Steerable antenna-based covert communication system transmission rate enhancement method and related equipment

Abstract

The embodiment of the invention provides a steerable antenna-based covert communication system transmission rate enhancement method and related equipment, and belongs to the technical field of wireless communication. The method comprises the following steps: introducing an antenna pointing vector and a deflection angle pair to represent the three-dimensional direction of a single steerable antenna, establishing a channel model related to the antenna deflection angle pair, and deducing a hidden rate expression of a legal user; deducing a hidden constraint condition expression of the illegal user side by using the channel model; according to the concealment rate expression and the concealment constraint condition expression, constructing a joint optimization problem taking maximization of the concealment rate of the legal user as a target and taking concealment constraint, transmitting power constraint and antenna steering angle constraint as conditions; and solving the joint optimization problem to obtain an optimized transmitting beam forming vector and a deflection angle pair of the steerable antenna. The antenna orientation is dynamically adjusted, the spatial degree of freedom is fully excavated, and the transmission rate of the system can be remarkably improved on the premise of strictly ensuring the communication concealment.

Description

Technical Field

[0001] This application relates to the field of wireless communication technology, and in particular to a method and related equipment for enhancing the transmission rate of a covert communication system based on a steerable antenna. Background Technology

[0002] Covert communication, also known as low-probability-of-detection communication, aims to conceal the existence of communication activities and represents a cutting-edge paradigm in wireless communication security. Unlike traditional encryption technologies that protect information content, covert communication strives to make it impossible for unauthorized eavesdroppers to detect the existence of communication signals, playing a crucial role in military, financial, and civilian scenarios with high privacy requirements.

[0003] Existing covert communication technologies are mostly based on fixed antenna systems, using methods such as power control and artificial noise injection to reduce the probability of detection. However, fixed antenna systems have limited spatial freedom; their antenna position and radiation direction cannot be dynamically adjusted, which fundamentally restricts further improvements in system performance. Specifically, fixed antennas struggle to dynamically and accurately focus signal energy onto legitimate users in complex environments while avoiding the detection areas of potential illegitimate users, making it difficult to achieve both covert transmission speed and reliability.

[0004] In recent years, reconfigurable antenna technology, such as steerable antennas, has attracted attention due to its ability to dynamically adjust its radiation pattern. Steerable antennas change the direction of the main lobe of a single antenna element mechanically or electronically, thereby introducing a new spatial dimension of freedom into the system. However, there are currently no systematic applications of steerable antennas in covert communication. Summary of the Invention

[0005] The main objective of this application is to propose a method, electronic device, storage medium, and program product for enhancing the transmission rate of a covert communication system based on steerable antennas. By jointly optimizing the transmit beamforming and the deflection angle of all steerable antennas, the directional gain pattern of the array is dynamically reconstructed, thereby significantly improving the transmission rate of legitimate users while ensuring the covertness of communication.

[0006] To achieve the above objectives, one aspect of this application proposes a method for enhancing the transmission rate of a covert communication system based on steerable antennas. This method is applied to a covert communication system comprising a transmitter, a legitimate user, and at least one unauthorized user. The transmitter is equipped with an antenna array consisting of multiple steerable antennas. The method includes the following steps: Antenna pointing vector and deflection angle pair are introduced to characterize the three-dimensional orientation of a single steerable antenna. A channel model related to the antenna deflection angle pair is established, and the covert rate expression of legitimate users is derived based on the channel model. Using the aforementioned channel model, the hidden constraint condition expression for the illegal user terminal is derived; Based on the covert rate expression of the legitimate user and the covert constraint expression, a joint optimization problem is constructed with the objective of maximizing the covert rate of the legitimate user and the conditions of covertness constraint, transmit power constraint and antenna turning angle constraint. The optimization variables of the joint optimization problem include the transmit beamforming vector and the deflection angle pairs of all steerable antennas. Solving the joint optimization problem yields an optimized transmit beamforming vector and a deflection angle pair for the steerable antenna, which can then be used for downlink transmission in the covert communication system.

