An anti-unmanned aerial vehicle radar beamforming method based on hybrid fundamental beam synthesis

Abstract

The application discloses a kind of based on hybrid base beam synthesis anti-UAV radar beam shaping methods, for each beam pointing only from each base beam group corresponding pointing base beam selects one base beam to participate in shaping, and the corresponding pointing base beam of other base beam group of this pointing is closed use, in the process of shaping, for the beam selection of the center part of shaping interval, fast attenuation base beam is shaped, for the beam selection of the two side parts except the center part in shaping interval, Taylor base beam is shaped, then each beam pointing base beam linearly weighted summation of the base beam participating in shaping is obtained The final synthesis directivity diagram;The application solves the problem that the beam shaping solution of anti-UAV radar is complex, precision is difficult to control, and sidelobe suppression is difficult.

Description

Technical Field

[0001] This invention belongs to the field of anti-drone radar waveform optimization design technology, and relates to an anti-drone radar beamforming method based on hybrid base beam synthesis. Background Technology

[0002] Anti-drone radar is commonly used to detect and track aerial targets such as drones. Therefore, it features a relatively unique and complex beam, typically consisting of a flat-top region and a cosecant fourth region. Within the flat-top region, the radar has a uniform transmit power to achieve uniform power search for the target. Within the cosecant fourth region, the radar has a transmit power that varies with angle according to a cosecant fourth curve, ensuring that the radar can track the target with uniform power as it approaches. However, the complex beam increases the difficulty of beamforming and sidelobe suppression.

[0003] Radar beamforming is essentially a complex optimization problem with high precision requirements. Solving this optimization problem typically falls into three categories: solving only the amplitude, solving only the phase, and solving both amplitude and phase. The first two methods sacrifice accuracy to reduce complexity, while the last method trades greater algorithmic complexity for higher accuracy. To address the trade-off between accuracy and complexity, many researchers have achieved good results with simple beams by modifying optimization functions, improving or adding constraints, and refining optimization algorithms. However, for the complex beams of anti-UAV radars, beamforming is more complex, and accuracy is more difficult to control; directly solving for amplitude and phase to achieve high-precision beamforming is even more challenging. Summary of the Invention

[0004] To achieve the above objectives, this invention provides a beamforming method for anti-UAV radar based on hybrid basis beamforming synthesis, which solves the problems of complex beamforming solution, difficulty in controlling accuracy, and difficulty in suppressing sidelobes in anti-UAV radar.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is a beamforming method for anti-UAV radar based on hybrid fundamental beam synthesis. For each beam direction, only one fundamental beam is selected from the corresponding directional fundamental beams of each fundamental beam group to participate in the beamforming, and the corresponding directional fundamental beams of other fundamental beam groups of that direction are turned off. During the beamforming process, the beam in the center part of the beamforming interval is beamformed by a fast attenuation fundamental beam, and the beams on both sides of the beamforming interval, excluding the center part, are beamformed by Taylor fundamental beams. Then, the fundamental beams of each beam direction participating in the beamforming are linearly weighted and summed to obtain the final synthesized radiation pattern.

[0006] The fast attenuation fundamental beam is:

[0007] E D,i(θ)=(ψ(θ)·α D ·β i )K(θ) T

[0008] α D =α T ·α M

[0009] In the formula, E D,i (θ) is the radiation pattern of the fast attenuation fundamental beam; ψ(θ) is the steering vector; α D β represents the amplitude premodulation of the rapidly attenuating fundamental beam; · represents element-wise multiplication between vectors; i The compensation phase modulation is for the i-th beam; K(θ) is the transmitted beam of each array element;

[0010] Where, α D =α T ·α M In the formula, α T For window function; α M α is the initial amplitude pre-modulation amount for rapidly attenuating the fundamental beam. M The objective function is obtained by solving for the objective function, which is:

[0011]

[0012] In the formula, ε v Let [θ] be the weight of the v-th optimization interval. vmax ,θ vmin ] represents the range of the v-th interval, θ e The beam pointing angle; The conjugate of the elements of ψ(θ) is indicated.

[0013] Furthermore, a genetic algorithm with real-number encoding is used to solve for the optimal weighting coefficients, thereby decoupling the actual amplitude modulation and phase modulation of each array element.

