Anti-interference beam forming control method for low-altitude aircraft

Abstract

The invention discloses an anti-interference beam forming control method for a low-altitude aircraft, and the method comprises the steps: firstly, optimizing an optimal beam angle range through building a three-dimensional attitude differentiation jitter model, achieving the cooperative balance of a beam alignment probability and an antenna gain, constructing an irregular multi-beam forming scheme, precisely matching multi-directional jitter distribution, and achieving the multi-directional jitter distribution. And finally, a virtual sub-array dynamic mapping mechanism is designed, the calculation complexity is reduced in combination with an array power distribution rule, and nonlinear distortion and beam distortion caused by non-uniform array element power loads are avoided. The method has excellent airflow disturbance resistance, low calculation overhead and engineering realizability, is suitable for high-reliability communication scenes of low-altitude aircrafts such as hovercars and unmanned aerial vehicles, and solves the technical problems of beam offset and channel capacity reduction caused by influence of low-altitude airflow on the low-altitude aircrafts.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, and specifically relates to an anti-interference beamforming control method for low-altitude aircraft. Background Technology

[0002] As a core component of future three-dimensional transportation, the communication reliability of low-altitude aircraft (such as flying cars) directly affects operational safety and service quality. Beamforming technology, by focusing signal energy, has become a key support for improving the performance of low-altitude communication links. However, the three-dimensional attitude jitter (pitch, roll, yaw) of aircraft caused by low-altitude airflow can lead to random beam shifts, severely deteriorating the communication link.

[0003] The main approaches to beam alignment under jitter fall into two categories: beam tracking and beam widening. Beam tracking methods often utilize machine learning and visual information to dynamically adjust the beam. For example, they employ multi-armed beam selection strategies, combining sparse Bayesian learning and Kalman filtering to track channel changes and achieve fast beam alignment. However, eVTOL users cannot afford such a large computational overhead for beam pointing. Beam widening schemes, on the other hand, reduce the impact of beam offset through beamforming optimization algorithms. For instance, the paper "W. Chen, et al., Adaptive Hybrid Beamforming for UAV mmWave Communications against Asymmetric Jitter. IEEE Transactions on Wireless Communications, early access" models the attitude changes of a large-scale uniform planar array caused by UAV jitter and designs a robust hybrid beamforming based on this model. The paper "W. Chen, et al., Adaptive Hybrid Beamforming for UAV mmWave Communications against Asymmetric Jitter. IEEE Transactions on Wireless Communications, early access" proposes an adaptive beamwidth control scheme for UAV millimeter-wave communication systems. Based on modeling the relationship between beamwidth and antenna gain, it calculates the optimal beamwidth for the system's maximum average transmission rate. While robust beamforming schemes are more suitable for eVTOL systems with low computational power, the aforementioned studies are all based on the assumption of unidirectional Gaussian random jitter, which is difficult to adapt to multi-directional random jitter caused by low airflow. Furthermore, these works simply extend the elliptical beam angle to match the irregular distribution of mechanical jitter. This coarse matching using a "minimum circumscribed ellipse" approach, while completely covering the jitter region, leads to significant redundancy in the signal radiation space and a severe decrease in beam directivity.

[0004] The beamforming technique inevitably leads to a decrease in beam gain, resulting in a deterioration in the signal-to-noise ratio (SNR) of the link. Therefore, it is necessary to increase the transmit power to ensure the receive SNR. However, existing beamforming research typically ignores the finite linear amplification range of the amplifiers at the array elements, and the nonlinear distortion of the devices gradually worsens with increasing operating frequency. Existing research considers the maximum power constraint at each array element and jointly optimizes the selection of the transmit beamformer and array elements to avoid nonlinear distortion in the power amplifier. However, the beamforming vector and waveform pattern are correlated through Fourier transform, and their power distribution exhibits regularity. Existing work directly searches the entire beamforming vector space, ignoring the regularity of the array power distribution, leading to high computational complexity.

[0005] In the face of airflow effects, real-time jitter detection for beam tracking control leads to significant terminal computational overhead. Existing beamwidth studies make overly simplistic assumptions about jitter, only considering a unidirectional Gaussian distribution, which fails to reflect the stochastic, multidirectional nature of jitter under turbulent conditions. Matching the beam projection shape to multidirectional jitter and balancing antenna gain with beam range require further investigation. To mitigate the gain reduction caused by beamwidth, increasing transmit power is necessary. However, the array suffers from amplifier nonlinear distortion, a factor that needs to be incorporated into the beamforming design. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides an anti-interference beamforming control method for low-altitude aircraft, which achieves reliable communication resistant to airflow disturbances through three-dimensional jitter modeling, beam angle optimization, irregular beam synthesis, and virtual subarray mapping.

