Covert communication method and system based on partitioned active intelligent reflecting surface and penalty function

Abstract

The invention discloses a covert communication method and system based on a partitioned active intelligent reflecting surface and a penalty function, and belongs to the technical field of wireless communication. According to the method, an optimization problem taking maximization of a security user hiding rate as a target is constructed, and combined optimization of base station mixed signal beam forming and RIS passive beam forming is carried out by combining hardware constraints (a module value in the same sub-block is constant) of block active RIS and utilizing a fractional planning strategy and an alternating optimization algorithm. In the optimization process, a penalty function method is adopted to decouple the non-convex constraint, the auxiliary variable and the penalty constant are updated through iteration, and finally the hiding rate of the system is maximized. Through the block active RIS design, the hardware cost is reduced, meanwhile, the covert communication quality is ensured, and the method is suitable for the safety transmission requirement in a complex wireless communication scene.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a covert communication method and system based on a block-based active intelligent reflecting surface (RIS) and a penalty function, for improving the rate and security of covert communication in a complex channel environment. Background Art

[0002] Reconfigurable Intelligent Surfaces (RIS) are considered a promising key technology candidate for future wireless communication systems. By deploying a large array of steerable phase-shifting elements, this technology dynamically reconfigures the propagation characteristics of wireless channels—directly reflecting incoming electromagnetic waves toward a target area with high array gain. With its low hardware cost and energy consumption advantages, RIS demonstrates significant potential for overcoming signal obstruction, increasing channel capacity, and reducing transmit power. However, the multiplicative fading effect introduced by RIS technology (i.e., the path loss of the transmitter-RIS-receiver link is the product of the transmitter-RIS link and the RIS-receiver link losses, rather than the sum of the two) results in significantly lower gain in the reflected link than in the direct link. In most practical scenarios where direct link strength is dominant, the expected capacity gains from RIS are often difficult to achieve effectively, posing a core issue that needs to be addressed. To overcome this multiplicative fading effect, researchers have proposed active RIS with signal amplification. Unlike traditional passive RIS (Passive RIS), which only supports phase control, active RIS integrates a power amplifier in each radiating element to achieve active gain control of the reflected signal. Theoretical studies have shown that this architecture can transform the channel fading characteristics from a multiplicative mode to an additive mode, thereby achieving significant capacity improvement under arbitrary direct link strength conditions.

[0003] Each RIS unit in active RIS is equipped with an independent power amplifier circuit. However, this architecture can lead to severe power consumption bottlenecks as the array scales. A sub-connected architecture, as an engineering solution for active RIS, allows multiple RIS units to share a single power amplifier module at the sub-array level (each unit still retains independent phase control capabilities). By optimizing hardware resource allocation, overall system power consumption is reduced while maintaining beamforming flexibility. Summary of the Invention

[0004] Technical problem: The purpose of the present invention is to provide a covert communication method and system based on block active intelligent reflecting surface (RIS) and penalty function, which can achieve reliable and secure information transmission while satisfying the power amplifier consistency constraint conditions within the block active RIS sub-block.

[0005] Technical solution: In order to solve the above technical problems, the specific technical solution of the present invention is as follows:

[0006] Step 1: Construct an initialization problem. In this initialization problem, the optimization goal is to maximize the security user and concealment rate, and the base station transmit beam is optimized with the constraints of limited base station transmit power, limited active RIS power, and constant internal modulus value of the same block of block RIS. and RIS passive beam Θ; where w k is the beamforming vector of the base station for the kth security user, K is the number of security users accessing the system, Θ is the block active RIS reflection diagonal matrix, where each RIS sub-block has T RIS units, and RIS is divided into sub-blocks, and M is the number of RIS units.

[0007] Step 2: Use fractional programming strategy and introduce Lagrange dual auxiliary variables and first-order Taylor expansion, transforming the initial fractional optimization problem into its lower bound expression.

[0008] Step 3: Based on the new optimization problem obtained in Step 2, an alternating optimization scheme is employed to jointly optimize the base station mixed-signal active beamforming and the block-based active RIS passive beamforming. In each iteration, a penalty function is employed to decouple the intra-block constant modulus constraint from the block-based active RIS.