[0014] Furthermore, the final composite pattern is as follows:

[0015] E a (θ)=W×E s (θ)

[0016] W = [w -I ,w -I+1 ,…,w i ,…w I ]

[0017]

[0018] Where W is the weighting coefficient, i∈[-I,I], and i represents the i-th fundamental beam; E s(θ) is the fundamental beam pattern matrix; CH l To select parameters for the fundamental beam group, CH l =diag(ch l,-I ,…,ch l,i ,…,ch l,I ), α l E represents the amplitude pre-modulation amount of the l-th base beam group in the L-group base beam group participating in beamforming; l (θ) represents the beam pattern of the l-th base beam group; CH l The value can be 0 or 1, where 1 means it participates in shaping and 0 means it does not participate in shaping.

[0019] Furthermore, the fitness function used to solve for the optimal weighting coefficients is:

[0020]

[0021] Among them, [θ f_min ,θ f_max ]、[θ c_min ,θ c_max ] are the shaping intervals for the flat-top region and the cosecant fourth power region, respectively, k p k y These are the weights for the flat-top region and the cosecant fourth power region, respectively, E r (θ) represents the desired radiation pattern.

[0022] Furthermore, the method for selecting the central portion is as follows: starting from the midpoint of the shaping interval, it expands continuously to both sides with a predetermined step size. During the expansion process, the sidelobe level of the fast attenuation fundamental beam is observed. When the sidelobe on any side of the fast attenuation fundamental beam rises, the expansion degree corresponding to the previous step size is the interval occupied by the central portion.

[0023] The beneficial effects of this invention are:

[0024] 1. The anti-UAV radar beamforming method based on hybrid fundamental beam synthesis proposed in this invention can utilize multiple fundamental beam synthesis for beamforming, fully leveraging the advantages of various fundamental beams during the beamforming process to achieve optimal beamforming effect; simultaneously, it employs a real-number encoded genetic algorithm for solving, improving the beamforming solution capability for complex beams; in anti-UAV radar beamforming with complex waveforms, it can achieve excellent sidelobe suppression effect without sacrificing beamforming accuracy and solution complexity.

[0025] 2. The fast attenuation fundamental beam of the present invention has fast attenuation sidelobes, which can cooperate with the Taylor fundamental beam to complete the shaping work, so that the sidelobes of the shaping result can be further reduced based on the window function used; at the same time, the main lobe width does not widen significantly, the main lobe width has little impact on accuracy, the sidelobes attenuate quickly, and the sidelobe region has little interference with shaping accuracy, which can ensure that the shaping accuracy is basically not lost.

[0026] 3. The hybrid fundamental beamforming parameter decoupling method of the present invention can decouple the actual amplitude modulation and phase modulation of each array element after solving for the optimal weighting coefficient of the fundamental beam, thereby modulating each antenna array element in the actual physical space and realizing the deployment of anti-UAV beams. Attached Figure Description

[0027] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 This is a schematic diagram of the beamforming result in the medium flat-top region of Embodiment 1 of the present invention.

[0029] Figure 2 This is a schematic diagram of the wide flat-top region beamforming result of Embodiment 2 of the present invention.

[0030] Figure 3 This is a schematic diagram of the narrow flat-top region beamforming result in Embodiment 3 of the present invention. Detailed Implementation

[0031] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] Radar detects targets by transmitting and receiving electromagnetic signals in a specified direction. Current radars primarily employ phased array antennas, which consist of multiple antenna elements with defined positional relationships. By beamforming modulating the amplitude and phase of the transmitted signals from each element, a signal of a specified strength can be transmitted in a designated direction, thus achieving a desired antenna beam. However, in the beamformed beam, the sidelobes in the non-beamformed regions also transmit and receive electromagnetic signals to some extent, interfering with radar angle detection. Therefore, radar sidelobes must be minimized as much as possible during radar beamforming to reduce radar angle detection interference.

