step processing and convergence guarantees for complex optimization problems.

[0056] The inner loop iterates over the two sub-problem modules. and Solve alternately. First, fix... This sub-question section, regarding To solve this problem, the optimization problem can be transformed into the following form:

[0057] ;

[0058] The nonconvexity of this subproblem stems from... Here, a first-order Taylor expansion method is used to transform these non-convex constraints into convex expressions.

[0059] ;

[0060] ;

[0061] ;

[0062] Finally, this sub-problem... The values ​​of the optimization variables obtained in the second iteration can be expressed as: .

[0063] Secondly, fixed right Solving this problem, the optimization subproblem can be represented as follows:

[0064] ;

[0065] In this subproblem, all constraints are non-convex. Here, we use the first-order Taylor expansion method to transform these non-convex constraints into convex constraints, as shown below:

[0066] ;

[0067] .

[0068] After the above transformation, this subproblem can be solved using the CVX package. However, the solution to this subproblem yields... It is not a symmetric unitary matrix. Here, we use a symmetric unitary projection method to map it into a symmetric unitary matrix. The definitions of symmetric projection and unitary projection are as follows:

[0069] ;

[0070] ;

[0071] in, and They are The left and right singular value matrices obtained by performing singular value decomposition are, i.e., , It is a diagonal matrix. Here... and Partitioning can yield and Therefore, we can obtain:

[0072] ;

[0073] in, , .

[0074] The calculation is obtained from the inner loop in the outer loop. right The penalty factor and dual variable are iteratively updated. Here, the constraint violation function is... Define:

[0075] ;

[0076] if In the outer loop In the next iteration, it is less than the preset value. Then the penalty factor The dual variable remains unchanged, while the dual variable remains unchanged. Updated based on gradient descent. The update criteria are expressed as follows:

[0077] ;

[0078] Conversely, if In the outer loop In the next iteration, it is greater than the preset value. Then the penalty factor Iterate using the following method:

[0079] ;

[0080] in, .

[0081] Step 208: Calculate the system's secure transmission rate based on the optimized satellite transmission beamforming vector and BD-RIS reflection coefficient matrix to enhance the system's security performance.

[0082] The system's secure transmission rate was calculated and analyzed using the optimized satellite transmission beamforming vector and BD-RIS reflection coefficient matrix. The results show that this scheme significantly improves system security performance while maintaining communication speed, effectively resisting eavesdropping threats and providing a feasible technical path for secure and efficient satellite communication transmission, thus verifying the effectiveness and reliability of this application.

[0083] The aforementioned method for improving the security performance of a BD-RIS-assisted satellite RSMA system involves using RSMA technology to split the information to be transmitted into a public stream and a private stream, and designing corresponding beamforming precoding matrices. Simultaneously, based on the CSI between the satellite and legitimate users and eavesdroppers, a Multi-Factor Optimization (MMF) problem is constructed with the objective of maximizing the worst-case security rate for legitimate users. This optimization problem sets multiple constraints, including user service quality requirements, symmetric unitary constraints on the BD-RIS reflection coefficient matrix, satellite transmit power limits, eavesdropper channel uncertainty range, and public rate constraints, ensuring that the optimization process aligns with the needs of actual communication scenarios. To address the complex non-convex nature of this optimization problem, a PDD algorithm with a dual-loop architecture is adopted as the core solution scheme. The inner loop uses the Block Coordinate Descent (BCD) method to decompose the joint optimization task into two sub-problems: satellite transmit beamforming vector design and BD-RIS reflection coefficient matrix optimization. Furthermore, the SCA algorithm is used to transform the original non-convex problem into a tractable convex optimization form. To address the challenge of directly solving the BD-RIS symmetric unitary constraints, this paper first relaxes them into convex constraints and incorporates them into the optimization process. After the problem is solved, a symmetric unitary projection operation is used to ensure that the BD-RIS reflection coefficient matrix satisfies the original constraints. Finally, using the optimized satellite transmit beamforming vector and the BD-RIS reflection coefficient matrix, in-depth calculations and analyses are performed on the system's secure transmission rate. Simulation experiments show that this application significantly enhances the system's security performance while effectively guaranteeing the communication rate, effectively resisting potential eavesdropping threats. It provides a practical technical path for achieving secure and efficient satellite communication in complex environments, fully verifying the effectiveness and reliability of this optimization scheme in practical applications.