[0007] In some embodiments, the yaw angle pair includes pitch and azimuth; The pointing vector of a steerable antenna is represented as:

[0008]

[0009]

[0010]

[0011] in, Indicates the pitch angle, Indicates the azimuth angle; The pitch angle is limited to a preset steering range: ; This indicates the maximum allowable deflection angle for a steerable antenna.

[0012] In some embodiments, the establishment of the channel model includes: Based on the inner product between the pointing vector and the unit direction vector pointing from the steerable antenna to the user, determine the first... The directional gain of the steerable antenna in the user direction is: ,in, For maximum main lobe gain, As a directional factor, For the first The angle between the line-of-sight vector of the steerable antenna and the user direction vector; No. A steerable antenna to the user The complex channel is represented as:

[0013] in, For the deflection angle pair, For channel power gain, For transmission distance, The carrier wavelength.

[0014] In some embodiments, deriving the hidden constraint expression of the unauthorized user terminal includes: Based on a binary hypothesis testing model, determine the minimum detection error probability of unauthorized users. Compared with the received signal power The relationship between them; By setting a lower bound for the minimum detection error probability, the concealment constraint is equivalently transformed into an explicit upper bound constraint on the received power of unauthorized users:

[0015] in, For the transmit beamforming vector, It is the conjugate transpose. Unauthorized user The channel vector, Let be the matrix consisting of the deflection angle pairs of all steerable antennas. The maximum received power threshold; This represents the total number of unauthorized users.

[0016] In some embodiments, the joint optimization problem is formulated as follows:

[0017] in, For legitimate users' channel vectors, For legitimate users' noise power, This is the maximum transmission power; This represents the total number of steerable antennas.

[0018] In some embodiments, solving the joint optimization problem employs an alternating optimization method, including: Sub-problem 1: The deflection angle of a fixed steerable antenna Optimize the transmit beamforming vector This subproblem is solved using a second-order cone programming method. Sub-problem 2: Fixed transmit beamforming vector Optimize the deflection angle of the steerable antenna This subproblem is solved using the continuous convex approximation method. Iteratively solve subproblems 1 and 2 until convergence.

[0019] In some embodiments, solving subproblem 2 using the continuous convex approximation method specifically includes: The objective function and constraints of subproblem 2 with respect to the deflection angle are Taylor expanded at the current solution to construct its convex approximation function. By solving the optimization problem corresponding to the convex approximation function, an approximate solution to subproblem 2 is obtained.

[0020] In some embodiments, the array of steerable antennas is a two-dimensional uniform planar array.

[0021] To achieve the above objectives, another aspect of this application provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the method described above.

[0022] To achieve the above objectives, another aspect of the embodiments of this application proposes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described above.

[0023] To achieve the above objectives, another aspect of the embodiments of this application proposes a computer program product, including a computer program that, when executed by a processor, implements the method described above.

[0024] Compared with the prior art, this application has the following significant advantages and beneficial effects: 1) Introducing new spatial degrees of freedom: This application creatively introduces steerable antennas into the covert communication system. By adjusting the deflection angle of each antenna element, it provides the system with spatial dimensional degrees of freedom that traditional fixed antennas do not have, enabling the system to actively "shape" the channel.

[0025] 2) Achieved synergistic performance improvement: By jointly optimizing beamforming and antenna deflection angle, this application can dynamically and accurately focus the transmitted energy in the direction of legitimate users (enhancing the main lobe gain), while forming zero traps or extremely low sidelobes in the direction of illegitimate users (suppressing leakage power). Thus, without violating the concealment constraint, it maximizes the transmission rate of legitimate users and solves the core contradiction between "concealment" and "rate" in covert communication.

[0026] 3) High feasibility and practicality: The alternating optimization framework adopted in this application decomposes the complex non-convex joint optimization problem into two sub-problems (SOCP and SCA) that can be solved efficiently. The algorithm has good convergence and controllable computational complexity, making it suitable for application in practical systems.

