Signal transmission method and device of movable antenna array and electronic equipment

Abstract

The embodiment of the invention provides a signal transmission method and device of a movable antenna array and electronic equipment, and belongs to the technical field of antenna communication. The method comprises the following steps: determining a plurality of monitoring parties and at least two target receiving ends; one target receiving end is in a near-field communication scene, and the other target receiving end is in a far-field communication scene; constructing a communication model based on the movable antenna array, the plurality of monitoring parties and the target receiving end; performing reachable rate analysis and concealment analysis based on the communication model to obtain reachable rate related data and concealment related data, and then constructing a target optimization problem; the position of each movable sub-array of the movable antenna array is adjusted, power distribution of the movable antenna array is adjusted, a target optimization problem is processed, target optimization information is obtained, and therefore signal transmission operation of the movable antenna array is adjusted. According to the embodiment of the invention, joint optimization of the covert communication rate and the concealment can be realized under the condition of a mixed field domain channel.

Description

Technical Field

[0001] This application relates to the field of antenna communication technology, and in particular to a signal transmission method, apparatus and electronic device for a movable antenna array. Background Technology

[0002] Covert communication is a communication method designed to hide the communication activity itself. Unlike physical layer security (PLS), which aims to prevent confidential information from being decoded by eavesdroppers, its goal is to make data transmission undetectable to non-target users (such as monitoring devices), attempting to hide the existence of the communication and thus providing stronger protection in terms of privacy and security.

[0003] In related technologies, for far-field covert communication, multi-input multi-output (MIMO) technology is widely used to generate narrow beams based on channel state information (CSI), thereby effectively reducing signal power leakage and improving transmission covertness. Reconfigurable antenna technologies such as movable antennas (MAs) and fluid antennas (FAs) can also significantly reduce channel spatial correlation through spatial degrees of freedom (such as the position movement of MAs and the port selection of FAs) to achieve covert transmission. In near-field covert communication, the near-field beam focusing characteristics can be utilized to effectively reduce power and information leakage to the monitoring party even when the legitimate user and the monitoring party are at the same angle.

[0004] However, the above methods only consider either far-field or near-field communication scenarios. In practical wireless systems, far-field and near-field users often coexist. Existing covert communication methods only consider a single far-field or near-field communication scenario, while research on more practical hybrid-field covert communication systems remains unclear. In covert communication scenarios, hybrid-field correlation effects may simultaneously affect the reachability rate between legitimate near-field and far-field users, as well as the transmission covertness between the near-field monitor and the legitimate far-field user. Therefore, how to balance these two types of performance indicators in hybrid-field channels remains a pressing scientific challenge. Summary of the Invention

[0005] The main objective of this application is to propose a signal transmission method, apparatus, and electronic device for a movable antenna array, aiming to achieve joint optimization of covert communication rate and covertness under mixed field channel conditions.

[0006] To achieve the above objectives, a first aspect of this application proposes a signal transmission method for a movable antenna array, applied to a movable antenna array comprising multiple movable subarrays, each of the movable subarrays comprising multiple antenna elements, the method comprising:

[0007] Multiple monitoring parties and at least two target receivers are identified; wherein at least one target receiver is in a near-field communication scenario and one of the target receivers is in a far-field communication scenario.

[0008] A communication model is constructed based on the movable antenna array, the multiple monitoring parties, and the target receiver;

[0009] Based on the communication model, reachability analysis is performed to obtain reachability-related data.

[0010] Based on the aforementioned communication model, a covertness analysis is performed to obtain covertness-related data;

[0011] Based on the achievable rate-related data and the concealment-related data, a target optimization problem is constructed;

[0012] By adjusting the position of each movable subarray of the movable antenna array and adjusting the power distribution of the movable antenna array, the target optimization problem is processed to obtain target optimization information;

[0013] Based on the target optimization information, the signal transmission operation of the movable antenna array is adjusted.

[0014] In some embodiments, the communication model includes a first channel model and a second channel model, and the construction of the communication model based on the movable antenna array, the multiple monitoring parties, and the target receiver includes:

[0015] Obtain the monitoring locations of multiple monitoring parties and the receiving locations of several target receiving terminals;

[0016] Based on the receiving positions of several target receivers, a first channel model including near-field communication scenarios and far-field communication scenarios is constructed;

[0017] The second channel model is constructed based on the monitoring locations of multiple monitoring parties in a near-field communication scenario.

[0018] In some embodiments, the target receiving end includes at least a first receiving end and a second receiving end, and the achievable rate analysis based on the communication model to obtain achievable rate-related data includes:

[0019] Based on the communication model, the power detection capabilities of multiple monitoring parties are analyzed to determine the covert communication requirements of the movable antenna array.

[0020] Based on the aforementioned covert communication requirements, the achievable total rate is obtained; the achievable total rate represents the sum of the communication rates of the first receiving end and the second receiving end.

[0021] Based on the influencing factors of the achievable total rate, the relevant data of the achievable rate corresponding to the achievable total rate are obtained.

[0022] In some embodiments, the step of performing covert analysis based on the communication model to obtain covert-related data includes:

[0023] Based on the aforementioned covert communication requirements, the covert communication factors are determined;

[0024] Based on the aforementioned covert communication factors, a covertness analysis is performed on the first receiving end and the second receiving end to obtain the covertness-related data.

[0025] In some embodiments, the process of addressing the target optimization problem by adjusting the position of each of the movable subarrays of the movable antenna array and adjusting the power distribution of the movable antenna array to obtain target optimization information includes:

[0026] The target optimization problem is decomposed into an outer problem and an inner problem, wherein the inner problem is related to the power allocation of the multiple movable subarrays, and the outer problem is related to the position of the multiple movable subarrays;

[0027] The outer layer problem is optimized by adjusting the position of each movable subarray of the movable antenna array, and the inner layer problem is optimized by adjusting the power distribution of the movable antenna array. The outer layer problem and the inner layer problem are optimized alternately until a preset convergence condition is met, thereby obtaining the target optimization information.

[0028] In some embodiments, the optimization of the outer layer problem by adjusting the position of each movable subarray of the movable antenna array, the optimization of the inner layer problem by adjusting the power distribution of the movable antenna array, and the alternating optimization of the outer layer problem and the inner layer problem until a preset convergence condition is met, to obtain the target optimization information, includes:

[0029] Based on the preset positions of the multiple movable subarrays, the outer layer problem is optimized, and the target transmit power of the multiple movable subarrays is determined;

[0030] Based on the target transmit power of the plurality of movable subarrays, the inner layer problem is optimized to determine the target adjustment position of the plurality of movable subarrays.

[0031] In some embodiments, adjusting the signal transmission operation of the movable antenna array based on the target optimization information specifically includes:

[0032] Based on the target optimization information, perform at least one of the following operations: update the positions of the plurality of movable subarrays of the movable antenna array, and update the communication power of the plurality of movable subarrays of the movable antenna array.

[0033] To achieve the above objectives, a second aspect of this application provides a signal transmission device for a movable antenna array, the device comprising:

[0034] A multi-terminal acquisition module is used to identify multiple monitoring parties and at least two target receiving terminals; wherein at least one of the target receiving terminals is in a near-field communication scenario and one of the target receiving terminals is in a far-field communication scenario.

[0035] A communication model construction module is used to construct a communication model based on the movable antenna array, the multiple monitoring parties, and the target receiver.

[0036] The reachability analysis module is used to perform reachability analysis based on the communication model and obtain reachability-related data.

[0037] The concealment analysis module is used to perform concealment analysis based on the communication model to obtain concealment-related data;

[0038] An optimization problem construction module is used to construct a target optimization problem based on the achievable rate-related data and the concealment-related data;

[0039] The optimization problem processing module is used to process the target optimization problem by adjusting the position of each of the movable subarrays of the movable antenna array and adjusting the power distribution of the movable antenna array, so as to obtain target optimization information.

[0040] The signal transmission adjustment module is used to adjust the signal transmission operation of the movable antenna array based on the target optimization information.

