A method and system for secure communication of frequency diversity array under eavesdropper position uncertainty
By constructing a protected area model for the location of eavesdroppers and an alternating optimization framework, the problem of decreased security performance of frequency diversity arrays under uncertain eavesdropper locations is solved, achieving improved security capacity and reduced computational complexity in the worst-case scenario in wireless communication systems.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SHANDONG UNIV
- Filing Date
- 2026-04-08
- Publication Date
- 2026-07-03
AI Technical Summary
In wireless communication environments where the location of eavesdroppers is uncertain or dynamically changing, the security performance of existing frequency diversity arrays deteriorates, failing to effectively improve the worst-case security capacity of the system.
A model of the protected area for the location of eavesdroppers is constructed. An alternating optimization framework is used to iteratively optimize the frequency increment design, beamforming vector optimization, and power allocation optimization, thereby reducing computational complexity and improving security capacity.
This approach effectively enhances the worst-case security capacity of the system under conditions where the location of the eavesdropper is uncertain, reduces computational complexity, and improves robustness and engineering feasibility.
Smart Images
Figure CN122340488A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of wireless communication physical layer security technology, specifically relating to a frequency diversity array secure communication method and system under conditions where the location of an eavesdropper is uncertain. Background Technology
[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.
[0003] With the development of wireless communication technology, mobile communication technology enables information transmission between devices through wireless channels. However, due to the broadcast characteristics of the channels, wireless communication systems are vulnerable to eavesdropping attacks. Therefore, physical layer security technology is widely used to improve the confidentiality of wireless communication systems.
[0004] Frequency diversity arrays are multi-antenna transmission structures that introduce minute frequency shifts between array elements to give the array pattern both range- and angle-dependent characteristics. Unlike traditional phased arrays, which only exhibit angle-dependent characteristics, frequency diversity arrays achieve angle-range coupling by setting different frequency increments between each element.
[0005] Currently, the transmit beam pattern performance of frequency diversity arrays is typically improved through frequency increment design and array weight optimization. However, existing technologies usually assume that the location of the eavesdropper or channel state information is known, but in real communication environments, the location of the eavesdropper is often unknown or dynamically changing, leading to a decrease in the security performance of existing methods. Summary of the Invention
[0006] To address the aforementioned problems, this invention proposes a frequency diversity array secure communication method and system for situations where the location of the eavesdropper is uncertain. This invention can effectively improve the worst-case security capacity of the system and reduce computational complexity under conditions where the location of the eavesdropper is uncertain.
[0007] According to some embodiments, the present invention adopts the following technical solution: A method for secure communication using a frequency diversity array when the location of an eavesdropper is uncertain includes the following steps: Construct a frequency diversity array communication system model and establish a protected area model for the location of eavesdroppers. Establish a worst-case signal-to-interference-plus-noise ratio (SIR) model for the eavesdropper and determine the boundary location of the eavesdropper in the worst-case scenario; Based on the determined boundary location of the eavesdropper, an optimization model for maximizing the confidentiality capacity is constructed. An alternating optimization framework is used to solve the optimization model. The original problem is decomposed into sub-problems of frequency increment design, beamforming vector optimization, and power allocation optimization, and the optimization results are obtained through iterative optimization.
[0008] As an alternative implementation, the process of constructing a frequency diversity array communication system model includes: a transmitter A equipped with a frequency diversity array of M antennas, a legitimate single-antenna user B, and a potential passive single-antenna eavesdropper E, wherein the spacing between adjacent units of transmitter A is [missing information]. ,in Indicates the carrier wavelength; each antenna element operates at a different frequency. Launch, among which This represents the element-specific frequency increment, oriented towards an angle in the narrowband far-field condition. and distance The target's launch steering vector is represented as:
[0009] No. The phase of each unit is:
[0010] in, For wave speed, This is the reference frequency.
[0011] As an alternative implementation method, the process of establishing a protected area model for the location of an eavesdropper includes: assuming that a legitimate receiver B can detect potential eavesdroppers within a protected area centered on itself and with a radius of r, the possible location area of the eavesdropper E is represented as follows:
[0012] in, The location of the eavesdropper E. The location of the legitimate recipient B.