[0007] The technical solution adopted in this invention is: an anti-interference beamforming control method for low-altitude aircraft, the specific steps of which are as follows:

[0008] S1. Collect three-dimensional attitude jitter data of low-altitude aircraft through sensors, establish a Gaussian mixture model of three-dimensional jitter, and realize the conversion of attitude angle to beam angle;

[0009] First, sensors onboard the low-altitude aircraft acquire three-dimensional attitude jitter data (pitch, roll, yaw), and statistically analyze the distribution characteristics of random beam shift. Then, based on the Jacobian matrix... Achieve attitude angle To beam angle The conversion, approximating the beam angle through a first-order Taylor expansion, is expressed as follows:

[0010] ;

[0011] in, This represents the average attitude angle. This represents the attitude angle deviation, and , , .

[0012] Then, a Gaussian mixture model of three-dimensional jitter is established. .

[0013] Among them, the mean vector covariance matrix , Let represent the variance of the three-dimensional attitude jitter, respectively. This indicates the transpose operation.

[0014] S2. Based on the antenna array response model, construct the channel capacity optimization problem and solve for the optimal irregular beam angle distribution range under jitter.

[0015] S3. Divide the optimal beam angle distribution range into sub-beams, determine the number of array elements and shaping vector of the sub-beams, and realize irregular multi-beamforming.

[0016] S4. By solving the beam power allocation through convex optimization and combining it with the virtual subarray mapping algorithm based on beam power sorting, physical element power equalization and distortion-free beamforming are achieved.

[0017] Based on the power distribution characteristics of array elements and the condition that the sub-beam centers do not coincide, the convex optimization solution to the beam power allocation problem is decomposed into beam power allocation and virtual sub-array mapping.

[0018] The power distribution characteristics of the array elements, i.e., the scale, are... The array, with the maximum power element located at The condition that the sub-beam centers do not coincide is when At that time, the virtual subarray centers of each subbeam in the optimal shaping vector do not coincide.

[0019] in, These represent the number of array elements along the x-axis and y-axis, respectively. This indicates a constraint on the upper limit of total transmit power. This represents the upper limit constraint on the power of a single array element. This indicates the number of elliptical sub-beams after sub-beam division in step S3.

[0020] Furthermore, step S2 is specifically as follows:

[0021] S21. Define the antenna array response model;

[0022] Based on beam angle The response vector of the antenna array in the x-axis and y-axis directions is constructed in the form of the Kronecker product, as shown in the following expression:

[0023] ;

[0024] in, These represent the number of array elements along the x-axis and y-axis, respectively. Indicates the spacing between array elements. Representing the carrier wavelength, similarly... . This represents the Kronecker product operation.

[0025] S22. Based on step S21, construct the channel capacity optimization target;

[0026] Combining path loss and transmit power Beam pointing probability and beam gain The ideal antenna model is expressed as follows:

[0027] ;

[0028] in, Indicates the base station beam gain. Indicates the beam gain of the aircraft; This indicates the range of irregular beam angle distributions corresponding to the maximum channel capacity.

[0029] Then, the channel capacity is expressed as a function of the beam angle range. The expression is as follows:

[0030] ;

[0031] in, This represents path loss. This represents Gaussian white noise in the channel.

[0032] S23. Based on step S21, solve for the optimal irregular beam angle distribution range under jitter.

[0033] A constrained optimization problem is constructed, with the constraint that the beam angle distribution range is not less than the array beam resolution. By solving the problem, the irregular beam angle distribution range corresponding to the maximum channel capacity is obtained. The expression is as follows:

[0034] ;

[0035] The constraint condition states that the minimum beam angle should not be less than the array beam angle at which the minimum beam angle is within the range of the array beam. and directional resolution and Then, the range of irregular beam angle distribution corresponding to the maximum channel capacity is obtained by solving the problem using a numerical iteration method.

[0036] Furthermore, step S3 is specifically as follows:

[0037] S31. Define multibeamforming modes;

[0038] The multibeamforming modes include:

[0039] (1) Array power domain multiplexing: All beams use all physical array elements;

[0040] (2) Orthogonal subarray: The physical array is divided into orthogonal virtual subarrays, each subarray corresponds to a sub-beam, and the virtual subarray and the physical array are dynamically mapped.

[0041] S32. Based on step S31, perform sub-beam division and geometric feature extraction;

[0042] First, the optimal beam angle distribution range is determined. Perform curvature analysis to extract geometric features, including convexity, concavity, and boundary curvature. Then, decompose the extracted features into... An elliptical sub-beam is defined, and the sub-beams are further defined. The parameters include: two-dimensional angles Central position .

[0043] S33. Based on step S32, establish the sub-beam optimization objective and determine the number of sub-beam array elements and the shaping vector.

[0044] Establish a sub-beam optimization objective, namely, coverage integrity. , overlap rate To constrain and minimize beam approximation error The expression is as follows:

[0045] ;

[0046] in, This indicates the minimum threshold for the coverage ratio of the target area. . This indicates a binary variable for sub-beam selection. Indicates the coverage area of ​​the sub-beam. Indicates the total area. This represents the area function of the region beyond the specified area. This represents the regularization parameter.

[0047] Channel capacity Approximately expressed as The expression is as follows:

[0048] ;

[0049] in, Indicates the first The power of each sub-beam Indicates the first Gain of individual beams This indicates the beam gain of the aircraft.

[0050] S34. Based on step S33, determine the shaping vectors of each sub-beamforming vector to achieve irregular multi-beamforming.

