A low-altitude integrated regional perception enhancement method and related device

Abstract

The embodiment of the application provides a low-altitude integrated area perception enhancement method and related equipment, and belongs to the technical field of wireless communication. The application deploys multiple independently rotatable steerable antennas on the base station side, jointly optimizes the communication transmit beamforming matrix, the probe signal covariance matrix and the pointing vector of each steerable antenna, maximizes the minimum received echo signal power of the potential target in the low-altitude perception area, and meets the minimum communication rate constraint of each user. For the case of single user and point target perception target, the closed-form solution of the optimal pointing vector of the steerable antenna is derived. For the case of multiple users and the perception target distributed in the extended low-altitude area, an alternating optimization algorithm is proposed, which uses semi-definite relaxation and continuous convex approximation iterative solution. The application can significantly improve the worst-case perception performance in the low-altitude area, expand the performance compromise area between communication and perception, and can be applied to low-altitude logistics monitoring and other scenes.

Description

Technical Field

[0001] This application relates to the field of wireless communication technology, and in particular to a low-altitude integrated sensing area perception enhancement method and related equipment. Background Technology

[0002] Sensing and communication integration is widely regarded as one of the core enabling technologies for sixth-generation wireless networks, aiming to integrate communication and sensing functions on the same hardware platform and spectrum resources. The rapid development of the low-altitude economy (such as drone logistics and air traffic management) has brought new challenges to ISAC systems, including three-dimensional coverage, high mobility adaptation, and air-ground cooperation.

[0003] Existing ISAC systems mostly use fixed antenna arrays (such as traditional downtilt antennas), whose radiation patterns are statically fixed, making it difficult to simultaneously cover ground users and low-altitude targets, resulting in significant elevation blind spots. Although multiple-input multiple-output (MIMO) technology can provide beamforming capabilities, it is still limited by the fixed antenna architecture and cannot dynamically adjust according to the spatial distribution of users and targets.

[0004] Reconfigurable antenna architectures proposed in recent years, such as movable antennas (MA), flowing antennas (FA), and six-dimensional movable antennas (6DMA), provide additional degrees of freedom through translation or rotation, respectively. However, MA / FA cannot change the antenna orientation, and 6DMA has excessively high hardware complexity. Rotatable antennas (RA), as a low-cost and compact solution, allow each antenna to independently adjust its line-of-sight orientation, showing potential in the fields of communication and sensing.

[0005] Existing research shows that ISAC systems assisted by steerable antennas mostly employ an array-wide rotation approach, where all antennas share the same orientation. This approach cannot simultaneously optimize multiple spatial regions when users and targets are distributed in different directions, limiting its flexibility. In low-altitude ISAC scenarios, ground users, air users, and low-altitude sensing targets are often distributed at different elevation and azimuth angles, making it difficult for the overall rotation to meet heterogeneous requirements. Summary of the Invention

[0006] The main objective of this application is to propose a low-altitude sensing integrated area perception enhancement method and related equipment. By independently optimizing the line-of-sight orientation of each antenna and jointly designing communication beamforming and detection signals, the method maximizes the minimum echo signal power of potential targets within the low-altitude sensing area while ensuring the minimum communication rate requirements of multiple users.

[0007] To achieve the above objectives, one aspect of this application proposes a low-altitude integrated sensing area perception enhancement method and related equipment, the method comprising the following steps: The communication transmit beamforming matrix, the detection signal covariance matrix, and the pointing vector of each steerable antenna are jointly optimized. The optimization objective is to maximize the minimum received echo signal power of potential targets within the low-altitude sensing area. This optimization must satisfy the minimum communication rate constraint for each user and the maximum power constraint for the base station to transmit sensing signals.

[0008] In some embodiments, joint optimization includes: In the special case of a single user and a single point target, maximum ratio transmission beamforming is adopted, and the optimization problem is transformed into a convex projection maximization problem, thereby deriving the closed-form solution of the optimal pointing vector for each steerable antenna.

[0009] In some embodiments, the closed-form solution satisfies that: the optimal pointing vector of the steerable antenna lies within the sector spanned by the user direction and the target direction, or lies on the cone surface of a spherical cone defined by the antenna rotation range constraint, and that the optimal pointing vectors of all steerable antennas are the same in the far-field region.

[0010] In some embodiments, for the general case of multiple users and the sensing targets being distributed over an extended low-altitude region, joint optimization further includes: Discretize the continuous low-altitude sensing area into multiple spatial sampling points; A relaxation optimization variable is introduced, which represents the minimum echo signal power within the sensing area; Using an alternating optimization algorithm, the following subproblems are executed sequentially in each iteration: The first sub-problem is to optimize the communication transmit beamforming matrix and the detection signal covariance matrix with a fixed pointing vector of the steerable antenna. The second sub-problem is to optimize the pointing vector of each steerable antenna while fixing the communication transmit beamforming matrix and the detection signal covariance matrix.

[0011] In some embodiments, the first subproblem is transformed into a semidefinite programming problem by a semidefinite relaxation method and the obtained solution is then restored to rank-one.

[0012] In some embodiments, the second subproblem is handled by a continuous convex approximation method, including: The non-convex Hermitian quadratic form constraint is approximated as a convex constraint based on its first-order Taylor expansion. Relax the unit norm constraint of the pointing vector into two inequality constraints and then linearize them; The approximate convex problem is solved iteratively until the objective function converges, and the solution is then normalized.

[0013] In some embodiments, the pointing vector of the steerable antenna satisfies a rotation range constraint, which is defined by the maximum permissible rotation angle of each antenna relative to its initial line of sight orientation.

[0014] In some embodiments, the received echo signal power is calculated based on a free-space propagation model and an antenna radiation pattern, wherein the directional gain of the antenna radiation pattern depends on the off-axis angle between the signal direction and the current line-of-sight orientation of the steerable antenna.

[0015] In some embodiments, the base station uses independent time-domain or frequency-domain resource blocks to simultaneously transmit communication signals and dedicated detection signals, and the channel conditions and geometric parameters of the sensing target remain approximately unchanged within the same coherent time block.

[0016] To achieve the above objectives, another aspect of this application proposes a low-altitude integrated sensing area perception enhancement system, comprising: The base station is equipped with multiple independently rotatable antennas; A communication transmission beamforming module is used to generate beamforming vectors for transmitting information symbols to users; The detection signal generation module is used to generate a dedicated detection signal to be transmitted to the low-altitude sensing area; The pointing vector optimization module is used to jointly optimize the communication transmit beamforming matrix, the detection signal covariance matrix, and the pointing vector of each steerable antenna, so as to maximize the minimum received echo signal power of potential targets in the low-altitude sensing area while satisfying the minimum communication rate constraint for each user and the base station transmit power constraint.

[0017] In some embodiments, the pointing vector optimization module further includes: An alternating optimization unit is used to optimize the communication transmit beamforming matrix and the detection signal covariance matrix by semi-definite relaxation when the pointing vector of the steerable antenna is fixed; and to optimize the pointing vector of each steerable antenna by continuous convex approximation when the communication transmit beamforming matrix and the detection signal covariance matrix are fixed.

[0018] To achieve the above objectives, another aspect of this application provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-described method.

[0019] To achieve the above objectives, another aspect of the embodiments of this application proposes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0020] To achieve the above objectives, another aspect of this application provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0021] The embodiments of this application include at least the following beneficial effects: By organically combining the independent rotation of the steerable antenna element by element with the joint optimization of sensing signal-antenna orientation, this application effectively solves the two major technical challenges of "communication coverage and sensing coverage conflict" and "elevation blind zone" in low-altitude ISAC systems without increasing the number of antennas, increasing transmission power, or changing the overall base station architecture. The proposed maximum-minimum area sensing enhancement strategy takes into account sensing uniformity, communication service quality assurance, and hardware implementation feasibility, providing a high-performance, low-cost technical solution for integrated sensing applications in low-altitude economic scenarios, with significant industrial application value and broad market prospects. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the low-altitude sensing integrated system architecture assisted by the steerable antenna of this application.

