Data transmission method of near field communication system and related equipment

Abstract

According to the data transmission method of the near field communication system and the related equipment, the near field communication system comprises a base station, a receiving end and an eavesdropping end, and the method comprises the following steps: acquiring an eavesdropping estimation position of the eavesdropping end, and obtaining an eavesdropping rate model based on a position error parameter of the eavesdropping end in a position uncertainty area and the eavesdropping estimation position; a secure transmission optimization model is obtained based on a receiving rate model and an eavesdropping rate model corresponding to the data information sent by the base station received by the receiving end and a beam forming vector parameter of the base station; and dividing the position uncertainty area into a plurality of sub-areas, generating robust security constraints based on the proxy position corresponding to each sub-area, and solving the secure transmission optimization model based on the robust security constraints to obtain an optimized beam forming vector so as to control the base station to transmit data information to the receiving end, thereby ensuring the high-security transmission probability and improving the transmission efficiency. And the achievable communication rate of the receiving end is obviously improved.

Description

Technical Field

[0001] This application relates to the field of wireless communication technology, and in particular to data transmission methods and related equipment for near-field communication systems. Background Technology

[0002] Physical Layer Security (PLS) communication systems utilize spatial diversity provided by multiple antennas, enabling base stations to direct directional beams towards legitimate users while suppressing information leakage from potential eavesdroppers. In PLS communication systems, multi-antenna base stations typically employ beamforming technology, based on acquired Channel State Information (CSI), to direct signals to legitimate users (i.e., the receivers) while simultaneously suppressing information leakage from potential eavesdroppers.

[0003] However, due to the non-cooperative nature of eavesdroppers, obtaining accurate channel state and location information from them is extremely challenging in practice. To address this issue, related technologies typically optimize worst-case security performance by establishing an uncertainty model (e.g., a norm-bounded uncertainty set) for the eavesdropper's channel state and location errors when the information is incomplete or inaccurate. Robust beamforming design is then employed to ensure reliable and secure communication.

[0004] However, due to the inherent "beam-focusing" capability of near-field systems, they are highly sensitive to the positional errors (especially angular errors) of eavesdroppers. This sensitivity stems from the "near-field angular error amplification effect" revealed in the scheme, where small positional uncertainties can evolve into significant angular deviations at close range. This leads to existing robust methods based on error limits (such as GSD or LMI) becoming extremely conservative due to the excessively large error limits. Consequently, the system is forced to significantly sacrifice communication rates to meet security requirements during the beamforming optimization design process. This results in existing physical layer secure communication systems having relatively low communication rates when using optimized beamforming for communication in order to ensure security. Summary of the Invention

[0005] This application provides a data transmission method and related equipment for a near-field communication system, which can improve the communication rate while ensuring the communication security of the physical layer secure communication system.

[0006] To achieve the above objectives, a first aspect of this application proposes a data transmission method for a near-field communication system, the near-field communication system including a base station, a receiver, and an eavesdropping terminal, the method comprising: The eavesdropping estimated location of the eavesdropping terminal is obtained, and based on the location error parameter of the eavesdropping terminal in the location uncertainty region and the eavesdropping estimated location, the eavesdropping location model of the eavesdropping terminal is obtained; Based on the eavesdropping location model, the eavesdropping rate model corresponding to the eavesdropping terminal receiving the data information sent by the base station to the receiving terminal is obtained; Based on the receiving rate model corresponding to the data information received by the receiving end from the base station, the eavesdropping rate model, and the beamforming vector parameters of the base station, a secure transmission optimization model is obtained. The location uncertainty region is divided into multiple sub-regions. Based on the proxy location corresponding to each sub-region, robust security constraints are generated. The secure transmission optimization model is then solved based on the robust security constraints to obtain the optimized beamforming vector. Based on the optimized beamforming vector, the base station is controlled to transmit data information to the receiving end.

[0007] In some embodiments, obtaining the eavesdropping rate model corresponding to the data information sent by the base station to the receiving end by the eavesdropping terminal based on the eavesdropping location model includes: Substituting the eavesdropping location model into the near-field channel steering vector model, we obtain the eavesdropping steering vector; Based on the product of the channel gain model between the eavesdropping terminal and the base station and the eavesdropping steering vector, the eavesdropping channel model between the eavesdropping terminal and the base station is obtained. Based on the eavesdropping channel model and the beamforming vector parameters, the eavesdropping rate model is obtained.

[0008] In some embodiments, obtaining a secure transmission optimization model based on the receiving rate model corresponding to the data information received by the receiving end from the base station, the eavesdropping rate model, and the beamforming vector parameters of the base station includes: Based on the receiving rate model that maximizes all the receiving ends, a target rate optimization function is obtained, wherein the receiving rate model includes the beamforming vector parameters. Obtain the beam power constraint of the beamforming vector parameters; Based on the numerical relationship between the eavesdropping rate model and the maximum eavesdropping rate threshold corresponding to all the eavesdropping terminals, security eavesdropping constraints are obtained. Based on the target rate optimization function, the beamforming vector parameters, the beam power constraint, and the security eavesdropping constraint, the secure transmission optimization model is obtained.

[0009] In some embodiments, dividing the location uncertainty region into multiple sub-regions and generating robust security constraints based on the proxy location corresponding to each sub-region includes: Based on the number of antennas of the base station, a regional angle threshold is obtained, and a maximum division angle error constraint for each sub-region is generated based on the regional angle threshold. Based on the maximum division angle error constraint, the position uncertainty region is divided into multiple sub-regions; Based on the midpoint of the angle of each sub-region, the proxy angle corresponding to the sub-region is obtained, and based on the midpoint of the distance range of each sub-region, the proxy distance corresponding to the sub-region is obtained; Based on the proxy angle and the proxy distance, the proxy position of the corresponding sub-region is obtained; Based on the proxy location corresponding to each sub-region, the robust security constraint corresponding to each geographic location is generated.

[0010] In some embodiments, generating robust security constraints for each geographic location based on the proxy location corresponding to each sub-region includes: For each of the sub-regions corresponding to the proxy location, a proxy channel steering vector is obtained based on the near-field channel steering vector model; Based on the first-order Taylor expansion of the proxy channel steering vector, an approximate steering vector model corresponding to each sub-region is obtained; Using the general symbolic determinism lemma, the approximate guiding vector model corresponding to the multiple sub-regions is transformed and expressed to obtain the robust safety constraint corresponding to each geographical location in the location uncertainty region.

[0011] In some embodiments, obtaining the approximate steering vector model corresponding to each sub-region based on the first-order Taylor expansion of the proxy channel steering vector includes: Based on the proxy location within the sub-region, the gradient of the channel steering vector with respect to the location is calculated to obtain the proxy gradient matrix; For each geographic location within the sub-region, determine the location error vector between the geographic location and the proxy location; Based on the product of the proxy gradient matrix and the position error vector, plus the proxy channel steering vector, the approximate steering vector model corresponding to the sub-region is obtained.

[0012] In some embodiments, solving the secure transmission optimization model based on the robust security constraints to obtain the optimized beamforming vector includes: Based on the continuous convex approximation technique, the target rate optimization function in the secure transmission optimization model is transformed into a substitute target optimization function; Based on the robust security constraints, the secure eavesdropping constraints in the secure transmission optimization model are replaced; Based on the updated secure transmission optimization model, an alternative transmission optimization model is obtained, and the alternative transmission optimization model is iteratively solved to obtain the optimized beamforming vector.

[0013] To achieve the above objectives, a second aspect of this application provides a data transmission apparatus for a near-field communication system, the near-field communication system including a base station, a receiver, and an eavesdropping terminal, wherein the method apparatus includes: The eavesdropping location module is used to obtain the eavesdropping estimated location of the eavesdropping terminal, and to obtain the eavesdropping location model of the eavesdropping terminal based on the location error parameter of the eavesdropping terminal in the location uncertainty area and the eavesdropping estimated location. The eavesdropping rate module is used to obtain the eavesdropping rate model corresponding to the data information sent by the base station to the receiving end by the eavesdropping terminal based on the eavesdropping location model. The optimization model module is used to obtain a secure transmission optimization model based on the receiving rate model corresponding to the data information received by the receiving end from the base station, the eavesdropping rate model, and the beamforming vector parameters of the base station. The beam optimization module is used to divide the location uncertainty region into multiple sub-regions, generate robust security constraints based on the proxy position corresponding to each sub-region, and solve the secure transmission optimization model based on the robust security constraints to obtain the optimized beamforming vector. The data transmission module is used to control the base station to transmit data information to the receiving end based on the optimized beamforming vector.

[0014] To achieve the above objectives, a third 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 data transmission method of the near-field communication system as described in the first aspect.

[0015] To achieve the above objectives, a fourth aspect of the present application provides a storage medium, which is a computer-readable storage medium storing a computer program that, when executed by a processor, implements the data transmission method of the near-field communication system described in the first aspect.

[0016] The data transmission method and related equipment of the near-field communication system proposed in this application include a base station, a receiver, and an eavesdropping device. The method includes: First, obtaining the eavesdropping estimated position of the eavesdropping device, and obtaining an eavesdropping position model of the eavesdropping device based on the position error parameter of the eavesdropping device in the position uncertainty region and the eavesdropping estimated position; then, obtaining an eavesdropping rate model corresponding to the eavesdropping device receiving data information sent by the base station to the receiver based on the eavesdropping position model; next, obtaining a secure transmission optimization model based on the receiving rate model, the eavesdropping rate model, and the beamforming vector parameters of the base station corresponding to the receiving device receiving data information sent by the base station; second, dividing the position uncertainty region into multiple sub-regions, generating robust security constraints based on the proxy position corresponding to each sub-region, and solving the secure transmission optimization model based on the robust security constraints to obtain an optimized beamforming vector; finally, controlling the base station to transmit data information to the receiver based on the optimized beamforming vector. This application's embodiments innovatively divide the entire uncertain region of the eavesdropping terminal's location into multiple sub-regions, and for the proxy location of each sub-region, use a first-order Taylor expansion to establish a high-precision approximate channel model, thereby generating refined robust security constraints. This effectively overcomes the technical problem that traditional robust methods become extremely conservative due to excessively large error bounds caused by the "near-field angle error amplification effect." This allows the solution in this application to avoid excessive suppression of the base station's transmission power without sacrificing security performance, solving the problem in related technologies where communication rates are forced to be significantly sacrificed to ensure security. Ultimately, while ensuring a high probability of secure transmission, it significantly improves the achievable communication rate of the receiving end.

[0017] Other features and advantages of this application will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the application. The objectives and other advantages of this application may be realized and obtained by means of the structures particularly pointed out in the description, claims and drawings. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the structure of a near-field communication system provided in an embodiment of this application.

[0019] Figure 2 This is a flowchart of a data transmission method for a near-field communication system provided in another embodiment of this application.

[0020] Figure 3 yes Figure 2 The flowchart for step 202.

[0021] Figure 4 yes Figure 2 The flowchart for step 203.

[0022] Figure 5This is a schematic diagram of a near-field angle error amplification effect provided in another embodiment of this application.

[0023] Figure 6 This is another embodiment of the present application, providing a CSV error limit and a corresponding simulation diagram of achievable rate and transmit power.

[0024] Figure 7 This is a schematic diagram illustrating the relationship between the square Euclidean norm of the first-order Taylor approximation error and the angle and distance errors, provided in another embodiment of this application.

[0025] Figure 8 yes Figure 2 The flowchart for step 204.

[0026] Figure 9 This is a schematic diagram of a sub-region division provided in another embodiment of this application.

[0027] Figure 10 yes Figure 8 The flowchart for step 805.

[0028] Figure 11 yes Figure 10 The flowchart for step 1002.

[0029] Figure 12 yes Figure 2 Another flowchart for step 204.

[0030] Figure 13 This is a beam simulation diagram of a different processing method provided in another embodiment of this application.