[0051] Based on the sub-beamwidth and pointing angle, the virtual sub-array size corresponding to each sub-beam is determined, and any beamforming scheme can satisfy the following conditions. , This indicates the level of sidelobe inhibition.

[0052] Furthermore, step S4 is specifically as follows:

[0053] S41. Solve beam power allocation using convex optimization;

[0054] First, an optimization problem model is performed. With the virtual subarray mapping relationship fixed, the goal is to maximize channel capacity, and a total transmit power upper limit constraint is set as follows: The upper limit of power for a single array element is constrained to be Construct optimization problem The expression is as follows:

[0055] ;

[0056] in, This indicates the power allocated to each beam. Indicates the i-th sub-beam in the physical array element ( The weight at point ).

[0057] Then, Lagrangian transformation and convex optimization are performed, introducing the signal-to-noise ratio variable. ,Will Convert to contain To solve the optimization problem, auxiliary variables are introduced. ,Will Transform into a convex optimization problem The expression is as follows:

[0058] ;

[0059] in, This represents the equivalent gain of the i-th sub-beam. Represents the real number field.

[0060] Then, taking the derivative yields the optimal solution for the auxiliary variable. The expression is as follows:

[0061] ;

[0062] Finally, the convex optimization problem will be addressed. Transform into a standard convex optimization problem The optimal beam power is obtained by solving the problem using the interior point method. And update alternately. and solving The process continues until the difference between two consecutive power allocations is less than a preset convergence threshold. After convergence, the optimal beam power allocation is output. .

[0063] S42. Combine the virtual subarray mapping algorithm based on beam power sorting to achieve physical array element power equalization and distortion-free beamforming.

[0064] First, we model the mapping problem, which aims to minimize the maximum power of the physical array elements while constraining the center of the virtual subarray to be located in a legal region. The optimization problem is then constructed as follows:

[0065] ;

[0066] in, This represents the center coordinates of the i-th virtual subarray. This indicates the size of the virtual subarray along the x / y axis.

[0067] Then, the optimization problem is solved using a virtual subarray mapping algorithm based on beam power sorting, as follows:

[0068] (1) Initialization: Input the optimal beam power allocation Sub-beam size , forming vector Initialize the physical array element shaping vector record Mapping Relationship Table ;

[0069] (2) Beam sorting: according to Arrange the beams in descending order to obtain the sorting index { And the maximum power beam is mapped first;

[0070] (3) Calculate the legal region: for each beam Calculate the legal region at the center of the virtual subarray. ,in, , ;

[0071] (4) Maximum power beam mapping: Map the first ranked beam Mapped to its legal region center ,renew and utilize its corresponding forming vector renew , = ;

[0072] (5) Other beam orthogonal avoidance processing: For the remaining beams Based on the orthogonality condition, sub-regions orthogonal to the mapped beam are selected from the legal regions. Ensure that the weight of the new beam is 0 at the maximum power point of the already mapped beam;

[0073] The orthogonality condition is: if and only if the array center point position ( , )satisfy or hour, , Represents any integer, [ , ] indicates beam The sampling result is a two-dimensional index of the center position of the sampling point, where the sampling result is 1. Beam The forming vector in the array element The value at that location is .

[0074] (6) Power verification and update: for each candidate center Calculate the maximum power of the physical array element after loading the shaping vector, and select the element with the maximum power that satisfies the following conditions. The center is used as the optimal mapping, and the update is performed. and ;

[0075] (7) Iteration Termination: After all beam mappings are completed, the final physical element shaping vector is output. .

[0076] The beneficial effects of this invention are as follows: This invention discloses an anti-interference beamforming control method for low-altitude aircraft. First, it optimizes the optimal beam angle range by establishing a three-dimensional attitude-differential jitter model, achieving a coordinated balance between beam alignment probability and antenna gain. Then, it constructs an irregular multi-beamforming scheme to accurately match multi-directional jitter distribution, reducing signal radiation redundancy. Finally, it designs a virtual subarray dynamic mapping mechanism, combining array power distribution patterns to reduce computational complexity and avoid nonlinear distortion and beam distortion caused by uneven array element power load. This invention's method combines excellent resistance to airflow disturbances, low computational overhead, and engineering feasibility, making it suitable for high-reliability communication scenarios for low-altitude aircraft such as flying cars and drones. It solves the technical problem of beam offset and channel capacity reduction caused by low-altitude airflow affecting low-altitude aircraft (such as flying cars).

[0077] This invention's method, for the first time, considers the differentiated jitter characteristics of an aircraft's three-dimensional attitude under airflow disturbances. It establishes a Gaussian mixture model of pitch, roll, and yaw jitter, jointly optimizing beam alignment probability and antenna gain to construct the optimal beam angle range that maximizes channel capacity. Furthermore, it employs a multi-beam synthesis scheme to match irregular jitter distribution ranges, replacing existing beam widening schemes. This improves beam gain while covering jitter areas, avoiding power waste. The proposed low-computational-complexity dynamic mapping scheme between virtual subarrays and physical arrays achieves element power balance through beam-level power optimization and element-level mapping iteration, avoiding beam pattern distortion caused by nonlinear distortion. Attached Figure Description

[0078] Figure 1 This is a flowchart of an anti-interference beamforming control method for low-altitude aircraft according to the present invention.