[0023] Figure 2 This is a schematic diagram of the region where the optimal pointing vector of the steerable antenna is located in a single-user point target scenario in this application: (a) is located within the fan-shaped region spanned by the user direction and the target direction; (b) is located on the cone surface of a spherical cone with a rotation range defined.

[0024] Figure 3 For a single-user point target scenario, this application presents simulation curves showing the variation of echo signal power with the user's minimum communication rate requirement under different antenna directivity factors.

[0025] Figure 4 This is a comparison chart showing the echo signal power of different systems (this application, fixed antenna, omnidirectional antenna) as a function of the target azimuth angle in a single-user point target scenario.

[0026] Figure 5 This is a comparison chart showing the user reachability rate of different systems as a function of the target azimuth angle in a single-user point target scenario.

[0027] Figure 6 This is a comparison chart showing the minimum echo signal power of this application versus three benchmark schemes (uniform orientation, random orientation, and fixed orientation) as a function of communication rate requirements in a multi-user target scenario.

[0028] Figure 7 A comparison of the minimum echo signal power of this application and the benchmark scheme as a function of the maximum antenna rotation angle in a multi-user target scenario.

[0029] Figure 8A comparison of the minimum echo signal power of this application and the baseline scheme as a function of antenna directivity factor in a multi-user extended target scenario.

[0030] Figure 9 For multi-user extended target scenarios, this application presents the curves showing the minimum echo signal power as a function of the sensing area side length under different directional factors. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit it. In the following description, when referring to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with those of this application; they are merely examples of apparatuses and methods consistent with some aspects of the embodiments of this application as detailed in the appended claims.

[0032] 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.

[0033] Before providing a detailed description of the embodiments of this application, some of the nouns and terms involved in the embodiments of this application will be explained first. The nouns and terms involved in the embodiments of this application are subject to the following interpretations.

[0034] 1) ISAC (Integrated Sensing and Communication): is a technology that deeply integrates wireless communication with environmental sensing functions, enabling the same set of hardware, spectrum and signals to both transmit data and detect the distance, speed, angle and imaging of targets like radar.

[0035] Integrated Sensing and Communication (ISAC) is generally considered one of the most important application scenarios and enabling technologies for sixth-generation wireless networks. Its core idea is to integrate communication and sensing functions on the same hardware platform and the same spectrum resources. This integrated design can reduce deployment costs and energy consumption, and support location-aware applications such as low-altitude economy, immersive virtual reality, and vehicle-to-everything (V2X) communication. To support ISAC and meet its diverse needs, Multiple-Input Multiple-Output (MIMO) technology is widely regarded as a key enabling technology because it can achieve spatial adaptation and waveform design through spatial multiplexing and beamforming. However, existing MIMO-enabled ISAC systems mainly rely on traditional fixed antenna architectures, which are difficult to adapt to changes in wireless channels and user distribution. This limits the performance and overall potential of ISAC systems, especially in highly dynamic environments. Furthermore, to meet the ever-increasing communication and sensing demands, future ISAC systems typically need to evolve towards large-scale antenna arrays, which inevitably leads to higher hardware costs, posing a challenge to building low-cost, high-performance ISAC systems. The rapid development of the low-altitude economy has further amplified the aforementioned challenges. Targets such as drones and low-altitude logistics vehicles typically exhibit characteristics such as three-dimensional distribution, high maneuverability, and rapidly changing trajectories, placing higher demands on the dynamic communication coverage and continuous sensing and tracking capabilities of ISAC systems. However, traditional fixed antennas are limited by static radiation direction and fixed coverage patterns, making it difficult to adjust the sensing beam in real time according to the spatial location and motion state of low-altitude targets. Therefore, there is an urgent need to introduce more flexible antenna architectures to support adaptive stereo sensing coverage in low-altitude scenarios.

[0036] To overcome the limitations of traditional fixed-antenna ISAC systems, several reconfigurable antenna architectures have been proposed in recent years to enhance the performance ceiling of ISACs. These include fluid antenna systems, movable antennas, six-dimensional movable antennas, and rotary antennas (RA). Specifically, fluid antenna systems and movable antennas can actively utilize spatial diversity and effectively reshape the wireless channel by flexibly adjusting the antenna position, thereby providing stronger spatial multiplexing capabilities for communication and higher angular resolution for sensing. Simultaneously, real-time adjustment of the antenna position enables ISAC systems to adapt to time-varying environmental conditions and heterogeneous communication and sensing requirements. Therefore, fluid antenna systems and movable antennas are potentially important technologies in ISAC applications, offering greater design flexibility and simultaneously delivering performance gains in both communication and sensing. However, since movable antennas cannot rotate the antenna or array, the performance improvements they provide are still somewhat limited. To address this issue, six-dimensional movable antennas, by flexibly adjusting the three-dimensional position and three-dimensional orientation of a distributed antenna array, are considered a potential enabling technology for fully exploiting the spatial degrees of freedom of ISAC systems. Besides enhancing the array gain for communication users, the six-dimensional movable antenna can also improve sensing and positioning accuracy by utilizing the inherent geometric gain of the distributed antenna array, as the relative geometric relationship between the target and the base station with deployed six-dimensional movable antennas can be adaptively configured. Therefore, if six-dimensional movable antennas are deployed reasonably according to communication and sensing requirements and the spatial distribution of users and targets, the overall ISAC performance can be significantly enhanced. However, the six-dimensional movable antenna architecture may lead to higher hardware overhead and system design complexity, prompting researchers to further develop a flexible antenna architecture that can achieve low-cost ISAC while retaining sufficient spatial adaptability.

[0037] Steering antenna technology is a recently proposed novel antenna architecture. While maintaining a fixed antenna position, it focuses solely on the flexibility gained from antenna orientation rotation, making it a low-cost and compact solution. It can also be considered a simplified yet promising member of the steering antenna / six-dimensional steering antenna / fluidic antenna system family. By independently rotating the three-dimensional orientation of each steering antenna, the array directional gain map can be reconstructed to meet the performance requirements of various applications such as secure communications, cognitive radio systems, and cell-free communications. From a communications perspective, the steering antenna architecture can dynamically rotate the antenna main lobe according to the user spatial distribution, thereby achieving more refined spatial beam management. Specifically, it can enhance array gain in desired directions while reducing radiated energy leakage in undesired directions, helping to strengthen target user links, suppress multi-user interference, and improve channel capacity and communication reliability in multi-user systems. From a sensing perspective, steering antennas can provide flexible directional control to adapt to different sensing targets. When multiple steering antennas are aligned with the same target or area, they can form a narrower, more focused sensing beam, thereby improving target illumination and increasing angular resolution. Conversely, when multiple steerable antennas are oriented in different directions, the sensing area can be effectively expanded, resulting in wider sensing coverage. This flexibility allows steerable antenna arrays to balance sensing accuracy and coverage according to actual needs. Therefore, the rotational freedom provided by steerable antennas offers new opportunities for ISAC systems to achieve significant gains compared to traditional fixed antenna architectures. It enhances spatial adaptability and improves signal directivity without increasing the number of antennas. Thus, by jointly optimizing antenna orientation, communication beamforming, and detection signals, steerable antenna architectures are expected to achieve a more flexible performance trade-off between communication and sensing while improving spectral and energy efficiency. This characteristic is highly compatible with the requirements of low-altitude ISAC systems. Unlike traditional terrestrial cellular communication, low-altitude ISAC systems need to provide communication and sensing services to ground users, air users, and low-altitude sensing targets simultaneously, exhibiting a more pronounced three-dimensional spatial distribution of the system's service targets. However, existing cellular base stations typically use fixed downtilt antennas, whose radiation direction is mainly oriented towards ground coverage. This lack of flexibility in the elevation dimension makes it difficult to effectively adapt to the dynamic distribution of low-altitude targets, easily leading to air coverage blind spots, weak sensing echoes, and limited air-to-ground coordination capabilities. In contrast, steerable antennas can adaptively adjust the antenna's line-of-sight orientation based on the spatial location of ground users, air users, and low-altitude sensing targets. This allows communication and sensing beams to be more flexibly aligned with key service areas in three-dimensional space, thus providing a new technical approach for air-to-ground coordinated communication and sensing in low-altitude ISAC systems.