[0013] As an alternative implementation, the process of establishing a worst-case eavesdropper signal-to-interference-plus-noise ratio (SINR) model and determining the worst-case eavesdropper boundary location includes: designing the system using worst-case security design criteria, where the worst-case eavesdropper SINR is defined as:
[0014] Based on the worst-case scenario, the security capacity is:
[0015] in, For the SINR received by Eve's eavesdropper, SINR for the legitimate recipient Bob, This represents the SINR received by Eve in the worst-case scenario.
[0016] As an alternative implementation, the process of constructing a confidentiality capacity maximization optimization model based on the determined eavesdropper boundary location includes: assuming the maximum SINR of E in the worst case occurs at a distance of B and E. At the boundary of the protected region, the SC maximization problem is constructed as follows:
[0017]
[0018] in, This represents the beamforming vector of a frequency diversity array radar. It is the power distribution factor of artificial noise. It is a frequency increment vector. To set a threshold.
[0019] As a further defined implementation method, frequency increment The design employs PGD to approximately minimize the spatial correlation of the eavesdropper. The frequency increment is recovered by calculating the gradient, adjusting the step size, using box projection, and reconstructing the phase.
[0020] As an alternative implementation method, an alternating optimization framework is used to solve the optimization model. The process of iteratively optimizing the original problem by decomposing it into sub-problems of frequency increment design, beamforming vector optimization, and power allocation optimization includes: using an alternating optimization framework to decompose the non-convex optimization problem into three sub-problems for iterative solution. Frequency increment design: fixed , The phase variable is updated using the projected gradient descent method. Minimize the spatial correlation between the received signals of B and E; Beamforming vector optimization; fixed Maximizing the confidentiality capacity is transformed into a generalized eigenvalue problem, and the optimal solution is the normalized eigenvector corresponding to the largest eigenvalue of the matrix. Power distribution optimization: fixed The SC optimization problem simplifies to a problem about The univariate optimization is unimodal and is solved using the golden section search method.
[0021] As a further defined implementation, the iterative optimization process includes updating the value using the projected gradient descent method. ; Update the worst-case position E and search for the maximum SINR point on the boundary; Update based on generalized eigenvalue solutions ; Search update based on the golden ratio search method ; Assess confidentiality capacity When the number of iterations exceeds the maximum value Or the change in confidentiality capacity meets , Stop iteration and output the optimal parameters when the convergence accuracy is reached. .
[0022] A frequency diversity array secure communication system for situations where the location of an eavesdropper is uncertain, comprising: The model building module is configured to build a frequency diversity array communication system model and establish a model of the protected area for the location of eavesdroppers. The boundary determination module is configured to build a worst-case eavesdropper signal-to-interference-plus-noise ratio model and determine the worst-case eavesdropper boundary location. The optimization solution module is configured to construct a confidentiality capacity maximization optimization model based on the determined eavesdropper boundary position. The optimization model is solved using an alternating optimization framework. The original problem is decomposed into sub-problems of frequency increment design, beamforming vector optimization, and power allocation optimization, and the optimization results are obtained through iterative optimization.
[0023] An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the steps in the method described above.
[0024] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention reduces the complexity of solving the problem by constructing a protected area model for eavesdroppers, transforming the uncertainty of eavesdropper location into a boundary optimization problem. By employing an alternating optimization framework, it jointly optimizes the beamforming vector, power allocation factor, and frequency increment, improving the system's security capacity performance in the worst-case scenario. Simultaneously, it avoids a complex global search process, reducing computational overhead and improving engineering feasibility. Therefore, this invention can effectively improve security capacity under conditions of uncertain eavesdropper location, demonstrating good robustness and application prospects.
[0025] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description
[0026] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.
[0027] Figure 1 This is a system communication model diagram; Figure 2It is the system's safety capacity under different protection radii; Figure 3 It is the system's transmit beamforming diagram; Figure 4 This is a flowchart illustrating how the present invention enhances security capacity. Figure 5 This is a comparison diagram of the safety capacity of different numbers of antennas in one embodiment. Detailed Implementation
[0028] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0029] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.
[0030] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.
[0031] Where there is no conflict, the embodiments and features described in this application may be combined with each other.