[0079] Figure 2 This is a schematic diagram of beam offset matching control in an embodiment of the present invention.

[0080] Figure 3 This is a flowchart of the virtual subarray mapping algorithm in an embodiment of the present invention.

[0081] Figure 4 This is a comparison diagram of array element power distribution and beam distortion in an embodiment of the present invention. Detailed Implementation

[0082] The method of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0083] like Figure 1 The flowchart of an anti-interference beamforming control method for low-altitude aircraft according to the present invention is shown below, and the specific steps are as follows:

[0084] S1. Collect three-dimensional attitude jitter data of low-altitude aircraft through sensors, establish a Gaussian mixture model of three-dimensional jitter, and realize the conversion of attitude angle to beam angle;

[0085] The directional narrow beam communication scenario applied in this embodiment is: a drone (transmitter, equipped with an array antenna) and a base station (receiver, at a fixed position) are transmitting high-definition images in a directional manner. The drone has slight attitude sway (causing beam alignment deviation).

[0086] First, the aircraft's pitch, roll, and yaw three-dimensional attitude jitter data are acquired using sensors mounted on the low-altitude aircraft. In this embodiment, a gyroscope is used to collect the jitter data, and the three-dimensional jitter variance is statistically obtained. Then, the distribution characteristics of the random beam offset are statistically analyzed. Finally, based on the Jacobian matrix... Achieve attitude angle To beam angle The conversion, approximating the beam angle through a first-order Taylor expansion, is expressed as follows:

[0087] ;

[0088] in, This represents the average attitude angle. Attitude angle deviation, and , , .

[0089] Then, a Gaussian mixture model of three-dimensional jitter is established. .

[0090] Among them, the mean vector covariance matrix , Let represent the variance of the three-dimensional attitude jitter, respectively. This indicates the transpose operation.

[0091] S2. Based on the antenna array response model, construct the channel capacity optimization problem and solve for the optimal irregular beam angle distribution range under jitter.

[0092] The array beam resolution is determined by the number of array elements and the carrier wavelength, and needs to be set reasonably according to the frequency resources of the actual communication scenario. .

[0093] S3, such as Figure 2 As shown, the optimal beam angle distribution range is divided into sub-beams, the number of array elements and the shaping vector of the sub-beams are determined, and irregular multi-beamforming is realized.

[0094] Figure 2 This demonstrates the array element power distribution under different offsets, and the final formation of the optimal irregular matched beam. Figure 2 In case (a), the offset direction is relatively concentrated, and coverage can be achieved by increasing the sub-beam width. Figure 2 In case (b), the offset directions are mainly concentrated in three directions around the origin. In this case, it is necessary to generate a narrower sub-beam to cover these three directions. This can be achieved by dividing the power of the array elements into three equal parts and having all array elements participate in the sub-beam formation in each direction, ultimately synthesizing a sub-beam with three directions. Figure 2 (c) In this case, the offset direction is the same as... Figure 2 (b) is the same, but the distribution is more dispersed, so a wider sub-beam can be used and divided according to array elements. Figure 2 In case (d), when the sub-beamwidth requirements are different, they can be mixed and divided according to power and array elements.

[0095] S4. By solving the beam power allocation through convex optimization and combining it with the virtual subarray mapping algorithm based on beam power sorting, physical element power equalization and distortion-free beamforming are achieved.

[0096] Based on the element power distribution characteristics and the condition that sub-beam centers do not coincide, the convex optimization problem of beam power allocation is decomposed into beam power allocation and virtual sub-array mapping. (Setting...) These represent the number of array elements along the x-axis and y-axis, respectively. This indicates a constraint on the upper limit of total transmit power. This represents the upper limit constraint on the power of a single array element. This indicates the number of elliptical sub-beams after sub-beam division in step S3.

[0097] The power distribution characteristics of the array elements, i.e., the scale, are... The array, with the maximum power element located at The details are as follows:

[0098] This embodiment employs a separable beamforming scheme, in which the beam... The weight components at the array element are represented as follows: Then analyze them independently. direction and Beamforming vector in the direction, Ideal waveform in direction Using a rectangular window format, the expression is as follows:

[0099] ;

[0100] in, Indicates the beam angle distribution range. Beamforming vector. With response function By constructing a Fourier transform pair, we can obtain the following expression:

[0101] ;

[0102] Therefore, the power expression can be obtained as follows:

[0103] ;

[0104] in, This indicates the conjugate transpose. .right The first derivative with respect to the array position, set to 0, is expressed as follows:

[0105] ;

[0106] Solving for the array elements yields the array elements. The power carried by the upper part is expressed as follows:

[0107]

[0108] because The point of maximum power is located at Location. Combined with sampling function. As can be seen from the form, the power on both sides of this point gradually decreases in a fluctuating manner. Similarly, it can be proven that... The point where the power is at its maximum in the direction is located Place.