[0033] Sidelobe level, as a crucial factor in beamforming, determines the radar's anti-jamming capability. In the problem of azimuth estimation of the receiving beam, existing algorithms obtain extremely low sidelobes by analyzing the array signal subspace. However, these algorithms cannot demodulate the actual amplitude and phase modulation parameters of each array element, thus making them unsuitable for practical antenna beamforming. Current single-fundamental beamforming achieves sidelobe suppression by adding a window function to the fundamental beam, but beam combining reduces the sidelobe suppression effect of the fundamental beam, resulting in limited effectiveness. Furthermore, increasing the sidelobe suppression capability of the window function leads to broadening of the main lobe of the fundamental beam, thus affecting beamforming accuracy.

[0034] To suppress sidelobe levels, reduce the difficulty of solving the problem, and ensure beamforming accuracy, this invention discloses a beamforming method for anti-UAV radar based on hybrid fundamental beam synthesis. For each beam direction, only one fundamental beam is selected from the corresponding fundamental beams of each fundamental beam group to participate in beamforming, and the corresponding fundamental beams of other fundamental beam groups for that direction are turned off. During the beamforming process, the beam in the center of the beamforming interval is beamformed using a fast attenuation fundamental beam, and the beams on both sides of the beamforming interval, excluding the center, are beamformed using Taylor fundamental beams. Then, the fundamental beams of each beam direction participating in the beamforming are linearly weighted and summed to obtain the final synthesized radiation pattern.

[0035] Then, a genetic algorithm with real-number encoding is used to solve for the optimal weighting coefficients, thereby decoupling the actual amplitude modulation and phase modulation of each array element. In the actual antenna, the transmitted signals of each antenna element are modulated according to the decoupled amplitude and phase modulation, thereby enabling the anti-UAV radar to generate a shaped beam with low sidelobes.

[0036] This invention achieves excellent sidelobe suppression by comprehensively selecting two types of fundamental beams for beam shaping, leveraging the advantages of each type while suppressing their disadvantages. This is done without compromising other performance metrics (such as accuracy and solution complexity). Furthermore, this invention achieves beam shaping by indirectly solving for the weights of each fundamental beam. The solution variables are higher-dimensional and have the same dimensions, reducing the solution complexity and improving the accuracy of the beam shaping.

[0037] Beamforming achieves its effect by solving for the amplitude and phase modulation of each element, causing the modulated signals of each element to interfere to a corresponding degree in a specified direction. This results in the shaped beam being as close as possible to the expected beam. Each element's transmitted signal has a path difference related to the element spacing and transmission angle. This path difference causes a phase difference in the transmitted signals. For a linear array antenna with N elements, an element spacing of d, a wavelength of λ, and a wavenumber of k = 2π / λ, when the beam points to θ, the phase difference between the elements is ψ(θ) = [0, e^(-θ / λ). jkdsinθ ,e j2kdsinθ ,…,e j(N -1)kdsinθ ], where j is the imaginary unit. For amplitude modulation α=[α1,α2,…,α N and phase modulation The modulated beam can be represented as:

[0038]

[0039] Where T is the matrix transpose, · represents element-wise multiplication between vectors, and K(θ) = [K1(θ), K2(θ), ..., K n (θ),K N [θ] represents the transmitted beam of each array element.

[0040] For traditional phased arrays, a single beam points to θ e The launch pattern is as follows:

[0041]

[0042] in Let ψ(θ) represent the conjugate of its elements. At this point, the amplitude premodulation of the fundamental beam (i.e., the MVDR window, the window function to be solved) is the initial amplitude premodulation α of the rapidly attenuating fundamental beam. M =[α 1,M ,α 2,M ,…,α N,M According to the pattern, the total power should be minimized, but the beam pointing in the pattern direction θ e There should be no decay, and considering the difficulty of solving, an unconstrained optimization model can be established, which yields:

[0043]

[0044] Meanwhile, to meet the shaping needs of different regions, the proportion of different shaping regions in the fitness function (optimization objective function) can be changed by weighting:

[0045]

[0046] Where ε vLet be the weight of the v-th optimization interval. The larger the weight, the stronger the suppression ability for this angle. [θ] vmax ,θ vmin ] represents the range of the v-th interval.

[0047] In this embodiment, the fundamental beam is a beam with a single beam direction, which is pre-modulated in amplitude using methods such as window functions.