[0041] 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 signal transmission method of the movable antenna array described in the first aspect.

[0042] The signal transmission method, apparatus, and electronic device for a movable antenna array proposed in this application determine multiple monitoring parties and at least two target receivers. A communication model is constructed based on the movable antenna array, multiple monitoring parties, and target receivers. Achievable rate analysis is performed based on the communication model to obtain achievable rate-related data. Stealth analysis is also performed based on the communication model to obtain stealth-related data. Based on the achievable rate-related data and the stealth-related data, a target optimization problem is constructed. The target optimization problem is then processed by adjusting the position of each movable subarray of the movable antenna array and adjusting the power distribution of the movable antenna array to obtain target optimization information. Based on the target optimization information, the signal transmission operation of the movable antenna array is adjusted. Therefore, this application, through a communication model constructed based on a movable antenna array, monitoring parties, and target receivers, conducts achievable rate analysis to evaluate the communication rate that a target receiver can achieve in a mixed-field environment, i.e., when there are target receivers in both near-field and far-field communication scenarios simultaneously, and obtains achievable rate-related data. Meanwhile, based on the communication model, a covertness analysis is conducted, focusing on how to reduce the probability of the monitoring party detecting the communication behavior, thereby obtaining covertness-related data. Then, based on the achievable rate-related data and the covertness-related data, an objective optimization problem is constructed, aiming to achieve joint optimization of covert communication rate and covertness under mixed field channel conditions by adjusting the position of each movable subarray in the movable antenna array and adjusting the power distribution of the movable antenna array. Attached Figure Description

[0043] Figure 1 This is a flowchart of the signal transmission method for the movable antenna array provided in the embodiments of this application;

[0044] Figure 2 yes Figure 1 The flowchart of step S102 in the document;

[0045] Figure 3 yes Figure 1 The flowchart of step S103 in the process;

[0046] Figure 4 This is a schematic diagram showing how the normalized beam gain varies with different spatial angles in the case of far-field beamforming.

[0047] Figure 5 yes Figure 1 The flowchart of step S104 in the process;

[0048] Figure 6 This is a schematic diagram showing the relationship between the objective function of problem (P3) and the near-field target receiver;

[0049] Figure 7 yes Figure 1The flowchart of step S106 in the process;

[0050] Figure 8 yes Figure 7 The flowchart of step S502 in the document;

[0051] Figure 9 This is a schematic diagram of the structure of the signal transmission device for the movable antenna array provided in the embodiments of this application;

[0052] Figure 10 This is a schematic diagram of the hardware structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0053] 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.

[0054] It should be noted that although functional modules are divided in the device schematic diagram and a 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. The terms "first," "second," etc., in the specification, claims, and the aforementioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0055] 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.

[0056] Covert communication is a communication method designed to hide the communication activity itself. Unlike physical layer security (PLS), which aims to prevent confidential information from being decoded by eavesdroppers, its goal is to make data transmission undetectable to non-target users (such as monitoring devices), attempting to hide the existence of the communication and thus providing stronger protection in terms of privacy and security.

[0057] In related technologies, multi-input multi-output (MIMO) technology is widely used in far-field covert communication to generate narrow beams based on channel state information (CSI), thereby effectively reducing signal power leakage and improving transmission covertness. Multiple antennas can be deployed at the interference source to generate artificial noise beams pointing towards the monitor (Willie) while ensuring the legitimate user (Bob) is located in the beam null region. However, these methods may fail when there is strong channel correlation between the legitimate user and the monitor (e.g., they are at the same angle). To address this problem, intelligent reflecting surfaces (IRS) technology exhibits unique advantages, as it can simultaneously enhance the received power of the legitimate user and suppress the signal strength of the monitor by intelligently controlling signal reflection. Reconfigurable antenna technology provides another effective solution. For example, movable antennas (MAs) and fluid antennas (FAs) can significantly reduce channel spatial correlation to achieve covert transmission through spatial degrees of freedom (e.g., the position movement of MAs and the port selection of FAs).

[0058] In related technologies, near-field covert communication can leverage near-field beam focusing characteristics to effectively reduce power and information leakage to the monitoring party even when the legitimate user and the monitoring party are at the same angle. Based on the characteristics of spherical wavefronts, a frequency diverse array (FDA) can be employed in the near-field covert communication system to generate a flexible and controllable beam pattern, thereby enhancing beam focusing for the legitimate user while suppressing power leakage in the monitoring party's direction.

[0059] However, the above methods only consider either far-field or near-field communication scenarios. In actual wireless systems, far-field and near-field users often coexist. For example, when a base station equipped with 256 antennas operates in the 30GHz band, its traditional Rayleigh distance, calculated based on inter-antenna phase changes, is approximately 325 meters, while the effective Rayleigh distance (more practically meaningful for rate performance evaluation), calculated based on array gain changes, is only 120 meters. In a system with a typical cell radius of 200 meters, this means that far-field and near-field users will coexist.

[0060] Discrete Fourier transform (DFT) beams directed at far-field users can cause significant interference to near-field users, even if their azimuth angles differ. This phenomenon stems from the non-orthogonality of the steering vectors of the near-field and far-field channels, resulting in far-field power leakage in the near-field region (a phenomenon known as the "energy diffusion effect").

[0061] Existing covert communication methods only consider single far-field or near-field communication scenarios; however, research on more practical hybrid-field covert communication systems remains unclear. In covert communication scenarios, hybrid-field correlation effects may simultaneously affect the reachability rate between legitimate near-field and far-field users, as well as the transmission covertness between the near-field monitor and the far-field user. Therefore, how to balance these two types of performance indicators in hybrid-field channels remains a pressing scientific challenge.

[0062] Furthermore, in traditional MAs-enabled far-field covert communication scenarios, the independent movement of each antenna element needs to be controlled, leading to a surge in hardware control complexity and algorithm computational complexity.

[0063] Based on this, embodiments of this application provide a signal transmission method, apparatus, and electronic device for a movable antenna array, aiming to achieve joint optimization of covert communication rate and covertness under mixed field channel conditions.

[0064] The signal transmission method, apparatus, and electronic device of the movable antenna array provided in this application are specifically described through the following embodiments. First, the signal transmission method of the movable antenna array in the embodiments of this application is described.

[0065] The signal transmission method for a movable antenna array provided in this application relates to the field of antenna communication technology. This method can be applied to a terminal, a server, or software running on either a terminal or a server. In some embodiments, the terminal can be a smartphone, tablet, laptop, desktop computer, etc.; the server can be configured as an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms; the software can be an application implementing the signal transmission method for the movable antenna array, but is not limited to the above forms.

[0066] This application can be used in a wide variety of general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices. This application can be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform specific tasks or implement specific abstract data types. This application can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0067] Figure 1 This is an optional flowchart of the signal transmission method for the movable antenna array provided in the embodiments of this application. Figure 1 The method may include, but is not limited to, steps S101 to S107.

[0068] Step S101: Identify multiple monitoring parties and at least two target receivers; wherein at least one target receiver is in a near-field communication scenario and one target receiver is in a far-field communication scenario.

[0069] Step S102: Construct a communication model based on the movable antenna array, multiple monitoring parties, and the target receiver;

[0070] Step S103: Perform reachability analysis based on the communication model to obtain reachability-related data;

[0071] Step S104: Perform concealment analysis based on the communication model to obtain concealment-related data;

[0072] Step S105: Based on reachability-related data and concealment-related data, construct the target optimization problem;

[0073] Step S106: By adjusting the position of each movable subarray of the movable antenna array and adjusting the power distribution of the movable antenna array, the target optimization problem is processed to obtain target optimization information;

[0074] Step S107: Adjust the signal transmission operation of the movable antenna array based on the target optimization information.