[0109] The condition that the sub-beam centers do not coincide is when At this time, the virtual subarray centers of each subbeam in the optimal shaping vector do not coincide, as follows:

[0110] beam The gain is approximately expressed as the beam. Activated aperture size The function, with the following expression:

[0111] ;

[0112] in, Indicates beam exist The number of active array elements in the direction, This indicates the element spacing. If the main lobe-to-side lobe gain ratio SL is set to a fixed value, then the beam... Gain The expression is as follows:

[0113] ;

[0114] The centers of each beam virtual subarray coincide. According to Theorem 1, the tight boundary of the power constraint appears at the center position, and it is easy to prove the channel capacity. Since it is a monotonically increasing function, all elements must be used for each beam to maximize gain. Assume... Let the optimal solution be defined as follows: (The solution is missing from the original text.) The expression is as follows:

[0115] ;

[0116] Orthogonal partitioning of each beam virtual subarray considering the original problem The optimal solution, combined with the minimum distance constraint, yields the optimal power of each beam, which can be expressed as: Assume the array can be divided into There are 1 orthogonal subarrays (each element serves only one beam), and the virtual array size is 1. Then the optimal solution to the original problem The condition expression is as follows:

[0117] ;

[0118] Obviously, when (Right now When ), there are .

[0119] In this embodiment, step S2 is specifically as follows:

[0120] S21. Define the antenna array response model;

[0121] Based on beam angle The response vector of the antenna array in the x-axis and y-axis directions is constructed in the form of the Kronecker product, as shown in the following expression:

[0122] ;

[0123] in, These represent the number of array elements along the x-axis and y-axis, respectively. Indicates the spacing between array elements. Representing the carrier wavelength, similarly, we can obtain... . This represents the Kronecker product operation.

[0124] S22. Based on step S21, construct the channel capacity optimization target;

[0125] Combining path loss and transmit power Beam pointing probability and beam gain The ideal antenna model is expressed as follows:

[0126] ;

[0127] in, Indicates the base station beam gain. Indicates the beam gain of the aircraft; This indicates the range of irregular beam angle distributions corresponding to the maximum channel capacity.

[0128] Then, the channel capacity is expressed as a function of the beam angle range. The expression is as follows:

[0129] R ;

[0130] in, This represents path loss. This represents Gaussian white noise in the channel.

[0131] S23. Based on step S21, solve for the optimal irregular beam angle distribution range under jitter.

[0132] A constrained optimization problem is constructed, with the constraint that the beam angle distribution range is not less than the array beam resolution. By solving the optimization problem, the irregular beam angle distribution range corresponding to the maximum channel capacity is obtained. The expression is as follows:

[0133] ;

[0134] The constraint condition states that the minimum beam angle should not be less than the array beam angle at which the minimum beam angle is within the range of the array beam. and directional resolution and This embodiment uses Matlab numerical iteration to obtain the range of irregular beam angle distributions corresponding to the maximum channel capacity.

[0135] In this embodiment, step S3 is specifically as follows:

[0136] S31. Define multibeamforming modes;

[0137] Multibeamforming is essentially a combination and superposition of single-beamforming vectors. Therefore, the multibeamforming modes include:

[0138] (1) Array power domain reuse: All beams use all physical array elements, and power superposition can easily lead to array element overload;

[0139] (2) Orthogonal subarray: The physical array is divided into orthogonal virtual subarrays, each subarray corresponds to a sub-beam, and the dynamic mapping between the virtual subarray (single-beam activated array element set) and the physical array must be satisfied.

[0140] S32. Based on step S31, perform sub-beam division and geometric feature extraction;

[0141] First, the optimal beam angle distribution range is determined. Perform curvature analysis to extract geometric features, including convexity, concavity, and boundary curvature. Then, decompose the extracted features into... An elliptical sub-beam is defined, and the sub-beams are further defined. The parameters include: two-dimensional angles Central position (Overlap area of ​​two sub-beams / Total area).

[0142] S33. Based on step S32, establish the sub-beam optimization objective and determine the number of sub-beam array elements and the shaping vector.

[0143] Establish a sub-beam optimization objective, namely, coverage integrity. , overlap rate To constrain and minimize beam approximation error The expression is as follows:

[0144] ;

[0145] in, This represents the minimum coverage threshold for the target area. In this embodiment... ; . This indicates the sub-beam selection binary variable (1 indicates selected). Indicates the coverage area of ​​the sub-beam. Indicates the total area. This represents the area function of the region beyond the specified area. This represents the regularization parameter (which controls the number of sub-beams).

[0146] Channel capacity Approximately expressed as The expression is as follows:

[0147] ;

[0148] in, Indicates the first The power of each sub-beam Indicates the first Gain of individual beams This indicates the beam gain of the aircraft.

[0149] S34. Based on step S33, determine the shaping vectors of each sub-beamforming vector to achieve irregular multi-beamforming.

[0150] Based on the sub-beamwidth and pointing angle, the virtual sub-array size corresponding to each sub-beam is determined, and any beamforming scheme must meet the following requirements. , This indicates the level of sidelobe inhibition. (Sidelobe inhibition level) It can be adjusted according to the interference intensity; the stronger the interference, the better. The larger the setting (e.g., 30dB), the more important it is to balance the number of array elements. The larger, The larger (the larger).