[0084] In one embodiment, the received signals received by the legitimate user receiving node and the illegitimate receiving node are as follows:

[0085] ;

[0086] ;

[0087] in, and They represent the first The first legitimate user and the The eavesdropper's received signal This represents the reflection coefficient matrix of BD-RIS. and Indicates BD-RIS to the 1st The user and the The channel vector of an eavesdropper This represents the channel matrix from the satellite to BD-RIS. and Indicates the first The user and the Additive white Gaussian noise at the location of the eavesdropper. , J / K represents the Boltzmann constant. Indicates the noise bandwidth. Indicates ambient temperature.

[0088] In one embodiment, RSMA technology is used to decompose the information to be transmitted into a public stream and a private stream, and the received signal-to-noise ratio at the legitimate user and the eavesdropper is calculated, including:

[0089] In the After receiving the signal, each user decodes the public rate and treats all private stream signals as interference. The public stream signal is eliminated, and the private stream signal is decoded to obtain the user's signal. The signal-to-noise ratio (SNR) of the public data stream and the SNR of the private data stream are:

[0090] ;

[0091] ;

[0092] middle, This indicates the calculation of the square of the modulus. This represents the reflection coefficient matrix of BD-RIS. Indicates BD-RIS to the 1st Channel vectors for each user, This represents the channel matrix from the satellite to BD-RIS. Indicates the satellite transmit beamforming vector. Represents the transmit beamforming vector of the public signal. The transmit beamforming vector representing the private signal. These represent the noise power at the legitimate user's location and the eavesdropper's location, respectively. J / K represents the Boltzmann constant. Indicates the noise bandwidth. Indicates ambient temperature;

[0093] Then calculate the first The eavesdropper accessed public streaming data and the first The signal-to-noise ratio of eavesdropping on a user's private stream data is:

[0094] ;

[0095] ;

[0096] in, Indicates BD-RIS to the 1st The channel vector of an eavesdropper Indicates the first The signal-to-noise ratio of a single eavesdropper listening to public streaming data. Indicates the first The eavesdropper on the first The signal-to-noise ratio of eavesdropping on a user's private stream data.

[0097] In one embodiment, calculating the public stream communication rate and private stream communication rate of the legitimate user, as well as the eavesdropping rate of the eavesdropper on the public stream data and the legitimate user, using the received signal-to-noise ratio at the legitimate user and the eavesdropper, includes:

[0098] Using legitimate users Received signal-to-noise ratio calculation for legitimate users The public stream communication rate and the private stream communication rate are respectively and ;

[0099] Calculate the first using the received signal-to-noise ratio at the eavesdropper's location. The eavesdropper accessed public streaming data and the first The eavesdropping rate for each user is and .

[0100] In one embodiment, a target function is constructed using the public stream communication rate and private stream communication rate of legitimate users, as well as the eavesdropping rate of the eavesdropper on the public stream data and the legitimate user, including:

[0101] The objective function is constructed by utilizing the public and private flow communication rates of legitimate users, as well as the eavesdropping rate of the eavesdropper on the public flow data and the legitimate user's eavesdropping rate:

[0102] ;

[0103] in, Indicates the first Secure transmission rate for each user Indicates the first The shared flow rate allocation coefficient for each user and satisfying the following conditions: , Indicates output Values ​​larger than 0 Indicates a legitimate user Public stream communication rate, Indicates the first The rate at which an eavesdropper can eavesdrop on public streaming data. Indicates a legitimate user Private stream communication rate, Indicates the first The eavesdropper on the first The eavesdropping rate per user This represents the public rate for legitimate users.

[0104] In one embodiment, an optimization model for the BD-RIS reflection coefficient and satellite transmitted beamforming vector is constructed based on the objective function and a pre-set loss function, including:

[0105] Based on the objective function and a pre-defined loss function, the optimization model for BD-RIS reflection coefficients and satellite transmitted beamforming vectors is constructed as follows:

[0106] ;

[0107] in, Indicates the first Secure transmission rate for each user Indicates a legitimate user Public stream communication rate, Indicates a legitimate user Private stream communication rate, Indicates the first The rate at which an eavesdropper can eavesdrop on public streaming data. Indicates the estimation error. This represents the reflection coefficient matrix of BD-RIS. Represents the identity matrix. Represents the set of public rates for legitimate users. Indicates a legitimate user public rate, This indicates that the eavesdroppers have gathered. This represents the satellite transmission beamforming matrix. Indicates the satellite's maximum transmission power. This indicates the service quality requirements of satellite users. Represents the set of legitimate users. It is a constant greater than zero.