[0009] Step 4: Based on the optimal active beamforming and RIS passive beamforming that meet the system constraints after iterative convergence, the current auxiliary variables are obtained The system concealment rate under .

[0010] Step 5: Update auxiliary variables Repeat steps 3 and 4 until the system concealment rate and RIS passive beamforming reach convergence conditions, and the optimal system concealment rate is obtained.

[0011] Furthermore, in step 1, the initialization problem is as follows:

[0012] The optimization goal is to maximize:

[0013]

[0014] The constraints are:

[0015]

[0016] Constraints C1 and C2 limit the maximum output power at the base station and RIS, and constraints C3 and C4 limit the feasible solutions for the phase and modulus of the RIS unit, respectively. Where log(·) represents the logarithm operation with the base being the natural logarithm, |·| represents the norm operation, and Represent the maximum transmit power of the base station and block active RIS respectively. represents the block active RIS reflection diagonal matrix, θ m represents the phase of the mth unit, a l is the modulus value of the lth sub-block. b,i , h w represents the cascade channel between the secure user and the potential eavesdropper, σ 2 In this scenario, assuming that the base station knows the channel state information of all links, each cascade channel is represented as:

[0017]

[0018] Furthermore, in step 2, a fractional programming strategy is adopted to introduce the Lagrangian dual auxiliary variable And Taylor expansion approximation, the initial fraction optimization problem is transformed into its lower bound expression. At the same time, in order to solve the high computational complexity caused by the constant module value of the block active RIS block, the auxiliary variable is introduced Decouple the modulus constraint. γ is a real penalty greater than 0. When γ is large, optimizing the objective function can make the RIS beamforming meet the modulus constraint. The initial optimization problem is transformed into a new linear optimization problem, which is equivalent to the following problem:

[0019]

[0020] The constraints are:

[0021]

[0022]

[0023] in, is the Lagrangian dual auxiliary variable introduced, (·) t Indicates the feasible solution obtained in the previous round. In each iteration, the auxiliary variable The update formula is given as follows:

[0024]

[0025] Furthermore, in step 3, an alternating optimization method is used according to the new optimized beamforming method obtained in step 2. In each iteration, the base station mixed signal and the block-based active RIS beamforming are jointly optimized.

[0026] In the tth iteration, the base station mixed signal beamforming optimization problem is described as follows:

[0027]

[0028] The constraints are:

[0029]

[0030] The above sub-problem P 2.1 In the linear optimization problem, the linear optimization problem can be further simplified as:

[0031]

[0032] Among them, v i , Q i is an intermediate variable related to the base station mixed signal beam, expressed as follows:

[0033]

[0034] The above sub-problems are reduced to quadratically constrained, quadratic programming (QCQP) problems, which can be solved by the optimizer. At the tth iteration, the block-wise active RIS beamforming optimization problem is described as follows:

[0035]

[0036] The constraints are:

[0037]

[0038] The above sub-problem P 2.2 In the linear optimization problem, we can further simplify it into:

[0039]

[0040] The constraints are:

[0041]

[0042] Among them, z, G, and T are intermediate variables related to the block active RIS beam, which are expressed as follows:

[0043]

[0044]

[0045] The above problem is transformed into a QCQP problem, which can be obtained through the Lagrange dual method:

[0046] u=(G+ηT) -1 z

[0047] Where η is the Lagrangian dual variable that satisfies the constraint of the active RIS transmission power of the constrained block, which can be obtained by the bisection method.

[0048] Then, in the tth iteration, with respect to the penalty vector The optimization problem is described as follows:

[0049]

[0050] The constraints are:

[0051]

[0052] Constraints C1, C2 represent The phase value of each unit of is the same as u, and The modulus values of T elements in each sub-block are consistent. To solve the above problem, a Lagrangian dual function is constructed.

[0053]

[0054] Among them, α n =Re{|u n,1 |+|u n,2 |+…+|u n,T |}, λ is a Lagrange multiplier greater than 0. The above function can be solved by the Lagrange multiplier method The modulus value of .