[0038] While several studies have investigated ISACs powered by steerable antennas, these works primarily focus on the overall array rotation, providing only coarse-grained directional control to balance array aperture gain between communication users and sensing targets. However, in low-altitude ISAC scenarios, the system needs to simultaneously serve ground users, airborne users, and low-altitude sensing targets, with communication and sensing objects being more widely and heterogeneously distributed in three-dimensional space. In this context, the spatial freedom provided by the overall array rotation may be insufficient, as the entire array, with only a single antenna orientation, cannot simultaneously adapt to service requirements across different elevation angles, azimuth angles, and spatial regions. Therefore, a more flexible steerable antenna ISAC system, implemented through element-by-element rotation, can provide fine-grained adaptive capabilities for low-altitude communication coverage and target sensing, but related research remains limited. This gap prompts us to further explore the performance gains of steerable antenna arrays in low-altitude ISAC systems and verify the advantages of element-by-element rotation in air-to-ground collaborative communication and sensing.

[0039] In view of this, this application provides a method for enhancing low-altitude sensing and communication integrated area perception with the assistance of a steerable antenna, comprising the following steps: Step S1: Deploy multiple independently rotatable and steerable antennas at the base station; Step S2: Establish a communication channel model and a round-trip sensing channel model that include the antenna line-of-sight orientation and antenna radiation pattern; Step S3: Construct the optimization problem: with the objective of maximizing the minimum echo signal power within the low-altitude sensing area, the constraints include the minimum communication rate for each user, the maximum transmit power of the communication and detection signals, the rotation range of each antenna, and the unit norm of the pointing vector; Step S4: For the special case of a single user and a single point target, the problem is transformed into a convex projection maximization problem by using maximum ratio transmission beamforming and Jensen's inequality. A closed-form solution with the same optimal pointing for all antennas is derived, and the condition that the optimal pointing vector is located in one of the two surface regions is given. Step S5: For the general case of multiple users and the sensing targets distributed in an extended low-altitude area, the continuous sensing area is discretized into multiple spatial sampling points. A relaxation variable is introduced to represent the minimum echo power, and an alternating optimization algorithm is used: With the antenna pointing vector fixed, the beamforming matrix and the detection covariance matrix are optimized through positive semidefinite relaxation (SDR). With fixed beamforming matrix and detection covariance matrix, the pointing vector of each antenna is optimized by continuous convex approximation (SCA). Step S6: Iterate until convergence, and output the optimal beamforming, probe signal covariance, and antenna pointing vector.

[0040] The solutions of the embodiments of this application will be described in detail below with reference to the accompanying drawings and specific application examples.

[0041] This embodiment studies a novel steerable antenna-enabled low-altitude ISAC system, such as... Figure 1 As shown, a step-by-step rotation mechanism is introduced to provide sufficient spatial degrees of freedom, thereby improving system performance. Specifically, a steerable antenna array is deployed on a dual-function base station, capable of communicating with multiple users simultaneously via the downlink and sensing potential air targets randomly distributed in the extended area by receiving uplink echo signals. To achieve ISAC functionality and enhance sensing capabilities in low-altitude areas, the ISAC beam transmitted by the base station and the line-of-sight orientation of each steerable antenna need to be jointly designed to uniformly improve sensing performance throughout the entire area where air targets may exist, while ensuring the communication performance of each user. To this end, this paper aims to maximize the minimum echo signal power of potential air targets within the sensing area by jointly optimizing the transmitted beamforming of user communication, the covariance matrix of the probe signal, and the line-of-sight orientation of all steerable antennas, while ensuring that the communication rate of each user is not lower than a preset threshold. The main contributions of the embodiments of this application are summarized as follows: 1) First, a communication channel and round-trip sensing channel model for the low-altitude ISAC system was established for antenna line-of-sight rotation. Based on this, a problem was proposed to maximize the echo signal power by jointly optimizing the communication transmit beamforming, the covariance matrix of the probe signal, and the pointing vector of the steerable antenna. The constraints are the minimum required user communication rate and the maximum power of the base station transmit sensing signal.

[0042] 2) For the special cases of single-user and point targets, the optimization problem can be transformed into a convex projection maximization problem based on maximum ratio transmission beamforming and Jensen's inequality. Furthermore, a closed-form solution for the optimal pointing vector of the steerable antenna is derived, showing that the optimal orientation can only lie in one of two surface regions, depending on the permissible range of steerable antenna rotation and the required minimum communication rate.

[0043] 3) For the general case of multiple users and extended targets, the continuous low-altitude sensing area is discretized into a set of spatial sampling points for optimization. An alternating optimization algorithm is then proposed to iteratively optimize the ISAC signal and the steerable antenna pointing vector. Specifically, the subproblem of optimizing the transmit beamforming matrix and the covariance matrix of the probe signal is solved using positive semidefinite relaxation, while the non-convex subproblem of optimizing the steerable antenna pointing matrix is ​​handled using a continuous convex approximation method.

[0044] 4) Simulation results are provided to evaluate the proposed optimization algorithm, demonstrating that the steerable antenna architecture achieves significantly better ISAC performance compared to various benchmark schemes. The results show that the proposed steerable antenna-enabled low-altitude ISAC system effectively expands the trade-off area between communication and sensing performance. Furthermore, even with a limited rotation range of the steerable antenna, the system can still significantly enhance echo signal power. Simultaneously, the antenna directivity should be appropriately adjusted to balance directional gain and radiation coverage.

[0045] (1) System Model and Problem Construction like Figure 1 As shown, this embodiment considers a low-altitude ISAC system, in which a ground dual-function base station is located at... - Deployed on the plane A steerable antenna for use with Individual users communicate simultaneously in a given low-altitude region. The system performs sensing tasks to detect potential aerial targets, with each user equipped with a single omnidirectional antenna. To achieve wireless sensing, it is assumed that the base station can simultaneously transmit and receive detection signals to estimate the position of aerial targets. For ease of representation, the set of steerable antennas and the set of users are denoted as follows: and steerable antenna and users The positions are respectively represented as and Each steerable antenna can independently and flexibly rotate its line-of-sight orientation, thereby reconstructing the array directional gain map to maximize ISAC performance given the spatial distribution of communication users and air targets. Furthermore, we assume the channel is a narrowband quasi-static channel, meaning the channel coherence time is long enough to ensure that the wireless environment remains approximately unchanged before and after antenna rotation.

[0046] To characterize the steerable antenna The orientation of the view axis is defined by a pointing vector as follows: (1) in , and They represent exist axis, shaft and The projection on the axis, and for normalization, we have Furthermore, if we assume that the initial line-of-sight orientation of each steerable antenna is the same as... If the axes are aligned in the positive direction, the following rotational constraints can be considered to limit the rotational range of each steerable antenna and alleviate coupling between antennas: (2) in and This represents the maximum permissible rotation angle of each steerable antenna relative to its initial line-of-sight orientation.