[0108] In one embodiment, before solving the BD-RIS reflection coefficient and satellite transmitted beamforming vector optimization model using the dual-loop PDD algorithm, the following steps are also included:

[0109] By introducing auxiliary variables , , The problem of solving the optimization model of BD-RIS reflection coefficient and satellite transmitted beamforming vector is transformed into the following optimization problem:

[0110] ;

[0111] in, , , , , , , , , , This represents the intermediate variables used in calculating the BD-RIS reflection coefficient and the satellite transmit beamforming vector. This represents the reflection coefficient matrix of BD-RIS. Indicates the first The shared flow rate allocation coefficient for each user Indicates the satellite transmit beamforming vector. Represents the transmit beamforming vector of the public signal. The transmit beamforming vector representing the private signal. These represent the noise power at the legitimate user's location and the eavesdropper's location, respectively. J / K represents the Boltzmann constant. Indicates the noise bandwidth. Indicates ambient temperature. This indicates the service quality requirements of satellite users. Indicates satellite to user Cascaded channels, Indicates satellite to eavesdropper Cascaded channels.

[0112] In one embodiment, a dual-loop PDD algorithm is used to solve the optimization model of BD-RIS reflection coefficient and satellite transmitted beamforming vector, including:

[0113] The double-loop PDD algorithm is adopted, and a penalty factor is introduced. Construct an augmented Lagrangian problem for the original optimization problem and introduce auxiliary variables. Come on This is converted into an equality constraint, i.e., Substituting the equality constraints as penalty terms into the objective function yields:

[0114] ;

[0115] Among them, the penalty factor , It is a dual variable.

[0116] In the double-loop PDD algorithm, the inner loop focuses on solving the augmented Lagrange problem, while the outer loop is responsible for updating the dual variable and the penalty factor.

[0117] In one embodiment, the BCD method is used to decompose the joint optimization problem into two sub-problems: satellite transmit beamforming vector design and BD-RIS reflection coefficient matrix optimization.

[0118] Using the BCD method, the joint optimization problem is decomposed into two sub-problems: satellite launch beamforming vector design and BD-RIS reflection coefficient matrix optimization. These sub-problems are then addressed separately. and Solve the problem.

[0119] The inner loop iterates over the two sub-problem modules. and Perform alternating solutions, first fix... This sub-question section, regarding Solving the problem, the optimization problem is transformed into the following form:

[0120] ;

[0121] Secondly, fixed right The optimization subproblem is represented as follows:

[0122] ;

[0123] in, Represents equality constraints, penalty factor , It is a dual variable. Indicates auxiliary variables;

[0124] The subproblems are solved using the CVX package.

[0125] In one embodiment, the calculation is obtained from the inner loop in the outer loop. right Iterative updates are performed on the penalty factor and dual variable, and the constraint violation function is updated. Defined as:

[0126] ;

[0127] in, Represents auxiliary variables. This indicates the number of reflective elements in BD-RIS;

[0128] if In the outer loop In the next iteration, it is less than the preset value. Then the penalty factor The dual variable remains unchanged, while the dual variable remains unchanged. Updated based on gradient descent The update criteria are expressed as follows:

[0129] ;

[0130] Conversely, if In the outer loop In the next iteration, it is greater than the preset value. Then the penalty factor The iteration is performed according to the following formula, expressed as:

[0131] ;

[0132] in, .