[0048] In this embodiment, the fundamental beam group is a group of fundamental beams with different directions that are modulated with the same amplitude pre-modulation amount.

[0049] In this embodiment, the initial amplitude premodulation amount α of the rapidly attenuating fundamental beam needs to be solved. M The solution is obtained using a genetic algorithm with real-number encoding. The specific solution process is as follows:

[0050] Step 1: Generate a specified number of Num values ​​within the range of possible values. b1 The initial population of individuals is used to calculate the fitness of individuals according to the fitness function of equation (4), and they are sorted according to their fitness values.

[0051] Step 2: Select the top Num according to the fitness function ranking. s1 Individuals participate in subsequent crossover and mutation, while other individuals are retained;

[0052] Step 3: Based on the crossover probability, select individuals exchange information through crossover to enhance population diversity. The specific rules for crossover are as follows:

[0053]

[0054] in These are two gene sequences involved in the crossover. Let μ be the gene sequence resulting from two crossovers, and μ be a random number in the range [0,1].

[0055] Step 4: To further increase population diversity, individuals after crossover need to be mutated according to the mutation probability. The specific mutation rules are as follows:

[0056]

[0057] Where L i U i To the current gene node w i The maximum and minimum values ​​can be obtained;

[0058] Step 5: Calculate the fitness function (Equation 4) for the individual samples after mutation in Step 4, the samples before mutation (individuals selected in Step 2), and the unselected individual samples in Step 2, and sort them, eliminating redundant individuals and retaining the top Num individuals. b1For individuals with a larger fitness function, determine whether the iteration stopping condition is met (i.e., whether the current iteration count exceeds the preset maximum iteration stopping count). If the condition is met, output the optimal individual; otherwise, input the retained individual into the selection step to start the next iteration.

[0059] In practical antenna arrays, the closer the angle is to the beam pointing direction, the stronger the interference between the array elements. Conversely, the farther away from the beam pointing direction, the smaller the interference effect due to the large phase difference between some elements, and the more easily attenuation occurs. Therefore, in the optimization results, within the optimization interval under the same weight, the farther away from the beam pointing direction, the higher the sidelobe attenuation and the lower the sidelobe level. At the same time, due to energy conservation, sidelobes closer to the beam pointing direction may have relatively higher levels of attenuation.

[0060] To control the level of the sidelobes near the beam pointing and to further smooth the beam, a window function α is used. T Windowing is applied (using the same window function as that used for Taylor baseband beams) to obtain the amplitude premodulation α of the fast attenuation baseband beam. D :

[0061] α D =α T ·α M #(8)

[0062] Furthermore, the rapidly attenuating fundamental beam is:

[0063] E D,i (θ)=(ψ(θ)·α D ·β i )K(θ) T #(9)

[0064] The rapidly attenuating fundamental beam has a relatively narrow main lobe width, further reducing the sidelobe level without loss during beamforming. Within a certain range near the beam pointing direction, it exhibits a relatively low sidelobe level compared to the unwindowed fundamental beam, but may still be higher than the Taylor windowed fundamental beam. Furthermore, it has a rapidly attenuating sidelobe level outside a certain range near the beam pointing direction. Therefore, this embodiment solves the problem of difficult sidelobe reduction caused by the complexity of anti-UAV radar beamforming.

[0065] In this embodiment, another type of fundamental beam used is the Taylor fundamental beam. This fundamental beam premodulates the amplitude of each array element directly through a certain Taylor window function, that is, the amplitude premodulation amount α of the Taylor beam is... T =[α 1,T ,α 2,T ,…,α N,T The Taylor window-based beam formed by its modulation is:

[0066] E T,i (θ)=(ψ(θ)·αT ·β i )K(θ) T #(10)

[0067] In this embodiment, the pointing angle of the fundamental beam group is uniformly distributed in sinusoidal space to ensure that adjacent fundamental beams with different pointing directions in the same group overlap evenly.