[0047] 1.1) Channel Model To characterize the effective directional gain, we consider the antenna radiation pattern of each steerable antenna as follows: (3) in These represent the elevation arrival / departure angle and azimuth arrival / departure angle of the signal relative to the current line of sight of the steerable antenna, respectively. The directionality factor is used to characterize the beamwidth of the main lobe. The direction of the line of sight (i.e.) The maximum gain on the radiation pattern is obtained to satisfy the law of power conservation. The directional gain of the radiation pattern in expression (3) depends on the off-axis angle between the signal direction and the antenna line-of-sight. .

[0048] Based on the free-space propagation model and the directional gain map in expression (3), for a given pointing vector steerable antenna With any spatial observation point The channel power gain between them can be expressed as: (4) in This represents the integer operation. Indicates reference distance Channel power gain at meters, For the signal wavelength, Indicates a steerable antenna With space observation points The distance between them Indicates a change from a steerable antenna Pointing to space observation point The normalized direction vector. Furthermore, express and The projection between them. Accordingly, the steerable antenna. The line-of-sight channel between the observation point and the observation point in space can be represented as: (5) By stacking the channel coefficients corresponding to all steerable antennas into a vector, the channel between the base station and any spatial observation point can be represented as: (6) in Let represent the pointing matrix of all steerable antennas. Based on the channel model defined by (4)-(6), the channels for wireless communication and target sensing are given below.

[0049] a) Communication channel: from base station to user The downlink communication channel is represented as: (7) For the multi-user communication system enabled by the steerable antenna under consideration, the spatial selectivity introduced by the antenna rotation helps to simultaneously enhance the directional gain in multiple desired user directions, thereby mitigating inter-user interference and improving spatial multiplexing gain.

[0050] b) Round-trip sensing channel: Unlike communication, since the single-base station sensing system under consideration relies on the echo signal received by the base station, the sensing of aerial targets requires consideration of the round-trip channel. Aerial targets are modeled as unstructured point targets for sensing low-altitude areas. The round-trip channel matrix of the potential target is denoted as It can be represented as: (8) in and These represent the location and radar cross section of a potential aerial target, respectively. It's important to note that for a single-base radar system, the departure and arrival directions of the detection signal are the same.

[0051] 1.2) ISAC Model In the considered low-altitude ISAC system, the base station simultaneously transmits communication signals and dedicated detection signals to perform multi-user downlink communication and airborne target sensing concurrently. To avoid self-interference between communication and sensing, we assume that they use independent time-domain or frequency-domain resource blocks while sharing the same base station architecture and the same steerable antenna orientation configuration. Let... This represents the total number of time slots within a sensing period. Furthermore, we assume that each sensing period does not exceed the length of a coherent time block, within which the channel conditions and the target's geometric parameters remain approximately constant.

[0052] a) Communication Model: Assuming the communication channel gain This has already been obtained by the base station using an effective channel estimation method. Let... Indicates that it is used to provide information to users. The transmit beamforming vector for transmitting information symbols is then in the time slot. , ,user The received communication signal can be represented as: (9) in Indicates user Independent and identically distributed information carrying symbols, satisfying ,and Indicates user The additive white Gaussian noise at the location has a mean of zero and a variance of . Accordingly, users The received signal-to-interference-plus-noise ratio can be expressed as: (10) in This represents the transmitted beamforming matrix. Therefore, the user... The achievable rate can be expressed as: (11) b) Perception Model: For any given steerable antenna pointing matrix In the time slot Inside, from potential aerial targets The received echo signal can be represented as: (12) in This indicates the detection signal transmitted by the base station. Let the vector of additive white Gaussian noise at the base station have the following variance: Accordingly, the power of the received echo signal from the air target at the base station can be expressed as: (13) in and This represents the covariance matrix of the dedicated detection signal. Since echo signal power is a universally measurable metric widely used in localization and detection tasks, this paper uses it to evaluate sensing performance. Generally, higher echo signal power results in a higher signal-to-noise ratio, leading to more accurate sensing information.

[0053] 1.3) Optimization Problem To balance the performance trade-offs between communication and sensing capabilities, and to achieve uniform sensing performance across the entire low-altitude target area, this paper aims to jointly optimize the pointing matrix of the steerable antenna. Transmit beamforming matrix and the covariance matrix of the detection signal To maximize the low-altitude sensing area The optimization problem is to find the minimum received echo power for the internal target while ensuring that the communication rate for each user is not lower than a given threshold. The resulting optimization problem can be formulated as follows:

[0054] Among them, constraint (14b) guarantees the user Able to achieve its required minimum communication rate Constraints (14c) and (14d) limit the average transmit power of communication and sensing, respectively. and Constraint (14e) limits the line-of-sight rotation of each steerable antenna to within the permissible range of rotation; Constraint (14f) guarantees is a unit norm vector. It should be noted that, given the geometric information of the low-altitude sensing region of interest, the round-trip sensing channel corresponding to any spatial point within that region can be determined according to expression (8). Therefore, as shown in (14a), the echo signal power within the entire low-altitude sensing region can be expressed as... and The function can be obtained without performing channel estimation for each spatial point. In the following sections, we present the solution methods for problem (P1) in the single-user point target case and the multi-user extended target case, respectively.

[0055] (2) Single-user and point-target scenarios In this section, we consider the special case of single-user communication and point target perception, namely... and low-altitude sensing area This is reduced to a single spatial point to gain basic insights from problem (P1). In this case, the positions of the user and the low-altitude target are represented separately. and And by omitting the user index for simplified representation, problem (P1) can be simplified to:

[0056] in This represents the minimum signal-to-interference-plus-noise ratio required by the user.

[0057] For any given pointing matrix of a steerable antenna In a single-user setup, maximum transmission ratio is the optimal transmit beamforming scheme for maximizing the signal-to-interference-plus-noise ratio on the left side of constraint (15b). Therefore, the optimal solution for problem (P2) is... It can be represented as Furthermore, in order to maximize the objective function in (15a), the optimal... It can be represented as .Will and Substituting into problem (P2), we get the following problem:

[0058]

[0059] in Furthermore, the constant term is omitted in the objective function (16a). and These represent steerable antennas. Distance between the user and the steerable antenna Distance to aerial targets, and These represent the steerable antennas respectively. Normalized direction vectors pointing to the user and the air target. Due to the nonconvexity of (14f), (16a), and (16b), problem (P3) is difficult to solve directly. To overcome this challenge, the following lemma is introduced.

[0060] Lemma 1: The optimal solution to problem (P3) must simultaneously satisfy the following two conditions: (17) as well as (18) Accordingly, the objective function in (16a) is... The upper bound is (16b), while the left side is (16b). The lower bound.

[0061] Proof: For the left side of (16b), since when hour, It is about For a concave function, based on Jensen's inequality, we have: (19) The equality holds if and only if condition (17) is satisfied. For the objective function in (16a), since... A about Since it is a convex function, we have: (20) The equality holds if and only if condition (18) is satisfied.

[0062] Comment 1: If both the user and the target are located in the far-field region of the base station, the signal transmission between the base station and the user / target can be characterized by a plane wave model. Therefore, the user / target has approximately the same distance and orientation relative to all steerable antennas in the array. In this case, we have as well as ,in Therefore, conditions (17) and (18) can both be approximated as This indicates that, when the far-field condition is met, the optimal pointing vectors of all steerable antennas are the same. Therefore, within the far-field region, the optimal pointing vectors of all steerable antennas are identical.

[0063] According to inequality (19) in Lemma 1, problem (P3) can be approximated as:

[0064] Furthermore, based on (17), problem (P4) can be decomposed into Each subproblem independently optimizes the pointing vector of a steerable antenna. For a steerable antenna... The corresponding subproblem can be represented as:

[0065] Among them, constraint (22b) is obtained from (21b). This indicates that the antenna can be rotated while meeting the user's communication needs. The pointer vector With user direction The maximum allowable angle between them; constraint (22c) is equivalent to (14e). It should be noted that... Will follow The rate increases as the rate decreases. Furthermore, considering the optimal steerable antenna pointing vector obtained by a single-user system propagating in free space, the maximum achievable rate for the user is: (twenty three) therefore, The maximum feasible value is Therefore, when At that time, it can be guaranteed and .