[0075] Steps S101 to S107 of this application embodiment involve determining multiple monitoring parties and at least two target receivers, constructing a communication model based on a movable antenna array, multiple monitoring parties, and target receivers, performing achievable rate analysis based on the communication model to obtain achievable rate-related data, performing concealment analysis based on the communication model to obtain concealment-related data, constructing a target optimization problem based on the achievable rate-related data and the concealment-related data, processing the target optimization problem by adjusting the position of each movable subarray of the movable antenna array and adjusting the power distribution of the movable antenna array to obtain target optimization information, and adjusting the signal transmission operation of the movable antenna array based on the target optimization information. Therefore, this application, through a communication model constructed based on a movable antenna array, monitoring parties, and target receivers, conducts achievable rate analysis to evaluate the communication rate that a target receiver can achieve in a mixed-field environment, i.e., when there are target receivers in both near-field and far-field communication scenarios simultaneously, and obtains achievable rate-related data. Meanwhile, based on the communication model, a covertness analysis is conducted, focusing on how to reduce the probability of the monitoring party detecting the communication behavior, thereby obtaining covertness-related data. Then, based on the achievable rate-related data and the covertness-related data, an objective optimization problem is constructed, aiming to achieve joint optimization of covert communication rate and covertness under mixed field channel conditions by adjusting the position of each movable subarray in the movable antenna array and adjusting the power distribution of the movable antenna array.

[0076] In step S101 of some embodiments, the setup of the monitoring party and the target receiver is first determined (step S101), which helps to clarify the participants in the communication system and their positional relationships. The monitoring party refers to the entity that monitors and receives the communication signals emitted by the communication system, and the target receiver refers to the legitimate user equipment that expects to receive the communication signals. Near-field communication scenarios refer to situations with short communication distances, while far-field communication scenarios refer to situations with long communication distances, where signal propagation conforms to the free-space attenuation model.

[0077] In step S102 of some embodiments, the communication model is constructed to simulate and analyze the behavior and performance of the communication system through mathematical or simulation means.

[0078] Please see Figure 2 In some embodiments, the communication model includes a first channel model and a second channel model, and step S102 may include, but is not limited to, steps S201 to S203:

[0079] Step S201: Obtain the monitoring locations of multiple monitoring parties and the receiving locations of several target receivers;

[0080] Step S202: Based on the receiving positions of several target receivers, construct a first channel model that includes near-field communication scenarios and far-field communication scenarios;

[0081] Step S203: Based on the monitoring locations of multiple monitoring parties, construct a second channel model for the near-field communication scenario.

[0082] In step S201 of some embodiments, the monitoring locations of multiple monitoring parties and the receiving locations of several target receivers are first obtained. Monitoring parties refer to entities that may attempt to detect communication activities, while target receivers refer to legitimate user equipment that expects to receive communication signals.

[0083] In step S202 of some embodiments, a first channel model is constructed based on the receiving location of the target receiver, encompassing near-field and far-field communication scenarios. The first channel model is used to describe the propagation characteristics of the signal from the transmitter (i.e., the movable antenna array) to the target receiver, including signal power attenuation, delay spread, etc.

[0084] In step S203 of some embodiments, a second channel model for a near-field communication scenario is constructed based on the monitoring locations of multiple monitoring parties. The second channel model is mainly used to describe the propagation characteristics of signals from the transmitter to the monitoring party, focusing on how the monitoring party perceives communication signals in a near-field environment, which helps to assess the stealth of the communication system.

[0085] Through steps S201 to S203, such a communication model can help analyze the achievable speed and stealth of a communication system.

[0086] In some specific embodiments, the communication system is configured with a movable antenna array consisting of N antenna elements, also known as a movable extremely large-scale array (XL-array), which is divided into M movable subarrays (denoted as...). Each movable subarray contains Each antenna element. Here we consider a practical and challenging mixed-field scenario where the target receiver is located in the near or far field of a movable antenna array, while the monitoring party is located in the near field, monitoring communication signals over a short distance.

[0087] The antenna spacing in each movable subarray is half a wavelength, and the position of each movable subarray can be flexibly controlled to enhance covert communication performance. Assume... Let M be the position vectors of the M movable subarrays, where This is the center position of the movable subarray m. Given that the antenna spacing in each movable subarray is half a wavelength, the nth antenna in the movable antenna array (or the nth antenna in the movable subarray m)... One antenna, of which The position can be represented as:

[0088]

[0089] The center positions of the movable subarrays i and j satisfy the following condition: In particular, when At this point, the movable antenna array degenerates into a fixed-position very large-scale antenna array (referred to as "fixed XL-array"), where the spacing between all antennas is half a wavelength. For a fixed XL-array, q = q U This indicates the center position of the movable subarray.

[0090] The boundaries between the near-field and far-field regions can be defined based on the effective Rayleigh distance. Where ν = 0.37, and D represents the aperture of the movable antenna array. It is worth noting that, compared to the classical Rayleigh distance based on phase change, Z(θ) describes the range boundary where the gain of the movable antenna array exhibits significant differences in far-field and near-field channel models.

[0091] For both near-field and far-field target receivers, a common near-field spherical wavefront channel model is used. Let... Let the channel from the movable antenna array to the b-th target receiver be represented. The first channel model is constructed as follows:

[0092]

[0093] It consists of a line-of-sight (LoS) path and L b It consists of several non-line-of-sight (non-LoS, NLoS) paths. Furthermore, g B,b and These are the line-of-sight path and the e-th... b The complex path gain of a non-line-of-sight path, with corresponding spatial angles and distances of {θ}. B,b ,r B,b}and Here, the channel steering vector (i.e. The following formula is given:

[0094]

[0095] in, Given {q m Let b be the near-field channel steering vector of the m-th movable subarray when θ ∈ [-1, 1]. Specifically, b m (q m (θ, r) is given by the following formula:

[0096]

[0097] It should be noted that for far-field beams, when r>Z(θ), the near-field channel steering vector in formula (3) simplifies to the far-field case. In this case, the quadratic phase term in formula (4) can be ignored and simply expressed as: That's all.

[0098] Similarly, the channel from the movable antenna array to the w-th monitoring party is denoted as... The second channel model is constructed as follows:

[0099]

[0100] Among them, g W,w ,θ W,w , and r W,w These represent the complex path gain, spatial angle, and distance of the direct path, respectively. Furthermore, and Representing the lth position of the wth monitoring party w Complex path gain, spatial angle, and distance of a non-direct path, L w Let represent the number of non-direct paths for the w-th monitoring party. Assume the movable antenna array can obtain perfect channel state information for both the target receiver and the monitoring party; this can be practically obtained using existing near-field and far-field channel estimation methods. Furthermore, a(q,θ) W,w ,r W,w )and These represent the channel steering vectors, respectively.

[0101] This movable antenna array considers a low-cost hybrid beamforming architecture, equipping the base station with B (B << N) radio frequency (RF) chains to serve B users. and Let represent the analog and digital beamforming matrices, respectively. Based on the above, the signal received by the b-th target receiver can be expressed as:

[0102]

[0103] in, It is a symbol vector sent to B target receivers. This is additive white Gaussian noise (AWGN) at the target receiver b. Therefore, the achievable rate (bits / second / hertz, bps / Hz) at the target receiver b can be expressed as:

[0104]

[0105] Among them, f D,b It is matrix F D Column b.

[0106] In step S103 of some embodiments, achievable rate analysis is performed based on the communication model to obtain achievable rate-related data. Achievable rate analysis determines the highest data transmission rate that the target receiver can achieve under given communication conditions. The achievable rate reflects the communication efficiency and performance of the system, referring to the maximum information transmission rate that the communication system can achieve under specific channel conditions and power constraints. The achievable rate-related data represents the influencing factors related to the achievable rate.

[0107] Please see Figure 3 In some embodiments, the target receiving end includes at least a first receiving end and a second receiving end, and step S103 may include, but is not limited to, steps S301 to S303:

[0108] Step S301: Analyze the power detection capabilities of multiple monitoring parties based on the communication model to determine the covert communication requirements for the mobile antenna array.

[0109] Step S302: Based on the covert communication requirements, the achievable total rate is obtained; the achievable total rate represents the sum of the communication rates of the first receiving end and the second receiving end.