[0027] 4) Strong robustness: Simulation results show that, under different numbers of antennas, transmission distances and transmission powers, the method proposed in this application can consistently outperform benchmark schemes such as fixed antennas, randomly oriented antennas and omnidirectional antennas, demonstrating superior environmental adaptability and performance robustness. Attached Figure Description

[0028] Figure 1 This is a flowchart of a method for enhancing the transmission rate of a covert communication system based on a steerable antenna, provided in an embodiment of this application. Figure 2 This is a schematic diagram of the covert communication system scenario based on the embodiments of this application.

[0029] Figure 3 This is a comparison graph showing the relationship between the legitimate user rate and the number of antennas in the embodiments of this application.

[0030] Figure 4 This is a comparison graph showing the relationship between the legitimate user rate and the distance from the legitimate user to the transmitter in the embodiments of this application.

[0031] Figure 5 This is a comparison graph showing the relationship between the legitimate user rate and the transmit power in the embodiments of this application. Detailed Implementation

[0032] 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 of this application and are not intended to limit it. In the following description, when referring to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with those of this application; they are merely examples of apparatuses and methods consistent with some aspects of the embodiments of this application as detailed in the appended claims.

[0033] Unless otherwise defined, 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 belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0034] Before providing a detailed description of the embodiments of this application, some of the nouns and terms involved in the embodiments of this application will be explained first. The nouns and terms involved in the embodiments of this application are subject to the following interpretations.

[0035] 1) Rotatable antenna (RA) is a technology that dynamically adjusts the orientation of the main lobe of an antenna through mechanical or electronic control. It is designed to improve the adaptability and performance of wireless communication systems, especially suitable for high dynamic scenarios such as 6G.

[0036] Over the past few decades, with the rapid development of global communication technologies and the continuous evolution from 5G to 6G, the demand for secure and undetectable data transmission in harsh environments has been growing. Therefore, covert communication (also known as low probability of detection communication, LPD communication) has become a cutting-edge security paradigm in modern wireless networks. Unlike traditional security technologies such as Physical Layer Security (PLS) and upper-layer encryption, which focus on protecting message content, covert communication aims to hide the existence of the communication itself, making it a key technology in corporate finance, military operations, and privacy-sensitive civilian communications. To improve the feasibility and performance of covert communication, the industry has explored various technical means, including uncertainty exploitation and artificial noise interference. However, existing technical solutions are mainly based on fixed antenna systems, whose spatial position and orientation remain unchanged. This fundamental limitation severely hinders the exploitation of spatial degrees of freedom (DoFs), thus restricting the improvement of system spectral efficiency and covert performance. Therefore, developing more flexible antenna architectures is urgently needed to achieve highly reliable and highly covert wireless transmission.

[0037] In recent years, flexible antenna technology (including Fluid Antenna Systems (FAS), Movable Antennas (MA), and Six-Dimensional Movable Antennas (6DMA)) has attracted widespread attention due to its ability to dynamically adjust various antenna configurations to improve wireless performance. Among them, steerable antenna technology stands out as a simplified and promising form. While maintaining a fixed antenna position, it emphasizes the flexibility of antenna line-of-sight rotation, providing a cost-effective and compact solution. By adjusting the three-dimensional orientation of individual antennas mechanically or electronically, steerable antenna technology enhances adaptability to dynamic transmission environments and unlocks additional spatial degrees of freedom. Specifically, arrays based on steerable antennas can dynamically reconstruct the overall directional gain pattern by independently controlling the rotation angle of each antenna element, thereby actively shaping the radiation pattern to enhance array gain in the target direction and improve communication or sensing performance. Currently, research on steerable antennas has preliminarily verified their enormous application potential, and their application areas have expanded to multiple scenarios such as secure wireless communication, integrated sensing and communication (ISAC), and terahertz (THz) beam deflection suppression. Because they can selectively enhance or suppress signal power in specific directions, steerable antennas are inherently suitable for scenarios with strict requirements for transmission concealment, especially in covert communication where they offer significant advantages. They can deflect signals away from potential transmission rate enhancement methods in covert communication systems based on steerable antennas, reducing the risk of unintended detection.