[0066] For problem (P5), constraint (22b) specifies the direction vector. It must be located within a spherical cone on a unit sphere, the spherical cone being oriented in the user direction. Let be the axis, and its half angle be . Meanwhile, constraint (22c) requires... Located inside another spherical cone on a unit sphere, this spherical cone... shaft (i.e.) ( ) is the axis, and its half angle is Two spherical cones can only intersect if the included angle between their axes is no greater than the sum of their half angles. This condition can be expressed as: ,in Indicates user direction and The angle between the axes. This condition must be satisfied to guarantee that problem (P5) has a feasible solution. Problem (P5) requires finding a unit norm vector such that it is perpendicular to the user's direction. The included angle is less than At the same time, get as close as possible to the target direction. Therefore, the optimal pointing vector Or located by and Within the formed sector (i.e., ,in and In particular, when and When orthogonal, there is ),like Figure 2 As shown in (a); or located on the cone surface of the spherical cone defined by (22c) (i.e., ),like Figure 2 As shown in (b). For any other arbitrary choice, we can always find a unit norm vector that gives it a larger value. Values. Next, we give the solutions to the problems (P5) corresponding to these two cases.

[0067] 2.1) Located in and Solution within the formed sector region By relaxing the constraint (22c), or equivalently making The optimal solution to problem (P5) is a solution located at... and Zhang Cheng's unit norm vector within the sector, such as Figure 2 As shown in (a), the vector is as close as possible to the constraint (22b) without violating it. Alignment. Therefore, optimal. With user direction The included angle between them is ,in, Indicates user direction and the direction of the target The angle between them. Based on the spherical linear interpolation method and the Slerp formula, the optimal... It can be represented as: (twenty four) in Therefore, substituting (24) into (22a), we can obtain the maximum value of the objective function. (25) in This represents the feasible set of problem (P5). In this case, the smaller minimum communication rate requirement... It will bring greater Thus expanding The feasible region. Therefore, Able to get closer to the target direction to obtain greater This results in a higher maximum value and thus a higher received echo signal power. This also demonstrates that in low-altitude ISAC systems powered by steerable antennas, relaxing communication rate requirements allows for greater flexibility in sensing.

[0068] 2.2) Located at half-angle Solution on the cone surface If the vector obtained from (24) If constraint (22c) is not satisfied, then the optimal solution to problem (P5) becomes a unit vector located on the spherical cap cone surface specified by (22c), such as... Figure 2 As shown in (b). In other words, the optimal pointing vector and The included angle between the axes is Accordingly, question (P5) can be transformed into the following question:

[0069] Among them, constraint (26b) is equivalent to (22b), and constraints (26c) and (26d) together define a unit norm vector, which is related to... The included angle between the axes is Specifically, express exist - The azimuth angle in the plane. Let Indicates user direction The azimuth angle, where , ,and It consists of sine components Sum and cosine components A definite arctangent function in the four quadrants. Therefore, Can represent Accordingly, constraint (26b) can be rewritten as: (27) in Under feasibility conditions Below, there is Therefore, we can obtain Therefore, constraint (27) is feasible. This means that if constraint (26b) is to be satisfied, the user direction... With the pointing vector The azimuth difference between them cannot exceed Consider vectors , and The geometric relationship between them, problem (P6) can be equivalently transformed into:

[0070] in Indicates the direction of the target exist - The azimuth angle in the plane is obtained from (27) by constraint (28b), and is equivalent to (26b).

[0071] It is important to note that the key to solving problem (P7) lies in determining the closest match within the feasible set defined by (28b). azimuth .make Indicates user direction and the direction of the target The azimuth difference between them, where and They represent and exist - The projection onto a plane. If... ,but It lies within the feasible set (28b). Therefore, when (29) If the condition is met, the optimal objective value of problem (P7) can be achieved. Otherwise, the optimal objective value of problem (P7) is achieved at the boundary of the feasible set, i.e.: (30) in, ,and ; ,and Both are equations Two solutions. Based on the above discussion, The maximum value can be expressed as: (31) in Indicates the direction of the target and The angle between axes.

[0072] Unlike the one derived from equation (25) in section 2.1 The maximum value when the locations of both the user and the target are given (i.e. and (fixed), obtained from equation (31) The maximum value is not only determined by The decision is made through the equation (27) shown. right The influence of [the system] determines [the outcome], and is also determined by [other factors]. Decision. First, in the second case of equation (31), The maximum value will vary with It increases with the increase of, and this corresponds to a smaller... Secondly, in both cases of equation (31), as... The increase, The maximum values ​​of all first increase and then decrease. Specifically, for a given... In the first case, the maximum value is In the second case, the maximum value is obtained at that time; This means that when... and At that time, and when and At that time, the optimal It will not lie on the cone surface of the spherical cone defined by (22c). Therefore, as discussed in subsection 2.1, the optimal... Only located by and Within the formed sector. Therefore, optimal It can be obtained from equation (24).

[0073] (3) Multi-user and extended target scenarios In this section, we consider a general steerable antenna-enabled low-altitude ISAC system, where the base station based on the steerable antenna architecture simultaneously performs multi-user communication and low-altitude area sensing, i.e. And the potential aerial target is located within the sensing area. As can be seen from problem (P1), a joint design of a steerable antenna pointing matrix is ​​required. Transmit beamforming matrix and the covariance matrix of the detection signal To maximize the entire low-altitude sensing area The minimum received echo signal power within the low-altitude sensing area. In other words, the considered max-min design aims to enhance worst-case sensing performance within this low-altitude region and suppress severe power imbalances between different spatial locations. Therefore, the objective function in (14a) involves semi-infinite terms because the low-altitude sensing area... The continuous nature of the low-altitude sensing region makes solving this problem challenging. To address this, the continuous low-altitude sensing region is first discretized into... Each spatial sampling point. Let ,in , indicating the first The location of each spatial sampling point. In the following text, let... and ,in , respectively representing the steerable antenna To users The propagation distance and normalized direction vector; at the same time, let and ,in , respectively representing the steerable antenna To the The propagation distance and normalized direction vector of each spatial sampling point.

[0074] By introducing relaxation optimization variables To represent the sensing area The minimum echo signal power within the range, problem (P1) can be approximated as:

[0075] Due to constraints (14b), (14f), and (32b) regarding the optimization variables , and Since the problem is non-convex, problem (P8) remains difficult to solve directly. To address this issue, we propose an alternating optimization algorithm based on block coordinate descent and continuous convex approximation techniques to obtain an efficient suboptimal solution to problem (P8). The main idea is to decompose problem (P8) into two subproblems. The first subproblem optimizes the beamforming matrix and covariance matrix given the pointing matrix of the steerable antenna. The second subproblem optimizes the pointing matrix of the steerable antenna given the beamforming matrix and covariance matrix. These two subproblems are then iteratively solved, resulting in a block coordinate descent algorithm that optimizes the pointing matrix of the steerable antenna. and Update alternately until the target value is reached. It converges within a preset precision range. For ease of representation, in the remainder of this paper, we will use... Indicates base station and user The channel vector between them, i.e. ; and use Indicates base station and sensing area Inner The channel vector between spatial sampling points, i.e. .

[0076] 3.1) Optimization of beamforming matrix and covariance matrix under fixed steerable antenna pointing matrix In this section, we optimize the transmit beamforming matrix with the pointing vectors of all steerable antennas fixed. and the covariance matrix of the detection signal Given a pointer matrix Problem (P8) can be simplified to:

[0077] in Indicates user The minimum signal-to-interference-plus-noise ratio required. Semi-definite relaxation can be used to overcome the non-convex constraint (33c). First, define the auxiliary variable. Its satisfaction and Subsequently, by relaxing the non-convex rank-one constraint, problem (P9) can be approximated as:

[0078] It should be noted that problem (P10) is a standard semidefinite programming problem, which can be optimally solved using the CVX solver.