[0110] Step S303: Based on the influencing factors of the achievable total rate, obtain the achievable rate-related data corresponding to the achievable total rate.

[0111] In step S301 of some embodiments, the power detection capabilities of multiple monitoring parties are first analyzed based on a communication model. Power detection capability refers to the magnitude of signal power that a monitoring party can detect, which is related to whether the monitoring party can detect communication behavior. Based on the power detection capabilities of the monitoring parties, the covert communication requirements when the movable antenna array communicates can be determined. The covert communication requirements aim to ensure that the power of the communication signal is low enough to avoid detection by the monitored party, while simultaneously ensuring that legitimate receivers can reliably receive the signal.

[0112] In step S302 of some embodiments, the achievable total rate is obtained based on the determined covert communication requirements. The achievable total rate refers to the sum of communication rates that all target receivers (such as the first receiver and the second receiver) can achieve under the condition of meeting the covert communication requirements. This step requires comprehensive consideration of factors such as the power constraints of the communication system, channel conditions, and covertness requirements to calculate the maximum communication rate achievable in the covert communication scenario.

[0113] In step S303 of some embodiments, achievable rate-related data is obtained based on factors influencing the achievable total rate. These factors may include channel state information, the configuration of the movable antenna array, the location and detection capabilities of the monitoring party, etc. The achievable rate-related data may include rate values ​​under different channel conditions, the relationship between rate and power allocation, etc., which helps to further optimize the performance of the communication system.

[0114] Steps S301 to S303 systematically analyze the communication rate achievable by the communication system while meeting concealment requirements. This helps optimize the performance of the communication system in concealed communication scenarios, ensuring efficient communication without being detected by the monitoring party.

[0115] In some specific embodiments, for covert communication, each monitoring party attempts to independently detect the existence of communication between the movable antenna array and several target receivers based on the Neyman-Pearson test, which can be formulated as a binary hypothesis testing problem. Specifically, for each monitoring party w, the signal received in time slot t is given by the following formula:

[0116]

[0117] in, This indicates that no communication was detected. This indicates that communication has been detected. Let w represent additive white Gaussian noise at the monitoring point. Since multiple monitoring points employ energy detection technology to determine the covert transmission between the movable antenna array and the target receiver, noise uncertainty needs to be considered, which affects covert performance. Here, a bounded uncertainty model is considered; based on this model, the noise power... The probability density function (PDF) is given by the following formula:

[0118]

[0119] Where ρ≥1 represents the noise uncertainty level, and Let w represent the nominal noise power. Based on the above, the average power of the signal received at monitoring point w can be expressed as:

[0120]

[0121] For each monitoring party w, the power detection threshold τ is appropriately set to determine whether covert transmission exists. Or there is no covert transmission Its expression is:

[0122]

[0123] In the energy detection described above, two types of errors may occur: false alarm (FA) and missed detection (MD), and their probabilities are given by the following formulas:

[0124]

[0125] in, This represents the average received power of the signal carrying the information. Therefore, given the parameter τ, the total detection error probability (DEP) of the monitoring method w is:

[0126]

[0127] Based on the first-order optimality condition, to minimize the total detection error probability, the optimal detection threshold at monitoring point w is... It should be set as follows:

[0128]

[0129] Will Substituting formula (9) into formula (13), we can obtain the minimum total detection error probability of the monitoring method w:

[0130]

[0131] set up This is a positive constant used to ensure the covert communication requirements of the system under consideration. Specifically, it is only when the minimum total detection error probability of all monitoring parties satisfies... Only then can covert communication be guaranteed. This condition can be equivalently rewritten as:

[0132]

[0133] It is worth noting that the inequality in formula (16) indicates that, in order to ensure concealment, the average received power of the information-carrying signal received by each monitoring party should be less than a certain threshold.

[0134] This application considers a typical mixed-field scenario where a movable antenna array communicates with both near-field and far-field target receivers, while the near-field monitoring party detects covert transmissions between the movable antenna array and the target receivers. In this scenario, the movable antenna array can effectively address energy diffusion effects in mixed-field conditions, thus significantly improving the achievable total data rate and covert capabilities compared to a fixed XL-array. Therefore, the following definitions are given first.

[0135] Definition 1: For a movable antenna array, given two positions {θ} i ,r i} and {θ j ,r j The correlation function of the two steering vectors given by formula (3) is defined as follows:

[0136]

[0137] Definition 2: For a fixed XL-array (i.e., q = q...) U ), given θ i =θ j =θ, the correlation function in equation (17) can be approximated as:

[0138]

[0139] in, as well as

[0140] Definition 3: For a fixed XL-array, given the near-field channel steering vector a(q) U ,θ i ,r i and far-field beamforming vector The μ-dB energy diffusion angle set is defined as follows:

[0141]

[0142] in, Indicates normalized beam gain. Specifically, μ = 10 corresponds to the 10-dB energy diffusion region, where This indicates that at a distance r j Peak normalized beam gain at (equivalent to 0.1f) peak Specifically, The corresponding normalized beam gain is greater than ιf peak The angle of support set.

[0143] It is worth noting that the defined μ-dB angle support has been used to characterize energy diffusion effects, facilitating performance analysis of hybrid field systems and beam training design based on the discrete Fourier transform (DFT). To illustrate this, in Figure 4 The figure shows the distance r under far-field beamforming w(θ). i =10 and r iThe normalized beam gain at point θ = 5 varies with different spatial angles θ. It can be seen that the normalized beam gain has a significantly large value within a certain range, accompanied by slight fluctuations, and generally increases as the distance decreases.

[0144] Regarding the achievable rate analysis, we first fix the total rate performance achievable by the XL-array without considering concealment constraints. To facilitate rate performance analysis in mixed-field channels, we consider the LoS scenario in the high-frequency band and adopt a low-complexity hybrid beamforming design. Specifically, analog beamforming is based on maximalratio transmission (MRT) (i.e., the beam is directed towards the target receiver), while power allocation is optimized in digital beamforming. More complex digital beamforming designs (such as zero-forcing (ZF) or minimum mean-squared error (MMSE) typically make the analysis more complex or even difficult to handle; therefore, power allocation design is considered in the performance analysis. Based on this, the beamforming vector is given below. as well as Where P B,1 and P B,2 Let P represent the transmit power allocated to the first receiver in the near field and the second receiver in the far field, respectively. B,1 +P B,2 =P. Based on the above conditions, the achievable rates of the near-field first receiver and the far-field second receiver can be rewritten as follows:

[0145]

[0146] in, This represents the correlation between the channel steering vectors of the first and second receivers. Furthermore, according to Definition 3, It can be approximated as:

[0147]

[0148] in, This refers to the 10-dB energy diffusion angle support set relative to the near-field target receiver. The 10-dB energy diffusion angle support set is used here to ensure that the angle support set... The correlation with other parameters is approximately 0.

[0149] The optimal transmit power allocation between the two target receivers that maximizes the total achievable rate can be obtained through an exhaustive search method. and Furthermore, the total achievable rate at the two target receivers can be bounded to the following:

[0150]

[0151] when The equation holds true.

[0152] Next, the rate performance gain brought by the movable antenna array (i.e., the movable XL-array) in this application is investigated. Specifically, the correlation function defined according to Equation (17) with respect to the position {q} of each movable subarray is investigated. m}(i.e., χ(q,{θ) i ,r i},{θ j ,r j The following rewrite is possible:

[0153]

[0154] in, And when r i and r j Greater than When, formula (23a) holds true.

[0155] For a movable antenna array, as shown in equation (23), its correlation function can be expressed as a function of the positions of the movable subarrays. By adjusting the position of each movable subarray, the phase term {φ} in equation (23) can be adjusted. m} and amplitude term {A m This controls the value of the correlation function, thereby determining the achievable rate correlation data. This suggests that movable antenna arrays have potential in resolving mixed-field interference caused by energy diffusion effects, as... The increase in R increases the achievable rate. B,1 and R B,2 It will decrease.