[0038] In view of this, this application provides a method, electronic device, storage medium, and program product for enhancing the transmission rate of a covert communication system based on a steerable antenna. This solution effectively improves the reception rate of legitimate users and reduces the detection probability of illegitimate users in a covert communication system by utilizing the new spatial degrees of freedom provided by the steerable antenna, thereby achieving better communication quality than covert communication systems based on traditional fixed antennas. Furthermore, the transmission rate of the covert communication system is enhanced by jointly optimizing the antenna element deflection angle and transmit beamforming.

[0039] This application provides a method for enhancing the transmission rate of a covert communication system based on a steerable antenna, relating to the field of wireless communication technology. This method can be applied to a terminal, a server, or software running on either a terminal or a server. In some embodiments, the terminal can be a smartphone, tablet, laptop, desktop computer, smart speaker, smartwatch, or vehicle terminal, but is not limited thereto. The server can be configured as an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms. The server can also be a node server in a blockchain network. The software can be an application implementing the method for enhancing the transmission rate of a covert communication system based on a steerable antenna, but is not limited to the above forms.

[0040] like Figure 1 As shown, this embodiment provides a method for enhancing the transmission rate of a covert communication system based on steerable antennas. The method is applied to a covert communication system including a transmitter, a legitimate user, and at least one unauthorized user. The transmitter is equipped with an antenna array consisting of multiple steerable antennas. The method specifically includes the following steps: Step S101: Introduce antenna pointing vector and deflection angle pair to characterize the three-dimensional orientation of a single steerable antenna, establish a channel model related to the antenna deflection angle pair, and derive the covert rate expression of legitimate users based on the channel model; Step S102: Using the channel model, derive the hidden constraint expression for the illegal user terminal; Step S103: Based on the covert rate expression of the legitimate user and the covert constraint expression, construct a joint optimization problem with the objective of maximizing the covert rate of the legitimate user and the conditions of covertness constraint, transmit power constraint and antenna turning angle constraint. The optimization variables of the joint optimization problem include the transmit beamforming vector and the deflection angle pairs of all steerable antennas. Step S104: Solve the joint optimization problem to obtain the optimized transmit beamforming vector and the deflection angle pair of the steerable antenna for downlink transmission of the covert communication system.

[0041] The solutions of the embodiments of this application will be described in detail below with reference to the accompanying drawings and specific application examples.

[0042] This embodiment provides a method for enhancing the transmission rate of a covert communication system based on a steerable antenna. It overcomes the drawback of low spatial freedom by reconstructing the antenna radiation orientation simply by rotating the antenna elements, without requiring additional rotation or movement of the antenna array. This reduces the probability of legitimate users being detected and effectively improves the system's transmission rate. The method specifically includes the following steps: S1. Introduce antenna pointing vector and deflection angle pair to characterize the three-dimensional direction of a single antenna, establish a channel model related to antenna deflection angle pair, and derive the expression for the covert rate of legitimate users.

[0043] In some embodiments, step S1 proceeds as follows: See Figure 2 This embodiment considers a covert communication system based on a steerable antenna, consisting of a transmitter Alice, a legitimate user Bob, and... The group consists of Willies, who employ an illegal method to enhance the transmission rate of a covert communication system based on a steerable antenna. Bob and all the Willies are equipped with a single antenna to receive signals; Alice is equipped with a... A two-dimensional uniform planar array (UPA) consisting of several steerable antennas, located in a three-dimensional Cartesian coordinate system. On a plane. The reference position of the array element is denoted as... , Bob's reference position relative to each of the Willies is denoted as follows: and , Therefore, the first The distance from each RA to Bob / Willie can be expressed as: (1) This invention uses an antenna pointing vector to describe the three-dimensional pointing of the antenna (RA). The pointing vectors of each RA are represented as: (2) To facilitate mechanical / electronic controllability of the RA, this invention uses a pair of deflection angles to describe the RA's three-dimensional attitude, where the pitch angle... Indicates the direction of the antenna's main lobe radiation and Axis angle; azimuth angle Indicates the direction of the antenna's main lobe radiation. Plane projection and Axis angle. Based on three-dimensional geometric relationships, the three components of the pointing vector satisfy: , , Furthermore, to ensure the achievable steering of the RA, the pitch angle of each RA is limited to the following steering range: (3) in This indicates the maximum allowable deflection angle for a steerable antenna.