[0032] Example 1 As described in the background section, in wireless communication systems, eavesdroppers are typically passive devices whose location is difficult to ascertain, preventing the transmitter from obtaining complete channel information and thus reducing system security. Under conditions where the eavesdropper's location is uncertain or the channel is rapidly changing, the security fluctuations of legitimate communication links increase, necessitating robust physical layer secure transmission and improved system security capacity.
[0033] This invention proposes a physical layer security capacity optimization method based on frequency diversity arrays. Frequency diversity arrays introduce frequency offsets between array elements, making the radiation pattern dependent on both distance and angle, extending the spatial degrees of freedom to the range domain. This reduces the signal-to-interference-plus-noise ratio (SIR) of the received signal from potential eavesdroppers, thereby improving the security capacity in the worst-case scenario. In this embodiment, as... Figure 3 As shown, it includes the following steps: (1) Construct a frequency diversity array communication system model and establish a model of the protected area for the location of the eavesdropper; (2) Establish a worst-case signal-to-interference-plus-noise ratio model for the eavesdropper and determine the boundary location of the eavesdropper in the worst case; (3) Construct a model for maximizing confidentiality capacity and define system optimization variables; (4) The optimization problem is solved by using an alternating optimization framework, and the original problem is decomposed into multiple sub-problems for iterative optimization.
[0034] In this embodiment, step (1) includes: Construct a frequency diversity array communication system model, such as Figure 1 As shown, the scenario includes a transmitter A equipped with a frequency diversity array of M antennas, a legitimate single-antenna user B, and a potential passive single-antenna eavesdropper E. The spacing between adjacent units of A is... ,in This indicates the carrier wavelength. Each antenna element operates at a slightly different frequency. Launch, among which This represents the frequency increment specific to an element. For example... Figure 2 As shown, under narrowband far-field conditions, the orientation is located at an angle and distance The target's launch steering vector can be expressed as:
[0035] Among them, the first The phase of each unit is given by the following formula:
[0036] To further enhance system security, assume that a legitimate receiver B can detect potential eavesdroppers within a protected area centered on itself and with a radius of r. Therefore, the possible location area of eavesdropper E can be represented as:
[0037] In this embodiment, step (2) includes: The system design adopts the worst-case security design principle. The worst-case SINR (Security Inquiry Rate) is defined as:
[0038] Based on the worst-case scenario, the security capacity is:
[0039] According to the theorem of this invention: the maximum SINR of E in the worst case occurs at a distance of B and E. The search space is reduced to the boundary of the protected area, thus significantly reducing the computational complexity of optimization.
[0040] In this embodiment, step (3) includes: Based on the worst-case E derived in the theorem The SC maximization problem can be constructed as follows:
[0041]
[0042] in This represents the beamforming vector of a frequency diversity array radar. It is the power distribution factor of artificial noise. It is the frequency increment vector. Because it involves multiple coupled variables and the SINR expression has a fractional structure with nested maximization operations, this optimization problem is non-convex.
[0043] In this embodiment, step (4) includes: The Alternating Optimization (AO) framework is used to decompose the non-convex optimization problem into three sub-problems for iterative solution: Frequency increment design: fixed , The phase variables are updated using the projected gradient descent (PGD) method. Minimize the spatial correlation between the received signals of B and E.
[0044] Beamforming vector optimization; fixed Maximizing the confidentiality capacity is transformed into a generalized eigenvalue problem, and the optimal solution is the normalized eigenvector corresponding to the largest eigenvalue of the matrix.
[0045] Power distribution optimization: fixed The SC optimization problem simplifies to a problem about The univariate optimization is unimodal and can be solved using the Golden Section Search (GSS) method.
[0046] In the above process, the system model includes a frequency diversity array transmitting base station A, a legitimate single-antenna receiver B, and a potential passive single-antenna eavesdropper E. To further improve system security, artificial noise is added to the transmitted signal, represented as:
[0047] in For beamforming vectors, For artificial noise matrix, Let be the power allocation factor, and s be the secure symbol transmitted per unit power. is the normalization factor for Q.