[0068] For example, for L groups of fundamental beams, each group contains 2I+1 directional fundamental beams (one at 0°, and I each for greater than 0° and less than 0°). Within each fundamental beam, there is a constant path difference between adjacent elements. This path difference results in a constant phase difference between adjacent elements. To make the antenna point at a specified angle θ, phase modulation is needed to compensate for the phase of each element. The unit compensation phase is Δβ = -kdsinθ. Simultaneously, for the same element, there is also a constant phase difference of -kdΔsinθ between two adjacent fundamental beams. Therefore, the unit compensation phase can be set as:

[0069] Δβ=-kdΔsinθ0#(11)

[0070] In the formula, k is the wave number and d is the element spacing.

[0071] Where Δsinθ0 is the sinusoidal angle deviation between adjacent fundamental beams, i.e.:

[0072]

[0073] The pointing angle ranges from [-θ] to [-θ]. max ,θ max ], i∈[-I,I]. Simultaneously, the pointing angle θ of the i-th beam. i For θ i =arcsin(iΔsinθ).

[0074] The compensated phase modulation for the i-th beam is:

[0075] β i =[0,iΔβ,…,i(N-1)Δβ]#(13)

[0076] In the L groups of fundamental beams involved in beam shaping, the amplitude premodulation of the l-th fundamental beam group is α. l =[α 1,l ,α 2,l ,…,α N,l The beam pattern of the i-th beam in the l-th fundamental beam group is:

[0077]

[0078] At this time, the l-th fundamental beam group is:

[0079]

[0080] This embodiment employs two types of fundamental beamforming, comprehensively considering the advantages and disadvantages of both types to maximize strengths and minimize weaknesses, further reducing sidelobes on the original basis. This invention selects the beam in the center of the beamforming interval as the rapidly attenuating fundamental beam, controlling the higher sidelobes near the beam's direction within the beamforming interval, while the rapidly attenuating sidelobes fall outside the interval. The portions on both sides of the beamforming interval are then shaped using Taylor window fundamental beamforming. Hybrid beamforming can achieve further optimized beamforming results based on single Taylor window beamforming without incurring other costs such as accuracy loss or reduced solution speed.

[0081] The method for selecting the central part is as follows: starting from the midpoint of the shaping interval, expand outwards to both sides with a predetermined step size. During the expansion process, observe the sidelobe level of the fast attenuation fundamental beam. When the sidelobe on either side of the fast attenuation fundamental beam rises, the expansion degree corresponding to the previous step size is the interval occupied by the central part.

[0082] The selection of the center part needs to be adjusted according to the actual effect. During the parameter adjustment process, the center part should be expanded from the midpoint of the shaping area to both sides to observe the sidelobe level of the shaping beam. When the sidelobe of the shaping beam is raised on one side, it means that the center part is adjusted too wide. A better shaping effect can be obtained by reducing the center area to a certain extent.

[0083] In this embodiment, for each beam pointing, only one beam from the L groups of fundamental beams needs to be selected for beamforming, while the remaining L-1 fundamental beams are turned off. Therefore, it is necessary to design the fundamental beam group selection parameter CH. l :

[0084] CH l =diag(ch l,-I ,…,ch l,i ,…,ch l,I )#(16)

[0085] Where ch l,i The value can only be 0 or 1, representing whether the i-th fundamental beam of the l-th fundamental beam group participates in beamforming. For beams whose beam pointing angle is outside the beamforming interval, their contribution to the sidelobes is much greater than that to the main lobe. Therefore, the corresponding beams of all fundamental beam groups do not participate in beamforming, i.e., ch l,i =0; For beam pointing angles within the shaping range, a reasonable selection should be made based on the beam shape and advantages / disadvantages of each basic beam group. CH l for ch l,i The diagonal matrix formed, after selection, results in the following fundamental beam pattern matrix:

[0086]

[0087] The final synthesized radiation pattern is obtained by linearly weighting and summing the fundamental beams for each pointing angle. The weighting coefficients are:

[0088] W = [w -I ,w -I+1 ,…,w i ,…w I ]#(18)

[0089] The final composite pattern is as follows:

[0090] E a (θ)=W×E s (θ)#(19)

[0091] The beam pattern synthesized by this method, after designing and selecting each set of basic beam groups, only requires solving the optimal weighting coefficient W for each beam pointing point to complete beamforming, which greatly reduces the difficulty of solving beamforming. At the same time, this method integrates multiple sets of basic beam groups, providing room for improvement in beamforming accuracy and sidelobe reduction.