[0044] To describe the characteristics of the radiation main lobe directional gain of RA as a function of deflection angle, this embodiment adopts the following general directional gain model: (4) in, This represents a pair of incident angles between the incident direction and the current main lobe direction of the RA radiation. This represents the maximum main lobe gain that satisfies power conservation. Represents the directivity factor, used to describe the main lobe beamwidth of the antenna. Therefore, the... A RA in Bob / Willie Directional gain in the direction is , among which angle Determined by the following inner product relationship It is represented as a unit direction vector pointing from RA to user / Willie.

[0045] This embodiment uses a free-space line-of-sight (LoS) channel model. RA to Bob / Willie The complex channel can be represented as: (5) in, For the first The deflection angle of each RA pair The channel power gain can be expressed as Indicates the physical effective area of ​​the antenna. Indicates the carrier wavelength.

[0046] Therefore, the first The channel vector consisting of the channels of each RA to Bob and all RAs can be expressed as follows: in This is the complete antenna deflection angle matrix. Assume Alice uses the transmit beamforming vector. Downlink transmission is performed; therefore, Bob's achievable covert communication rate can be expressed as: (6) in, Let be the additive white Gaussian noise power of Bob.

[0047] This concealment rate clearly characterizes the ability of the steerable antenna to actively enhance the Bob channel gain in three dimensions, laying the foundation for subsequent concealment rate maximization optimization.

[0048] S2. Using the relevant channel model established above, derive the expression for the covert constraint condition of the illegal user terminal.

[0049] In some embodiments, step S2 proceeds as follows: To ensure that communication activities are not detected by the probe Willie, this invention constructs concealment constraints based on a binary hypothesis testing model. Willie determines the presence of a signal through power detection; his decision problem can be expressed as: a) Null hypothesis Alice remains silent, while Willie only receives noise; b) Alternative Hypothesis Alice is sending a signal to Bob.

[0050] For the first A Willie, at a certain time slice (sample index) The received signal model is as follows: (7) in, The baseband symbols sent for Alice satisfy ,noise Willie used the average received energy of the samples and compared it with the detection threshold. Compare ,in / They respectively represent the judgment as / .

[0051] To characterize the noise uncertainty, we assume that the noise standard deviation has an uncertainty factor. This uncertainty affects the selection of the optimal threshold and detection performance. Let Willie... The received signal power is expressed as follows: Assuming equal prior probabilities (both 0.5) and that sampling and noise statistics satisfy the aforementioned assumptions, Willie's minimum detection error probability (DEP) can be expressed in closed form as follows: (8) in This represents the nominal noise power (the nominal value when noise uncertainty is not introduced). Equation (1) shows that: The larger the value, the lower Willie's minimum DEP. The smaller the value (i.e., the easier it is to detect the presence of transmission).

[0052] To meet the system's preset concealment tolerance, the minimum DEP for each Willie must be no less than [a certain value]. ,Right now ,in Let be the maximum detectable probability allowed by the system. In summary, the concealment constraint can be equivalently expressed as the constraint on the th... Explicit upper bound constraints on the received power of each Willie: (9) in, This indicates that in this covert communication system, Willie meets the maximum received power threshold under the covert constraints.

[0053] S3. Based on steps S1 and S2, formulate the problem of maximizing the covert rate of legitimate users. Under the constraints of covertness, transmit power, and antenna turning angle, jointly optimize the transmit beamforming and the deflection angle pairs of all steerable antennas.