[0055] Furthermore, in step 4, based on the base station mixed signal and block active RIS beamforming obtained in step 3, the system safety capacity under the current beam is calculated and updated. Lagrange dual auxiliary variables.

[0056] Furthermore, in step 5, according to the system safety capacity obtained in step 4 and the auxiliary penalty vector obtained in step 3 Repeat steps 3 and 4 while increasing the penalty constant γ. During each iteration, multiply the penalty constant γ by a constant greater than 1. This continues until the new system's concealment rate reaches convergence and the block-level active RIS modulus satisfies the constraints. The maximum system concealment rate is then determined based on the resulting base station mixed signal active beamforming and RIS passive beamforming.

[0057] In the concealment scenario, the present invention provides a penalty function-based optimization method for maximizing the concealment rate of a block-based active RIS-assisted system, which has the following advantages:

[0058] (1) This invention divides the active RIS into multiple sub-blocks. RIS units within each sub-block share a single power amplifier, and hardware simplification is achieved through unified control of the modulus. Sharing the power amplifier module reduces the number of power amplifiers, significantly reducing hardware complexity and manufacturing costs. Sub-block-level power control avoids the redundant energy consumption of independent unit-level power amplifiers. The consistent modulus within the same sub-block provides a physical basis for subsequent beam optimization.

[0059] (2) The Lagrangian duality and penalty function method adopted in the present invention can achieve the optimal solution of non-convex problems with lower complexity.

[0060] (3) The present invention takes into account the impact of RIS hardware limitations on covert communication performance and adopts a penalty function method to optimize the block-based active RIS phase and modulus, thereby achieving a higher system covert rate while reducing the number of RIS power amplifiers. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 This is a model diagram of a beam optimization method for maximizing the system concealment rate with the assistance of block-based active RIS in the covert communication scenario provided in the first embodiment of the present invention.

[0062] Figure 2 The present invention provides a first embodiment of a covert communication scenario, providing a block-based active RIS-assisted beam optimization method for maximizing the system concealment rate.

[0063] Figure 3 FIG1 is a schematic diagram of simulation results of a beam optimization method for maximizing the system concealment rate with the assistance of block-based active RIS in the covert communication scenario provided in the first embodiment of the present invention. DETAILED DESCRIPTION

[0064] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention.

[0065] The present invention provides a beam optimization method for maximizing the system concealment rate in a covert communication scenario using block-based active RIS assistance. This solution is suitable for scenarios with limited hardware limitations for RIS power amplifiers. The base station sends a mixed communication signal:

[0066]

[0067] By designing the base station to transmit beams and the block active RIS beamforming matrix Θ, which satisfies the base station power constraint, the active RIS power limitation and the constant inner modulus value of the same block of block RIS are the constraints, maximizing the system concealment rate.

[0068] Specifically, in this example, the process of the beam optimization method for maximizing the system concealment rate is as follows: Figure 1 As shown, the specific steps include:

[0069] Step 1: Construct the initialization problem. In this initialization problem, the optimization goal is to maximize the security user and concealment rate, and the base station transmit power is limited, the active RIS power is limited, and the block RIS has a constant internal modulus value. and RIS passive beam Θ; where w k is the beamforming vector of the base station for the kth security user, K is the number of security users accessing the system, Θ is the block active RIS reflection diagonal matrix, where each RIS sub-block has T RIS units, and RIS is divided into sub-blocks, and M is the number of RIS units.