[0156] According to formula (20), maximizing the total achievable rate is equivalent to minimizing the relevant function in formula (20) by optimizing the position of the movable subarray. This problem can be expressed mathematically as follows:

[0157]

[0158] Constraints (24a) and (24b) specify the allowed movement areas and the minimum spacing between adjacent movable subarrays.

[0159] It is worth noting that, due to the complexity of the near-field steering vector, problem (P1) is a non-convex optimization problem, making it difficult to obtain the optimal solution. To solve this problem, we first solve a relaxed problem (P2), as shown below, which does not consider the movement region constraint in (24b).

[0160]

[0161] Given Ω θ and Ω r An optimal solution to problem (P2) is given by the following

[0162]

[0163] make and Ω m The value should meet the following conditions

[0164]

[0165] Ω m =2q m Ω r +Ω θ Substituting into equation (25), we can obtain the optimal solution.

[0166] On the other hand, for the original problem (P1) with the moving region constraint, its optimal solution is usually difficult to obtain directly in a closed form, but a high-quality suboptimal solution can be obtained by using efficient algorithms such as differential evolution (DE).

[0167] This shows that by adjusting the position of the movable subarray, the movable antenna array achieves rate performance close to its upper limit, indicating that interference cancellation is almost achieved across the entire angular domain even with aperture constraints.

[0168] In step S104 of some embodiments, a covertness analysis is performed based on the communication model to obtain covertness-related data. Covertness analysis refers to evaluating the covert performance of a communication system, i.e., the difficulty for a monitoring party to detect communication behavior. Covertness measures the ability of a communication system to avoid detection by unauthorized monitoring parties, and covertness-related data represents influencing factors related to covertness.

[0169] Please see Figure 5 In some embodiments, step S104 may include, but is not limited to, steps S401 to S402:

[0170] Step S401: Based on the need for covert communication, determine the factors of covert communication;

[0171] Step S402: Based on covert communication factors, perform covertness analysis on the first receiving end and the second receiving end to obtain covertness-related data.

[0172] In step S401 of some embodiments, covert communication factors are determined by covert communication requirements. Covert communication requirements refer to the conditions that must be met during communication to prevent detection by the monitored party, such as limiting the detectability of the signal. Covert communication factors represent the relevant factors that affect covert communication conditions.

[0173] In step S402 of some embodiments, a covertness analysis is performed on the first and second receivers based on these covert communication factors to obtain covertness-related data. Covertness analysis refers to assessing the ability of a communication system to avoid detection by a monitored party under given covert communication factors. Covertness-related data represents the influencing factors related to covertness.

[0174] Steps S401 to S402 help analyze the impact of the communication system on the concealment of different receiving ends when meeting different covert communication requirements.

[0175] This embodiment analyzes the covert transmission performance under a mixed-field setup. Since the minimum total detection error probability of each monitoring party is independent of each other, the following performance analysis first considers only the case of one monitoring party, and the results can be easily generalized to the case of multiple monitoring parties.

[0176] For a fixed XL-array system, the information carrier signal f received by the monitoring party Co,1 The average received power can be expressed as:

[0177]

[0178] in, Represents the channel steering vector a(q) U ,θ W,1 ,r W,1 ) and a(q U ,θ B,b ,r B,b The correlation between (b, 2) and (b ∈ {1, 2}). Given a positive constant. The following lemma provides the conditions for ensuring covert transmission.

[0179] For a fixed XL-array system, given the location of the monitoring party and Covert transmission is guaranteed when the following conditions are met:

[0180]

[0181] Therefore, the following factors can be seen to affect covert transmission conditions: 1) Complex path gain g W,1 The weaker the path gain, 1) The higher the value, the more relaxed the covert transmission conditions; 2) The higher the detection error probability requirement ∈: the more stringent the covert transmission conditions; 3) Transmission power P B,b b∈{1,2}: The greater the transmission power, the more stringent the conditions for covert transmission; 4) Correlation Correlation The higher the value, the less likely the conditions for covert transmission will be met.

[0182] Among these factors, correlation This is particularly crucial, as it directly affects the location of the monitoring party, concealment requirements, and transmission power P. B,b Given that b∈{1,2}, the conditions for covert transmission are as follows. For ease of analysis, we first consider... The value categorizes the mixed-field covert communication scenario into the following four cases.

[0183] Case 1 (No power leakage): The steering vectors between the first and second receivers and the monitoring party are almost orthogonal (i.e., and This can be mathematically represented as:

[0184]

[0185] Case 2 (Power Leakage at Far-Field Target Receiver): Only the correlation between the far-field target receiver and the monitoring party is not negligible (i.e., and Its expression is:

[0186]

[0187] Case 3 (Power Leakage at Near-Field Target Receiver): Only the correlation between the target receiver and the monitoring party in the near field is not negligible (i.e., and Its expression is:

[0188]

[0189] Case 4 (Power Leakage at Two Target Receivers): For the two target receivers, the correlation between their channel steering vectors and the channel steering vector of the monitoring receiver is not negligible (i.e., and This can be expressed as:

[0190]

[0191] In case 1, the conditions for covert transmission can always be met.

[0192] In scenario 2, energy leakage caused by energy diffusion makes... The value increases significantly. Next, we will first give the covert transmission conditions for case 2.

[0193] Given the position of the near-field monitoring object, when θ B,1 ≠θ W,1 and Then, the covert transmission condition in Lemma 2 simplifies to:

[0194] Therefore, the channel correlation between the near-field monitoring party and the far-field target receiver caused by energy effects should be sufficiently small to ensure concealment. Furthermore, as ∈ increases, Δ2(∈) decreases (i.e., the concealment transmission condition becomes more stringent). Moreover, since a(q U ,θ B,2 ,r B,2 It can be approximated as the far-field steering vector. The covert transmission conditions of a far-field target receiver depend on its spatial angle. Based on the above, the covert transmission angle of the far-field target receiver is described to ensure the covertness of its transmission.

[0195] Given the position of the near-field monitoring object, when θ B,1 ≠θ W,1 and At this time, the covert transmission angle of the far-field target receiver can be obtained by the following formula:

[0196] {θ B,2 ≤Ξ left (θ W,1 ,r W,1 ,Δ2(∈))}∪{θ B,2 ≥Ξ right (θ W,1 ,r W,1 ,Δ2(∈))}. (34)

[0197] Here, Ξ left (θ W,1 ,r W,1 ,Δ2(∈)) and Ξ right (θ W,1 ,r W,1 ,Δ2(∈)) respectively represent the following equations f(w(θ),θ W,1 ,r W,1 The two solutions of ) = Δ2(∈).

[0198] To ensure covert transmission conditions, the spatial angle difference between the monitoring party and the target receiver in the far field must exceed the threshold determined by Δ2(∈).

[0199] Based on formula (34), we can obtain information about {θ} W,1 ,r W,1 The minimum and maximum spatial angles Ξ of Δ2(∈)} leftand Ξ right To meet the covert transmission requirements of the far-field target receiver, the permissible spatial angle should be less than Ξ. left or greater than Ξ right To ensure channel correlation Below the threshold determined by Δ2(∈). Furthermore, given a larger ∈ (a more stringent covert transmission condition), a larger spatial angle difference (a smaller Ξ) is required. left and larger Ξ right This ensures concealment.

[0200] For case 3, when the near-field target receiver and the near-field monitoring party are at the same angle, their channel correlation will be affected by their respective distances, and its characteristics are as follows.

[0201] Given the position of the near-field monitoring object, when θ B,1 =θ W,1 and The covert transmission conditions of the near-field target receiver are given below.

[0202]

[0203] This gives us the covert transmission distance of the target receiver in the near field. Within this area, the covert transmission capability can be guaranteed, which is the covert transmission distance.

[0204] Let β Δ To satisfy |G(β) Δ The non-negative constant of |θ| is given by the position of the monitoring party. W,1 ,r W,1}, when θ W,1 =θ B,1 At this time, the covert transmission distance of the target receiver is given by the following formula.