[0092] In this embodiment, a genetic algorithm with real-number encoding is used to solve for the optimal weighting coefficient W. The anti-UAV radar beam has a flat-top region and a cosecant fourth-order region, with different beam-forming difficulties in different regions. Therefore, the fitness function used for solving the problem is the minimum weighted sum of the normalized squared errors of the two regions, i.e.:

[0093]

[0094] Where [θ f_min ,θ f_max ]、[θ c_min ,θ c_max ] are the shaping intervals for the flat-top region and the cosecant fourth power region, respectively, k p k y These are the weights for the flat-top region and the cosecant fourth power region, respectively, E r (θ) represents the desired radiation pattern. The fitness function used for solving can obtain the balanced flat-top region and cosecant fourth power region shaping, and the shaping regions are normalized so that they can be applied to the shaping waveforms under different designs, thereby improving the robustness of the design.

[0095] The specific process of the real-number encoded genetic algorithm for solving the optimal weighting coefficients W of the fundamental beam in this embodiment is as follows:

[0096] Step 1: Generate a specified number of Num values ​​within the given range. b2 The initial population of individuals is calculated based on the fitness function of equation (20), and individuals are sorted according to their fitness values.

[0097] Step 2: Select the top Num values ​​based on their fitness scores. s2 Individuals participate in subsequent crossover and mutation, while other individuals are preserved;

[0098] Step 3: Based on the crossover probability, the selected individuals exchange information through crossover to enhance population diversity. The specific crossover rules are shown in Equations (5) and (6).

[0099] Step 4: In order to further increase the diversity of the population, the individuals after crossover need to be mutated according to the mutation probability. The specific rules for mutation are as shown in equation (7).

[0100] Step 5: Calculate the fitness function (Equation 20) for the individual samples after mutation in Step 4, the samples before mutation (i.e., the individuals selected in Step 2), and the individual samples not selected in Step 2, and sort them, eliminating redundant individuals and retaining the top Num individuals. b2 For individuals with larger fitness function values, determine whether the iteration stopping condition is met (i.e., whether the current iteration count exceeds the preset maximum iteration stopping count). If the condition is met, output the optimal individual; otherwise, input the retained individual into the selection step to start the next iteration.

[0101] After solving for the optimal weighting coefficient W of the fundamental beam, the actual amplitude modulation and phase modulation of each array element are decoupled, thereby modulating each antenna array element in the actual physical space to realize the deployment of anti-UAV beams, which has practical application value.

[0102] Final composite pattern E a (θ), which can be rewritten as:

[0103]

[0104] In equation (21), each term involved in the summation of l and i can be equivalent to a complex number. Therefore, the summation part can also be equivalent to a complex number, and can be rewritten in amplitude and phase form using Euler's formula, i.e.:

[0105]

[0106] Where α n β n Let the amplitude modulation and phase modulation (the phase value of each element's modulation) be the values ​​of the nth array element, respectively. Then the final radiation pattern is:

[0107]

[0108] This embodiment achieves optimal amplitude modulation α = [α1, α2, ..., α] for each array element. N and phase modulation Subsequently, the antenna elements need to be modulated in the actual antenna to obtain the actual anti-drone radar antenna beam. For example, the transmission signal modulation of each element can be completed in the analog domain by controlling the signal transmission line length and power amplifier of each element, or the transmission signal modulation of each element can be completed in the digital domain by using digital phase shifters, thereby achieving low sidelobe anti-drone beam deployment.

[0109] Beamforming using single-fundamental beamforming with windowless fundamental beams and beamforming using Taylor-based fundamental beams were used as comparative methods to compare and analyze the effectiveness of this invention with other methods, thus verifying the effectiveness of this invention. In the experiment, the simulated radar carrier frequency was 9.6 GHz, the radar antenna was a 16-element linear array, and the antenna spacing was 0.0155 m. The genetic algorithm population was set to 50 individuals, with 20 individuals selected per iteration, a crossover probability of 0.99, and a mutation probability of 0.05.