[0031] Figure 14 This is a simulation diagram illustrating how the rate and probability of secure transmission change with position error, provided in another embodiment of this application.

[0032] Figure 15 This is a simulation diagram illustrating the relationship between the total rate and the number of iterations, provided in another embodiment of this application.

[0033] Figure 16 This is a beam simulation diagram of a data transmission scheme for a near-field communication system provided in another embodiment of this application.

[0034] Figure 17 This is a simulation diagram illustrating the variation of rate and secure transmission probability with position error in a near-field communication system provided in another embodiment of this application.

[0035] Figure 18 This is a simulation diagram illustrating the variation of data rate and secure transmission probability with power ratio in an electronic device provided in another embodiment of this application.

[0036] Figure 19 This is a schematic diagram of the data transmission device of a near-field communication system provided in another embodiment of this application.

[0037] Figure 20 This is a schematic diagram of the hardware structure of an electronic device provided in another embodiment of this application. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0039] It should be noted that although functional modules are divided in the device schematic diagram and the logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart.

[0040] 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.

[0041] First, let's analyze some of the terms used in this application: Physical layer security (PLS) is a technology that utilizes the physical characteristics of the wireless channel itself (such as fading, noise, and interference) to achieve secure information transmission. It does not rely on high-level encryption algorithms, but rather uses signal processing and coding techniques to ensure that the channel quality for a legitimate receiver is superior to that of an eavesdropper, thereby achieving secure communication.

[0042] A base station (BS) is a core infrastructure in mobile communication networks, responsible for providing wireless coverage within a specific geographical area (i.e., a cellular network). It acts as a bridge between mobile terminals (such as mobile phones) and the core network, handling the transmission and reception of wireless signals, resource allocation, and handover control.

[0043] Multiple-input multiple-output (MIMO) is a wireless technology that uses multiple antennas at both the transmitting and receiving ends of a communication system. By utilizing spatial dimensions, it can significantly improve channel capacity and data transmission rate without increasing bandwidth or transmit power.

[0044] Channel state information (CSI) is a dataset that describes the physical path characteristics of a wireless signal as it travels from the transmitter to the receiver. It typically includes information such as signal attenuation, phase changes, and multipath delay, and is fundamental to advanced technologies such as beamforming and resource allocation.

[0045] Intelligent reflecting surfaces (IRSs) are artificial electromagnetic surfaces composed of numerous low-cost, passive reflecting elements. They can intelligently control the amplitude and phase of incident electromagnetic waves through software programming, thereby actively reconstructing the wireless propagation environment to improve communication quality.

[0046] Integrated sensing and communications (ISAC) is an emerging wireless technology paradigm that aims to integrate wireless communication with radar sensing capabilities within the same hardware platform and signal framework. This technology allows systems to perceive their surroundings (such as target detection, localization, and tracking) while transmitting data, enabling resource sharing and complementary performance.

[0047] General sign-definiteness (GSD) is a mathematical concept in convex optimization and control theory used to analyze specific types of quadratic matrix inequalities. It is frequently used as a lemma or tool to handle non-convex constraints involving uncertain parameters in robust optimization problems, transforming them into solvable convex constraints.

[0048] In communication systems, degrees of freedom (DoF) measure the maximum number of data streams that a system can transmit simultaneously and independently. It represents the signal dimensions that the system can utilize, such as the time domain, frequency domain, or spatial domain in MIMO systems.

[0049] Extremely large-scale arrays (XL-arrays) are array systems equipped with an extremely large number of antenna elements (usually hundreds or thousands or even more). The huge aperture of such arrays gives them near-field propagation characteristics, enabling unprecedented high spatial resolution and "beam focusing" capabilities.

[0050] Line-of-sight (LoS) is a radio wave propagation scenario where there is a direct path between the transmitting and receiving antennas without any physical obstacles. In the LoS scenario, signal propagation is primarily direct wave propagation, and the channel characteristics are relatively stable and predictable.

[0051] Non-line-of-sight (NLoS) is a radio wave propagation scenario where the direct path between the transmitting and receiving antennas is blocked by obstacles such as buildings. In NLoS scenarios, signals propagate to the receiver primarily through multiple paths, including reflection, diffraction, and scattering, resulting in more complex channel characteristics and more severe fading.

[0052] Additive white Gaussian noise (AWGN) is an idealized channel noise model used in communication theory to simplify analysis. "Additive" means that it is added to the signal, "Gaussian" means that its amplitude is distributed in a Gaussian manner, and "white" means that its power is uniformly distributed across all frequencies.

[0053] Linear matrix inequalities (LMIs) are a form of constraint in convex optimization that requires an affine symmetric matrix with respect to decision variables to be positive semidefinite. Many complex system control and signal processing problems can be transformed into LMI problems and solved using efficient algorithms such as the interior-point method.

[0054] A second-order cone (SOC) is a specific set of convex cones in mathematical optimization, typically defined as ||Ax + b||_2 <= c^T x + d. Optimization problems involving second-order cone constraints are called second-order cone programming (SOCP), an important and efficiently solvable class of problems in convex optimization.

[0055] The channel steering vector (CSV) (also often simply called the steering vector) is a complex vector that characterizes the response of an antenna array to plane or spherical waves from a specific direction or location. It is a core component of beamforming and direction-of-arrival (DOA) algorithms, determining how the antenna array focuses or receives the energy of a specific spatial signal.

[0056] Successive convex approximation (SCA) is a powerful iterative algorithm for solving complex nonconvex optimization problems. Its core idea is to approximate the original nonconvex problem into a more easily solvable convex problem in each iteration by performing Taylor expansion or other methods at the current point, and then iteratively approximate the optimal solution of the original problem. Physical Layer Security (PLS) communication systems utilize spatial diversity provided by multiple antennas, enabling base stations to direct directional beams towards legitimate users while suppressing information leakage from potential eavesdroppers. In PLS communication systems, multi-antenna base stations typically employ beamforming technology, based on acquired Channel State Information (CSI), to direct signals to legitimate users (i.e., the receivers) while simultaneously suppressing information leakage from potential eavesdroppers.

[0057] However, due to the non-cooperative nature of eavesdroppers, obtaining accurate channel state and location information from them is extremely challenging in practice. To address this issue, related technologies typically optimize worst-case security performance by establishing an uncertainty model (e.g., a norm-bounded uncertainty set) for the eavesdropper's channel state and location errors when the information is incomplete or inaccurate. Robust beamforming design is then employed to ensure reliable and secure communication.

[0058] However, due to the inherent "beam-focusing" capability of near-field systems, they are highly sensitive to the positional errors (especially angular errors) of eavesdroppers. This sensitivity stems from the "near-field angular error amplification effect" revealed in the scheme, where small positional uncertainties can evolve into significant angular deviations at close range. This leads to existing robust methods based on error limits (such as GSD or LMI) becoming extremely conservative due to the excessively large error limits. Consequently, the system is forced to significantly sacrifice communication rates to meet security requirements during the beamforming optimization design process. This results in existing physical layer secure communication systems having relatively low communication rates when using optimized beamforming for communication in order to ensure security.

[0059] To improve communication speed while ensuring communication security in a physical layer secure communication system, this application innovatively divides the entire uncertain region of the eavesdropping terminal's location into multiple sub-regions. For the proxy location of each sub-region, a high-precision approximate channel model is established using a first-order Taylor expansion, thereby generating refined robust security constraints. This effectively overcomes the technical problem that traditional robust methods become extremely conservative due to excessively large error bounds caused by the "near-field angle error amplification effect." This allows the solution in this application to avoid excessive suppression of base station transmission power without sacrificing security performance, solving the problem of forced significant sacrifice of communication speed in related technologies to ensure security. Ultimately, while ensuring a high probability of secure transmission, it significantly improves the achievable communication speed of the receiving end.

[0060] To better describe the data transmission method of the near-field communication system provided in this application, the near-field communication system applied to the data transmission method of the near-field communication system is described first below. (Refer to...) Figure 1This is a schematic diagram of a near-field communication system provided in an embodiment of this application. Figure 1 As shown, a near-field communication system includes a base station equipped with an ultra-large-scale antenna array (XL-array), multiple legitimate users (Bobs, i.e., the receivers in the following text), and multiple eavesdropping users (Eves, i.e., the eavesdropping ends in the following text). According to this model, the base station possesses perfect location information for the legitimate users (Bobs), but can only obtain imperfect location information for the eavesdropping users (Eves). The purpose of this application is to design a robust beamforming scheme using the near-field beam focusing capability of the XL-array in situations where the eavesdropper's location is uncertain, to ensure that signal energy (shown as the blue beam in the figure) is accurately transmitted to the Bobs, while suppressing information leakage within the uncertainty region where the Eves are located.

[0061] In such Figure 1 In the near-field communication system shown, there is The base station (BS) with one antenna is in the downlink. Each single-antenna Bob (i.e., the receiver) provides service, and these Bobs use a set of It indicates. At the same time, there is... Each single-antenna Eve (i.e., the eavesdropping device) is used in a set This indicates that the XL array is located near a base station to intercept legitimate communications over short distances. Without loss of generality, the XL array is positioned... On the axis, its array center is located Assuming the antenna spacing is half a wavelength, the first... The position of the root antenna is determined by Given, among which ,here , Indicates the carrier frequency.

[0062] The propagation channel associated with the XL-array of the base station is modeled based on a spherical wavefront. Therefore, in the near-field communication system of this application embodiment, any wavefront located in a Cartesian coordinate system is considered. The receiving end at the location .use Indicates the receiving end The channel received from the base station has the following channel model as shown in formula (1).

[0063] (1) The channel consists of a line-of-sight (LoS) path and It consists of several non-line-of-sight (non-LoS, NLoS) paths. Represents the complex channel gain. The reference channel gain at a distance of 1 meter. For legitimate users (i.e., the receiving end) The distance from the center of the XL-array. Furthermore, and Do not represent path The complex channel gain and scatterer location. In the embodiments of this application, a high-frequency scenario is considered, in which the power of the NLoS path can be ignored due to severe path loss and shadowing effects. It is worth noting that in multipath scenarios, the NLoS component can be bounded to its maximum power. Therefore, the receiver... The channel can be approximated by its LoS component in equation (1), i.e. Among them, the near-field channel steering vector (CSV) is the near-field channel steering vector model. , is given by the following formula (2).

[0064] (2) Here, Indicates the receiving end With the The distance between the XL-array antennas can be obtained by the Fresnel approximation method as shown in the following formula (3).

[0065] (3) in, and Bob represents the base station and the receiver, respectively. The distance and (physical) angle between them are given by the following formula (4).

[0066] (4) Therefore, the near-field channel steering vector model in equation (2) It can also be expressed as and The function is shown in (5).

[0067] (5) Similarly, from the base station to the... The channel of the eavesdropping terminal is denoted as... It can be modeled as shown in the following formula (6).

[0068] (6) in, This represents the complex-valued channel gain, while That is the location of the eavesdropping device. By using... as well as eavesdropping terminal The near-field channel steering vector model can also be expressed as .

[0069] Based on the aforementioned near-field communication system, the data transmission method and related equipment of the near-field communication system provided in the embodiments of this application will be further described below. The data transmission method of the near-field communication system provided in the embodiments of this application can be applied to the controller in the base station or the control processor (such as a server, smart terminal, etc.) connected to the near-field communication system.

[0070] The data transmission method of the near-field communication system in the embodiments of this application will be described in detail below. (Refer to...) Figure 2 This is an optional flowchart of a data transmission method for a near-field communication system provided in an embodiment of this application. Figure 2 The method may include, but is not limited to, steps 201 to 205. It is also understood that this embodiment... Figure 2 The order of steps 201 to 205 is not specifically limited. The order of steps can be adjusted or some steps can be reduced or added according to actual needs.

