A method for anti-uav attitude jitter robust beamforming based on a rotatable antenna

Abstract

The application discloses a kind of anti-UAV attitude jitter robust beam forming methods based on rotatable antenna.First, the UAV attitude jitter model considering yaw, pitch and roll three-dimensional independent Gaussian jitter is established.Second, the UAV point-to-point line-of-sight channel model based on uniform plane rotatable antenna is constructed.On this basis, with the maximum ergodic transmission rate as the target, under the constraints of transmit power, constant modulus and rotation angle feasible region, the optimization problem model of joint optimization of receiving end and transmitting end beam forming vector and antenna rotation angle is established.Finally, a two-stage robust beam forming method is proposed: the first stage is to rotate the coordinate system by optimizing the rotation angle, and to symmetrize the asymmetric jitter distribution;The second stage is to construct a two-dimensional flat-top beam based on the symmetrization result using the principle of linear frequency modulation to achieve robust coverage.Compared with the prior art, it can effectively resist asymmetric attitude jitter and has significant advantages in ergodic transmission rate and communication reliability.

Description

Technical Field

[0001] This invention pertains to wireless communication technology, specifically a robust beamforming method for combating UAV attitude jitter based on a rotatable antenna. Background Technology

[0002] Low-altitude wireless networks have rapidly developed as an integrated paradigm covering diverse activities in airspace below 1,000 meters. Through the deployment of drones and other aerial platforms, they are widely used in logistics, environmental monitoring, and smart city services. Drones, with their three-dimensional maneuverability, flexible deployment, and line-of-sight (Line-of-Sight) link-dominated communication characteristics, have become a core component of low-altitude wireless networks. To fully utilize these capabilities and support high-capacity services, aerial networks typically employ millimeter-wave communication combined with high-gain directional beamforming technology to maintain reliable connections between drones. However, drone beamforming design faces a key challenge: drone attitude jitter. Due to external disturbances (such as gusts and turbulence) and internal factors (such as sensor noise and mechanical vibration), drone platforms experience continuous high-frequency fluctuations in yaw, pitch, and roll attitude angles. These attitude jitters cause AoD and AoA to deviate from their nominal values, resulting in inaccurate transmit and receive beams. In practical applications, the rapid changes in drone attitude make accurate AoD / AoA acquisition difficult, making instantaneous beam tracking and alignment extremely challenging.

[0003] To address the challenges posed by attitude jitter, existing research has proposed various robust beamforming schemes. Among them, beam widening technology has been widely used, such as... The guidelines extend beam coverage and design wide beams by activating some antenna elements. Furthermore, some studies employ heuristic algorithms such as the artificial bee colony algorithm to search for the optimal beamforming vector under jitter conditions. In practical applications, the coupling of yaw, pitch, and roll jitter causes non-uniform fluctuations in the AoD / AoA along the array's horizontal and vertical axes. This phenomenon, known as "asymmetric jitter," more accurately reflects the impact of attitude fluctuations in 3D UAVs but limits the effectiveness of robust solutions designed for simplified symmetrical scenarios.

[0004] In recent years, rotatable antennas have emerged as a novel array architecture, introducing additional rotational degrees of freedom compared to traditional fixed arrays. By dynamically adjusting the geometric layout of antenna elements, rotatable antennas provide a new physical layer solution for low-altitude wireless network communication. Based on the granularity of rotation, rotatable antennas can be categorized into array-level rotation and element-level rotation: array-level rotation reshapes spatial channel characteristics through global rotation, while element-level rotation allows each element to rotate independently for finer beam and polarization control. Leveraging these capabilities, rotatable antennas demonstrate significant potential in improving spatial resolution, suppressing interference, enhancing received power, and optimizing coverage performance. Summary of the Invention

[0005] This invention proposes a robust beamforming method for combating UAV attitude jitter based on a rotatable antenna. By jointly optimizing the rotation angle of the rotatable antenna and the beamforming vector, the method effectively solves the problem of communication quality degradation caused by UAV attitude jitter.

[0006] The technical solution to achieve the purpose of this invention is: a robust beamforming method for anti-UAV attitude jitter based on a rotatable antenna, the specific steps of which are as follows:

[0007] Step 1: Based on the UAV point-to-point communication system, establish a UAV attitude jitter model. The UAV attitude jitter model considers the independent Gaussian jitter of the UAV at the three attitude angles of yaw, pitch and roll. The attitude jitter is mapped to the two-dimensional cosine angle domain through the Jacobian matrix.