[0079] Although the question (P10) may not be able to provide information about While we can find a rank-one solution, we can always construct the following rank-one solution, which achieves the same objective function value: (35) in This indicates the result obtained by solving problem (P10). The globally optimal solution. Therefore, The rank-one solution can be expressed as .

[0080] 3.2) Optimization of the pointing matrix of a steerable antenna under fixed beamforming matrix and covariance matrix In this section, with the transmit beamforming matrix and the detect signal covariance matrix fixed, the pointing matrix is ​​optimized. Given the transmit beamforming matrix and the covariance matrix of the detection signal Problem (P8) can be simplified to:

[0081] Where constraint (36c) is equivalent to (14e). Since constraints (36b) and (34b) are related to... Since the problem is non-convex and the equality constraint (14f) is not affine, the above subproblems are difficult to solve directly. Specifically, the main challenge in solving problem (P11) lies in dealing with the Hermitian quadratic forms present in constraints (36b) and (34b).

[0082] First of all, let and These represent the communication channel vectors respectively. The amplitude components and phase shift components. Therefore, It can be represented as: (37) in and The The elements are respectively and ,in Indicates user With steerable antenna The channel coefficients of the link between them. Furthermore, the equation... This holds true for column vectors of the same size. and ,have Similarly, the sensing channel vector The amplitude and phase shift components are respectively expressed as: and ,in , ,and Represents the sensory region Inner Spatial sampling points and steerable antenna The channel coefficients of the links between them, then It can be written as: (38) Subsequently, to address the nonconvexity of problem (P11), we introduce the following proposition.

[0083] Proposition 1: For Hermitian quadratic form in (34b) about It is convex.

[0084] Proof: According to (37) and (38), It can be written as: (39) in, The equation holds true because for and have Since the Hadamard product of two positive semi-definite matrices is also a positive semi-definite matrix, we have It is a positive semi-definite matrix, where and Therefore, in (39) about It is convex.

[0085] Similarly, by defining Hermitian quadratic form in (36b) It can be written as: (40) This can also be proven. It is a positive semi-definite matrix, therefore, about It is convex.

[0086] To transform the problem (P11) into a more manageable form, we introduce auxiliary variables. , , as well as The problem (P11) is restructured into the following form.

[0087]

[0088] Among them, we utilized (39) and (40) and defined Let be the set of all optimization variables. To facilitate convex reconstruction, let... The right side of (36b) can be equivalently rewritten as the convex quadratic-over-linear form in (41b). Since when hour, about Monotonically increasing, therefore, in (P12) maximize This is equivalent to maximizing the original variable in (P11). In (41e) and (41f), and They represent and The There are 14 elements. Furthermore, we can prove by contradiction that problem (P12) is equivalent to problem (P11). Due to the nonconvexity of constraints (14f) and (41b)-(41f), problem (P12) remains nonconvex. Therefore, we will next perform appropriate transformations and approximations on these nonconvex constraints to facilitate tractable optimization.

[0089] Due to the Hermitian quadratic forms on the left side of (41b) and (41c) and Regarding respectively and Since the function is convex, we can handle the non-convexity of constraints (41b) and (41c) by applying a continuous convex approximation. This allows us to replace the non-convex constraints with appropriate convex approximations and iteratively solve the approximation problem until its objective function converges. Because the first-order Taylor expansion of a convex function is its global lower bound, if... and Defined respectively as the first In the next iteration and The solution is... and Can be in and We use its first-order Taylor expansion to estimate the lower bound. Therefore, we have: (42) (43) It should be noted that in (42) and (43), if and only if and The equality holds when each condition is true. Correspondingly, in the first... In the next consecutive convex approximation iteration, constraints (41b) and (41c) are approximated as the following two convex quadratic constraints: (44) (45) Similarly, due to about It is convex, and constraint (41d) can be approximated as: (46) In (46), if and only if When the equality holds, the equation is true.

[0090] In addition, through Perform a first-order Taylor expansion on the non-affine terms to the right of (41e) and (41f), where Indicates the first Obtained in the next iteration The solution, constraints (41e) and (41f), can be linearized as follows: (47) (48) in, and They represent the first The result obtained in the next iteration and The value of ; and They represent and Compared to The first derivative.

[0091] Furthermore, for the equality constraint (14f), by introducing two sufficiently small positive constants... and This can be transformed into the following two inequality constraints: (49) (50) It is important to note that when and When (49) and (50) are equivalent to the equality constraint (14f), similar to (46), the non-convex constraint (50) can be approximated as: (51) Among them, if and only if When the equality holds, the equation is true.

[0092] Based on the above derivation, by replacing constraints (41b)-(41f) with the convex approximations given in (44)-(48), and relaxing the equality constraint (14f) according to (49) and (51), the first... The approximation problem in the next iteration is as follows:

[0093] It can be verified that problem (P13) is a convex optimization problem, which can be solved by the CVX solver. Since problem (P13) may not yield a pointer vector with the unit norm due to the relaxation of the equality constraint (14f), we employ normalization. ,in, This indicates the result obtained by solving problem (P13). The solution. Furthermore, after solving problem (P13), the objective value of the original subproblem, i.e., problem (P11), can be restored to... .

[0094] 3.3) Overall Algorithm Based on the solution methods for the two subproblems mentioned above, we propose an alternating optimization algorithm based on block coordinate descent to solve problem (P8). Specific details are summarized in Algorithm 1. Since problems (P10) and (P13) are optimally solved in each iteration of Algorithm 1, the objective value... The iteration process is non-decreasing and is constrained by a finite upper bound. Therefore, Algorithm 1 guarantees convergence to a local optimum, as shown in Table 1 below.

[0095] Subproblems (P10) and (P13) can be solved by the CVX solver, with time complexity orders of respectively. and ,in, and Let represent the number of optimization variables and the preset precision tolerance of the interior point method, respectively. Therefore, the complexity order of Algorithm 1 is . ,in This indicates the number of iterations required for the algorithm to converge.

[0096] Table 1

[0097] (4) Simulation results In this section, we present simulation results to evaluate the performance of the proposed steerable antenna-enabled low-altitude ISAC system and the proposed optimization algorithm. In the simulation, we consider a system containing... One communication user and a size of The ISAC system with a square low-altitude sensing area, in which This indicates the side length of the low-altitude sensing area. The system operates in the 2.4 GHz frequency band, corresponding to a wavelength of... m. The base station is equipped with a unit consisting of A uniform planar array consisting of steerable antennas, with an element spacing of [missing information]. Furthermore, this uniform planar array is deployed in a Cartesian coordinate system. - On a plane, centered at the origin. Assume the noise power is the same at the base station and all users, i.e. dBm, The maximum average transmit power of the communication signal and the detection signal are respectively set to... dBm and dBm. Unless otherwise specified, the maximum permissible rotation angle for each steerable antenna is set to The antenna directivity factor is set to The side length of the low-altitude sensing area is set to m. Furthermore, the minimum communication rate required by all users is given as m. ,in It can be varied under different simulation settings.