[0071] Step 201: Obtain the eavesdropping estimated location of the eavesdropping terminal, and based on the location error parameter of the eavesdropping terminal in the location uncertainty area and the eavesdropping estimated location, obtain the eavesdropping location model of the eavesdropping terminal.

[0072] Step 201 will be described in detail below.

[0073] In near-field line-of-sight-dominated scenarios, accurately acquiring channel state information from both the receiver and the eavesdropping device is crucial for efficient beamforming design, which largely depends on location information. In this embodiment, it is assumed that the base station possesses precise location information of the receiver, as legitimate users can typically cooperate with the base station to acquire channel state information and share location information. Existing near-field localization methods, as well as classic methods such as time-of-arrival, received signal strength, and radio fingerprinting, can be used to practically acquire the receiver's location. Furthermore, since eavesdroppers typically conceal their presence, it must be assumed that their location information is inaccurate, and this information can be obtained through non-cooperative localization methods. For example, the eavesdropper's location can be estimated by monitoring the power leakage of the local oscillator at the receiver's RF front-end. However, this method is susceptible to environmental interference and received noise, often leading to inaccurate location estimation.

[0074] Therefore, in near-field communication systems, before optimizing the beamforming vector parameters of the base station, it is necessary to properly model the location of the eavesdropping device to facilitate subsequent optimization calculations. Based on this, the estimated location of the eavesdropping device is first obtained. (Indicates the first) (Location estimation of the eavesdropping device), which is obtained, for example, through a non-cooperative localization method. Subsequently, based on this eavesdropping estimated location... and the positional error parameters of the eavesdropping device in the region of positional uncertainty. The eavesdropping location model of the eavesdropping terminal is jointly established as shown in the following formula (7).

[0075] (7) Specifically, this eavesdropping location model describes the actual location of the eavesdropping device as its estimated location. With a bounded position error vector The sum of these factors constrains the error vector to a bounded spherical region of uncertainty centered on the estimated position, with a radius determined by the position error parameter and the confidence level. Inside.

[0076] in, This represents the position error parameter in the Cartesian coordinate system. By adopting a non-cooperative positioning method, the position error parameter vector can be modeled as a two-dimensional Gaussian distribution as shown in the following formula (8).

[0077] (8) in, , and They represent and The mean. Furthermore, It is the covariance matrix, given by the following formula (9).

[0078] (9) in, and They are and The variance, and This represents the correlation coefficient between the two variables. In the embodiments of this application, positional error is considered. and With a mean of zero and a variance of The case of independent Gaussian variables. For , as well as In this situation, the uncertainty area of ​​the eavesdropping end Depend on Given this elliptical uncertainty region, the proposed robust beamforming method can be directly extended to this general case. Therefore, the distribution of the position error parameter vector is as shown in the following formula (10).

[0079] (10) Step 202: Based on the eavesdropping location model, obtain the eavesdropping rate model corresponding to the data information sent by the base station to the receiving end.

[0080] Step 202 will be described in detail below.

[0081] In the embodiments of this application, it is set that as well as For the receiving end These represent the information sent by the base station to each receiver. The transmitted data information corresponds to the signal and beamforming vector parameters. Therefore, the receiving end... The received signal can be represented as shown in the following formula (11).

[0082] (11) in, This represents the received additive white Gaussian noise (AWGN). Therefore, the receiver... The receiving rate model corresponding to the achievable rate (in bits / second / hertz, bps / Hz) is shown in the following formula (12).

[0083] (1) Based on this, for the eavesdropping end, based on the eavesdropping location model (7) established in the previous step, the eavesdropping rate model is further derived. Specifically, the eavesdropping rate is a function of the eavesdropping channel between the base station and the eavesdropping device. In near-field line-of-sight dominant scenarios, the eavesdropping channel is jointly determined by the channel gain and the near-field channel steering vector (CSV). The near-field channel steering vector is a direct function of the eavesdropper's physical location. Therefore, since the eavesdropping location model (7) constrains the location of the eavesdropping device to an uncertain region... Inside, It is also represented by the rate at which information can be eavesdropped at any point within this uncertainty region, as described below.

[0084] Reference Figure 3 Based on the position error parameters of the eavesdropping terminal in the position uncertainty area and the eavesdropping estimated position, the eavesdropping position model of the eavesdropping terminal is obtained, including the following steps 301 to 303.

[0085] Step 301: Substitute the eavesdropping location model into the near-field channel steering vector model to obtain the eavesdropping steering vector.

[0086] Step 302: Based on the product of the channel gain model between the eavesdropping terminal and the base station and the eavesdropping steering vector, obtain the eavesdropping channel model between the eavesdropping terminal and the base station.

[0087] Step 303: Based on the eavesdropping channel model and beamforming vector parameters, obtain the eavesdropping rate model.

[0088] Steps 301 to 303 are described in detail below.

[0089] In some embodiments, the known eavesdropping location model (i.e., the eavesdropper is located in a bounded region of uncertainty) is used. Substituting this fact into the near-field channel steering vector model The near-field channel steering vector model is a key mathematical model that maps the geometric positions between transceivers (especially the angles and distances relied upon in near-field communication) to specific response vectors of the antenna array. By substituting this into the model, the eavesdropping steering vector can be obtained. The eavesdropping steering vector is a function of the eavesdropper's uncertain location, and it characterizes the channel spatial characteristics from the base station antenna array to the eavesdropper's uncertain location.

[0090] Then, based on the channel gain model between the eavesdropping device and the base station And the eavesdropping guidance vector obtained in the previous step The product of these two equations yields the eavesdropping channel model between the eavesdropping device and the base station. This eavesdropping channel model (i.e., the complete near-field channel vector as shown in equation (6)) encapsulates the complete path propagation characteristics from the base station to the eavesdropper. Since this model relies on an uncertain eavesdropping steering vector, the eavesdropping channel model itself is also an unknown vector that varies with location within the uncertainty region defined by the eavesdropping location model.

[0091] Therefore, for Eves, the eavesdropping terminal attempting to intercept the transmission of confidential information, the eavesdropping terminal... The received signal is shown in the following formula (13).

[0092] (13) in Indicates at the eavesdropping end The received additive white Gaussian noise. Consider a scenario where each eavesdropper can eliminate all multi-user interference without cooperation and then decode legitimate information, posing a practical challenge to secure communication. The most challenging worst-case scenario is considered, characterizing the lower bound of system performance under the assumption that channel state information at all receivers is perfect. The proposed method is applicable to residual interference due to imperfect or incomplete elimination of channel state information, as well as inherent multi-user interference, by introducing auxiliary variables.

[0093] Based on this, and the eavesdropping channel model obtained in the previous step... The eavesdropping rate model is obtained by combining the beamforming vector parameters configured by the base station for legitimate users with the following formula (14).

[0094] (14) Specifically, the rate at which an eavesdropper can intercept a specific user's signal is a function of the received signal-to-interference-to-noise ratio (SINR). This SINR depends on the square of the inner product modulus of the eavesdropping channel model and the corresponding beamforming vector parameters, as well as the noise power of the eavesdropping device. The resulting eavesdropping rate model (as shown in Equation (14)) is a key performance indicator, which is also a function of the eavesdropper's location because the eavesdropping channel model it relies on is uncertain.

[0095] Through steps 301 to 303 above, a physical-level, geometrically based uncertainty (i.e., the eavesdropping location model) is mapped and mathematically represented layer by layer. First, the location uncertainty is transformed into the uncertainty of channel spatial characteristics (i.e., the eavesdropping steering vector) through a near-field channel steering vector model. Then, combined with the channel gain model, a complete eavesdropping channel model is obtained, and finally, the uncertainty of communication performance indicators (i.e., the eavesdropping rate model) is derived. The effectiveness of this process lies in its successful mathematical binding of the eavesdropper's physical location uncertainty with the system's security performance (i.e., the eavesdropping rate). This provides a necessary and computable model foundation for establishing robust security constraints and designing beamforming schemes that can suppress the eavesdropping rate in the worst case in subsequent steps.

[0096] Step 203: Based on the receiving rate model, eavesdropping rate model, and beamforming vector parameters of the base station corresponding to the data information received by the receiving end from the base station, a secure transmission optimization model is obtained.

[0097] Step 203 will be described in detail below.

[0098] In some embodiments, a secure transmission optimization model needs to be constructed in order to perform reasonable optimization in the near-field communication system.

[0099] In this embodiment of the application, the objective is to ensure that the amount of information leakage from each eavesdropping device is below a specified threshold. Simultaneously, we maximize the sum rate of all legitimate users (i.e., receivers) while considering the uncertainty of the eavesdropping device's location. Specifically, to facilitate robust beamforming design in the worst-case scenario, we consider each eavesdropping device... Bounded spherical uncertainty region of position error (instead of the unbounded region corresponding to the original formula (10), where It is the center of the uncertainty region, and its uncertainty radius is given by the following formula (15).

[0100] (15) Here, Let represent the inverse cumulative distribution function of a chi-square distribution with 2 degrees of freedom. Indicates the confidence level (e.g., (Corresponding to a 95% confidence level). Region Ensure the The actual location of the eavesdropping device is, for example, within that area with a 95% probability. Let... and They represent the first The estimated distance and angle of each eavesdropping device.

[0101] Based on the aforementioned spherical uncertainty region, each eavesdropping terminal The angle and distance errors are denoted as follows: and It satisfies the following formula (16) (16) The secure transmission optimization model is an optimization problem with the objective function of maximizing the total rate of all receivers (i.e., the receiver rate model (12)), as described below.

[0102] Reference Figure 4 Based on the receiving rate model, eavesdropping rate model, and beamforming vector parameters of the base station corresponding to the data information received by the receiving end, a secure transmission optimization model is obtained, including the following steps 401 to 404.

[0103] Step 401: Based on the model that maximizes the receiving rate of all receivers, obtain the target rate optimization function. The receiving rate model includes beamforming vector parameters.

[0104] Step 402: Obtain the beam power constraint of the beamforming vector parameters.

[0105] Step 403: Based on the numerical relationship between the eavesdropping rate model and the maximum eavesdropping rate threshold corresponding to all eavesdropping terminals, obtain the security eavesdropping constraints.

[0106] Step 404: Based on the target rate optimization function, beamforming vector parameters, beam power constraints, and security eavesdropping constraints, a secure transmission optimization model is obtained.

[0107] Steps 401 to 404 are described in detail below.

[0108] In some embodiments, an optimization objective is first constructed, namely, a target rate optimization function is obtained based on maximizing the receiver rate model (12) corresponding to all receivers. The receiver rate model (as shown in Equation (12)) is a mathematical model for calculating the achievable communication rate of legitimate users, which depends on the channel, interference, and noise power of legitimate users. Since the signal power of the receiver is directly related to the beamforming gain of the base station, the receiver rate model includes beamforming vector parameters. By summing the rate models of all legitimate receivers and setting them as the maximization objective, the target rate optimization function is obtained, which characterizes the overall throughput performance of the system.

[0109] Furthermore, obtain the beamforming vector parameters. The beam power constraint is an inherent characteristic of the base station's physical hardware. It stipulates that the total transmit power of the base station (BS) used to transmit all beamforming signals cannot exceed a preset maximum power value. Mathematically, this constraint is typically represented by all beamforming vector parameters. The sum of the squares of the second norm must be less than or equal to This is a fundamental prerequisite for ensuring the practical feasibility of the optimization model.

[0110] Simultaneously, based on the system's security requirements, security eavesdropping constraints are established. These constraints are based on the eavesdropping rate model corresponding to all eavesdropping terminals (as shown in Equation (14)) and the maximum eavesdropping rate threshold. The numerical relationship is used to determine this. Specifically, to ensure robust security, this numerical relationship is set as follows: in areas where the eavesdropper's location is uncertain... The maximum eavesdropping rate achievable at all possible locations must be less than or equal to that maximum eavesdropping rate threshold. This constraint ensures that even if an eavesdropper is in the most advantageous position within their uncertain area, their ability to steal information is strictly limited to a preset security level.