[0133] It should be understood that, although Figure 2 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 2 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0134] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0135] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for improving the security performance of a BD-RIS-assisted satellite RSMA system, characterized in that, The method is applied to a BD-RIS-assisted satellite RSMA system, which includes a satellite transmitting node configured with multiple antennas, a BD-RIS equipped with multiple reflector units, a legitimate user receiving node with a direct link that is blocked, and an illegal receiving node with multiple potential eavesdroppers. Based on the concatenated channel coefficients from the satellite transmitting node to the legitimate user receiving node and the illegitimate receiving node, RSMA technology is used to decompose the information to be transmitted into a public stream and a private stream, and the received signal-to-noise ratio at the legitimate user and the eavesdropper is calculated. The public stream communication rate and private stream communication rate of the legitimate user, as well as the eavesdropping rate of the eavesdropper on the public stream data and the legitimate user, are calculated using the received signal-to-noise ratio at the legitimate user and the eavesdropper. An objective function is constructed using the public and private flow communication rates of the legitimate users and the eavesdropping rate of the eavesdropper on the public flow data and the legitimate users. Based on the objective function and a pre-set loss function, an optimization model for the BD-RIS reflection coefficient and satellite transmission beamforming vector is constructed. The dual-loop PDD algorithm is used to solve the optimization model of the BD-RIS reflection coefficient and the satellite transmission beamforming vector. Using the BCD method, the joint optimization problem is decomposed into two sub-problems: satellite transmission beamforming vector design and BD-RIS reflection coefficient matrix optimization. The symmetric unitary constraint on the BD-RIS reflection coefficient matrix is ​​first relaxed and optimized by SCA to handle non-convexity, and then symmetric unitary projection is performed to satisfy the original constraint, so as to obtain the optimized satellite transmission beamforming vector and BD-RIS reflection coefficient matrix. The system's secure transmission rate is calculated based on the optimized satellite transmission beamforming vector and the BD-RIS reflection coefficient matrix to enhance the system's security performance. Based on the objective function and a pre-set loss function, an optimization model for the BD-RIS reflection coefficient and satellite transmission beamforming vector is constructed, including: Based on the objective function and the pre-set loss function, an optimization model for BD-RIS reflection coefficient and satellite transmission beamforming vector is constructed as follows: in, Indicates the first Secure transmission rate for each user Indicates a legitimate user Public stream communication rate, Indicates a legitimate user Private stream communication rate, Indicates the first The rate at which an eavesdropper can eavesdrop on public streaming data. Indicates the estimation error. This represents the reflection coefficient matrix of BD-RIS. Represents the identity matrix. Represents the set of public rates for legitimate users. Indicates a legitimate user public rate, This indicates that the eavesdroppers have gathered. This represents the satellite transmission beamforming matrix. Indicates the satellite's maximum transmission power. This indicates the service quality requirements of satellite users. Represents the set of legitimate users. It is a constant greater than zero; Before using the dual-loop PDD algorithm to solve the BD-RIS reflection coefficient and satellite transmitted beamforming vector optimization model, the following steps are also included: By introducing auxiliary variables , , The problem of solving the BD-RIS reflection coefficient and satellite transmitted beamforming vector optimization model is transformed into the following optimization problem: in, , , , , , , , , , This represents the intermediate variables used in calculating the BD-RIS reflection coefficient and the satellite transmit beamforming vector. This represents the reflection coefficient matrix of BD-RIS. Indicates the first The shared flow rate allocation coefficient for each user Indicates the satellite transmit beamforming vector. Represents the transmit beamforming vector of the public signal. The transmit beamforming vector representing the private signal. These represent the noise power at the legitimate user's location and the eavesdropper's location, respectively. J / K represents the Boltzmann constant. Indicates the noise bandwidth. Indicates ambient temperature. This indicates the service quality requirements of satellite users. Indicates satellite to user Cascaded channels, Indicates satellite to eavesdropper Cascaded channels; The dual-loop PDD algorithm is used to solve the optimization model of the BD-RIS reflection coefficient and the satellite transmitted beamforming vector, including: The double-loop PDD algorithm is adopted, and a penalty factor is introduced. Construct an augmented Lagrangian problem for the original optimization problem and introduce auxiliary variables. Come on This is converted into an equality constraint, i.e., Substituting the equality constraints as penalty terms into the objective function yields... Among them, the penalty factor , It is a dual variable. Indicates the number of elements in BD-RIS; In the described double-loop PDD algorithm, the inner loop focuses on solving the augmented Lagrange problem, while the outer loop is responsible for updating the dual variable and the penalty factor.

2. The method according to claim 1, characterized in that, The received signals obtained by the legitimate user receiving node and the illegitimate receiving node are respectively in, and They represent the first The first legitimate user and the The eavesdropper's received signal This represents the reflection coefficient matrix of BD-RIS. and Indicates BD-RIS to the 1st The user and the The channel vector of an eavesdropper This represents the channel matrix from the satellite to BD-RIS. and Indicates the first The user and the Additive white Gaussian noise at the location of the eavesdropper. , J / K represents the Boltzmann constant. Indicates the noise bandwidth. Indicates ambient temperature. Symbols representing signals transmitted by satellites.