[0205]

[0206] in, Among them, there are as well as This indicates that to ensure covert transmission, the distance difference between the near-field target receiver and the monitoring party must exceed a certain threshold, which is related to Π. Furthermore, because... As Δ1(∈) decreases, it increases, so the stricter covert transmission conditions in Equation (35) (i.e., lower Δ1(∈)) will lead to a larger Π, which means that the distance difference between the near-field target receiver and the monitoring party needs to be larger.

[0207] For the more challenging scenario 4, to ensure covert transmission, the total correlation between the monitoring party and the target receiver (i.e., ) must be kept at the threshold corresponding to ∈ (i.e. The following is a breakdown of the covert transmission conditions for the far-field target receiver, given the positions of the near-field target receiver and the monitoring party:

[0208]

[0209] By replacing Δ2(∈) in formula (34) with Similarly, the concealed transmission angle of the far-field target receiver in case 4 can be obtained. Because In this situation, there is always This indicates that a greater angular difference is needed between the monitoring party and the target receiver in the far field to ensure concealment.

[0210] For the movable antenna array (movable XL-array system) of this application, channel correlation can be reduced by flexibly adjusting the position of the movable subarrays. To this end, an optimization problem is constructed to minimize the information-carrying signal f. Co,1 The average received power is increased, thereby reducing power leakage from the target receiver in both the near and far fields. Accordingly, the equivalent optimization problem can be formulated as follows:

[0211]

[0212] Problem (P3) is a nonconvex optimization problem because The expression is non-convex. To address this challenge, efficient algorithms (such as the DE algorithm) can be used to solve problem (P3). Since closed-form solutions to problem (P3) are difficult to obtain, an example will be provided below to demonstrate the effectiveness of movable antenna arrays in reducing the correlation between the target receiver and the monitoring party to enhance stealth.

[0213] exist Figure 6 middle, Figure 6 It shows when θ B,1 =θ B,2 =θ W,1 =0, r W,1 =25 meters, r B,2 At a range of 150 meters, the relationship between the objective function of problem (P3) and the range of the near-field target receiver is examined. It is observed that for a fixed XL-array, the objective function of problem (P3) exceeds 0.1, indicating a strong correlation between the monitoring party and multiple target receivers. In contrast, for a movable antenna array, the objective function of problem (P3) decreases significantly and approaches zero. However, its value remains relatively high when the monitoring party's range is between 20 and 30 meters. This is due to the strong channel correlation between the near-field monitoring party and target receivers, which is difficult to address within the constraints of the array aperture.

[0214] In summary, movable antenna arrays can be used to increase the achievable total data rate or enhance transmission concealment. However, in covert communication within hybrid field systems, simultaneously improving communication performance and transmission concealment is more challenging, requiring a trade-off between the two.

[0215] Mobility of mobile subarrays: For sum and rate performance, the movement of mobile subarrays should be designed to minimize channel correlation between target receivers. However, to enhance transmission concealment, the main principle of adjusting the movement of mobile subarrays is to minimize channel correlation between the target receiver and the monitoring party.

[0216] Power Allocation: To maximize the achievable total rate of fire, all available transmit power should be fully utilized. Conversely, to ensure stealth, using lower transmit power can reduce the risk of detection.

[0217] In step S105 of some embodiments, a target optimization problem is constructed based on achievable rate-related data and stealth-related data. The target optimization problem is a mathematical framework used to find the optimal balance among multiple objectives, in this case, between communication rate and stealth, to maximize the stealth of the communication process while satisfying certain communication performance requirements.

[0218] In step S106 of some embodiments, target optimization problem is addressed by adjusting the position of each movable subarray of the movable antenna array and adjusting the power allocation of the movable antenna array to obtain target optimization information. A movable subarray refers to the portion of the movable antenna array whose position can be changed to dynamically adjust the signal propagation direction and strength. Power allocation refers to the rational distribution of limited transmission power to different antennas or different communication directions to optimize system performance. By changing the position and power allocation of the movable subarrays, the signal propagation characteristics can be affected, thereby affecting achievable speed and stealth. The target optimization information includes setting information related to the position and transmission power of each movable subarray.

[0219] Please see Figure 7 In some embodiments, step S106 may include, but is not limited to, steps S501 to S502:

[0220] Step S501: Based on the objective optimization problem, decompose it into an outer layer problem and an inner layer problem. The inner layer problem is related to the power allocation of multiple movable subarrays, and the outer layer problem is related to the position of multiple movable subarrays.

[0221] Step S502: The outer layer problem is optimized by adjusting the position of each movable subarray of the movable antenna array, and the inner layer problem is optimized by adjusting the power distribution of the movable antenna array. The outer layer problem and the inner layer problem are optimized alternately until the preset convergence condition is met, and the target optimization information is obtained.

[0222] In step S501 of some embodiments, the target optimization problem is decomposed into an outer layer problem and an inner layer problem. The inner layer problem relates to the power allocation of multiple movable subarrays, while the outer layer problem relates to the positions of the multiple movable subarrays. Power allocation refers to how to rationally distribute limited transmit power to different antennas or different communication directions in a communication system to optimize system performance. A movable subarray refers to the portion of a movable antenna array whose position can be changed; by adjusting the positions of multiple movable subarrays, the signal propagation direction and coverage area can be dynamically changed.

[0223] In step S502 of some embodiments, the outer layer problem is optimized by adjusting the position of each movable subarray of the movable antenna array, while the inner layer problem is optimized by adjusting the power distribution of the movable antenna array. This process employs an alternating optimization method, that is, while optimizing the outer layer problem, the variables of the inner layer problem remain unchanged, and iteration continues until a preset convergence condition is met. The convergence condition refers to the condition that, during the iterative optimization process, when the change in the solution is less than a certain set threshold, or when the maximum number of iterations is reached, the optimization process is considered to have converged, and iteration can be stopped. The final target optimization information includes the optimized movable subarray positions and power distribution scheme, and the target optimization information will be used to guide the actual signal transmission operation of the movable antenna array.

[0224] Steps S501 to S502 provide an optimization method that enables the communication system to achieve an optimal performance balance by adjusting the position and power allocation of the movable subarray while meeting the requirements of concealment and achievable speed.

[0225] In this embodiment, an objective optimization problem is designed, and the hybrid beamforming matrix {F} is designed jointly. A ,F D The objective optimization problem can be formulated as follows: ...and the position q of the movable subarray to maximize the covert transmission rate.

[0226]

[0227] in, It is a weighting factor. Here, (39a) ensures covert transmission between the movable antenna array and the target receiver, (39b) is the unit mode constraint for simulating beamforming, and (39c) limits the maximum transmit power.

[0228] To solve problem (P4), it is first transformed into two subproblems, corresponding to optimizing the hybrid beamforming matrix {F} given the positions of the subarrays. A ,F D The inner layer problem of}, and the outer layer problem of further optimizing the subarray position q.

[0229] Inner Layer Problem: Given any feasible location of the movable subarray q, the inner layer problem for beamforming optimization is given by the following.

[0230]

[0231] st(39a),(39b),(39c).

[0232] Outer layer problem: Let and The solutions to problem (P5) are shown below. The outer problem of optimizing the position of the movable subarray can be expressed as follows:

[0233]

[0234] st(24a),(24b).

[0235] Please see Figure 8 In some embodiments, step S502 may include, but is not limited to, steps S601 to S605:

[0236] Step S601: Based on the preset positions of multiple movable subarrays, optimize the outer layer problem and determine the target transmission power of multiple movable subarrays;

[0237] Step S602: Based on the target transmit power of multiple movable subarrays, optimize the inner layer problem and determine the target adjustment position of multiple movable subarrays.

[0238] In step S601 of some embodiments, outer-layer optimization is performed based on preset positions of multiple movable subarrays to determine the target transmit power. Preset positions refer to the initial positions of the movable subarrays set before optimization begins. Outer-layer optimization focuses on determining the optimal transmit power that the movable subarrays should use at a specific location to meet the performance objectives of the communication system, such as stealth and reachability.