[0111] Finally, by integrating all the aforementioned components, the secure transmission optimization model is obtained as shown in the following formula (17).

[0112] (17) The model is a complete mathematical programming problem (as shown in problem (17)), with the obtained target rate optimization function as the maximization objective; at the same time, it must satisfy beam power constraints and security eavesdropping constraints; and the solution variables of the entire model are the beamforming vector parameters; among which constraint (17a) limits the maximum transmit power of the base station to The constraint (17b) ensures that positional errors exist. In the worst-case scenario, the eavesdropping rate of each eavesdropping terminal against any legitimate receiver will not exceed the prescribed threshold. .

[0113] In summary, the overall effectiveness of steps 401 to 404 lies in systematically and rigorously transforming a complex near-field physical layer secure communication scenario into a well-defined mathematical optimization problem, namely, a secure transmission optimization model. This model precisely quantifies the relationship between the core objective of the system design (i.e., the target rate optimization function) and the physical constraints (i.e., beam power constraints) and security performance indicators (i.e., security eavesdropping constraints) that must be followed. By constructing this model, this invention provides the necessary and computable mathematical foundation for subsequent steps to solve for the optimized beamforming vector using advanced techniques such as region partitioning and LMI, thereby achieving a balance between maximizing communication rate and ensuring robust security in the worst-case scenario.

[0114] Problem (P1) is a non-convex optimization problem, so it is usually difficult to obtain the optimal solution because: 1) the objective function is relative to the beamforming vector 1) It is non-concave; 2) Due to the continuous set of uncertainties, the positional uncertainty of the eavesdropping end introduces infinitely many non-convex constraints in (17b). In order to solve these problems and gain useful insights, the following embodiments of this application first consider the case of a single Bob and a single Eve, and propose an effective method to solve the problem (P1) for this case, and then further generalize the method to the general case.

[0115] For the case of a single Bob and a single Eve (i.e., a near-field communication system with only a single receiver and a single eavesdropping device), this application first introduces two traditional methods and points out their main limitations. Then, an efficient two-stage robust beamforming method is proposed to effectively overcome these limitations and the aforementioned challenges in solving the problem (P1). For brevity, the indices for Bob and Eve are omitted in this section.

[0116] First, for the case under consideration, problem (P1) simplifies to the following formula (18).

[0117] (18) in, However, since the objective function is non-concave and (18b) has infinitely many constraints, problem (P2) remains difficult to solve. To address these issues, the successful convex approximation (SCA) technique is first employed to approximate (P2). Construct a concave substitution function, as shown in the following formula.

[0118]

[0119] in It is the first Feasible beamforming vectors in the next SCA iteration. Next, for the non-convex constraint in constraint (18b), there are two typical solutions in existing schemes: 1) using the continuous uncertainty set... Discretize the constraint (18b) into a finite number of samples, and 2) approximate the constraint (18b) as a single linear matrix inequality using the channel error bound. Details of these two methods are described below.

[0120] 1) Sampling-based method: Considering the spherical uncertainty region The uniform location sampling method is widely used in China. Let... This represents the total number of sampling points, where the possible locations for Eve (i.e., the eavesdropping device) are... Sampling was conducted at the location. Therefore, constraint (18b) can be approximated as shown in formula (19).

[0121] (19) This transformation converts constraint (18b) into... The sampling method employs convex quadratic constraints, allowing the use of standard convex optimization tools to solve this convex optimization problem. However, the performance of this sampling-based method is critically dependent on the number of sampling points. Insufficient sampling points prevent adequate traversal of the continuous uncertainty set. Therefore, it is impossible to guarantee the eavesdropping rate constraint within the uncertainty set. On the other hand, a large number of sampling points can more accurately approximate the uncertainty set, but this will bring extremely high computational complexity proportional to the number of sampling points, making it unacceptable in practical applications.

[0122] 2) Error-bound-based methods: For error-bound-based methods, the CSV error bound is used to transform an infinite number of constraints into a single linear matrix inequality. Specifically, by using the position... A first-order Taylor expansion at a given location, for any location... The CSV of Eve is approximated as follows, as shown in Equation (20).

[0123] (20) in, and They are about and The gradient of CSV. Based on the above, the maximum error of CSV can be bounded by the following formula (21).

[0124] (twenty one) Among them, due to the triangle inequality, we have Based on equation (21), by using GSD, the constraint (18b) can be rewritten as the following linear matrix inequality (22).

[0125] (twenty two) in It is an auxiliary variable.

[0126] For the position error model considered in equation (7), given the position error parameters (or When the estimated distance to the eavesdropper is relatively small, the angle error (i.e.) The error can become very large, which is known as the near-field angle error amplification effect.

[0127] Reference Figure 5 This is a schematic diagram illustrating a near-field angle error amplification effect provided in an embodiment of this application. For example... Figure 5 The figure illustrates the key technical problem this application aims to solve: "near-field angle error amplification effect." The attached figure shows two circular regions with the same radius representing possible locations of eavesdropping users (Eves), but at different distances from the base station (the origin). Figure 5 As shown, the range of angular uncertainty corresponding to the blue solid line area closer to the base station is significantly larger than the range of angular uncertainty corresponding to the red dashed line area farther from the base station. This effect indicates that, in the near-field situation, a fixed position error leads to an amplified angular error, which causes the traditional robust beamforming method based on the first-order Taylor approximation to fail due to inaccurate approximation, thus highlighting the necessity of the "region division" strategy adopted in this application.

[0128] This effect introduces two limitations to the performance of error-bound methods. First, at point ( ) The first-order Taylor approximation (see Equation (20)) is likely applicable to all potential eavesdropper locations. Neither is accurate, when the angle error ( ) and / or distance error ( When the error bound is relatively large, the approximation error becomes significant. Secondly, the performance of methods based on error bounds is affected by the size of the error bound (i.e., ...). Due to the limitations of the effective range, and the amplification effect of angular errors, this error boundary often varies with the effective range. The decrease in density leads to an increase in density, which in turn leads to a more conservative beamforming design under confidentiality requirements.

[0129] Reference Figure 6This is a simulation diagram illustrating a CSV error limit provided in an embodiment of this application, along with the corresponding achievable rate and transmit power. For example... Figure 6 As shown in the figure, two sub-figures demonstrate, through data, the core technical problem to be solved by this application: the failure of traditional robust beamforming methods based on error limits in near-field communication. Sub-figure (a) shows the relationship between the channel steering vector (CSV) error limit and the estimated distance of the eavesdropper (Eve). It clearly shows that when the eavesdropper is very close to the base station (e.g., less than 50 meters), the CSV error caused by the "near-field angle error amplification effect" increases sharply. Sub-figure (b) further reveals the severity of this consequence: as demonstrated in Proposition 1 of this application, as the CSV error increases, the optimized transmission power (red line) of the traditional robust method to meet security constraints will rapidly decrease; this conservative power strategy directly leads to the achievable rate (blue line) also plummeting to almost zero, thus proving that the existing technology cannot balance security and rate under near-field uncertainty, highlighting the necessity of the region partitioning and fine LMI reconstruction adopted in this application.

[0130] Proposition 1: For error-bound methods, given Error bound in equation (21) And the estimated location of the eavesdropper Beamforming vector It should satisfy the following under the LMI constraint (22): .

[0131] Proof: A necessary condition for the optimization problem corresponding to the error bound method to be feasible is that To ensure The following inequalities should be satisfied.

[0132]

[0133] based on We have as well as This can be rewritten as Thus, the proof is completed.

[0134] like Figure 6 As shown in (b), the estimated location of Eve is... The optimized transmit power of the method based on the error bound decreases monotonically with respect to the error bound, as stated in Proposition 1. It is noteworthy that even for relatively small CSV error bounds (e.g., 0.1, much smaller than...), the error remains constant. Figure 6 The values ​​in (a) also mean that the transmit power allocated to the base station approaches zero, resulting in a significant decrease in the achievable rate.

[0135] Step 204: Divide the location uncertainty region into multiple sub-regions, generate robust security constraints based on the proxy location corresponding to each sub-region, and solve the secure transmission optimization model based on the robust security constraints to obtain the optimized beamforming vector.

[0136] Based on this, this application proposes an efficient near-field robust safety beamforming method. This method achieves superior PLS performance with low complexity, thus outperforming the traditional methods mentioned above. Essentially, the method proposed in this application first determines an effective region where the first-order Taylor approximation of the CSV is sufficiently accurate. Then, based on this, the uncertain region is divided into a finite number of sub-regions to design robust beamforming. The conditions for the accuracy of the first-order Taylor approximation are described below.

[0137] 1) Conditions for the accuracy of the first-order Taylor approximation: In order to overcome the limitations of the error-boundary-based methods mentioned above, we first describe the CSV error caused by angle and distance deviations, and then establish the conditions for the accuracy of the first-order Taylor approximation.

[0138] Specifically, in the spherical uncertainty region In the case of the eavesdropping terminal, the CSV error is shown in the following formula (23).

[0139] (twenty three) Then, assuming no distance / angle error, the CSV error in the angle / distance domain is obtained.

[0140] Lemma 1 (Distance Domain CSV Error): Given a spherical region of uncertainty as well as The CSV error of Eve, the eavesdropping device, is given by the following formula. (twenty four) in, ,and Furthermore, when When smaller (e.g., In equation (24) It can be approximated by the following formula (25).

[0141] (25) in .

[0142] Proof: When At that time, Xiang It can be approximated as ,in , ,as well as Based on the above, item Can be rewritten as Thus, we obtain the equation (24) .

[0143] when Small enough to ensure At that time, for ,have And in equation (24) It can be approximated by the following formula.

[0144]

[0145] therefore, It can be rewritten as shown in the following formula.

[0146]

[0147] Will Substituting into the above formula, we obtain the following formula.

[0148]

[0149] And in (For example, Under the condition of ), utilize The above equation holds true, thus completing the proof.

[0150] Lemma 2 (Angular Domain CSV Error): Given a spherical uncertainty region as well as Eve's CSV error is given by the following formula (26).

[0151] (26) in, (27) In addition, when When, in equation (26) It can be approximated by the following formula (28).

[0152] (28) in .

[0153] Proof: When At that time, due to the relatively small angle error, the approximate formula is... Therefore, the item is valid. It can be approximated by the following formula.

[0154]

[0155] Given In the interval arrive The upper part is monotonically decreasing, and in The value reaches its minimum near the nearest point, thus we obtain the value in equation (27). .

[0156] make Then the terms in equation (27) It can be represented as Known and Then there is as well as Using approximate formulas (when (time) and (when hour), It can be approximately expressed as shown in the following formula.

[0157]

[0158] therefore, It can be rewritten as shown in the following formula.

[0159]

[0160] in And because for small ,have and Therefore, (c) holds true (i.e., the above equation), thus completing the proof.

[0161] The two lemmas above show that when Very small and hour, and They can be expressed as about and The linear function is given. Based on this, the conditions for the first-order Taylor approximation of CSV to be approximately accurate are obtained.

[0162] Proposition 2 (Condition for the first-order Taylor approximation to be accurate): When Very small (e.g., )and When the first-order Taylor approximation is given by the following formula.

[0163]

[0164] It is accurate. Among them, and They are CSV about and The gradients are expressed as shown in the following formula (29).

[0165] (29) And this includes,

[0166]

[0167]

[0168] Proof: Let The squared Euclidean norm, representing the approximation error, is expressed as follows.

[0169]

[0170] By introducing intermediate variables , It can be rewritten as shown in (30).

[0171] (30) Considering that when the error range is small, there is Therefore, the proof of proposition 2 can be equivalently accomplished by proving the following equation (31).

[0172] (31) make ,as well as These represent the approximate CSV error in the angular and distance domains, respectively. When... Very small and At that time, it was found that as well as This is because the CSV error in the range domain obtained through the Taylor approximation (i.e., ) can be represented as shown below.