[0008] Step 2: Construct a point-to-point channel model for UAVs based on a rotatable antenna;

[0009] Step 3: Construct an optimization problem model with the goal of maximizing the traversal transmission rate. The problem jointly optimizes the transmit and receive beamforming vectors and the rotation angle of the rotatable antenna. Under the constraints of transmit power, constant mode constraint and feasible region of rotation angle, the optimization is carried out to address the uncertainty of the transmit and receive angles caused by asymmetric attitude jitter.

[0010] Step 4: Symmetricalize the asymmetric jitter distribution by using the optimal rotation angle, and then construct a two-dimensional beam using linear frequency modulation based on the symmetry result to obtain the array rotation angle and beamforming vector of the receiver and transmitter.

[0011] Compared with the prior art, the significant advantages of this invention are:

[0012] The robust beamforming method for anti-UAV attitude jitter based on a rotatable antenna proposed in this invention adaptively covers the asymmetric jitter region without instantaneous tracking by jointly optimizing the rotation angle of the rotatable antenna and the beamforming vector. Compared with existing narrow beam and wide beam reference schemes, it has significant advantages in traversal transmission rate and communication reliability.

[0013] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description

[0014] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0015] Figure 1 This is a schematic diagram of a UAV point-to-point communication system based on a rotatable antenna, as studied in this invention. Figure 1 (a) in the diagram represents a point-to-point communication scenario between drones. Figure 1 (b) in the figure represents the attitude jitter of the UAV (local coordinate system). Figure 1 (c) In-plane rotation model of the antenna array.

[0016] Figure 2 This is a flowchart of the present invention.

[0017] Figure 3 The normalized beamforming performance of the robust beamforming scheme proposed in this invention is illustrated in the diagrams under different UAV states.

[0018] Figure 4 The diagram shows a comparison of the traversal transmission rate performance of the robust beamforming scheme proposed in this invention and a benchmark scheme under different jitter intensities. Detailed Implementation

[0019] It is readily understood that, based on the technical solution of this invention, various embodiments of the invention can be conceived by those skilled in the art without altering the essential spirit of the invention. Therefore, the following detailed embodiments and accompanying drawings are merely illustrative examples of the technical solution of this invention and should not be considered as the entirety of the invention or as limitations or restrictions on the technical solution of this invention. Rather, these embodiments are provided to enable those skilled in the art to gain a more thorough understanding of the invention. Preferred embodiments of the invention are described below in conjunction with the accompanying drawings, which form part of this application and, together with the embodiments of the invention, serve to illustrate the innovative concept of the invention.

[0020] UAV point-to-point communication systems based on rotatable antennas, such as Figure 1 As shown.

[0021] like Figure 2 As shown, a robust beamforming method for anti-UAV attitude jitter based on a rotatable antenna is described, with the following specific steps:

[0022] Step 1: Establish a UAV attitude jitter model. The UAV attitude jitter model considers the independent Gaussian jitter of the UAV at three attitude angles: yaw, pitch and roll. The attitude jitter is mapped to the two-dimensional cosine angle domain through the Jacobian matrix to obtain the transmitter angle and receiver angle (AoD / AoA).

[0023] Initialize system parameters, such as Figure 1 As shown in (a), the UAV point-to-point communication system comprises indexes respectively. The three-dimensional coordinates of the UAV transmitter and receiver are shown as follows: The transmitting and receiving ends are each equipped with a scale of and A uniform planar rotatable antenna array.

[0024] Establish a model for the attitude angle jitter of a UAV, such as Figure 1 As shown in (b), the drone The attitude is determined by the attitude yaw angle. Attitude and pitch angle and attitude roll angle Composition, denoted as Due to attitude jitter, the instantaneous attitude angle is decomposed into the sum of the nominal attitude angle and the random jitter component:

[0025]

[0026] in, Indicates the drone index. Indicates the transmitting end. Indicates the receiving end; This is the instantaneous attitude angle vector; The nominal attitude angle vector is the command from the flight control system. Let $\frac{ ...

[0027]

[0028] in, These are the variances of attitude yaw, attitude pitch, and attitude roll jitter, respectively. Based on the geometric positional relationship between the transmitter and receiver, the relative pitch angle between the transmitter and receiver is... and azimuth The calculation is as follows:

[0029]

[0030] in, The three-dimensional coordinates of the launching UAV; The three-dimensional coordinates of the receiving drone.