[0098] 4.1) Single-user and point-target scenarios First, consider a single-user point target system, where the positions of the aerial target and the user are set as follows: m and m. Figure 3 Demonstrates different antenna directivity factors Under the given value, the power of the echo signal received from the air target varies with the required minimum communication rate. The results show that as the required minimum communication rate increases, for all considered... The value of the echo signal will decrease. This is expected because higher communication rates require the steerable antenna to tilt towards the user to provide more radiated energy to support the communication link between the base station and the user, thus inevitably reducing the directional gain in the direction of the air target. Furthermore, it can be observed that when the required minimum communication rate is relatively low, i.e. A larger antenna directivity factor (bps / Hz) is more conducive to obtaining higher echo signal power. Conversely, when the required minimum communication rate is relatively high, i.e. At bps / Hz, the opposite trend can be observed. This phenomenon reflects the trade-off between directional gain and spatial radiation coverage. Specifically, antennas with higher directivity factors have narrower main lobes and larger line-of-sight directional gain, thus enabling them to concentrate more radiated energy toward the airborne target by rotating the antenna, resulting in higher echo signal power. In contrast, antennas with lower directivity factors provide a wider spatial radiation coverage, which is more beneficial for balancing sensing and communication performance. Furthermore, compared to omnidirectional antenna systems, steerable antennas enable low-altitude ISAC systems to achieve higher target detection echo signal power and meet more stringent communication requirements. This is because steerable antenna arrays can flexibly adjust the spatial radiation energy distribution according to the required communication and sensing performance.

[0099] Figure 4 and Figure 5 They respectively gave when At bps / Hz, the echo signal power received from the target and the achievable rate of the user in different ISAC systems vary with the target azimuth angle. The changes. For example Figure 4 As shown, except for the two lateral regions of the steerable antenna array, i.e. The proposed steerable antenna-enabled low-altitude ISAC system achieves significantly higher echo signal power than conventional fixed and omnidirectional antenna reference schemes in all azimuth angles. However, in the two lateral regions mentioned above, its performance advantage is somewhat diminished due to the limited antenna rotation range. Furthermore, in the region... Within the proposed steerable antenna-enabled low-altitude ISAC system, the echo signal power remains approximately constant, demonstrating the significant area scanning and sensing capabilities of the steerable antenna architecture. This is because, thanks to the additional spatial degrees of freedom provided by antenna rotation, the steerable antenna can concentrate radiated energy onto the desired observation point to adaptively enhance the echo signal power while meeting the user's communication needs. In contrast, the effective sensing area of ​​a fixed antenna system is very limited because the radiated energy of the base station can only be concentrated in the fixed forward direction of the array. Although omnidirectional antenna systems can provide relatively uniform sensing performance throughout the space, their radiated energy is uniformly distributed, resulting in lower echo signal power in any particular direction.

[0100] exist Figure 4 In this process, the user's achievable rate always exceeds the minimum required communication rate. This demonstrates that even with a significant angular deviation between the user's direction and the target's direction, the steerable antenna-enabled system can still significantly improve echo signal power while maintaining the quality of user communication services. This result highlights the unique advantages of steerable antenna architecture in low-altitude ISAC applications.

[0101] 4.2) Multi-user and Extended Target Scenarios Next, we consider a typical multi-user and extended target scenario, which includes... One communication user, and the horizontal low-altitude sensing area is located - In the plane, its center is Specifically, three users are evenly distributed in three different directions in front of the base station, each at a horizontal distance of 40 m, and all are located on a plane. m. Furthermore, uniformly select within the low-altitude sensing area. There are spatial sampling points, among which and They represent along shaft and The number of spatial sampling points along the axial direction. To ensure that sensing regions of different sizes have the same spatial sampling density, we set... To verify the performance advantages of the proposed steerable antenna-enabled low-altitude ISAC system, we consider the following three benchmark systems for comparison: 1) Uniform Orientation Design: In this scheme, all steerable antennas are constrained to have the same orientation. This is achieved by imposing additional constraints in problem (P1). The maximum and minimum received echo signal power of this scheme can also be obtained using Algorithm 1. It should be noted that when the low-altitude sensing area and the user are located in the far field area of ​​the base station, the performance of the low-altitude ISAC system empowered by the steerable antenna based on the overall rotation of the array can be approximately characterized by this scheme.

[0102] 2) Random Orientation Design: In this scheme, the orientation of each steerable antenna is randomly generated within the rotation range specified in (2). The simulation results of this scheme are obtained by averaging over 100 independent pointing vector implementations.

[0103] 3) Fixed Orientation Design: In this design, the orientation of all steerable antennas is fixed to their reference orientation, i.e. .

[0104] For the three benchmark schemes mentioned above, given the pointing vector of the steerable antenna, the transmit beamforming vectors and the covariance matrix of the probe signals for all users are obtained by solving problem (P4).

[0105] Figure 6This demonstrates the minimum echo signal power achievable by the considered system as a function of the minimum required communication rate. The proposed steerable antenna-enabled low-altitude ISAC system consistently outperforms the baseline system in terms of minimum echo signal power and supported communication rates within the sensing area. This is because the steerable antenna can adaptively reconstruct the array directional gain map by adjusting its line-of-sight orientation according to the wireless environment and ISAC requirements, thereby significantly expanding the area characterizing the performance trade-off between communication and sensing. In contrast, although the baseline system with a uniform orientation design can improve echo signal power compared to random and fixed orientation designs, it cannot independently control the orientation of each antenna, resulting in limited spatial degrees of freedom and thus inferior performance to the proposed steerable antenna-enabled low-altitude ISAC system.

[0106] Figure 7 The minimum echo signal power as a function of the maximum rotatable angle is depicted. The changes can be observed in several ways. Firstly, with... With the increase in amplitude, the proposed steerable antenna-enabled low-altitude ISAC system can obtain more spatial degrees of freedom and greater flexibility to balance communication and sensing performance, thereby increasing the minimum echo signal power obtained. Secondly, since a steerable antenna with random orientation can statistically radiate power in any direction around the base station, it can bring a certain gain in sensing performance compared to a fixed-orientation design. However, when… At that time, the echo signal power of the randomly oriented design will change with The value decreases as the value increases. This result highlights the importance and effectiveness of antenna orientation design in ISAC systems, especially... At higher altitudes, inappropriate and uncontrolled orientation design can lead to a decline in ISAC performance. Third, even with a small range of rotation for adjusting the orientation of the steerable antenna, steerable antennas can still significantly improve the echo signal power of low-altitude ISAC systems.

[0107] exist Figure 8 In the previous section, we showed that the minimum echo signal power of the considered system as a function of the antenna directivity factor... The changes are as follows. It can be observed that the minimum echo signal power of the proposed steerable antenna-enabled low-altitude ISAC system changes with... It increases with the increase of [something]. This is because the larger [something]... This results in a narrower main lobe and higher directional gain along the antenna's line of sight, enabling base stations based on steerable antennas to more effectively focus their radiated power, providing strong directional illumination of low-altitude sensing areas of interest while meeting the communication needs of all users. Therefore, when At higher altitudes, the proposed steerable antenna-enabled low-altitude ISAC system can generate more adaptive and customized ISAC beams through optimized transmit beamforming and dedicated probe signals, thereby achieving higher echo signal power. In contrast, when , and At that time, the echo signal power of uniform orientation design, random orientation design and fixed orientation design will respectively change with The power decreases as the directivity factor increases. Furthermore, although a uniform orientation design can rotate all antennas to the same optimized orientation, its received echo signal power eventually drops to levels approaching those of a fixed orientation design. This is because, with the increase in the directivity factor... With increasing orientation, the radiated power of reference systems based on uniform and fixed orientation designs will be more concentrated in the array's main pointing direction because all antennas in both systems share the same orientation. Therefore, their ability to balance communication and sensing performance will be significantly weakened. For random orientation designs, a larger... This leads to more irregular directional gain patterns and ISAC beamforming, making it more difficult to improve ISAC performance. The proposed steerable antenna-enabled low-altitude ISAC system outperforms all benchmark systems, and its performance advantage over a uniform orientation design will increase with... The size increases with the size of the antenna. This further demonstrates that the proposed steerable antenna-enabled low-altitude ISAC system is of great significance for making full use of available spatial degrees of freedom, especially when the antenna has strong directivity.