[0173]

[0174] Based on antenna location , which can be represented as shown below.

[0175]

[0176] Therefore, CSV error Rewritten as shown below.

[0177]

[0178] Right now, Similarly, the CSV error obtained in the angle domain via Taylor approximation. It can be expressed as the following formula.

[0179]

[0180] because It is small enough that (d) (i.e., the above equation) holds. Given the following formula.

[0181]

[0182] It can be concluded that Equation (31) holds, because, let ,but The square norm is given by the following formula.

[0183]

[0184] According to formula (31) For the specific expression, we have the following formula.

[0185]

[0186] In this equation, equation (e) holds because the quadratic term is sufficiently small, and equation (f) holds by using... Equation (g) holds true when Under these conditions, based on the above, we conclude... Similarly, it can be easily proven that... Detailed proof is omitted here. Based on the above, we conclude... Thus, the proof is completed.

[0187] It is worth noting that, under the considered position error model, it is easy to prove that when the angle error satisfies At that time, the corresponding distance error It always holds true, because The results are significantly smaller. The above findings indicate that, in order to ensure the accuracy of the first-order Taylor approximation, the angle error can satisfy the constraint condition shown in the following formula (32).

[0188] (32) In this case, the original uncertainty region It is divided into multiple sub-regions. This will be used for subsequent undetermined region partitioning.

[0189] Reference Figure 7This diagram illustrates the relationship between the squared Euclidean norm of the approximation error of a first-order Taylor approximation and the angle and distance errors, as provided in an embodiment of this application. Simulation data visually verifies the theoretical basis of the region division in this application, namely, the accuracy condition of the first-order Taylor approximation. The diagram uses a three-dimensional surface to show how the approximation error of the channel steering vector (CSV) changes with the angle and distance errors. It is clearly observed from the diagram that the approximation error is highly sensitive to the angle error. When the angle error exceeds a certain threshold (e.g., the condition represented by the magenta line in the diagram), the approximation error increases sharply (the color changes from dark to bright yellow), indicating that the first-order Taylor approximation fails in this region. Therefore, this diagram strongly demonstrates that the present invention must divide the uncertainty region into multiple sub-regions to ensure that the angle error in each sub-region is less than the threshold, thereby guaranteeing the accuracy of the subsequently generated robust security constraints.

[0190] In such Figure 7 In the example shown, to evaluate the accuracy of the first-order Taylor approximation method, we... Figure 7 The squared Euclidean norm between the actual CSV and its Taylor approximation vector is plotted in the figure. The main observations are as follows.

[0191] (1) When hour, The value remains relatively small, indicating that the Taylor approximation accurately describes CSV within this range.

[0192] (2) Once The approximation error will increase significantly, indicating that the Taylor approximation becomes inaccurate and is therefore unsuitable for characterizing regions with large angular errors.

[0193] Step 204 is described in detail below.

[0194] Therefore, in this scheme, based on the exact Taylor approximation condition, we propose an efficient two-stage robust beamforming method. In the first stage, the method cleverly divides the spherical uncertainty region, and then in the second stage, it uses the first-order Taylor approximation and GSD technique to reformulate and solve the resulting optimization problem.

[0195] In some embodiments, to address the non-convexity problem caused by the worst-case eavesdropping rate constraint (e.g., (17b)) in the secure transmission optimization model (e.g., problem (P1) or problem (P2)) in step 203, this application employs a two-stage solution method. First, region partitioning is performed, that is, dividing the location uncertainty region into multiple sub-regions. The criterion for this partitioning is to overcome the "near-field angle error amplification effect" and ensure that the first-order Taylor approximation of the channel steering vector (CSV) maintains sufficient accuracy in each sub-region. Next, robust security constraints are generated based on the proxy location corresponding to each sub-region. This generation process specifically includes: performing a first-order Taylor expansion of the CSV at the proxy location, and using the General Symbolic Determinism (GSD) lemma to transform the original non-convex constraints into a set of refined and efficiently solvable convex constraints, such as linear matrix inequalities (LMI). Finally, the secure transmission optimization model is solved based on robust security constraints. At this point, the original problem (P1) has been transformed into a convex optimization problem, which can be solved iteratively by continuous convex approximation (SCA) and convex optimization tools (such as CVX) to finally obtain the optimized beamforming vector.

[0196] The following is a detailed description.

[0197] Reference Figure 8 The location uncertainty area is divided into multiple sub-regions, and robust security constraints are generated based on the agent location corresponding to each sub-region, including the following steps 801 to 805.

[0198] Step 801: Based on the number of antennas of the base station, obtain the regional angle threshold, and generate the maximum division angle error constraint for each sub-region based on the regional angle threshold.

[0199] Step 802: Divide the region of position uncertainty into multiple sub-regions based on the maximum division angle error constraint.

[0200] Step 803: Based on the midpoint of the angle of each sub-region, obtain the proxy angle corresponding to the sub-region, and based on the midpoint of the distance range of each sub-region, obtain the proxy distance corresponding to the sub-region.

[0201] Step 804: Based on the proxy angle and proxy distance, obtain the proxy position of the corresponding sub-region.

[0202] Step 805: Generate robust security constraints for each geographic location based on the proxy location corresponding to each sub-region.

[0203] Steps 801 to 805 are described in detail below.

[0204] In some embodiments, the regional angle threshold is first obtained based on the number of antennas N of the base station. The region angle threshold is determined to ensure the accuracy of the first-order Taylor approximation of the channel steering vector (CSV), as shown in Propositions 2 and 3, and its accuracy condition is related to the number of antennas N. Subsequently, based on the region angle threshold... Generate the maximum partitioning angle error constraint for each sub-region This constraint specifies the upper limit of the angular span that each subregion must satisfy when subsequently dividing the region.

[0205] Based on the maximum division angle error constraint generated in the previous step The region with uncertain location (i.e., the original circular region) is divided into multiple sub-regions. This division process involves cutting the original region along the angular dimension to ensure that the angular span of each newly generated fan-shaped sub-region satisfies the maximum division angular error constraint.

[0206] To ensure the accuracy of the Taylor approximation in characterizing the CSV at the location of the eavesdropping device's uncertainty, the proposed solution first defines the original spherical uncertainty region. The area is divided into multiple sector-shaped sub-regions to ensure that the maximum angular error within each sub-region is minimized. The constraints are then addressed. An alternative location is selected for each uncertain sub-region to facilitate robust beamforming design.

[0207] Reference Figure 9 This is a schematic diagram of sub-region division provided in an embodiment of this application. For example... Figure 9 As shown in the diagram, the core technical feature of this application is the division of the location-uncertain region into multiple sub-regions. For example... Figure 9 As shown, the original circular region of positional uncertainty is divided into multiple sector-shaped sub-regions by a series of angle lines based on the maximum partitioning angle error constraint. The purpose of this partitioning operation is to ensure the accuracy of the first-order Taylor approximation within each sub-region, thereby providing a foundation for subsequently generating accurate and robust safety constraints based on the surrogate location.

[0208] Next, a representative sampling point needs to be determined for each sub-region divided in the previous step. First, based on the midpoint of the angle of each sub-region, the agent angle corresponding to the sub-region is obtained; and based on the midpoint of the distance range of each sub-region, the agent distance corresponding to the sub-region is obtained.

[0209] For the angular range: First, given the estimated location of the eavesdropping device... and its uncertainty area The maximum and minimum angles that enable an accurate Taylor approximation can be determined as follows: and Then, the region of angular uncertainty... Divided into Each angle sub-region has a (center) sampling angle (i.e., the midpoint of the angle) as shown in the following formula (33).

[0210] (33) Specifically, each angular sub-region is related to its sampling angle. Symmetry, in which ,and and These are its maximum and minimum angles, respectively. To ensure that the maximum angular error within each sub-region is constrained by... The angle sampling points and their corresponding maximum and minimum angles are set as shown in the following formula (34).

[0211] (34) also, ,in ; ,in ;and .

[0212] Distance range: Next, for each region of uncertainty... The corresponding distance uncertainty region can be obtained. .in, and These represent the regions of overall uncertainty. and angle sub-region Within this region, we find the maximum and minimum distances to Eve. Therefore, we obtain a sector-shaped uncertain sub-region. Its mathematical expression is shown in the following formula (35).

[0213] (35) Then, based on the surrogate angle and surrogate distance obtained in the previous step, the two are combined to obtain the surrogate position of the corresponding sub-region. This surrogate position will serve as the representative of the sub-region and will be used for subsequent Taylor approximation and constraint construction.

[0214] That is, for each sub-region Sampling angle It is retained as the alternative angle (i.e., the surrogate angle). Furthermore, the midpoint of the region of distance uncertainty is set as the alternative distance (i.e., the surrogate distance), that is... Based on the above, each sub-region The alternative position is set as Therefore, for each sub-region, given an alternative location... ,exist The maximum absolute angle and distance error within the range satisfy the following formula (36).

[0215] (36) Subsequently, robust security constraints are generated for each geographic location based on the surrogate location corresponding to each sub-region. This generation process is the core of robust beamforming design. It utilizes a first-order Taylor approximation model at the surrogate location and combines it with generalized sign determinism (GSD) to transform the non-convex eavesdropping constraints for an infinite number of geographic locations within the sub-region into a single (or a set of) solvable convex constraints (e.g., linear matrix inequalities, LMIs). This LMI is the robust security constraint, and its mathematical construction guarantees that the security requirements for each geographic location within the sub-region are satisfied, as described below.

[0216] Phase 2 (Robust beamforming design based on fine linear matrix inequalities): Based on the division of the uncertainty region, the optimization problem (P2) is reformulated as the problem (P3) shown in the following formula (37).

[0217] (37) It is worth noting that, although constraint (18b) has been restated as A continuous set of uncertainties, but due to the infinite number of constraints (37) in problem (P3), the problem remains difficult to solve. Based on the analysis, after sub-regional division, Eve's CSV It can be done in We approximate this using a first-order Taylor expansion. Furthermore, to address the problem of conservative beamforming design in error-bounded methods, where near-field angle error amplification leads to significant error limits, we propose an improved LMI method, as shown below, to achieve higher secure transmission rates.

[0218] Reference Figure 10 Based on the proxy location corresponding to each sub-region, robust security constraints are generated for each geographic location, including the following steps 1001 to 1003.

[0219] Step 1001: For the proxy location corresponding to each sub-region, obtain the proxy channel steering vector based on the near-field channel steering vector model.

[0220] Step 1002: Based on the first-order Taylor expansion of the proxy channel steering vector, obtain the approximate steering vector model corresponding to each sub-region.

[0221] Steps 1001 to 1002 are described in detail below.

[0222] In some embodiments, firstly, for the proxy location corresponding to each sub-region... Based on the near-field channel steering vector model, a specific channel steering vector is obtained by substituting the coordinate parameters of the proxy position. This vector is the proxy channel steering vector. It will serve as the reference point and zeroth-order term for subsequent Taylor expansions.

[0223] Then, based on the proxy channel steering vector obtained in the previous step (as the zeroth-order term of the Taylor series), and combined with the gradient matrix calculated at the surrogate location. A first-order Taylor expansion is constructed. This expansion is the approximate steering vector model for each sub-region. This model is a linear function that can approximate the true channel steering vector of any geographic location with high accuracy using the location error vector relative to the proxy location. The accuracy of this approximation is guaranteed by the preceding region partitioning steps, as described below.

[0224] Reference Figure 11 Based on the first-order Taylor expansion of the proxy channel steering vector, an approximate steering vector model corresponding to each sub-region is obtained, including the following steps 1101 to 1103.

[0225] Step 1101: Based on the agent location within the sub-region, calculate the gradient of the channel steering vector with respect to the location to obtain the agent gradient matrix.

[0226] Step 1102: For each geographic location within a sub-region, determine the location error vector between the geographic location and the proxy location.