[0031] Establish a mapping relationship between attitude jitter and the two-dimensional cosine angular domain, where the actual beam direction is determined by the elevation angle. Azimuth and attitude angle Together, they determine the first dimension component of the two-dimensional AoD / AoA vector. Second dimension component In the cosine angle domain:

[0032]

[0033] in, This represents the first dimension component of the two-dimensional AoD / AoA vector in the cosine angle domain. This is the second-dimensional component of the two-dimensional AoD / AoA vector in the cosine angle domain; This refers to the attitude yaw angle; The pitch angle is the attitude angle. For attitude roll angle; The relative elevation angle between the receiver and the transmitter; This refers to the relative azimuth angle between the receiver and the transmitter.

[0034] For small-scale jitter, a first-order Taylor expansion is used. and Approximation:

[0035]

[0036] in, It is a two-dimensional AoD / AoA vector; A nominal two-dimensional AoD / AoA vector; This is the random fluctuation vector of the attitude angle. and The nominal attitude angles of the transmitter and receiver are respectively. The first and second dimensions are specifically represented as follows:

[0037] The Jacobian matrix is ​​represented as follows:

[0038]

[0039] in, , , They are respectively Partial derivatives with respect to attitude yaw angle, attitude pitch angle, and attitude roll angle; , , They are respectively Partial derivatives with respect to attitude yaw, pitch, and roll angles; subscript This indicates the values ​​of each partial derivative at the nominal attitude angle.

[0040] Therefore, the two-dimensional AoD / AoA vector follows a Gaussian distribution:

[0041]

[0042] Among them, the mean covariance matrix Specifically:

[0043]

[0044] in, It is a Jacobian matrix; Represents a diagonal matrix; , , These are the variances of yaw, pitch, and roll jitter, respectively; superscript This indicates the matrix transpose.

[0045] Step 2: Construct a point-to-point channel model for UAVs based on rotatable antennas. The UAV point-to-point channel is a line-of-sight dominant channel, and both the transmitter and receiver use uniform planar rotatable antenna arrays.

[0046] The UAV point-to-point channel matrix based on a rotatable antenna Represented as:

[0047]

[0048] in, For carrier wavelength, The distance between the two drones; To account for the guide vector of array rotation, and These are the in-plane rotation angles of the transmitting and receiving ends, respectively; the geometric center of the uniform planar array is used as the rotation center and reference point; taking the receiving array as an example, its guiding vector... The The elements are:

[0049]

[0050] in, Antenna spacing; and They represent the first The horizontal axis normalized position index and the vertical axis normalized position index of each antenna element relative to the geometric center of the uniform planar array; The rotation angle within the receiving end face; and Define the first and second dimensions of the two-dimensional AoA matrix at the receiving end; define the in-plane rotation matrix. and index matrix for:

[0051]

[0052] Receive guide vector It can be compactly represented as:

[0053]

[0054] in, This is the receiver index matrix; This is the rotation matrix within the receiving end face; The receiving end is a two-dimensional AoA vector; Antenna spacing; This is the carrier wavelength. Similarly, the transmit steering vector... Represented as:

[0055]

[0056] in, This is the transmitter index matrix; This is the rotation matrix within the transmitting end face; The transmitter's two-dimensional AoD vector; The rotation angle within the transmitting end face; Antenna spacing; The carrier wavelength.

[0057] Step 3: Construct an optimization problem model with the goal of maximizing the traversal transmission rate. The problem jointly optimizes the transmit and receive beamforming vectors and the rotation angle of the rotatable antenna. Under the constraints of transmit power, constant mode constraint and the feasible region of rotation angle, the AoD / AoA uncertainty caused by asymmetric attitude jitter is optimized.