[0048] In radius Within the range, a malicious eavesdropping user E can be detected, and the location of E with the maximum SINR occurs between B and E at a distance equal to the radius. The location. Its SINR can be expressed as:
[0049] in , , For the number of antennas, This represents the received noise power of E.
[0050] Since SINR follows Monotonically increasing, worst case E corresponds to Maximum, that is .
[0051] Furthermore, in this embodiment, the SC maximization problem is constructed as follows:
[0052] Frequency increment The design employs PGD to approximately minimize the spatial correlation of the eavesdropper. The frequency increment is recovered by calculating the gradient, adjusting the step size, using box projection, and reconstructing the phase.
[0053] Under power constraints The optimization problem is now transformed into:
[0054]
[0055] in , .
[0056] The optimal solution to this optimization problem is: , where vector It is a matrix The normalized eigenvector corresponding to the largest eigenvalue.
[0057] The SC optimization problem is simplified to a problem about Univariate optimization:
[0058]
[0059] in in .function exist The surface is smooth, and the numbers are optimal. It can be obtained through GSS.
[0060] In some embodiments, the complete process of solving the proposed optimization problem is as follows: Initialize the frequency increment, beamforming vector, power allocation factor, iteration index, and tolerance.
[0061] Repeat the following steps until convergence: Update using PGD algorithm ; Update the worst-case position E and search for the maximum SINR point on the boundary; Update based on generalized eigenvalue solutions ; Search and update based on GSS method ; Assess confidentiality capacity When the number of iterations exceeds the maximum value Or the change in confidentiality capacity meets When the time is right, stop the iteration and output the optimal parameters. .
[0062] To verify the effectiveness of the present invention, such as Figure 4 As shown, a simulation was performed using MATLAB. The spatial observation area was set to an angle. ,distance The SC generated by this scheme is compared with four other benchmark schemes. The results show that for all configurations, after applying the method of this invention, the SC increases accordingly. It increases monotonically. For SC and protection radius... The relationship between SC and SC was observed. The SINR increases with spatial correlation. Since the SINR of the eavesdropper increases monotonically with respect to spatial correlation, reducing this correlation directly lowers the SINR of the worst-case E, thereby increasing SC.
[0063] Example 2 A frequency diversity array secure communication system for situations where the location of an eavesdropper is uncertain, comprising: The model building module is configured to build a frequency diversity array communication system model and establish a model of the protected area for the location of eavesdroppers. The boundary determination module is configured to build a worst-case eavesdropper signal-to-interference-plus-noise ratio model and determine the worst-case eavesdropper boundary location. The optimization solution module is configured to construct a confidentiality capacity maximization optimization model based on the determined eavesdropper boundary position. The optimization model is solved using an alternating optimization framework. The original problem is decomposed into sub-problems of frequency increment design, beamforming vector optimization, and power allocation optimization, and the optimization results are obtained through iterative optimization.
[0064] Example 3 An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the steps in the method provided in Embodiment 1.
[0065] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of one or more computer-usable storage media (including, but not limited to, disk storage, etc.) containing computer-usable program code. CD - ROM It takes the form of a computer program product implemented on (such as optical memory, etc.).
[0066] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0067] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0068] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0069] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made by those skilled in the art without creative effort within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A frequency diversity array secure communication method under conditions where the location of the eavesdropper is uncertain, characterized in that, Includes the following steps: Construct a frequency diversity array communication system model and establish a protected area model for the location of eavesdroppers. Establish a worst-case signal-to-interference-plus-noise ratio (SIR) model for the eavesdropper and determine the boundary location of the eavesdropper in the worst-case scenario; Based on the determined boundary location of the eavesdropper, an optimization model for maximizing the confidentiality capacity is constructed. An alternating optimization framework is used to solve the optimization model. The original problem is decomposed into sub-problems of frequency increment design, beamforming vector optimization, and power allocation optimization, and the optimization results are obtained through iterative optimization.
2. The frequency diversity array secure communication method under uncertain eavesdropper location as described in claim 1, characterized in that, The process of constructing a frequency diversity array communication system model includes: a transmitter A equipped with a frequency diversity array of M antennas, a legitimate single-antenna user B, and a potential passive single-antenna eavesdropper E. The spacing between adjacent units of transmitter A is... ,in Indicates the carrier wavelength; each antenna element operates at a different frequency. Launch, among which This represents the element-specific frequency increment, oriented towards an angle in the narrow-band far-field condition. and distance The target's launch steering vector is represented as: No. The phase of each unit is: in, For wave speed, This is the reference frequency.