[0227] Step 1103: Based on the product of the proxy gradient matrix and the position error vector, plus the proxy channel steering vector, the approximate steering vector model corresponding to the sub-region is obtained.

[0228] Steps 1101 to 1103 are described in detail below.

[0229] In some embodiments, based on the agent location within a sub-region Calculate the gradient of the channel steering vector (CSV) with respect to location. This location typically includes two dimensions: angle and distance. Therefore, this gradient describes the instantaneous rate of change of the channel steering vector at the proxy location with respect to angle and distance. Combining these gradient vectors yields the proxy gradient matrix. This matrix represents the coefficients of the linear terms in the subsequent first-order Taylor expansion.

[0230] Then, for each geographic location within the sub-region, the location error vector between the geographic location and the proxy location is determined. The position error vector is a variable. Its weight and These represent the deviations in angle and distance between the geographical location and the proxy location, respectively. Since the sub-region has been divided in the previous steps, the range of values ​​for this location error vector is ensured to be within a sufficiently small limit, which is the basis for guaranteeing the accuracy of the Taylor approximation.

[0231] Then, based on the obtained surrogate gradient matrix With a determined position error vector The product (i.e.) (forming the first-order correction term of the Taylor expansion), plus the proxy channel steering vector (i.e., the zeroth-order term of the Taylor expansion), to obtain the approximate guiding vector model corresponding to the sub-region. The model is a linear function of the position error vector, used to approximate the true, nonlinear channel steering vector with high accuracy within a sub-region.

[0232] In summary, the overall effectiveness of steps 1101 to 1103 lies in transforming a complex, nonlinear near-field channel steering vector model into a simple, linear approximate steering vector model. This transformation constructs a high-precision linear approximation function by calculating the channel's sensitivity to location changes at the surrogate location (i.e., the surrogate gradient matrix) and combining this with the deviation of that point from other geographical locations within the sub-region (i.e., the location error vector). This approximate steering vector model is the key mathematical foundation for subsequent steps to utilize the general symbolic determinism lemma for convex optimization, as it transforms a non-convex channel uncertainty problem into a linear uncertainty problem that can be handled within a convex optimization framework.

[0233] Therefore, in the scheme of this application, based on the Taylor approximation of CSV in equation (20), the constraint condition (37) can be rewritten as shown in the following formula (38) (also an approximate guided vector model).

[0234] (38) in, It is the gradient matrix. It is the error vector, and .

[0235] Proof: For any condition satisfying of The constraint is satisfied if and only if the following conditions are met.

[0236]

[0237] When equation (38) holds true, the above equation can be rewritten as shown in the following formula.

[0238]

[0239] Given and According to the GSD lemma, constraint (38) can be rewritten as the linear matrix inequality in equation (39). and It is an auxiliary variable. ,as well as Thus, the proof is complete.

[0240] Then, for the sake of simplicity, let it be written as By using the GSD lemma, the nonconvex constraint (38) can be reformulated as follows in a more refined form. The linear matrix inequalities are expressed in formula (39). (39) in, and It is an auxiliary variable. ,as well as .

[0241] Step 1003: Using the general symbolic determinism lemma, the approximate guided vector model corresponding to multiple sub-regions is transformed and expressed to obtain the robust safety constraints corresponding to each geographical location in the region of location uncertainty.

[0242] Step 1003 will be described in detail below.

[0243] Based on the above description, substituting the obtained approximate steering vector model into the original security eavesdropping constraint will form a new infinite constraint that must hold for all bounded position error vectors within the sub-region (as shown in Equation (38)). To handle this infinite constraint, this invention utilizes the mathematical tool of the General Symbolic Determinism Lemma (GSD Lemma) to transform the security eavesdropping constraint (applied with the approximate steering vector model) into a transformed expression. The essence of this transformation expression is to equivalently transform a quadratic inequality that must hold for infinitely many uncertain variables into a constraint of finite dimension and convex form, such as a linear matrix inequality (LMI) (as shown in Equation (39)). After performing this transformation on multiple sub-regions, the resulting set of LMIs constitutes the robust security constraint corresponding to each geographical location in the final location uncertainty region. This constraint is convex and can be solved efficiently.

[0244] In summary, the overall effectiveness of steps 1001 to 1003 lies in realizing a refined method that transforms the non-convex security eavesdropping constraints containing infinitely many points in the original secure transmission optimization model into a finite set of efficiently solvable convex constraints (i.e., robust security constraints). This method, by establishing a high-precision approximate steering vector model and utilizing the key mathematical transformation of the general symbolic determinism lemma, successfully transforms a robust optimization problem (such as problem P1) that cannot be directly solved into a solvable convex optimization problem, thus providing an accurate, reliable, and computationally feasible mathematical foundation for the final solution of the optimized beamforming vector.

[0245] In summary, steps 801 to 805 implement a refined strategy for dividing the uncertainty region and constructing constraints. The overall effectiveness of this strategy lies in its proactive overcoming the severe inaccuracy of the first-order Taylor approximation throughout the uncertainty region caused by the "near-field angle error amplification effect" by dividing the positional uncertainty region based on the maximum division angle error constraint. By decomposing a large, approximately inaccurate non-convex problem into multiple small, approximately accurate sub-problems, and generating refined robust safety constraints for each sub-region based on the surrogate location, the scheme in this application avoids the overly conservative design caused by excessively large error bounds in traditional methods, providing accurate and solvable convex constraint conditions for subsequent solving of optimized beamforming vectors.

[0246] The following section will further describe how to solve the secure transmission optimization model using robust security constraints.

[0247] Reference Figure 12 The optimization model for secure transmission is solved based on robust security constraints to obtain the optimized beamforming vector, including the following steps 1201 to 1203.

[0248] Step 1201: Based on the continuous convex approximation technique, the target rate optimization function in the secure transmission optimization model is transformed into a substitute target optimization function.

[0249] Step 1202: Replace the security eavesdropping constraints in the secure transmission optimization model based on robust security constraints.

[0250] Step 1203: Based on the updated secure transmission optimization model, obtain the replacement transmission optimization model, and iteratively solve the replacement transmission optimization model to obtain the optimized beamforming vector.

[0251] Steps 1201 to 1203 are described in detail below.

[0252] As shown above, the objective function in problem (P2) is transformed using continuous convex approximation techniques to obtain... Similarly, because the target rate optimization function (i.e., the sum rate of legitimate users) in the original secure transmission optimization model (e.g., as shown in problem (P1)) is a non-concave function, the entire model is non-convex and difficult to solve directly. Therefore, this application, based on the continuous convex approximation technique (SCA), constructs a compact and solvable concave approximation function for the non-concave target rate optimization function in each iteration. The concave approximation function is transformed into the alternative objective optimization function.

[0253] Then, the non-convex constraints in the original optimization model are processed in parallel. The security eavesdropping constraint in the original secure transmission optimization model (e.g., as shown in constraint (17b)) is a worst-case constraint that needs to be satisfied throughout the entire uncertainty region, thus containing infinitely many non-convex constraints that cannot be solved directly. Based on robust security constraints (i.e., a finite set of convex linear matrix inequalities LMI, as shown in equation (39)), the present invention replaces the security eavesdropping constraint in the secure transmission optimization model, thereby transforming an infinite non-convex constraint problem into a finite convex constraint problem as shown in problem (P4) corresponding to the following equation (40).

[0254] (40) in as well as .

[0255] The replacement transmission optimization model (P4) is a standard convex optimization problem in each SCA iteration (e.g., an LMI problem solvable by CVX). Therefore, this application iteratively solves the replacement transmission optimization model, updating the replacement objective optimization function and solving the convex problem in each iteration until the algorithm converges, ultimately obtaining an optimized beamforming vector that satisfies all constraints and maximizes the original objective function.

[0256] In summary, the overall effectiveness of steps 1201 to 1203 lies in providing a complete algorithmic framework for transforming a complex, non-convex secure transmission optimization model into an efficiently solvable convex optimization problem. This framework handles the non-concave target rate optimization function using Continuous Convex Approximation (SCA) and replaces the infinite non-convex security eavesdropping constraint with a Robust Security Instraint (LMI) constraint. This transformation allows the original problem to be solved efficiently through iterative solutions, thus computationally feasible to obtain an optimized beamforming vector that maximizes the communication rate while satisfying worst-case security performance.

[0257] Compared to traditional methods, the near-field robust beamforming design proposed in this application has two key advantages. First, unlike existing methods, which rely on their CSV error bound (e.g., ... or The error bound is used to characterize the location uncertainty. When the range of Eve is relatively small, the error bound increases significantly. The proposed method incorporates an alternative CSV in Equation (38). and its associated gradient space Both of these characteristics define the location uncertainty region of Eve. Therefore, the method proposed in this application can design efficient beamforming vectors to reduce information leakage within the uncertainty region of Eve, rather than reducing the base station's transmit power, thereby achieving higher data rates. Secondly, compared to the matrix in the error bound method... The dimension is (See Equation (22)) In comparison, the proposed improved LMI method only introduces a gradient matrix of dimension 4. This effectively transforms the matrix in equation (39) The dimension from The computational complexity was reduced to 4 (see Proposition 3 for details), thus significantly reducing the computational complexity.

[0258] Reference Figure 13 This is a beam simulation diagram illustrating a different processing method provided in an embodiment of this application. Figure 13 As shown in the figure, four sub-figures compare the beamforming power distribution of the present invention with that of three reference schemes in space, aiming to intuitively demonstrate the beneficial effects of the present application. All sub-figures show how the base station (located at the origin of the coordinate system) can evade the "estimated Eve location" (eavesdropping end, red dot) while sending signals to the "Bob location" (legitimate user, black star).

[0259] Figure 13 Subplot (a) “Non-robust method” shows that although the beam achieves high gain at the “Bob position”, it also produces severe power leakage (bright red area) at the “estimated Eve position” due to the failure to consider position uncertainty, resulting in extremely low safety performance. Figure 13 Subgraph (c), “The Error Boundary-Based Method,” illustrates the opposite extreme: this method becomes overly conservative to meet security constraints, drastically suppressing its total transmission power (as shown by the color bars). This results in the signal at the legitimate user's “Bob location” being almost zero, severely sacrificing communication speed. This contrasts sharply with… Figure 6 This is consistent with the conclusion shown in (b).

[0260] Figure 13 While the subgraph (b) "sampling-based method" maintains high power at Bob and forms an effective null trap at Eve, as in the scheme, this method relies on a large number of sampling points, resulting in extremely high computational complexity. In contrast, Figure 13Subgraph (d) “The proposed method”—that is, the result obtained by the present invention using region partitioning and refined constraints—achieves an optimal balance: it not only maintains high power gain at the “Bob location” (maximum value of 0.5 in the color bar), but also successfully suppresses power leakage (dark blue area) around the “estimated Eve location” and its uncertainty region. Figure 13 This strongly demonstrates that while solving the computational complexity problem, this application overcomes the conservatism of traditional methods and achieves efficient data transmission while ensuring robust security.

[0261] Reference Figure 14 This is a simulation diagram illustrating how the rate and probability of secure transmission change with position error, as provided in an embodiment of this application. Figure 14 As shown in the figure, simulation data was used to compare the performance of the proposed method with three other benchmark schemes in terms of "reachable rate" and "secure transmission probability" as a function of the eavesdropper's "position error". Subfigure (a) shows that the traditional "error-boundary-based method" (red dashed line) experiences an immediate drop in "reachable rate" to zero when any "position error" ($\sigma_c>0$) exists; while the "non-robust method" (black square line), although having the highest rate, Figure 14 Subgraph (b) shows that its "secure transmission probability" collapses rapidly to near zero as the error increases.