[0058] Construct a signal transmission model, and represent the baseband received signal after beamforming at the receiving end as follows:

[0059]

[0060] in, For transmission power, The emitted symbol satisfies ; Transmit beamforming vector and receive beamforming vector Satisfying constant modulus constraints and ; The receiver uses additive white Gaussian noise with a noise power of , and These are the in-plane rotation angles of the transmitting and receiving ends, respectively. The instantaneous transmission rate is:

[0061]

[0062] in, Instantaneous transmission rate; Transmission power; For receiving beamforming vectors; The channel matrix; For transmitting beamforming vectors; superscript Indicates conjugate transpose; Noise power; Equivalent signal-to-noise ratio; This is the guide vector for the receiving end; For receiver beamforming gain; The transmitting end steering vector; For the transmitter beamforming gain. To maximize the traversal transmission rate, the transmit beamforming vector is jointly optimized. Receive beamforming vector and the rotation angle of the rotatable antenna and , construct an optimization problem:

[0063]

[0064] The constraints include constant mode constraints on the transmit beamforming vector and the receive beamforming vector, as well as feasible region constraints on the rotation angle. and ; This represents the expected operation of the statistical characteristics of the uncertainty of the transmitting and receiving angles. The traversal rate objective function depends on the AoD / AoA deviation caused by the attitude jitter of the UAV.

[0065] Step 4: A two-stage robust beamforming method is adopted. In the first stage, the asymmetric jitter distribution is symmetricized by optimizing the rotation angle. In the second stage, a two-dimensional beam is constructed based on the symmetry result using linear frequency modulation. Since the attitude jitter of the transmitter and receiver are independent of each other, the traversal rate can be decomposed into two independent single-UAV subproblems. Taking the receiver as an example, the specific process is as follows; the transmitter uses the same method to jointly optimize the beamforming vector and rotation angle.

[0066] Step 4.1: The first stage is rotation angle optimization to symmetricize the asymmetric jitter distribution;

[0067] Based on the current nominal attitude angle of the drone at the receiving end And the jitter variance in the three directions of attitude yaw, attitude pitch, and attitude roll. Calculate the initial covariance matrix of the two-dimensional AoA vector:

[0068]

[0069] in, It is a Jacobian matrix; Represents a diagonal matrix; , , These are the variances of yaw, pitch, and roll jitter, respectively; superscript This indicates the matrix transpose.

[0070] The in-plane rotational degrees of freedom of the rotatable antenna are used to compensate for the asymmetric tilt, and the optimal rotation angle to eliminate the axial offset is determined by eigenvalue decomposition. :

[0071] like ,Pick ;

[0072] like ,Pick ;

[0073] The receiver's uniform planar antenna array is physically rotated around its normal by the optimal rotation angle. This makes the rotated two-dimensional AoA vector Diagonalization of the corresponding covariance matrix:

[0074]

[0075] in and Let each represent the rotated covariance matrix. The eigenvalues; thus symmetricizing the asymmetric jitter distribution, the mean vector in the new coordinate system is... ;

[0076] The same steps are performed on the launching UAV to obtain the optimal rotation angle of the launching end. .

[0077] Step 4.2: The second stage is the robust beam coverage design based on linear frequency modulation;

[0078] Based on the diagonalized jitter distribution from the first stage of step 4.1, and according to the covariance matrix after symmetry transformation and diagonalization... Select confidence level , with point Centered on the ellipse, determine the major axis coverage width and minor axis coverage width of the confidence ellipse:

[0079]

[0080] in To find the quantiles of a chi-square distribution with 2 degrees of freedom, take... Make the ellipse contain the region where the jitter probability is concentrated;

[0081] To be within a defined angular range It provides uniform gain and synthesizes a flat-top beam under constant mode constraint using the linear frequency modulation principle; robust beamforming vector. Construct the Kronecker product of two one-dimensional vectors:

[0082]

[0083] in, and These are the linear frequency modulation beamforming vectors along the major and minor axes in the rotated coordinate system, respectively.

[0084] Based on the mapping relationship between linear frequency modulation sequences and desired spatial coverage, the sequence is designed. The Each element aligns the center angle. And adjust the coverage area to ;Will Decomposed into the Hadamard product of two sequences:

[0085]

[0086] in, It is represented as the component used to determine the center pointing of the beam, and its first... Each element is represented as ; Represented as the broadening component used to broaden the beam to the desired coverage area, its first... Each element is represented as ; The Each element is represented as:

[0087]

[0088] when from Change to At that time, the beam coverage area is ;

[0089] Solve for the range of angles Boundary condition determination coefficients and :

[0090]

[0091] in, The frequency modulation slope is used to control the degree of beam widening. This is the initial frequency compensation coefficient, used to ensure that the beam center is aligned with the nominal angle; The coverage width along the major axis in the rotating coordinate system; This refers to the number of elements in the horizontal direction of the receiving antenna array;

[0092] Linear frequency modulated beamforming vector The The elements are:

[0093]

[0094] in, This indicates the number of antenna elements in the vertical direction of the receiver array; The vertical component of the two-dimensional mean vector AoA in the rotated coordinate system; This represents the beam coverage width corresponding to the short axis direction; For the index of the vertical array cell;

[0095] Two one-dimensional beamforming vectors are combined using the Kronecker product to generate a two-dimensional robust receiving beamforming vector:

[0096]

[0097] The transmitter adopts the same two-stage design, jointly optimizing the transmitted beamforming vector. and rotation angle .