[0108] exist Figure 9 In the middle, we examined the side length of the sensing region. The impact of the proposed steerable antenna on the minimum echo signal power of the low-altitude ISAC system was investigated, and the directivity factors of different antennas were compared. The performance at that point. It can be observed that, with... The increase of [amount], for all considerations With each change in value, the echo signal power obtained by a low-altitude ISAC system powered by a steerable antenna decreases. This is expected because a larger sensing area naturally presents greater challenges to the design of the detection signal and the adjustment of the steerable antenna orientation, making it more difficult for the system to form a sensing beam that can cover the entire sensing area. Furthermore, due to the conservation of radiated energy, expanding the sensing area inevitably reduces the minimum echo signal power over the entire sensing area. Further, when the sensing area is small (i.e.... m), larger This can increase the minimum echo signal power. This is because a higher directivity factor results in a narrower main lobe and higher directional gain along the antenna's line of sight, allowing the base station to concentrate more radiated power onto the sensing area. However, when the sensing area increases (i.e.,...) m), increase Conversely, this may reduce the minimum echo signal power. This is because a narrower beam covers a smaller spatial area, making it difficult to effectively illuminate the entire sensing area. As a result, some locations far from the line-of-sight of the steerable antenna receive significantly less detection power, thus worsening worst-case sensing performance in that area. This reveals a practical trade-off between radiated energy focusing and spatial coverage: higher directivity is advantageous for compact sensing areas, but for large sensing areas, it may weaken sensing performance due to reduced coverage uniformity.

[0109] (5) Summary This paper investigates a novel steerable antenna-enabled low-altitude area sensing (ISAC) system to simultaneously improve communication and sensing performance. Specifically, to support both multi-user communication and low-altitude area sensing, while meeting the minimum communication rate requirements of users, we maximize the minimum received echo signal power within the sensing area where potential airborne targets may be randomly located. For the single-user and point target case, a closed-form optimal steerable antenna pointing vector is derived. For the general multi-user and extended target case, an efficient alternating optimization algorithm is proposed to jointly optimize transmit beamforming, the probe signal covariance matrix, and the steerable antenna pointing vector. Simulation results show that, compared with various benchmark schemes, the proposed steerable antenna-enabled low-altitude ISAC system significantly expands the region representing the trade-off between communication and sensing. The results also demonstrate a trade-off between directional gain and radiation coverage when selecting the antenna directivity factor.

[0110] Compared with the prior art, this application has at least the following advantages and beneficial effects: 1) Enhanced low-altitude coverage: By independently rotating the antenna element by element, the elevation blind spot of traditional downtilt antennas is effectively eliminated, enabling the base station to serve both ground users and low-altitude sensing areas simultaneously.

[0111] 2) Improve worst-case perception performance: With the goal of maximizing the minimum echo signal power within the perception area, ensure uniform perception capability throughout the entire area and avoid detection blind spots.

[0112] 3) Flexible balance between communication and sensing: The joint optimization framework can adaptively adjust the antenna orientation and beamforming to maximize sensing performance while meeting the communication rate threshold, thus expanding the trade-off range between communication and sensing performance.

[0113] 4) Low implementation complexity: Compared with a six-dimensional movable antenna, this solution only requires antenna rotation, with minimal hardware modifications and low cost; the proposed replacement optimization algorithm has polynomial time complexity and can be practically deployed.

[0114] 5) Wide applicability: Supports various scenarios such as single-user / multi-user, point target / extended target, and can adapt to different antenna directivity factors and rotation range limitations.

[0115] This application also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-described method. This electronic device can be any smart terminal, including tablet computers, in-vehicle computers, etc.

[0116] It is understood that the content of the above method embodiments is applicable to this device embodiment. The specific functions implemented by this device embodiment are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0117] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0118] It is understood that the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0119] 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.

[0120] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0121] It is understood that the content of the above method embodiments is applicable to the embodiments of this program product. The specific functions implemented in the embodiments of this program product are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments. The executable computer program code or "code" used to perform the various embodiments can be written in high-level programming languages ​​such as C, C++, Python, Smalltalk, Java, JavaScript, Visual Basic, Structured Query Language (e.g., Transact-SQL), Perl, or in various other programming languages.

[0122] 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.

[0123] 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.

[0124] 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.

[0125] 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.

[0126] 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.

[0127] 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.

[0128] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of the units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0129] 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.

[0130] 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.

[0131] 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.

[0132] 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 low-altitude integrated sensing area perception enhancement method, characterized in that, Applied to a base station, wherein the base station is equipped with multiple independently rotatable antennas, the method includes the following steps: Jointly optimize the communication transmit beamforming matrix, the detection signal covariance matrix, and the pointing vector of each steerable antenna; The optimization objective is to maximize the minimum received echo signal power of potential targets within the low-altitude sensing area. This optimization must satisfy the minimum communication rate constraint for each user and the maximum power constraint for the base station to transmit sensing signals.

2. The method according to claim 1, characterized in that, Joint optimization includes: In the special case of a single user and a single point target, maximum ratio transmission beamforming is adopted, and the optimization problem is transformed into a convex projection maximization problem, thereby deriving the closed-form solution of the optimal pointing vector for each steerable antenna.

3. The method according to claim 2, characterized in that, The closed-form solution satisfies the following: the optimal pointing vector of the steerable antenna lies within the sector spanned by the user direction and the target direction, or on the cone surface of a spherical cone constrained by the antenna rotation range constraint, and in the far-field region, the optimal pointing vectors of all steerable antennas are the same.

4. The method according to claim 1, characterized in that, For the general scenario of multiple users and perceived targets distributed across an extended low-altitude region, joint optimization includes: Discretize the continuous low-altitude sensing area into multiple spatial sampling points; A relaxation optimization variable is introduced, which represents the minimum echo signal power within the sensing area; Using an alternating optimization algorithm, the following subproblems are executed sequentially in each iteration: The first sub-problem is to optimize the communication transmit beamforming matrix and the detection signal covariance matrix with a fixed pointing vector of the steerable antenna. The second sub-problem is to optimize the pointing vector of each steerable antenna while fixing the communication transmit beamforming matrix and the detection signal covariance matrix.

5. The method according to claim 4, characterized in that, The first subproblem is transformed into a semidefinite programming problem by a semidefinite relaxation method, and the obtained solution is restored to rank-one.

6. The method according to claim 4, characterized in that, The second subproblem is addressed using a continuous convex approximation method, including: The non-convex Hermitian quadratic form constraint is approximated as a convex constraint based on its first-order Taylor expansion. Relax the unit norm constraint of the pointing vector into two inequality constraints and then linearize them; The approximate convex problem is solved iteratively until the objective function converges, and the solution is then normalized.

7. The method according to claim 1, characterized in that, The pointing vector of the steerable antenna satisfies a rotation range constraint, which is defined by the maximum permissible rotation angle of each antenna relative to its initial line of sight.

8. The method according to claim 1, characterized in that, The received echo signal power is calculated based on a preset propagation model and antenna radiation pattern. The directional gain of the antenna radiation pattern depends on the off-axis angle between the signal direction and the current line-of-sight orientation of the steerable antenna.

9. A low-altitude integrated sensing and perception enhancement system, characterized in that, include: The base station is equipped with multiple independently rotatable antennas; A communication transmission beamforming module is used to generate beamforming vectors for transmitting information symbols to users; The detection signal generation module is used to generate a dedicated detection signal to be transmitted to the low-altitude sensing area; The pointing vector optimization module is used to jointly optimize the communication transmit beamforming matrix, the detection signal covariance matrix, and the pointing vector of each steerable antenna, so as to maximize the minimum received echo signal power of potential targets in the low-altitude sensing area while satisfying the minimum communication rate constraint for each user and the base station transmit power constraint.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 8.

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