[0262] The comparative results in this figure strongly demonstrate the beneficial effects of the present invention. The "proposed method" (blue circle line) of this application successfully solves the aforementioned technical problems; it... Figure 14 In subgraph (b), the same 100% "secure transmission probability" as the "error bounds-based method" is achieved, while in Figure 14 The subgraph (a) maintains a high "reachable rate" similar to that of the "sampling-based method". This indicates that by adopting the strategy of "dividing the positional uncertainty region into multiple sub-regions" and "generating robust safety constraints", this application overcomes the excessive conservatism caused by the "near-field angle error amplification effect" in traditional methods, and achieves high-speed data transmission while ensuring robust safety.

[0263] The above appendix Figure 13 and attached Figure 14 The examples demonstrate the beammaps, achievable rates, and secure transmission probabilities of different methods, among which... , , rice, as well as Meters. Key observations are summarized and described below.

[0264] (1) Non-robust method: This method implements Figure 14The highest rate is shown in (a), but due to severe power leakage around the estimated location (e.g. Figure 13 As shown in (a), its probability of secure transmission is low (see [a]). Figure 14 (b)).

[0265] (2) Sampling-based method: This method achieves the second-highest achievable rate when the probability of secure transmission exceeds 80% (see Figure 14 (The rate and feasibility in the process). For example... Figure 13 As shown in (b), it significantly reduces power leakage around the estimated location, but the computational cost is enormous.

[0266] (3) Error bounds-based method: This method ensures a secure transmission probability of 1 by conservatively limiting the base station's transmit power, such as... Figure 13 As shown in (c), this results in the lowest achievable rate (see...). Figure 14 (a)).

[0267] (4) Proposed Method: The method proposed in this application achieves a similar success rate to sampling-based methods while ensuring a secure transmission probability of 1, such as... Figure 14 As shown. By dividing the uncertainty region and applying an improved beamforming design based on linear matrix inequalities, it suppresses power leakage in the potential Eve region, such as Figure 13 As shown in (d).

[0268] The robust beamforming design solution of this application will be further extended to a more general scenario with multiple Bob and multiple Eve (i.e., near-field communication scenarios including multiple receivers and multiple eavesdropping devices).

[0269] It is worth noting that near-field robust beamforming design in general is more challenging than the single-user case described above because: 1) the worst-case eavesdropping rate of each Bob at each Eve must be guaranteed, and 2) multi-user interference further complicates the beamforming design.

[0270] To address these issues, in this scenario, the problem (P1) is first restated as shown in the problem (P5) corresponding to the following formula (41).

[0271] (41) in, To solve this non-convex problem, consistent with step 1201 above, the SCA technique is used to obtain the desired value in the objective function. The concave approximation function is expressed as shown in formula (2) below.

[0272] (42) in , , as well as .in, Indicates from the first The beamforming vector obtained in the SCA iteration. Based on the above, for... A tight concave boundary (i.e.) was constructed. ).

[0273] Next, to address the non-convex constraint (41) caused by continuous uncertainty sets, the method designed in steps 1001 to 1003 is extended to this more general case. Specifically, for any eavesdropping device... spherical uncertainty region Divided into multiple sub-regions Their replacement positions are shown in the following formula (43).

[0274] (43) Here, ,in ,and For eavesdropping The number of angle sampling points. Based on proposition 3, constraint (41) can be restated as follows.

[0275] Corollary 1: By performing Taylor expansion on the CSV at each alternative position, the constraint (41) can be re-expressed as shown in the following formula (44).

[0276] (44) in, , ,as well as Its value can be determined according to the methods proposed above.

[0277] According to Proposition 3, the above constraint (44) can be transformed into the following more refined linear matrix inequality as shown in formula (45).

[0278] (45) in It is given by the following formula (46).

[0279] (46) Here, and It is an auxiliary variable. ,as well as .

[0280] Therefore, problem (P5) can be restated as the problem (P6) shown in the following formula.

[0281]

[0282] in, and These are auxiliary matrices, respectively satisfying and At this point, problem (P6) becomes a convex optimization problem, which can be solved efficiently using the CVX tool to obtain the optimal solution.

[0283] In the embodiments of this application, firstly, the convergence performance of the proposed algorithm is analyzed. Since the total achievable rate obtained in each SCA iteration is non-decreasing, i.e. Therefore, the convergence of the proposed algorithm is guaranteed. Secondly, we evaluate the computational complexity. In problem (P6), the proposed algorithm involves... A linear matrix inequality constraint of size 4, and a constraint of size 4. The second-order cone (SOC) constraint. Because... Typically much smaller The main order of magnitude of the variable is ,in The computational complexity of solving problem (P6) is... The order of magnitude, of which This is the predefined precision of the CVX solver. This indicates the number of SCA iterations.

[0284] In multipath scenarios, it is assumed that the base station can obtain Bob's perfect CSI using existing channel estimation methods. However, Eve's channel state information... It is given by the following formula (47).

[0285] (47) These are typically difficult to obtain. Given that only Eve's approximate location is available, and that the power of the NLoS path is generally much weaker than that of the LoS path, we assume that the NLoS component is subject to the following constraints: ,in This represents the maximum possible power of the NLoS path, while This represents the power ratio between the NLoS path and the LoS path. Therefore, a conservative confidentiality constraint can be obtained as shown in the following formula (48).

[0286] (48) Based on the above, the proposed scheme can be used for robust beamforming design in multipath scenarios.

[0287] For scenarios considering Bobs' position uncertainty, the objective function becomes more complex due to this uncertainty, making robust beamforming design more challenging. We consider the worst-case sum rate maximization problem, whose optimization objective is... We present a formula that aims to maximize the sum of the minimum achievable rates under Bobs position uncertainty. To address this challenge, we first reformulate it in the following equivalent form.

[0288]

[0289] in, and These are auxiliary variables. Although this is a more complex problem, the proposed two-stage robust beamforming method can be extended to this scenario using SCA and S-Procedure techniques.

[0290] Step 205: Based on the optimized beamforming vector, control the base station to transmit data information to the receiving end.

[0291] Step 205 is described in detail below.

[0292] In some embodiments, the base station will use the optimized beamforming vector obtained in step 204 to configure its antenna array. Specifically, in the downlink, the base station weights and precodes the data information sent to each legitimate receiver based on the optimized beamforming vector, and then controls the base station to transmit the data information to the receiver.

[0293] To further verify the reliability of the data transmission method of the near-field communication system provided in this application, numerical results are given in the embodiments of this application to demonstrate the efficiency of the proposed robust beamforming scheme in ensuring secure near-field transmission.

[0294] In this embodiment, a near-field communication system is considered to be equipped with The XL array system with one antenna, in At a frequency of GHz Bob provides services, and simultaneously exists There are 10 Eves. The estimated locations of the Eves are as follows: Mihe Meters, the positional error is the same, all are meters. Bob is randomly distributed in a radius of meters. Within a circular area of ​​meters, the center of the area is located At a distance of meters. Unless otherwise specified, system parameters are set to... watt, bits per second per hertz decibels and milliwatts, and .

[0295] The following benchmark schemes were considered for performance comparison.

[0296] Non-robust approach: This approach designs beamforming vectors based solely on the estimation of Eve's location, without considering the uncertainty of location.

[0297] Sampling-based approach: In this approach, for regions with angular uncertainty... Perform uniform sampling, with a sample size of... Based on this, beamforming vectors are designed.

[0298] Error-bounded scheme: In this scheme, the beamforming vector is based on the GSD lemma and combined with a precise error bound. To carry out the design.

[0299] Uncertainty-only region partitioning scheme: For this scheme, the uncertainty region is divided into multiple sector-shaped sub-regions. Then, the CSV error bound (i.e., ...) for each sub-region is defined. (This is used for beamforming design by rewriting the conventional LMI.)

[0300] Only the refined LMI scheme is used: This scheme uses a refined linear matrix inequality reformulation in robust beamforming design, but does not divide the uncertainty region.

[0301] Reference Figure 15 This is a simulation diagram illustrating the relationship between the total rate and the number of iterations, provided in an embodiment of this application. Figure 15 The figure shows the convergence performance of the proposed algorithm, corresponding to the iterative solution process of the replacement transport optimization model in the scheme. The figure plots the reachability and rate as a function of the number of iterations under different location error conditions. Figure 15 As shown, the reachability and rate of all curves are non-decreasing and converge rapidly to a stable point within the last 10 iterations. This strongly demonstrates that the iterative algorithm based on Continuous Convex Approximation (SCA) used in this invention is efficient and convergent. Reference Figure 16 This is a beam simulation diagram of a data transmission scheme for a near-field communication system provided in an embodiment of this application. Figure 16 The diagram illustrates the proposed scheme in two locations. Mihe The beam pattern at Bob's location is shown. It can be seen that even when one of Bobs is occupied by Eve with the same spatial angle, both Bobs still achieve satisfactory beam gain. This is attributed to the near-field effect, which allows for flexible beamforming design in the joint angle-range domain. Importantly, the beam gain at the estimated Eve location and its surrounding area is significantly suppressed because our robust beamforming design effectively minimizes energy leakage within the uncertainty region of each Eve, thus satisfying the worst-case confidentiality constraint.

[0302] Reference Figure 17 This is a simulation diagram illustrating how the rate and secure transmission probability can vary with position error, provided in an embodiment of this application. Figure 17 As shown in the diagram, to illustrate the impact of positional error, we... Figure 17 (a) and Figure 17 (b) plots the total achievable rate and secure transmission probability of all schemes within a small error range as a function of position error. The changing curve. The non-robust scheme achieves the highest total rate by enforcing secrecy constraints only at the estimated eavesdropper locations. While this improves the achievable total rate, it also... Figure 17 As shown in (b), its secure transmission probability is significantly reduced. On the other hand, the scheme based on error limits and the scheme with only uncertainty region partitioning... With the increase of [something], its rate performance decreases significantly, when [something] At this point, the rate drops to almost zero. This is because, even within a small error range, the optimized base station transmit power is severely limited by the large CSV error bound. The proposed scheme, the improved LMI scheme, and the sampling-based scheme show similar achievable rates, such as... Figure 17 As shown in (a). However, for the latter two schemes, as With the increase of uncertainty, the probability of secure transmission is much lower. These results indicate that both the partitioning of the uncertainty region and the refined reformulation of linear matrix inequalities contribute to the improvement in confidentiality performance.

[0303] Furthermore, with positional error Increasing the value from 0.02 to 0.1 renders the uncertainty region partitioning scheme unsuitable due to its poor rate performance and high computational complexity. Figure 17 Other schemes in (c) and 17(d) exhibit similar performance trends to those observed in the small error range. Among these, although the total achievable rate of the proposed schemes increases with... While its performance gradually decreases with increasing location uncertainty, it achieves a good balance between rate performance and security requirements, significantly outperforming other benchmark schemes in both robustness and rate performance. Reference Figure 18This is a simulation diagram illustrating how the rate and secure transmission probability can change with the power ratio, as provided in an embodiment of this application. Figure 18 The diagram illustrates the performance of different schemes at the maximum possible non-line-of-sight path power. Similar observations emerge: the non-robust schemes achieve the highest achievable total rate, but their secure transmission probability is very low. In contrast, the scheme proposed in this application ensures a secure transmission probability of 1 while achieving good rate performance. Furthermore, the achievable total rate of all five schemes increases with power ratio. The rate decreases with increasing non-line-of-sight components. These results indicate that in multipath scenarios, stronger non-line-of-sight components impose more conservative confidentiality constraints, thereby reducing the achievable summation rate, particularly for sampling-based schemes and the scheme proposed in this application.