[0151] In this embodiment, assuming a uniform array, the positive pointing angle of the main lobe beam is approximately assumed to be as follows:

[0152] ;

[0153] Therefore, based on the target coverage angle range Calculate the number of array elements required for the subarray.

[0154] Similarly, this embodiment employs Bisherff synthesis to achieve minimum sidelobe gain with a fixed main lobe width, adapting to the requirement of "full main lobe interference suppression": based on sub-beams beamwidth ( , ), pointing angle ( And the sidelobe suppression level SL, the number of array elements required for the sub-beam is derived through Chebyshev synthesis, for The direction (corresponding to the X direction of the array) is expressed as follows:

[0155] ;

[0156] Calculation of single beamforming vectors based on Chebyshev polynomials To ensure the main lobe covers the sub-beam region, and the side lobe gain... .

[0157] In this embodiment, step S4 is specifically as follows:

[0158] S41. Solve beam power allocation using convex optimization;

[0159] Convex optimization solutions can be obtained by calling the "cvx_solve" function from the Matlab CVX toolbox. This method offers fast convergence and meets real-time requirements.

[0160] First, an optimization problem model is performed. With the virtual subarray mapping relationship fixed, the goal is to maximize channel capacity, and a total transmit power upper limit constraint is set as follows: The upper limit of power for a single array element is constrained to be (i.e., the linear distortion threshold), construct the optimization problem The expression is as follows:

[0161] ;

[0162] in, This indicates the power allocated to each beam. Indicates the i-th sub-beam in the physical array element ( The weight at point ).

[0163] Then, Lagrangian transformation and convex optimization are performed, introducing the signal-to-noise ratio variable. ,Will Convert to contain The optimization problem involves introducing auxiliary variables. ,Will Transform into a convex optimization problem The expression is as follows:

[0164] ;

[0165] in, This represents the equivalent gain of the i-th sub-beam. Represents the real number field.

[0166] Then, taking the derivative yields the optimal solution for the auxiliary variable. The expression is as follows:

[0167] ;

[0168] Finally, the convex optimization problem will be addressed. Transform into a standard convex optimization problem The optimal beam power is obtained by solving the problem using the interior point method. And update alternately. and solving The process continues until the difference between two consecutive power allocations is less than a preset convergence threshold. After convergence, the optimal beam power allocation is output. .

[0169] S42. Combine the virtual subarray mapping algorithm based on beam power sorting to achieve physical array element power equalization and distortion-free beamforming.

[0170] First, we model the mapping problem, which aims to minimize the maximum power of the physical array elements while constraining the center of the virtual subarray to be located in a legal region (avoiding element boundaries). The optimization problem is then constructed as follows:

[0171] ;

[0172] in, This represents the center coordinates of the i-th virtual subarray. This indicates the size of the virtual subarray along the x / y axis.

[0173] Then as Figure 3 As shown, the virtual subarray mapping algorithm based on beam power sorting solves the optimization problem as follows:

[0174] (1) Initialization: Input the optimal beam power allocation Sub-beam size , forming vector Initialize the physical array element shaping vector record Mapping Relationship Table ;

[0175] (2) Beam sorting: according to Arrange the beams in descending order to obtain the sorting index { And the maximum power beam is mapped first;

[0176] (3) Calculate the legal region: for each beam Calculate the legal region at the center of the virtual subarray. ,in, , ;

[0177] (4) Maximum power beam mapping: Map the first ranked beam Mapped to its legal region center ,renew and utilize its corresponding forming vector renew , ( ),:,:)= (Update the physical array element weight record table);

[0178] (5) Other beam orthogonal avoidance processing: For the remaining beams Based on the orthogonality condition, sub-regions orthogonal to the mapped beam are selected from the legal regions. Ensure that the weight of the new beam is 0 at the maximum power point of the already mapped beam;

[0179] The orthogonality conditions are as follows:

[0180] If and only if the array center point is located ( , )satisfy or hour, .

[0181] in, Represents any integer, [ , ] indicates based on A uniform sampling point (the number of sampling points equals the array size), beam The sampling result is a two-dimensional index of the center position of the sampling point, where the sampling result is 1. Beam The forming vector in the array element The value at that location is .

[0182] Since the ideal beam takes a value of 1 within the target direction range and a value of 0 in other ranges, the beam can be... The region where the sampling result is 1 is defined as ,in and Represents an ideal beam exist direction and The number of sampling points with a value of 1 in the direction. Based on this, the beam... exist weight at the point The derivation process is expressed as follows:

[0183] ;

[0184] in, , .

[0185] when For a condition to be true, the denominator must be non-zero (otherwise the weights would be meaningless), therefore the following condition must be met:

[0186] ;

[0187] The condition that the weight is zero is equivalent to the numerator being zero. We will discuss two cases:

[0188] Case 1: The first part of the molecule is zero.

[0189] ;

[0190] Case 2: The second part of the molecule is zero:

[0191] ;

[0192] because ,when The denominator of the time fraction is never zero. Furthermore, because... Since the number is rational, case 1 is clearly not true.