[0054] In some embodiments, step S3 proceeds as follows: Based on steps S1 (channel model of the steerable antenna and Bob's covert rate expression) and S2 (equivalent to Willie's energy detection and covertness requirement as the upper bound of received power η), the problem of maximizing the covert transmission rate of the legitimate user (Bob) is formulated as follows:

[0055] question It is about continuous complex variables With multidimensional angle variables This is a joint nonconvex optimization problem where the objective function is nonconvex with respect to both variables, and the implicit constraints make the problem difficult to solve directly. To solve this problem efficiently, this invention employs an alternating optimization (AO) strategy, decomposing the problem into two easily manageable subproblems that are alternately optimized until convergence.

[0056] S4. Using the alternating optimization method, the problem is decomposed into two subproblems, and then solved by second-order cone programming and continuous convex approximation methods respectively.

[0057] In some embodiments, step S4 proceeds as follows: Subproblem 1: Fixed Optimized Spread Beamforming (SOCP) For a fixed antenna rotation angle Subproblem 1 can be written as:

[0058] Since the goal is only to maximize And for Multiplying by the same phase factor does not change the constraints, therefore it can be assumed that... Let the numbers be real numbers and introduce slack variables. :

[0059] question Constraints , All are standard second-order cone constraints or linear constraints, thus the problem This belongs to the second-order cone programming problem. It can be solved efficiently using an existing optimizer.

[0060] Subproblem 2: Fixed Slewing antenna angle optimization (SCA) For a fixed emission vector The objective of subproblem 2 is to maximize the received power with respect to the angle variable:

[0061] This subproblem is related to To obtain a solvable form, this invention employs Successive Convex Approximation (SCA) combined with Second-Order Taylor (SOT) expansion to construct convex / concave substitution functions for the objective and constraints, thereby transforming the subproblem into an approximate problem that can be solved by a convex optimizer (such as CVX).

[0062] Specifically, based on the channel model and the definition of antenna directivity gain, the target can be represented as a double summation form: (14) in, , , Note the constant term. This does not affect the concavity of the objective function; therefore, we only need to... By performing a second-order Taylor expansion, we can derive an easily tractable substitution function. Specifically, we first use a second-order Taylor expansion at the current initial point... place as Find a concave lower bound: (15) in, , The gradient vector, It is a Hessian matrix. Because... The second derivative of is bounded (absolute value ≤ 1), and can be replaced by conservative substitution. use By substitution, a concave lower bound is obtained: (16) Based on this, By performing a first-order extension and replacing the lower bound mentioned above, we obtain: Linear-quadratic lower bound expression: (17) Similarly for A similar lower bound expression can also be obtained: (18) All Xiang Daihui By retaining the second-order and linear terms, we can further obtain a concave quadratic approximation of the objective function: (19) in constant term linear terms All three, including the Hessian matrix term A, can be explicitly calculated, specifically expressed as follows: , The n Each element can be represented as ,as well as ,in .

[0063] Regarding the Hessian matrix We ignore the cross-coupling effect between different antennas and only retain the diagonal blocks of the matrix to reduce computational complexity. Each diagonal block Scaling with non-positive second derivatives and non-negative weights ensures that all eigenvalues ​​of the matrix are non-positive. From this, we can derive... The conclusion is that this property guarantees the concavity of the quadratic approximation of the objective function.

[0064] Received power constraints for each Willie Similarly, the Hessian matrix is ​​bounded by an upper bound. By substitution, we can obtain: (20) in Therefore, equation (19) above is a convex quadratic constraint.

[0065] From (18) and (19), subproblem 2 can be approximated as:

[0066] because (The objective function is a concave quadratic function) and each (The constraint function is convex quadratic), problem It is a convex quadratic optimization problem, which can be solved directly using CVX.

[0067] In terms of algorithm complexity, solving subproblem 1 has a complexity of O(n log n). The time complexity of solving subproblem 2 is... ,in Let represent the convergence accuracy threshold for subproblem 2. Therefore, the overall complexity of this algorithm is O(n log n). ,in This represents the number of iterations required for the algorithm to converge.