[0239] In step S602 of some embodiments, the target transmit power obtained in step S601 is used to optimize the inner-layer problem to determine the target adjustment position of the movable subarray. Optimizing the inner-layer problem involves adjusting the position of the movable subarray under a given power allocation to further optimize the performance of the communication system. The target adjustment position refers to the movable subarray position, after optimization calculation, that enables the system to achieve optimal performance.

[0240] Through steps S601 to S602, the coordinated optimization of the position and power allocation of the movable subarray of the movable antenna array is achieved, ensuring that the achievable rate of the system is maximized while meeting the needs of covert communication.

[0241] In one embodiment, the following is for solving the inner-layer problem: designing the simulated beamforming matrix F. A To maximize the signal power received by each target receiver. Specifically, based on the Loss of Path (LoS) of each target receiver, The b-th column is denoted as It can be represented as:

[0242]

[0243] Given simulated beamforming Next, the digital beamforming matrix is ​​optimized. Specifically, the obtained... The effective channels for all target receivers and monitoring parties are given below.

[0244]

[0245] With an effective channel, the achievable rate at the target receiver b and the covert transmission constraints on the monitoring party w can be rewritten as follows:

[0246]

[0247] Based on the above, the inner-layer problem of beamforming optimization can be simplified to the following digital beamforming optimization problem:

[0248]

[0249] st(39c),(44b).

[0250] Because the objective function in problem (P7) is about F D Since it is nonconvex, a concave substitute function is obtained through the technique of successful convex approximation (SCA) to approximate the nonconvex term, i.e., the one in problem (P7). Specifically, The substitution function, denoted as Given by the following formula:

[0251]

[0252] in, as well as Here, It is the digital beamforming matrix obtained in the k-th consecutive convex approximation iteration. By providing... Construct a tight concave lower bound (i.e. The original problem (P7) can be approximated as the following convex optimization problem:

[0253]

[0254] st(39c),(44b).

[0255] This problem can be solved efficiently using the CVX solver. Iterative updates... Until convergence, a suboptimal digital beamforming matrix can be obtained.

[0256] The following describes the solution to the outer layer problem: In the initial stage of the differential evolution algorithm, G feasible position vectors are randomly generated within a predefined solution space. These vectors represent a movable antenna array, and their expression is:

[0257]

[0258] in, Let represent the g-th candidate position vector of the movable antenna array. Let G represent the population index set, and G be the population size. Let Let g be the position vector in the i-th DE iteration, where g is the position vector. I represents the maximum number of iterations. This indicates its index set.

[0259] For each candidate position vector The corresponding hybrid beamforming matrix This can be obtained by solving problem (P5). Based on the above, the following fitness function is used to... The quality was evaluated.

[0260]

[0261] It is worth noting that the first term corresponds to the objective function in problem (P6), while the second term is a penalty function introduced to ensure that constraint (24a) is satisfied. Specifically, for any position vector q, the set Let q be the set of all pairs of elements in vector q that violate constraint (24a), and let its expression be:

[0262]

[0263] The degree of constraint violation of q is described, and it is defined as follows:

[0264]

[0265] also, Represents a set The cardinality is η, and η>0 represents the scaling factor.

[0266] Then, in each DE iteration, the following three operations are performed: "mutation", "crossover" and "selection" to update the individual (i.e., the candidate position of the subarray).

[0267] (a) Mutation: A mutation vector is generated by the following method.

[0268]

[0269] in, and From Two different vectors are randomly selected from the given vectors, and r1 and r2 satisfy the following conditions: also, This refers to the position vector with the highest fitness function value, while F is used for...

[0270] The mutation factor that controls the global search capability and convergence speed of the differential evolution algorithm.

[0271] (b) Crossover: After mutation, crossover is performed by mutating individuals. With the current individual Gene exchange between them to generate an experimental vector The process of crossover can be mathematically represented as follows:

[0272]

[0273] Among them, C R ∈[0,1] is the cross factor. It is a random index used to ensure at least one crossover occurs, while rand(1) represents a random variable that satisfies To satisfy boundary constraints (22b), the test vector is restricted to... Its mathematical expression is:

[0274]

[0275] (c) Selection: After the crossover operation is completed, the experimental position vector is evaluated using a fitness function to generate the next generation population determined by it.

[0276]

[0277] After I iterations, the suboptimal solution to problem (P6) is denoted as q.* ,Right now

[0278] Consider the convergence of the algorithm used to solve problem (P4). For the update From the inner problem, we can obtain:

[0279]

[0280] Since the objective function of problem (P8) is non-decreasing after each iteration, the convergence of the inner problem is guaranteed. For the differential evolution algorithm to solve the outer problem, The update during the iteration process satisfies

[0281] Since there is an upper limit to the achievable total rate, the convergence of the proposed algorithm can be guaranteed. Next, the computational complexity of the proposed algorithm is analyzed, which is derived from optimizing F... D The complexity is determined by both the inner-level problem and the outer-level problem of updating q. The complexity of solving the problem using the interior-point method (P8) is... The order of magnitude of ξ is given by ξ, where ξ is the accuracy required by the CVX solver. Considering that the fitness evaluation times in the differential evolution algorithm are GI, the total computational complexity of the proposed algorithm is O(n log n). The order of magnitude is , where I1 represents the number of iterations for the continuous convex approximation.

[0282] In step S107 of some embodiments, the signal transmission operation of the movable antenna array is adjusted based on the obtained target optimization information. According to the preceding analysis and optimization results, the parameters and operation mode of the movable antenna array are actually adjusted to achieve optimized communication performance and stealth.

[0283] Based on the target optimization information, perform at least one of the following operations: update the positions of multiple movable subarrays of the movable antenna array, and update the communication power of multiple movable subarrays of the movable antenna array.

[0284] This application's embodiments determine multiple monitoring parties and at least two target receivers. A communication model is constructed based on a movable antenna array, multiple monitoring parties, and target receivers. Achievable rate analysis is performed based on the communication model to obtain achievable rate-related data. Stealth analysis is also performed based on the communication model to obtain stealth-related data. Based on the achievable rate-related data and the stealth-related data, a target optimization problem is constructed. By adjusting the position of each movable subarray of the movable antenna array and adjusting the power distribution of the movable antenna array, the target optimization problem is processed to obtain target optimization information. Based on the target optimization information, the signal transmission operation of the movable antenna array is adjusted. Therefore, this application, through a communication model constructed based on a movable antenna array, monitoring parties, and target receivers, conducts achievable rate analysis to evaluate the communication rate that a target receiver can achieve in a mixed-field environment, i.e., when there are target receivers in both near-field and far-field communication scenarios simultaneously, and obtains achievable rate-related data. Meanwhile, based on the communication model, a covertness analysis is conducted, focusing on how to reduce the probability of the monitoring party detecting the communication behavior, thereby obtaining covertness-related data. Then, based on the achievable rate-related data and the covertness-related data, an objective optimization problem is constructed, aiming to achieve joint optimization of covert communication rate and covertness under mixed field channel conditions by adjusting the position of each movable subarray in the movable antenna array and adjusting the power distribution of the movable antenna array.

[0285] Please see Figure 9 This application also provides a signal transmission device for a movable antenna array, which can realize the above-described signal transmission method for a movable antenna array. The device includes:

[0286] The multi-terminal acquisition module is used to identify multiple monitoring parties and at least two target receivers; wherein at least one target receiver is in a near-field communication scenario and one target receiver is in a far-field communication scenario.

[0287] The communication model building module is used to build a communication model based on a mobile antenna array, multiple monitoring parties, and a target receiver.

[0288] The reachability analysis module is used to perform reachability analysis based on the communication model and obtain reachability-related data.

[0289] The concealment analysis module is used to perform concealment analysis based on the communication model and obtain concealment-related data.

[0290] The optimization problem construction module is used to construct the target optimization problem based on reachability-related data and concealment-related data;

[0291] The optimization problem processing module is used to process the target optimization problem by adjusting the position of each movable subarray of the movable antenna array and adjusting the power distribution of the movable antenna array, so as to obtain the target optimization information.