[0304] This application also provides a data transmission device for a near-field communication system, which can implement the data transmission method of the above-described near-field communication system, as described above. Figure 19 The device 1900 includes: The eavesdropping location module 1910 is used to obtain the eavesdropping estimated location of the eavesdropping terminal, and to obtain the eavesdropping location model of the eavesdropping terminal based on the location error parameter of the eavesdropping terminal in the location uncertainty area and the eavesdropping estimated location. The eavesdropping rate module 1920 is used to obtain the eavesdropping rate model corresponding to the data information sent from the base station to the receiver by the eavesdropping terminal based on the eavesdropping location model. The optimization model module 1930 is used to obtain a secure transmission optimization model based on the receiving rate model, the eavesdropping rate model, and the beamforming vector parameters of the base station corresponding to the data information received by the receiving end from the base station. The beam optimization module 1940 is used to divide the location uncertainty area into multiple sub-regions, generate robust security constraints based on the agent position corresponding to each sub-region, and solve the secure transmission optimization model based on the robust security constraints to obtain the optimized beamforming vector. The data transmission module 1950 is used to control the base station to transmit data information to the receiving end based on the optimized beamforming vector.

[0305] In some embodiments, the eavesdropping rate module 1920 is further configured to: Substituting the eavesdropping location model into the near-field channel steering vector model, we obtain the eavesdropping steering vector; Based on the product of the channel gain model between the eavesdropping terminal and the base station and the eavesdropping steering vector, the eavesdropping channel model between the eavesdropping terminal and the base station is obtained. Based on the eavesdropping channel model and beamforming vector parameters, the eavesdropping rate model is obtained.

[0306] In some embodiments, the optimization model module 1930 is further configured to: Based on the model that maximizes the receiving rate of all receivers, the target rate optimization function is obtained. The receiving rate model includes beamforming vector parameters. Obtain beam power constraints for beamforming vector parameters; Based on the numerical relationship between the eavesdropping rate model corresponding to all eavesdropping terminals and the maximum eavesdropping rate threshold, security eavesdropping constraints are obtained. Based on the target rate optimization function, beamforming vector parameters, beam power constraints, and security eavesdropping constraints, a secure transmission optimization model is obtained.

[0307] In some embodiments, the beam optimization module 1940 is further configured to: Based on the number of antennas at the base station, the regional angle threshold is obtained, and the maximum division angle error constraint for each sub-region is generated based on the regional angle threshold. The region of positional uncertainty is divided into multiple sub-regions based on the maximum division angle error constraint. Based on the midpoint of the angle of each sub-region, the agent angle corresponding to the sub-region is obtained, and based on the midpoint of the distance range of each sub-region, the agent distance corresponding to the sub-region is obtained; Based on the proxy angle and proxy distance, the proxy position of the corresponding sub-region is obtained; Based on the proxy location corresponding to each sub-region, robust security constraints are generated for each geographic location.

[0308] In some embodiments, the beam optimization module 1940 is further configured to: For each sub-region corresponding to the agent location, the agent channel steering vector is obtained based on the near-field channel steering vector model; Based on the first-order Taylor expansion of the proxy channel steering vector, an approximate steering vector model corresponding to each sub-region is obtained; Using the general symbolic determinism lemma, the approximate guided vector model corresponding to multiple sub-regions is transformed and expressed to obtain the robust safety constraints corresponding to each geographical location in the region of location uncertainty.

[0309] In some embodiments, the beam optimization module 1940 is further configured to: Based on the agent location within the sub-region, the gradient of the channel steering vector with respect to the location is calculated to obtain the agent gradient matrix; For each geographic location within a sub-region, determine the location error vector between the geographic location and the proxy location; Based on the product of the surrogate gradient matrix and the position error vector, plus the surrogate channel steering vector, an approximate steering vector model corresponding to the sub-region is obtained.

[0310] In some embodiments, the beam optimization module 1940 is further configured to: Based on the continuous convex approximation technique, the target rate optimization function in the secure transmission optimization model is transformed into a substitute target optimization function; Based on robust security constraints, the security eavesdropping constraints in the secure transmission optimization model are replaced; Based on the updated secure transmission optimization model, an alternative transmission optimization model is obtained, and the alternative transmission optimization model is iteratively solved to obtain the optimized beamforming vector.

[0311] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, the specific implementation of the data transmission device of the near-field communication system is basically the same as the specific implementation of the data transmission method of the near-field communication system described above, and will not be repeated here.

[0312] This application also provides an electronic device, including: At least one memory; At least one processor; At least one program; The program is stored in a memory, and the processor executes the at least one program to implement the data transmission method of the near-field communication system described above. The electronic device can be any smart terminal, including mobile phones, tablets, personal digital assistants (PDAs), and in-vehicle computers.

[0313] Please see Figure 20 , Figure 20 The hardware structure of an electronic device according to another embodiment is illustrated. The electronic device includes: The processor 2001 can be implemented using a general-purpose CPU (Central Processing Unit), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this application. The memory 2002 can be implemented in the form of ROM (Read-Only Memory), static storage device, dynamic storage device, or RAM (Random Access Memory). The memory 2002 can store the operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 2002 and is called and executed by the processor 2001 using the data transmission method of the near-field communication system of the embodiments of this application. Input / output interface 2003 is used to implement information input and output; The communication interface 2004 is used to enable communication and interaction between this device and other devices. Communication can be achieved through wired means (such as USB, network cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.). Bus 2005 transmits information between various components of the device (e.g., processor 2001, memory 2002, input / output interface 2003, and communication interface 2004); The processor 2001, memory 2002, input / output interface 2003 and communication interface 2004 are connected to each other within the device via bus 2005.

[0314] This application embodiment also provides a storage medium, which is a computer-readable storage medium, storing a computer program that, when executed by a processor, implements the data transmission method of the near-field communication system described above.

[0315] 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.

[0316] 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.

[0317] 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.

[0318] 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.

[0319] 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 suitable combinations thereof.

[0320] 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.

[0321] 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.

[0322] 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. The coupling or direct coupling or communication connection between the shown or discussed units may be through some interfaces, or indirect coupling or communication connection between the apparatus or units, and may be electrical, mechanical, or other forms.

[0323] 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.

[0324] 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.

[0325] 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.

[0326] 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 data transmission method for a near-field communication system, characterized in that, The near-field communication system includes a base station, a receiver, and an eavesdropping device; the method includes: The eavesdropping estimated location of the eavesdropping terminal is obtained, and based on the location error parameter of the eavesdropping terminal in the location uncertainty region and the eavesdropping estimated location, the eavesdropping location model of the eavesdropping terminal is obtained; Based on the eavesdropping location model, the eavesdropping rate model corresponding to the eavesdropping terminal receiving the data information sent by the base station to the receiving terminal is obtained; Based on the receiving rate model corresponding to the data information received by the receiving end from the base station, the eavesdropping rate model, and the beamforming vector parameters of the base station, a secure transmission optimization model is obtained. The location uncertainty region is divided into multiple sub-regions. Based on the proxy location corresponding to each sub-region, robust security constraints are generated. The secure transmission optimization model is then solved based on the robust security constraints to obtain the optimized beamforming vector. Based on the optimized beamforming vector, the base station is controlled to transmit data information to the receiving end.

2. The data transmission method of the near-field communication system according to claim 1, characterized in that, The step of obtaining the eavesdropping rate model corresponding to the data information sent by the base station to the receiving end by the eavesdropping terminal based on the eavesdropping location model includes: Substituting the eavesdropping location model into the near-field channel steering vector model, we obtain the eavesdropping steering vector; Based on the product of the channel gain model between the eavesdropping terminal and the base station and the eavesdropping steering vector, the eavesdropping channel model between the eavesdropping terminal and the base station is obtained. Based on the eavesdropping channel model and the beamforming vector parameters, the eavesdropping rate model is obtained.

3. The data transmission method of the near-field communication system according to claim 1, characterized in that, The secure transmission optimization model is obtained based on the receiving rate model corresponding to the data information received by the receiving end from the base station, the eavesdropping rate model, and the beamforming vector parameters of the base station, including: Based on the receiving rate model that maximizes all the receiving ends, a target rate optimization function is obtained, wherein the receiving rate model includes the beamforming vector parameters. Obtain the beam power constraint of the beamforming vector parameters; Based on the numerical relationship between the eavesdropping rate model and the maximum eavesdropping rate threshold corresponding to all the eavesdropping terminals, security eavesdropping constraints are obtained. Based on the target rate optimization function, the beamforming vector parameters, the beam power constraint, and the security eavesdropping constraint, the secure transmission optimization model is obtained.

4. The data transmission method of the near-field communication system according to claim 1, characterized in that, The step of dividing the location uncertainty region into multiple sub-regions and generating robust security constraints based on the proxy location corresponding to each sub-region includes: Based on the number of antennas of the base station, a regional angle threshold is obtained, and a maximum division angle error constraint for each sub-region is generated based on the regional angle threshold. Based on the maximum division angle error constraint, the position uncertainty region is divided into multiple sub-regions; Based on the midpoint of the angle of each sub-region, the proxy angle corresponding to the sub-region is obtained, and based on the midpoint of the distance range of each sub-region, the proxy distance corresponding to the sub-region is obtained; Based on the proxy angle and the proxy distance, the proxy position of the corresponding sub-region is obtained; Based on the proxy location corresponding to each sub-region, the robust security constraints corresponding to each geographic location are generated.

5. The data transmission method of the near-field communication system according to claim 4, characterized in that, The step of generating robust security constraints for each geographic location based on the proxy location corresponding to each sub-region includes: For each of the sub-regions corresponding to the proxy location, a proxy channel steering vector is obtained based on the near-field channel steering vector model; Based on the first-order Taylor expansion of the proxy channel steering vector, an approximate steering vector model corresponding to each sub-region is obtained; Using the general symbolic determinism lemma, the approximate guiding vector model corresponding to the multiple sub-regions is transformed and expressed to obtain the robust safety constraint corresponding to each geographical location in the location uncertainty region.

6. The data transmission method of the near-field communication system according to claim 5, characterized in that, The first-order Taylor expansion based on the proxy channel steering vector yields an approximate steering vector model for each sub-region, including: Based on the proxy location within the sub-region, the gradient of the channel steering vector with respect to the location is calculated to obtain the proxy gradient matrix; For each geographic location within the sub-region, determine the location error vector between the geographic location and the proxy location; Based on the product of the proxy gradient matrix and the position error vector, plus the proxy channel steering vector, the approximate steering vector model corresponding to the sub-region is obtained.

7. The data transmission method of the near-field communication system according to claim 3, characterized in that, Solving the secure transmission optimization model based on the robust security constraints to obtain the optimized beamforming vector includes: Based on the continuous convex approximation technique, the target rate optimization function in the secure transmission optimization model is transformed into a substitute target optimization function; Based on the robust security constraints, the secure eavesdropping constraints in the secure transmission optimization model are replaced; Based on the updated secure transmission optimization model, an alternative transmission optimization model is obtained, and the alternative transmission optimization model is iteratively solved to obtain the optimized beamforming vector.

8. A data transmission device for a near-field communication system, characterized in that, The near-field communication system includes a base station, a receiver, and an eavesdropping terminal; the method apparatus includes: The eavesdropping location module is used to obtain the eavesdropping estimated location of the eavesdropping terminal, and to obtain the eavesdropping location model of the eavesdropping terminal based on the location error parameter of the eavesdropping terminal in the location uncertainty area and the eavesdropping estimated location. The eavesdropping rate module is used to obtain the eavesdropping rate model corresponding to the data information sent by the base station to the receiving end by the eavesdropping terminal based on the eavesdropping location model. The optimization model module is used to obtain a secure transmission optimization model based on the receiving rate model corresponding to the data information received by the receiving end from the base station, the eavesdropping rate model, and the beamforming vector parameters of the base station. The beam optimization module is used to divide the location uncertainty region into multiple sub-regions, generate robust security constraints based on the proxy position corresponding to each sub-region, and solve the secure transmission optimization model based on the robust security constraints to obtain the optimized beamforming vector. The data transmission module is used to control the base station to transmit data information to the receiving end based on the optimized beamforming vector.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the data transmission method of the near-field communication system according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the data transmission method of the near-field communication system according to any one of claims 1 to 7.

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