[0068] Figure 3 This is a graph showing the relationship between the legal user rate and the number of antennas provided in the embodiments of this application. The maximum transmit power P... max = 30 dBm, distance r between base station and legitimate user b = 20 m. The results show that the system performance based on the steerable antenna consistently outperforms other benchmark schemes. This is because the steerable antenna can dynamically adjust the array directivity gain pattern by optimizing the antenna rotation angle, thereby concentrating the radiated power in the target direction and improving the covert transmission rate. In contrast, the fixed antenna scheme radiates energy in a fixed direction and cannot provide effective gain for legitimate users by adjusting the line-of-sight direction; the random antenna orientation scheme does not strategically design the antenna orientation, and the array gain in the direction of legitimate users is lower than that of the steerable antenna-based scheme proposed in this invention. The above results verify the effectiveness of the proposed steerable antenna scheme in flexibly reconstructing the array directivity gain pattern, thereby improving the performance of covert communication.

[0069] Figure 4 This is a graph showing the relationship between the legitimate user rate and the distance from the legitimate user to the base station, provided in an embodiment of this application. The number of antennas N=16, and the maximum transmit power P... max= 30 dBm. It can be observed that the covert transmission rate decreases with increasing distance for all schemes. This is because increased distance leads to increased path loss, which in turn reduces the received signal power at the legitimate user. Nevertheless, even at longer transmission distances, the system based on steerable antennas continues to achieve the highest covert transmission rate of all schemes. This is because the system can dynamically adjust the orientation of each antenna, thereby achieving directional gain and mitigating the effects of path loss more effectively than other benchmark schemes.

[0070] Figure 5 This is a graph showing the relationship between the legitimate user rate and the transmit power provided in an embodiment of this application. The number of antennas is N=16, and the distance r between the base station and the legitimate user is... b = 20 m. The results show that with the maximum transmit power P max As P increases, the covert transmission rate of all schemes exhibits a monotonically increasing trend. It is noteworthy that the system based on the steerable antenna consistently maintains a performance advantage over other benchmark schemes, and this advantage increases with P. max The increase in power is becoming increasingly significant. This is because higher transmit power amplifies the benefits of optimized antenna orientation, allowing steerable antenna-based solutions to better suppress energy leakage to eavesdroppers while concentrating energy on legitimate users, thus achieving a much higher covert transmission rate than other solutions.

[0071] In summary, this embodiment proposes a method for enhancing the transmission rate of a covert communication system based on steerable antennas. This method can flexibly adjust the line-of-sight direction of each antenna to dynamically reconstruct the overall directional gain pattern, thereby improving the system's covert transmission rate. Specifically, this application designs an efficient alternating optimization algorithm by jointly optimizing the transmit beamforming and the deflection angle of each steerable antenna. This algorithm maximizes the covert transmission rate of legitimate users while satisfying the covertness constraints of each eavesdropper. The results show that the proposed method for enhancing the transmission rate of a covert communication system based on steerable antennas can still achieve a significantly higher covert transmission rate than various benchmark schemes, even under complex and unfavorable conditions with multiple eavesdroppers. This highlights its great potential in future covert communication scenarios.

[0072] This application also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-described method. This electronic device can be any smart terminal, including tablet computers, in-vehicle computers, etc.

[0073] It is understood that the content of the above method embodiments is applicable to this device embodiment. The specific functions implemented by this device embodiment are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0074] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0075] It is understood that the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0076] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0077] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0078] It is understood that the content of the above method embodiments is applicable to the embodiments of this program product. The specific functions implemented in the embodiments of this program product are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments. The executable computer program code or "code" used to perform the various embodiments can be written in high-level programming languages ​​such as C, C++, Python, Smalltalk, Java, JavaScript, Visual Basic, Structured Query Language (e.g., Transact-SQL), Perl, or in various other programming languages.

[0079] The embodiments described in this application are for the purpose of more clearly illustrating the technical solutions of the embodiments of this application, and do not constitute a limitation on the technical solutions provided by the embodiments of this application. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by the embodiments of this application are also applicable to similar technical problems.