[0292] The signal transmission adjustment module is used to adjust the signal transmission operation of the movable antenna array based on target optimization information.

[0293] The specific implementation of the signal transmission device for the movable antenna array is basically the same as the specific implementation of the signal transmission method for the movable antenna array described above, and will not be repeated here.

[0294] This application also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the signal transmission method of the aforementioned movable antenna array. This electronic device can be any smart terminal, including tablet computers, in-vehicle computers, etc.

[0295] Please see Figure 10 , Figure 10 The hardware structure of an electronic device according to another embodiment is illustrated. The electronic device includes:

[0296] The processor 1001 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.

[0297] The memory 1002 can be implemented as a read-only memory (ROM), static storage device, dynamic storage device, or random access memory (RAM). The memory 1002 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 1002 and is called and executed by the processor 1001 to execute the signal transmission method of the movable antenna array of the embodiments of this application.

[0298] Input / output interface 1003 is used to implement information input and output;

[0299] The communication interface 1004 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.).

[0300] Bus 1005 transmits information between various components of the device (e.g., processor 1001, memory 1002, input / output interface 1003, and communication interface 1004);

[0301] The processor 1001, memory 1002, input / output interface 1003 and communication interface 1004 are connected to each other within the device via bus 1005.

[0302] 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.

[0303] The signal transmission method, apparatus, and electronic device for a movable antenna array provided in this application determine multiple monitoring parties and at least two target receivers. A communication model is constructed based on the movable antenna array, the multiple monitoring parties, and the target receivers. Achievable rate analysis is performed based on the communication model to obtain achievable rate-related data. Stealth analysis is also performed based on the communication model to obtain stealth-related data. Based on the achievable rate-related data and the stealth-related data, a target optimization problem is constructed. The target optimization problem is processed by adjusting the position of each movable subarray of the movable antenna array and adjusting the power distribution of the movable antenna array to obtain target optimization information. Based on the target optimization information, the signal transmission operation of the movable antenna array is adjusted. Therefore, this application, through a communication model constructed based on a movable antenna array, monitoring parties, and target receivers, conducts achievable rate analysis to evaluate the communication rate that a target receiver can achieve in a mixed-field environment, i.e., when there are target receivers in both near-field and far-field communication scenarios simultaneously, and obtains achievable rate-related data. Meanwhile, based on the communication model, a covertness analysis is conducted, focusing on how to reduce the probability of the monitoring party detecting the communication behavior, thereby obtaining covertness-related data. Then, based on the achievable rate-related data and the covertness-related data, an objective optimization problem is constructed, aiming to achieve joint optimization of covert communication rate and covertness under mixed field channel conditions by adjusting the position of each movable subarray in the movable antenna array and adjusting the power distribution of the movable antenna array.

[0304] 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.

[0305] 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.

[0306] 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.

[0307] 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.

[0308] 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.

[0309] 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.

[0310] 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.

[0311] 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.

[0312] 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.

[0313] 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.

[0314] 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 signal transmission method for a movable antenna array, characterized in that, Applied to a movable antenna array, the movable antenna array comprising multiple movable subarrays, each of the movable subarrays comprising multiple antenna elements, the method comprising: Multiple monitoring parties and at least two target receivers are identified; wherein at least one target receiver is in a near-field communication scenario and one of the target receivers is in a far-field communication scenario. A communication model is constructed based on the movable antenna array, the multiple monitoring parties, and the target receiver; Based on the communication model, reachability analysis is performed to obtain reachability-related data. Based on the aforementioned communication model, a covertness analysis is performed to obtain covertness-related data; Based on the achievable rate-related data and the concealment-related data, a target optimization problem is constructed; By adjusting the position of each movable subarray of the movable antenna array and adjusting the power distribution of the movable antenna array, the target optimization problem is processed to obtain target optimization information; Based on the target optimization information, the signal transmission operation of the movable antenna array is adjusted.

2. The method according to claim 1, characterized in that, The communication model includes a first channel model and a second channel model. The construction of the communication model based on the movable antenna array, multiple monitoring parties, and the target receiver includes: Obtain the monitoring locations of multiple monitoring parties and the receiving locations of several target receiving terminals; Based on the receiving positions of several target receivers, a first channel model including near-field communication scenarios and far-field communication scenarios is constructed; The second channel model is constructed based on the monitoring locations of multiple monitoring parties in a near-field communication scenario.

3. The method according to claim 1, characterized in that, The target receiving end includes at least a first receiving end and a second receiving end. The achievable rate analysis based on the communication model to obtain achievable rate-related data includes: Based on the communication model, the power detection capabilities of multiple monitoring parties are analyzed to determine the covert communication requirements of the movable antenna array. Based on the aforementioned covert communication requirements, the achievable total rate is obtained; the achievable total rate represents the sum of the communication rates of the first receiving end and the second receiving end. Based on the influencing factors of the achievable total rate, the relevant data of the achievable rate corresponding to the achievable total rate are obtained.

4. The method according to claim 3, characterized in that, The stealth analysis based on the communication model yields stealth-related data, including: Based on the aforementioned covert communication requirements, the covert communication factors are determined; Based on the aforementioned covert communication factors, a covertness analysis is performed on the first receiving end and the second receiving end to obtain the covertness-related data.

5. The method according to claim 1, characterized in that, The process of adjusting the position of each movable subarray of the movable antenna array and adjusting the power distribution of the movable antenna array to address the target optimization problem and obtain target optimization information includes: The target optimization problem is decomposed into an outer problem and an inner problem, wherein the inner problem is related to the power allocation of the multiple movable subarrays, and the outer problem is related to the position of the multiple movable subarrays; The outer layer problem is optimized by adjusting the position of each movable subarray of the movable antenna array, and the inner layer problem is optimized by adjusting the power distribution of the movable antenna array. The outer layer problem and the inner layer problem are optimized alternately until a preset convergence condition is met, thereby obtaining the target optimization information.

6. The method according to claim 5, characterized in that... The optimization of the outer layer problem by adjusting the position of each movable subarray of the movable antenna array, and the optimization of the inner layer problem by adjusting the power distribution of the movable antenna array, alternately optimizing the outer layer problem and the inner layer problem until a preset convergence condition is met, to obtain the target optimization information, includes: Based on the preset positions of the multiple movable subarrays, the outer layer problem is optimized, and the target transmit power of the multiple movable subarrays is determined; Based on the target transmit power of the plurality of movable subarrays, the inner layer problem is optimized to determine the target adjustment position of the plurality of movable subarrays.

7. The method according to claim 4, characterized in that, The adjustment of the signal transmission operation of the movable antenna array based on the target optimization information specifically includes: Based on the target optimization information, perform at least one of the following operations: update the positions of the plurality of movable subarrays of the movable antenna array, and update the communication power of the plurality of movable subarrays of the movable antenna array.

8. A signal transmission device for a movable antenna array, characterized in that, An apparatus for use with a movable antenna array, the movable antenna array comprising multiple movable subarrays, each of the movable subarrays comprising multiple antenna elements, the apparatus comprising: A multi-terminal acquisition module is used to identify multiple monitoring parties and at least two target receiving terminals; wherein at least one of the target receiving terminals is in a near-field communication scenario and one of the target receiving terminals is in a far-field communication scenario. A communication model construction module is used to construct a communication model based on the movable antenna array, the multiple monitoring parties, and the target receiver. The reachability analysis module is used to perform reachability analysis based on the communication model and obtain reachability-related data. The concealment analysis module is used to perform concealment analysis based on the communication model to obtain concealment-related data; An optimization problem construction module is used to construct a target optimization problem based on the achievable rate-related data and the concealment-related data; The optimization problem processing module is used to process the target optimization problem by adjusting the position of each of the movable subarrays of the movable antenna array and adjusting the power distribution of the movable antenna array, so as to obtain target optimization information. The signal transmission adjustment module is used to adjust the signal transmission operation of the movable antenna array based on the target optimization information.

9. An electronic device, characterized in that, The electronic device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the signal transmission method of the movable antenna array according to any one of claims 1 to 7.

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