[0098] Example 1

[0099] This invention is mainly verified using computer simulation methods, and all steps and conclusions have been verified to be correct using MATLAB.

[0100] The specific steps for signal generation are as follows:

[0101] 1) Initialization of system-related parameters

[0102] The carrier frequency is set to 28 GHz; the noise power of the receiving drone is -80 dBm, and the transmit power of the transmitting drone is... 30dBm; both drones are equipped with A rotatable antenna (RA) array with antenna spacing Half wavelength; the transmitting drone is fixed at the coordinates At point m, the receiving drone is located At point m; the nominal attitude angles are respectively set to m. rad and rad; assuming the two drones have the same jitter intensity, i.e. Each simulation data point was passed through The average value of the Monte Carlo experiments was obtained.

[0103] 2) Simulation analysis of method performance

[0104] Figure 2The normalized beam pattern of the proposed solution is shown in two representative UAV states. Observation reveals that, in both states, the main lobe of the beam consistently covers the asymmetric uncertainty region, demonstrating robustness to different asymmetric jitter conditions. This indicates that the proposed solution can adapt the effective angular coverage to asymmetric jitter without requiring instantaneous attitude tracking, while simultaneously maintaining concentrated high gain within the most probable fluctuation region. Figure 3 It shows that the traversal transmission rate varies with jitter intensity. The variation curves (ranging from 0.03 rad to 0.1 rad) are shown. Two benchmark schemes are introduced in the comparative analysis: benchmark scheme 1 uses a narrow beam design, and benchmark scheme 2 uses a wide beam design without array rotation. With... As the beamwidth increases, the ergonomic rate degrades in all schemes due to increased beam mismatch. The narrow-beam reference scheme is the most vulnerable due to its limited angular redundancy. Importantly, even with the same effective beamwidth, the scheme of this invention achieves a higher ergonomic rate than the two reference schemes. This further verifies that aligning the beam with the dominant angular uncertainty through rotatable antenna rotation is superior to simple beam widening techniques in combating asymmetric jitter.

[0105] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto.

[0106] Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this invention should be included within the protection scope of this invention.

[0107] It should be understood that, in order to simplify the present invention and help those skilled in the art understand its various aspects, in the above description of exemplary embodiments of the present invention, various features of the present invention are sometimes described in a single embodiment or with reference to a single figure. However, the present invention should not be construed as including all features in the exemplary embodiments as essential technical features of the claims of this patent.

[0108] It should be understood that the modules, units, components, etc., included in the device of one embodiment of the present invention can be adaptively changed to be placed in a device different from that embodiment. Different modules, units, or components included in the device of the embodiment can be combined into a single module, unit, or component, or they can be divided into multiple sub-modules, sub-units, or sub-components.