[0070] The initialization problem is as follows:

[0071] The optimization goal is to maximize:

[0072]

[0073] The constraints are:

[0074]

[0075] Constraints C1 and C2 limit the maximum output power at the base station and RIS, and constraints C3 and C4 limit the feasible solutions for the phase and modulus of the RIS unit, respectively. Where log(·) represents the logarithm operation with the base being the natural logarithm, |·| represents the norm operation, and Represent the maximum transmit power of the base station and block active RIS respectively. represents the block active RIS reflection diagonal matrix, θ m represents the phase of the mth unit, a l is the modulus value of the lth sub-block. b,i , h w represents the cascade channel between the secure user and the potential eavesdropper, σ 2 In this scenario, assuming that the base station knows the channel state information of all links, each cascade channel is represented as:

[0076]

[0077] Step 2: Use fractional programming strategy and introduce Lagrange dual auxiliary variables And Taylor expansion, the initial fraction optimization problem is transformed into its lower bound expression. At the same time, in order to solve the high computational complexity caused by the constant module value in the block active RIS block, the auxiliary variable is introduced Decouple the modulus constraint. γ is a penalty greater than 0. When γ is large, optimizing the objective function can make the RIS passive beam meet the constraint conditions. The initial optimization problem is transformed into a new linear optimization problem, which is equivalent to the following problem:

[0078]

[0079] The constraints are:

[0080]

[0081]

[0082] in, is the Lagrangian dual auxiliary variable introduced, (·) t Represents the feasible solution obtained in the previous round.

[0083] Step 3: Based on the new optimized beamforming method obtained in step 2, an alternating optimization method is used. In each iteration, the base station mixed signal and block-based active RIS beamforming are jointly optimized.

[0084] In the tth iteration, the base station mixed signal beamforming optimization problem is described as follows:

[0085]

[0086] The constraints are:

[0087]

[0088] The above sub-problem P 2.1 In the linear optimization problem, the linear optimization problem can be further simplified as:

[0089]

[0090] Among them, v i , Q i is an intermediate variable related to the base station mixed signal beam, expressed as follows:

[0091]

[0092] The above subproblems are reduced to quadratically constrained, quadratic programming (QCQP) problems, which can be solved by an optimizer.

[0093] In the tth iteration, the block-based active RIS beamforming optimization problem is described as follows:

[0094]

[0095] The constraints are:

[0096]

[0097] The above sub-problem P 2.2 In the linear optimization problem, we can further simplify it into:

[0098]

[0099] The constraints are:

[0100]

[0101] Among them, z, G, and T are intermediate variables related to the block active RIS beam, which are expressed as follows:

[0102] The above problem is transformed into a QCQP problem, which can be obtained by Lagrange dual method.

[0103]

[0104] Where η is the Lagrangian dual variable that satisfies the constraint of the active RIS transmission power of the constrained block, which can be obtained by the bisection method.

[0105] Then, in the tth iteration, with respect to the penalty vector The optimization problem is described as follows:

[0106]

[0107] The constraints are

[0108]

[0109] Constraints C1, C2 represent The phase value of each unit of is the same as u, and The modulus values of T elements in each sub-block are consistent. To solve the above problem, a Lagrangian dual function is constructed.

[0110]

[0111] Among them, α n =Re{|u n,1 |+|u n,2 |+…+|u n,T |}, λ is a Lagrange multiplier greater than 0. The above function can be solved by the Lagrange multiplier method The modulus value of .

[0112] Step 4: Based on the base station mixed signal and block active RIS beamforming obtained in step 3, calculate the system safety capacity under the current beam and update Lagrange dual auxiliary variables. In each iteration, the auxiliary variables The update formula is given as follows:

[0113]

[0114] Step 5: Based on the system safety capacity obtained in step 4 and the auxiliary penalty vector obtained in step 3 Repeat steps 3 and 4 while increasing the penalty constant γ. During each iteration, multiply the penalty constant γ by a constant greater than 1. This continues until the new system's concealment rate reaches convergence and the block-level active RIS modulus satisfies the constraints. The maximum system concealment rate is then determined based on the resulting base station mixed signal active beamforming and RIS passive beamforming.