[0193] For case 2: when When, the equation naturally holds true; when When rearranged, the expression can be obtained as follows:

[0194] ;

[0195] The same derivation applies to the Y direction. Following the same derivation of the condition that the numerator of the direction weight is zero, we can obtain the following expression:

[0196] ;

[0197] (6) Power verification and update: for each candidate center Calculate the maximum power of the physical array element after loading the shaping vector, and select the element with the maximum power that satisfies the following conditions. The center is used as the optimal mapping, and the update is performed. and ;

[0198] (7) Iteration Termination: After all beam mappings are completed, the final physical element shaping vector is output. (i.e., multibeamforming vector).

[0199] In this embodiment, the element power distribution-beam distortion pair is as follows: Figure 4As shown, the power distribution under two methods (virtual subarray mapping method and array full reuse method) and the degree of distortion compared to the ideal waveform are compared, illustrating the effectiveness of the method of the present invention in resisting nonlinear distortion.

[0200] In summary, the method of this invention has strong resistance to airflow disturbances. Through three-dimensional differentiated jitter modeling and optimal beam angle optimization, the beam alignment probability is improved compared to existing solutions, effectively suppressing beam drift caused by low airflow. Furthermore, the method of this invention decomposes the high-dimensional optimization problem into three sub-problems, and the computational complexity of the convex optimization solution and mapping algorithm is O(n log n). It can run in real time on an embedded platform of an aircraft, with low complexity and engineering feasibility; at the same time, the orthogonal avoidance mechanism of the virtual subarray ensures that the maximum power of the array elements is ≤ The beam pattern distortion rate caused by nonlinear distortion is reduced, and it has the advantages of distortion-free operation and power balance. It supports various low-altitude aircraft such as flying cars and drones, and can adapt to different airflow turbulence intensities without modifying the core algorithm (by adjusting SL and ).

[0201] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. An anti-interference beamforming control method for low-altitude aircraft, comprising the following steps: S1. Collect three-dimensional attitude jitter data of low-altitude aircraft through sensors, establish a Gaussian mixture model of three-dimensional jitter, and realize the conversion of attitude angle to beam angle; First, the three-dimensional attitude jitter data of the fuselage pitch, roll, and yaw are acquired using sensors mounted on the low-altitude aircraft, and the distribution characteristics of random beam offset are statistically analyzed; then, based on the Jacobian matrix... Achieve attitude angle to beam angle The conversion, approximating the beam angle through a first-order Taylor expansion, is expressed as follows: ； in, This represents the average attitude angle. This represents the attitude angle deviation, and , , ; Then, a Gaussian mixture model of three-dimensional jitter is established. ; Among them, the mean vector covariance matrix , Let represent the variance of the three-dimensional attitude jitter, respectively. Indicates the transpose operation; S2. Based on the antenna array response model, construct the channel capacity optimization problem and solve for the optimal irregular beam angle distribution range under jitter. S3. Divide the optimal beam angle distribution range into sub-beams, determine the number of array elements and shaping vector of the sub-beams, and realize irregular multi-beamforming. S4. By solving the beam power allocation through convex optimization and combining it with the virtual subarray mapping algorithm based on beam power sorting, physical element power equalization and distortion-free beamforming are achieved. Based on the power distribution characteristics of array elements and the condition that the sub-beam centers do not coincide, the convex optimization solution of the beam power allocation problem is decomposed into beam power allocation and virtual sub-array mapping. The power distribution characteristics of the array elements, i.e., the scale, are... The array, with the maximum power element located at The condition that the sub-beam centers do not coincide is when At that time, the virtual subarray centers of each subbeam in the optimal shaping vector do not coincide; in, These represent the number of array elements along the x-axis and y-axis, respectively. This indicates a constraint on the upper limit of total transmit power. This represents the upper limit constraint on the power of a single array element. This indicates the number of elliptical sub-beams after sub-beam division in step S3.

2. The anti-interference beamforming control method for low-altitude aircraft according to claim 1, characterized in that, Step S2 is as follows: S21. Define the antenna array response model; Based on beam angle The response vector of the antenna array in the x-axis and y-axis directions is constructed in the form of the Kronecker product, as shown in the following expression: ； in, These represent the number of array elements along the x-axis and y-axis, respectively. Indicates the spacing between array elements. Representing the carrier wavelength, similarly... This represents the Kronecker product operation; S22. Based on step S21, construct the channel capacity optimization target; Combining path loss and transmit power Beam pointing probability and beam gain The ideal antenna model is expressed as follows: ； in, Indicates the base station beam gain. Indicates the beam gain of the aircraft; This represents the range of irregular beam angle distributions corresponding to the maximum channel capacity; Then, the channel capacity is expressed as a function of the beam angle range. The expression is as follows: ； in, Indicates path loss; This represents Gaussian white noise in the channel; S23. Based on step S21, solve for the optimal irregular beam angle distribution range under jitter. A constrained optimization problem is constructed, with the constraint that the beam angle distribution range is not less than the array beam resolution. By solving the problem, the irregular beam angle distribution range corresponding to the maximum channel capacity is obtained. The expression is as follows: ； The constraint condition states that the minimum beam angle should not be less than the array beam angle at which the minimum beam angle is within the range of the array beam. and directional resolution and Then, the range of irregular beam angle distribution corresponding to the maximum channel capacity is obtained by solving the numerical iteration method.