Claims

1. A robust beamforming method for anti-UAV attitude jitter based on a rotatable antenna, characterized in that, The specific steps are as follows: Step 1: Based on the UAV point-to-point communication system, establish a UAV attitude jitter model. The UAV attitude jitter model considers the independent Gaussian jitter of the UAV at the three attitude angles of yaw, pitch and roll. The attitude jitter is mapped to the two-dimensional cosine angle domain through the Jacobian matrix. Step 2: Construct a point-to-point channel model for UAVs based on a rotatable antenna. Specifically: ； in, For carrier wavelength, The distance between the two drones; To account for the guide vector of array rotation, and These are the in-plane rotation angles of the transmitting and receiving ends, respectively. Represented as the imaginary unit; Rotation center and reference point are both based on the geometric center of the uniform planar array; receive array guide vector. The element Specifically: ； in, Antenna spacing; and They represent the first The horizontal and vertical axis normalized position indices of each antenna element relative to the geometric center of the uniform planar array. M represents the total number of antenna elements equipped at the receiver. This is the first dimension component of the angle of the two-dimensional receiver in the cosine angle domain; This is the second-dimensional component of the angle of the two-dimensional receiver in the cosine angle domain; Define the in-plane rotation matrix and index matrix for: ； Receive guide vector Represented as: ； in, This is the receiver index matrix; This is the rotation matrix within the receiving end face; This is a two-dimensional receiver angle vector; Antenna spacing; For carrier wavelength, Represented as the imaginary unit; Launch guidance vector Represented as: ； in, This is the transmitter index matrix; This is the rotation matrix within the transmitting end face; This is a two-dimensional transmitter angle vector; The rotation angle within the transmitting end face; Antenna spacing; The carrier wavelength; Step 3: Construct an optimization problem model with the goal of maximizing the traversal transmission rate. The problem jointly optimizes the transmit and receive beamforming vectors and the rotation angle of the rotatable antenna. Under the constraints of transmit power, constant mode constraint and feasible region of rotation angle, the optimization is carried out to address the uncertainty of the transmit and receive angles caused by asymmetric attitude jitter. Step 4: Symmetricalize the asymmetric jitter distribution by using the optimal rotation angle, and then construct a two-dimensional beam using linear frequency modulation based on the symmetry result to obtain the array rotation angle and beamforming vector of the receiver and transmitter.

2. The robust beamforming method for anti-UAV attitude jitter based on a rotatable antenna according to claim 1, characterized in that, The UAV point-to-point communication system includes a UAV transmitter and a receiver; the transmitter is equipped with a [missing information - likely a device or receiver]. A uniform planar rotatable antenna array composed of antenna elements, wherein the receiver is equipped with a... A uniform planar rotatable antenna array composed of antenna elements. , , , All are natural numbers.

3. The robust beamforming method for anti-UAV attitude jitter based on a rotatable antenna according to claim 1, characterized in that, The specific method for establishing a UAV attitude jitter model is as follows: The instantaneous attitude angle is decomposed into the sum of the nominal attitude angle and the random jitter component: ； in, Indicates the drone index. Indicates the transmitting end. Indicates the receiving end; The instantaneous attitude angle vector. For attitude yaw angle, For attitude pitch angle and For attitude roll angle; The nominal attitude angle vector is the command from the flight control system. The vector representing random fluctuations caused by drone jitter; Calculate the relative elevation angle between the transmitter and receiver based on their geometric positions. azimuth angles relative to the receiver and transmitter ; A mapping relationship between attitude jitter and the two-dimensional cosine angle domain is established, where the two-dimensional transmitter angle and receiver angle are represented in the cosine angle domain as follows: and : ； in, Let be the first-dimensional component of the two-dimensional transmitter angle and receiver angle in the cosine angle domain; This represents the second-dimensional component of the two-dimensional transmitter and receiver angles in the cosine angle domain. For small-scale jitter, a first-order Taylor expansion is used. and Approximation: ； in, It is a two-dimensional AoD / AoA vector; A nominal two-dimensional AoD / AoA vector; The attitude angle is a random fluctuation vector; and The nominal attitude angles of the transmitter and receiver are respectively. The first and second dimensions are specifically represented as follows: 。 4. The robust beamforming method for anti-UAV attitude jitter based on a rotatable antenna according to claim 3, characterized in that, Calculate the relative elevation angle between the transmitter and receiver based on their geometric positions. Azimuth angle relative to the receiver and transmitter The specific formula is: ； in, The three-dimensional coordinates of the launching UAV; The three-dimensional coordinates of the receiving drone.

5. The robust beamforming method for anti-UAV attitude jitter based on a rotatable antenna according to claim 1, characterized in that, The specific method for constructing an optimization problem model with the objective of maximizing the traversal transmission rate is as follows: A signal transmission model is constructed to determine the baseband received signal at the receiver after beamforming, specifically represented as follows: in, For transmission power, The emitted symbol satisfies , Symbol representing mathematical expectation; For the transmitted beamforming vector, To receive beamforming vectors, and Satisfying constant modulus constraints and , The total number of antenna elements equipped at the receiver. The total number of antenna elements equipped for the transmitting end; Additive white Gaussian noise at the receiving end. and These are the in-plane rotation angles of the transmitting and receiving ends, respectively. Channel matrix; superscript Indicates conjugate transpose; The formula for calculating the instantaneous transmission rate is as follows: in, Instantaneous transmission rate; Transmission power; Noise power; Equivalent signal-to-noise ratio; This is the guide vector for the receiving end; For the sending end steering vector, This is a two-dimensional receiver angle vector. This is a two-dimensional transmitter angle vector; With the goal of maximizing the traversal transmission rate, the transmit beamforming vector is jointly optimized. Receive beamforming vector And the rotation angle of the rotatable antennas at the transmitting and receiving ends. and , construct an optimization problem: In the formula, , These are feasible region constraints for the rotation angles of the rotatable antennas at the transmitting and receiving ends, respectively. This represents the expectation operation on the statistical characteristics of the uncertainty of the transmitting and receiving angles.