3. The method according to claim 1, characterized in that, RSMA technology is used to decompose the information to be transmitted into a public stream and a private stream, and the received signal-to-noise ratio at the legitimate user and the eavesdropper is calculated, including: In the After receiving the signal, each user decodes the public rate and treats all private stream signals as interference. The public stream signal is eliminated, and the private stream signal is decoded to obtain the user's signal. The signal-to-noise ratio of the public data stream and the signal-to-noise ratio of the private data stream are: in, This indicates the calculation of the square of the modulus. This represents the reflection coefficient matrix of BD-RIS. Indicates BD-RIS to the 1st Channel vectors for each user, This represents the channel matrix from the satellite to BD-RIS. Indicates the satellite transmit beamforming vector. Represents the transmit beamforming vector of the public signal. The transmit beamforming vector representing the private signal. These represent the noise power at the legitimate user's location and the eavesdropper's location, respectively. J / K represents the Boltzmann constant. Indicates the noise bandwidth. Indicates ambient temperature; Then calculate the first The eavesdropper accessed public streaming data and the first The signal-to-noise ratio of eavesdropping on a user's private stream data is: in, Indicates BD-RIS to the 1st The channel vector of an eavesdropper Indicates the first The signal-to-noise ratio of a single eavesdropper listening to public streaming data. Indicates the first The eavesdropper on the first The signal-to-noise ratio of eavesdropping on a user's private stream data.

4. The method according to claim 3, characterized in that, Calculating the public stream communication rate and private stream communication rate of the legitimate user, as well as the eavesdropping rate of the eavesdropper on the public stream data and the legitimate user, using the received signal-to-noise ratio at the legitimate user and the eavesdropper, includes: Using the aforementioned legitimate user Received signal-to-noise ratio calculation for legitimate users The public stream communication rate and the private stream communication rate are respectively and ; Calculate the first using the received signal-to-noise ratio at the eavesdropper's location. The eavesdropper accessed public streaming data and the first The eavesdropping rate for each user is and .

5. The method according to claim 1, characterized in that, A target function is constructed using the public stream communication rate and private stream communication rate of the legitimate users, as well as the eavesdropping rate of the eavesdropper on the public stream data and the legitimate users, including: The objective function is constructed using the public and private flow communication rates of the legitimate users, as well as the eavesdropping rate of the eavesdropper on the public flow data and the legitimate users. in, Indicates the first Secure transmission rate for each user Indicates the first The shared flow rate allocation coefficient for each user and satisfying the following conditions: , Indicates output Values ​​larger than 0 Indicates a legitimate user Public stream communication rate, Indicates the first The rate at which an eavesdropper can eavesdrop on public streaming data. Indicates a legitimate user Private stream communication rate, Indicates the first The eavesdropper on the first The eavesdropping rate per user This represents the public rate for legitimate users.

6. The method according to claim 1, characterized in that, Using the BCD method, the joint optimization problem is decomposed into two sub-problems: satellite transmission beamforming vector design and BD-RIS reflection coefficient matrix optimization, including: Using the BCD method, the joint optimization problem is decomposed into two sub-problems: satellite launch beamforming vector design and BD-RIS reflection coefficient matrix optimization. These sub-problems are then addressed separately. and Solve the problem. The inner loop iterates over the two sub-problem modules. and Perform alternating solutions, first fix... This sub-question section, regarding Solving the optimization problem, the problem is transformed into the following form: Secondly, fixed right The optimization subproblem is solved as follows: in, Represents equality constraints, penalty factor , It is a dual variable. Indicates auxiliary variables; The subproblems are solved using the CVX package.

7. The method according to claim 1, characterized in that, The method further includes: The calculation is obtained from the inner loop in the outer loop. right Iterative updates are performed on the penalty factor and dual variable, and the constraint violation function is updated. Define as in, Represents auxiliary variables. Indicates the number of elements in BD-RIS; if In the outer loop In the next iteration, it is less than the preset value. Then the penalty factor The dual variable remains unchanged, while the dual variable remains unchanged. Updated based on gradient descent The update criteria are expressed as follows: Conversely, if In the outer loop In the next iteration, it is greater than the preset value. Then the penalty factor The iteration is performed according to the following formula, expressed as: in, .

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