[0080] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of this application, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0081] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0082] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or appropriate combinations thereof.

[0083] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0084] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0085] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of the units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0086] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0087] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0088] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes multiple instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing programs, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0089] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. A method for enhancing the transmission rate of a covert communication system based on a steerable antenna, characterized in that, A covert communication system comprising a transmitter, a legitimate user, and at least one unauthorized user, wherein the transmitter is equipped with an antenna array consisting of multiple steerable antennas, the method comprising the following steps: Antenna pointing vector and deflection angle pair are introduced to characterize the three-dimensional orientation of a single steerable antenna. A channel model related to the antenna deflection angle pair is established, and the covert rate expression of legitimate users is derived based on the channel model. Using the aforementioned channel model, the hidden constraint condition expression for the illegal user terminal is derived; Based on the covert rate expression of the legitimate user and the covert constraint expression, a joint optimization problem is constructed with the objective of maximizing the covert rate of the legitimate user and the conditions of covertness constraint, transmit power constraint and antenna turning angle constraint. The optimization variables of the joint optimization problem include the transmit beamforming vector and the deflection angle pairs of all steerable antennas. Solving the joint optimization problem yields an optimized transmit beamforming vector and a deflection angle pair for the steerable antenna, which can then be used for downlink transmission in the covert communication system.

2. The method according to claim 1, characterized in that, The deflection angle pair includes pitch angle and azimuth angle; the first The pointing vector of a steerable antenna is represented as: in, Indicates the pitch angle, Indicates the azimuth angle; The pitch angle is limited to a preset steering range: ; This indicates the maximum allowable deflection angle for a steerable antenna.

3. The method according to claim 2, characterized in that, The establishment of the channel model includes: Based on the inner product between the pointing vector and the unit direction vector pointing from the steerable antenna to the user, determine the first... The directional gain of the steerable antenna in the user direction is: ,in, For maximum main lobe gain, As a directional factor, For the first The angle between the line-of-sight vector of the steerable antenna and the user direction vector; No. A steerable antenna to the user The complex channel is represented as: in, For the deflection angle pair, For channel power gain, For transmission distance, The carrier wavelength.

4. The method according to claim 1, characterized in that, The derivation of the hidden constraint expression for the illegal user terminal includes: Based on a binary hypothesis testing model, determine the minimum detection error probability of unauthorized users. Compared with the received signal power The relationship between them; By setting a lower bound for the minimum detection error probability, the concealment constraint is equivalently transformed into an explicit upper bound constraint on the received power of unauthorized users: in, For the transmit beamforming vector, It is the conjugate transpose. Unauthorized user The channel vector, Let be the matrix consisting of the deflection angle pairs of all steerable antennas. The maximum received power threshold; This represents the total number of unauthorized users.

5. The method according to claim 1, characterized in that, The joint optimization problem is expressed as follows: in, For legitimate users' channel vectors, For legitimate users' noise power, This is the maximum transmission power; This represents the total number of steerable antennas.

6. The method according to claim 5, characterized in that, The solution to the joint optimization problem employs an alternating optimization method, including: Sub-problem 1: The deflection angle of a fixed steerable antenna Optimize the transmit beamforming vector This subproblem is solved using a second-order cone programming method. Sub-problem 2: Fixed transmit beamforming vector Optimize the deflection angle of the steerable antenna This subproblem is solved using the continuous convex approximation method. Iteratively solve subproblems 1 and 2 until convergence.

7. The method according to claim 6, characterized in that, The method of solving subproblem 2 using the continuous convex approximation method specifically includes: The objective function and constraints of subproblem 2 with respect to the deflection angle are Taylor expanded at the current solution to construct its convex approximation function. By solving the optimization problem corresponding to the convex approximation function, an approximate solution to subproblem 2 is obtained.

8. The method according to any one of claims 1-7, characterized in that, The array of steerable antennas is a two-dimensional uniform planar array.

9. An electronic device, characterized in that, The electronic device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the method according to any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 8.

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