6. The robust beamforming method for anti-UAV attitude jitter based on a rotatable antenna according to claim 1, characterized in that, The specific method for symmetricizing the asymmetric jitter distribution using the optimal rotation angle is as follows: Based on the current nominal attitude angle of the drone at the receiving end And the jitter variance in the three directions of attitude yaw, attitude pitch, and attitude roll. Calculate the initial covariance matrix of the two-dimensional AoA vector: in, It is a Jacobian matrix; Represents a diagonal matrix; , , These are the variances of yaw, pitch, and roll jitter, respectively; superscript Indicates matrix transpose. These are the nominal yaw angle, nominal pitch angle, and nominal roll angle, respectively. The in-plane rotational degrees of freedom of the rotatable antenna are used to compensate for the asymmetric tilt, and the optimal rotation angle to eliminate the axial offset is determined by eigenvalue decomposition. : like ,Pick ; like ,Pick ; Represented as a matrix The first row and first column element, Represented as a matrix The element in the second row and second column; The receiver's uniform planar antenna array is physically rotated around its normal by the optimal rotation angle. This makes the rotated two-dimensional AoA vector Diagonalization of the corresponding covariance matrix: in, and Let each represent the rotated covariance matrix. The eigenvalues ​​are used to symmetricize the asymmetric jitter distribution, thus obtaining the mean vector in the new coordinate system. ; The launching UAV uses the same method to obtain the optimal rotation angle at the launching end. And the symmetrical two-dimensional AoD vector distribution.

7. The robust beamforming method for anti-UAV attitude jitter based on a rotatable antenna according to claim 6, characterized in that, The specific method for constructing a two-dimensional beam using linear frequency modulation based on the symmetry result is as follows: Based on the symmetric diagonalized covariance matrix Select confidence level , with point Centered on the ellipse, determine the major axis coverage width and minor axis coverage width of the confidence ellipse: ； in Let be the quantiles of a chi-square distribution with 2 degrees of freedom. These are represented as the first and second components of the nominal attitude angle of the receiver after rotation, respectively. A flat-top beam is synthesized under constant mode constraint using the principle of linear frequency modulation; a robust beamforming vector is then used. Construct the Kronecker product of two one-dimensional vectors: ； in, and These are the linear frequency modulation beamforming vectors along the major and minor axes in the rotated coordinate system, respectively. Based on the mapping relationship between linear frequency modulation sequences and desired spatial coverage, the sequence is designed. The Each element aligns the center angle. And adjust the coverage area to ;Will Decomposed into the Hadamard product of two sequences: ； in, This is represented as the component used to determine the center pointing direction of the beam. The Each element is represented as ; This is represented as the beam-widening component used to broaden the beam to the desired coverage area. The Each element is represented as , For frequency modulation slope, These are the initial frequency compensation coefficients; This is represented as the first component of the nominal attitude angle of the receiver after rotation. in, The Each element is represented as: ； when from Change to At that time, the beam coverage area is , This refers to the number of elements in the horizontal direction of the receiving antenna array; Solve for the range of angles Boundary condition determination coefficients and : ； in, The coverage width along the major axis in the rotating coordinate system; Determine the linear frequency modulated beamforming vector The The elements are: ； in, This indicates the number of antenna elements in the vertical direction of the receiver array; This is represented as the second component of the nominal attitude angle of the receiver after rotation. This represents the beam coverage width corresponding to the short axis direction; For the index of the vertical array cell; Two one-dimensional beamforming vectors are combined by Kronecker product to generate a two-dimensional robust receiving beamforming vector. The transmitter uses the same linear frequency modulation method as the receiver to construct a two-dimensional transmit beamforming vector. .

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