3. The anti-interference beamforming control method for low-altitude aircraft according to claim 2, characterized in that, Step S3 is as follows: S31. Define multibeamforming modes; The multibeamforming modes include: (1) Array power domain multiplexing: All beams use all physical array elements; (2) Orthogonal subarray: The physical array is divided into orthogonal virtual subarrays, each subarray corresponds to a sub-beam, and the dynamic mapping between the virtual subarray and the physical array is satisfied; S32. Based on step S31, perform sub-beam division and geometric feature extraction; First, the optimal beam angle distribution range is determined. Perform curvature analysis to extract geometric features, including convexity, concavity, and boundary curvature. Then, decompose the extracted features into... An elliptical sub-beam is defined, and the sub-beams are further defined. The parameters include: two-dimensional angles Central position ; S33. Based on step S32, establish the sub-beam optimization objective and determine the number of sub-beam array elements and the shaping vector. Establish a sub-beam optimization objective, namely, coverage integrity. , overlap rate To constrain and minimize beam approximation error The expression is as follows: ； in, This indicates the minimum threshold for the coverage ratio of the target area. This indicates a binary variable for sub-beam selection. Indicates the coverage area of ​​the sub-beam. Indicates the total area. This represents the area function beyond the region. Represents the regularization parameter; Channel capacity Approximately expressed as The expression is as follows: ； in, Indicates the first The power of each sub-beam Indicates the first Gain of individual beams Indicates the beam gain of the aircraft; S34. Based on step S33, determine the shaping vectors of each sub-beamforming vector to achieve irregular multi-beamforming. Based on the sub-beamwidth and pointing angle, the virtual sub-array size corresponding to each sub-beam is determined, and any beamforming scheme can satisfy the following conditions. , This indicates the level of sidelobe inhibition.

4. The anti-interference beamforming control method for low-altitude aircraft according to claim 3, characterized in that, Step S4 is as follows: S41. Solve beam power allocation using convex optimization; First, an optimization problem model is performed. With the virtual subarray mapping relationship fixed, the goal is to maximize channel capacity, and a total transmit power upper limit constraint is set as follows: The upper limit of power for a single array element is constrained to be Construct optimization problem The expression is as follows: ； in, This indicates the power allocated to each beam. Indicates the i-th sub-beam in the physical array element ( The weight at point ); Then, Lagrangian transformation and convex optimization are performed, introducing the signal-to-noise ratio variable. ,Will Convert to contain To solve the optimization problem, auxiliary variables are introduced. ,Will Transform into a convex optimization problem The expression is as follows: ； in, This represents the equivalent gain of the i-th sub-beam. Represents the real number field; Then, taking the derivative yields the optimal solution for the auxiliary variable. The expression is as follows: ； Finally, the convex optimization problem will be addressed. Transform into a standard convex optimization problem The optimal beam power is obtained by solving the problem using the interior point method. And update alternately. and solving The process continues until the difference between two consecutive power allocations is less than a preset convergence threshold. After convergence, the optimal beam power allocation is output. ; S42. Combine the virtual subarray mapping algorithm based on beam power sorting to achieve physical array element power equalization and distortion-free beamforming. First, we model the mapping problem, which aims to minimize the maximum power of the physical array elements while constraining the center of the virtual subarray to be located in a legal region. The optimization problem is then constructed as follows: ； in, This represents the center coordinates of the i-th virtual subarray. Indicates the size of the virtual subarray along the x / y axis; Then, the optimization problem is solved using a virtual subarray mapping algorithm based on beam power sorting, as follows: (1) Initialization: Input the optimal beam power allocation Sub-beam size , forming vector Initialize the physical array element shaping vector record Mapping Relationship Table ; (2) Beam sorting: according to Arrange the beams in descending order to obtain the sorting index { And the maximum power beam is mapped first; (3) Calculate the legal region: for each beam Calculate the legal region at the center of the virtual subarray. ,in, , ; (4) Maximum power beam mapping: Map the first ranked beam Mapped to its legal region center ,renew and utilize its corresponding forming vector renew , = ; (5) Other beam orthogonal avoidance processing: For the remaining beams Based on the orthogonality condition, sub-regions orthogonal to the mapped beam are selected from the legal regions. Ensure that the weight of the new beam is 0 at the maximum power point of the already mapped beam; The orthogonality condition is: if and only if the array center point position ( , )satisfy or hour, , Represents any integer, [ , ] indicates beam The sampling result is a two-dimensional index of the center position of the sampling point of 1; beam The forming vector in the array element The value at that location is ; (6) Power verification and update: for each candidate center Calculate the maximum power of the physical array element after loading the shaping vector, and select the element with the maximum power that satisfies the following conditions. The center is used as the optimal mapping, and the update is performed. and ; (7) Iteration Termination: After all beam mappings are completed, the final physical element shaping vector is output. .

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