3. The frequency diversity array secure communication method under uncertain eavesdropper location as described in claim 1, characterized in that, The process of establishing a protected area model for the location of an eavesdropper includes: assuming that a legitimate receiver B can detect potential eavesdroppers within a protected area centered on itself and with a radius of r, the possible location area of the eavesdropper E is represented as follows: in, The location of the eavesdropper E. The location of the legitimate recipient B.
4. The frequency diversity array secure communication method under uncertain eavesdropper location as described in claim 1, characterized in that, The process of establishing a worst-case eavesdropper signal-to-interference-plus-noise ratio (SINR) model and determining the worst-case eavesdropper boundary location includes: system design using worst-case security design criteria, where the worst-case eavesdropper SINR is defined as: Based on the worst-case scenario, the security capacity is: in, For the SINR received by Eve's eavesdropper, SINR for the legitimate recipient Bob, This represents the SINR received by Eve in the worst-case scenario.
5. The frequency diversity array secure communication method under uncertain eavesdropper location as described in claim 1, characterized in that, The process of constructing a confidentiality capacity maximization optimization model based on the determined eavesdropper boundary location includes: assuming the maximum SINR of E in the worst case occurs at a distance of B and E. At the boundary of the protected region, the SC maximization problem is constructed as follows: in, This represents the beamforming vector of a frequency diversity array radar. It is the power distribution factor of artificial noise. It is a frequency increment vector. To set a threshold.
6. A frequency diversity array secure communication method for situations where the location of an eavesdropper is uncertain, as described in claim 5, characterized in that the frequency... Increment The design employs PGD to approximately minimize the spatial correlation of the eavesdropper. The frequency increment is recovered by calculating the gradient, adjusting the step size, using box projection, and reconstructing the phase.
7. The frequency diversity array secure communication method under uncertain eavesdropper location as described in claim 1, characterized in that, The optimization model is solved using an alternating optimization framework. The process of iteratively optimizing the original problem by decomposing it into sub-problems of frequency increment design, beamforming vector optimization, and power allocation optimization includes: using an alternating optimization framework to decompose the non-convex optimization problem into three sub-problems for iterative solution. Frequency increment design: fixed , The phase variable is updated using the projected gradient descent method. Minimize the spatial correlation between the received signals of B and E; Beamforming vector optimization; fixed Maximizing the confidentiality capacity is transformed into a generalized eigenvalue problem, and the optimal solution is the normalized eigenvector corresponding to the largest eigenvalue of the matrix. Power distribution optimization: fixed The SC optimization problem simplifies to a problem about The univariate optimization is unimodal and is solved using the golden section search method.
8. The frequency diversity array secure communication method under uncertain eavesdropper location as described in claim 7, characterized in that, The iterative optimization process includes updating the value using the projected gradient descent method. ; Update the worst-case position E and search for the maximum SINR point on the boundary; Update based on generalized eigenvalue solutions ; Search update based on the golden ratio search method ; Assess confidentiality capacity When the number of iterations exceeds the maximum value Or the change in confidentiality capacity meets the requirements When the time is right, stop the iteration and output the optimal parameters. .
9. A frequency diversity array secure communication system for situations where the location of an eavesdropper is uncertain, characterized in that, include: The model building module is configured to build a frequency diversity array communication system model and establish a model of the protected area for the location of eavesdroppers. The boundary determination module is configured to build a worst-case eavesdropper signal-to-interference-plus-noise ratio model and determine the worst-case eavesdropper boundary location. The optimization solution module is configured to construct a confidentiality capacity maximization optimization model based on the determined eavesdropper boundary position. The optimization model is solved using an alternating optimization framework. The original problem is decomposed into sub-problems of frequency increment design, beamforming vector optimization, and power allocation optimization, and the optimization results are obtained through iterative optimization.
10. An electronic device, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, perform the steps of the method according to any one of claims 1-8.