[0115] Application examples:

[0116] To verify the performance of the active and passive beam optimization method for maximizing the system concealment rate provided in this embodiment, a simulation was conducted. This simulation assumes that the concealed users are evenly distributed within a circle with a radius of 5 at coordinates (50, -5). The base station is located at (0, -5) and the RIS is located at (45, 0). We also assume that there is an eavesdropper in this scenario, located at (45, -5). Other simulation parameters are shown in the following table:

[0117] Table 1. Simulation experiment parameter settings

[0118] parameter Value Number of active RIS units in blocks 256 Number of RIS sub-block units [1,4,16] Active RIS maximum power 35dBm*256 Number of hidden users 4 Maximum power of base station 20dBm Base station fixed power consumption 2dBW Ambient additive white Gaussian noise -90dBm RIS phase quantization bits 2

[0119] Figure 2 Comparison results from simulation experiments. To compare the performance of our proposed penalty function-based block-based active RIS beam optimization method with the method proposed in the article "Active Reconfigurable Intelligent Surface: Fully-Connected or Sub-Connected?" Simulation results demonstrate that the proposed active and passive beam optimization scheme significantly improves system concealment efficiency when compared to different beam optimization schemes in the scenario with an increased number of base station antennas.

[0120] It will be understood that the present invention is described by way of certain embodiments, and it will be appreciated by those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to suit specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are intended to be protected by the present invention.

Claims

1. A covert communication method based on block-based active intelligent reflective surface and penalty function, characterized in that: The following steps are involved: Step 1: Construct an initialization problem with the optimization objective of maximizing the concealment rate of the secure user. Constraints include the base station transmit power limit, the active RIS power limit, and the constant modulus value within the same sub-block of the block RIS. Optimize the base station transmit beam and the RIS passive beam. Step 2: Using the fractional programming strategy, introduce Lagrangian dual auxiliary variables, transform the initial fractional optimization problem into a lower bound expression, and introduce auxiliary variables to decouple the block RIS module value constraints; Step 3: Jointly optimize the base station mixed signal beamforming and block-based active RIS beamforming using an alternating optimization method, using a penalty function approach to handle non-convex constraints in each iteration. Step 4: Calculate the system concealment rate based on the optimized beamforming and update the auxiliary variables; Step 5: Repeat steps 3 and 4, increasing the penalty constant until convergence, and obtain the optimal beamforming and maximum concealment rate that meet the constraints.

2. The method according to claim 1, characterized in that The optimization goal in step 1 is to maximize the sum of the secure user concealment rates, and the constraints include: (1) The base station transmission power does not exceed the preset threshold; (2) The total transmission power of the block-based active RIS does not exceed the preset threshold; (3) The phase of the RIS unit satisfies the discrete phase constraint; (4) The modulus values of all units in the same RIS sub-block are the same.

3. The method according to claim 1, characterized in that In step 2, a fractional programming strategy is adopted, and Lagrangian dual auxiliary variables are introduced to transform the initial fractional problem into a lower bound form. At the same time, a penalty function is introduced to transform the block RIS sub-block module value constraint into a penalty term in the objective function, and the constraint condition is gradually approached by adjusting the penalty constant.

4. The method according to claim 1, wherein The alternating optimization in step 3 includes: (1) Fixed RIS passive beamforming to optimize base station mixed signal beamforming; (2) Fixed base station beamforming, optimized block active RIS passive beamforming.

5. The method according to claim 4, characterized in that The block-wise active RIS passive beamforming optimization is solved by Lagrangian dual method and bisection method.

6. The method according to claim 1, characterized in that The penalty constant in step 5 is increased by a fixed multiple in each iteration until the concealment rate and the RIS modulus constraint meet the convergence condition.

7. A covert communication system, characterized in that: include: a base station configured to generate a mixed signal and transmit it to the block active RIS; Block-based active RIS, consisting of multiple sub-blocks, where the RIS units in each sub-block have the same modulus and adjustable phase, used to reflect signals to secure users; A processing unit configured to execute the method according to any one of claims 1 to 6 to optimize base station beamforming and RIS reflection parameters.

8. A block-based active RIS device, used to execute the covert communication method according to any one of claims 1 to 6, characterized in that: include: Multiple sub-blocks, each sub-block contains several RIS units; Power amplifier, each sub-block shares one power amplifier; Phase controller, which independently adjusts the phase of each RIS unit; Among them, the modulus value of all RIS units in the same sub-block is the same.

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