[0110] Example 1

[0111] The beam used in Example 1 has a flat-top region of [-25°, -15°] and a cosecant fourth-order region of [-15°, 25°], making it a medium-flat-top beam. All schemes use a 30dB Taylor window function, and the beamforming results are as follows: Figure 1 As shown in the figure. According to the experimental results, the beamforming method using windowless fundamental beamforming for single-fundamental beamforming has an average error of 0.9838 dB and an average sidelobe of -17.5252 dB; the beamforming method using Taylor-based fundamental beamforming for single-fundamental beamforming has an average error of 0.5923 dB and an average sidelobe of -21.1260 dB; the beamforming method for anti-UAV radar based on hybrid fundamental beamforming in this embodiment has an average error of 0.4439 dB and an average sidelobe of -27.0338 dB. It can be seen that this embodiment can significantly reduce the sidelobe level and improve the radar's anti-jamming capability while ensuring no loss of beamforming accuracy, based on the window function used.

[0112] The final control pattern obtained by decoupling and remodulating the amplitude and phase modulation of each array element is as follows: Figure 1 As shown, the radiation pattern is basically consistent with the optimized beam pattern, thus proving that the shaping method of this embodiment can control the actual antenna array elements to obtain a beam with the expected effect.

[0113] Example 2

[0114] The beam used in Example 2 has a flat-top region of [-25°, -5°] and a cosecant fourth-order region of [-5°, 25°], making it a wide flat-top beam. All schemes use a 30dB Taylor window function. The beamforming results for each scheme are as follows: Figure 2As shown in the figure. According to the experimental results, the beamforming method using windowless fundamental beamforming for single-fundamental beamforming has an average error of 0.0502 dB and an average sidelobe of -13.5796 dB; the beamforming method using Taylor-based fundamental beamforming for single-fundamental beamforming has an average error of 0.1083 dB and an average sidelobe of -16.5343 dB; the beamforming method for anti-UAV radar based on hybrid fundamental beamforming of this invention has an average error of 0.4820 dB and an average sidelobe of -22.5585 dB. It can be seen that the method in this embodiment can significantly reduce the sidelobe level and improve the radar's anti-jamming capability while ensuring no loss of beamforming accuracy, based on the window function used.

[0115] The final radiation pattern obtained by decoupling and remodulating the amplitude and phase modulation of each array element is as follows: Figure 2 As shown, the radiation pattern is basically consistent with the optimized beam pattern, thus proving that this embodiment can control the actual antenna array elements to obtain a beam with the expected effect.

[0116] Example 3

[0117] The beam used in Example 3 has a flat-top region of [-25°, -20°] and a cosecant fourth-order region of [-20°, 25°], making it a narrow flat-top beam. To demonstrate that the method in this example can reduce sidelobes for different window functions, the window function used in each scheme is a 40dB Taylor window function. The beamforming results of each scheme are as follows: Figure 3 As shown in the figure. According to the experimental results, the beamforming method using windowless fundamental beamforming for single-fundamental beamforming has an average error of 1.3336 dB and an average sidelobe of -23.3806 dB; the beamforming method using Taylor-based fundamental beamforming for single-fundamental beamforming has an average error of 0.7181 dB and an average sidelobe of -30.7459 dB; the beamforming method for anti-UAV radar based on hybrid fundamental beamforming proposed in this invention has an average error of 0.2257 dB and an average sidelobe of -40.5148 dB. It can be seen that the method in this embodiment can significantly reduce the sidelobe level and improve the radar's anti-jamming capability while ensuring no loss of beamforming accuracy, based on the window function used.

[0118] The final control pattern obtained by decoupling and remodulating the amplitude and phase modulation of each array element is as follows: Figure 3 As shown, the radiation pattern is basically consistent with the optimized beam pattern, thus proving that this embodiment can control the actual antenna array elements to obtain a beam with the expected effect. Three sets of experiments demonstrate that this embodiment can achieve excellent sidelobe suppression effects for different types of fundamental beams under different window functions, and has practical application value.

Claims

1. A method for beamforming anti-UAV radar based on hybrid fundamental beam synthesis, characterized in that, For each beam pointing, only one fundamental beam is selected from the corresponding fundamental beams of each fundamental beam group to participate in the beam shaping, and the corresponding fundamental beams of other fundamental beam groups of that beam pointing are turned off. During the beam shaping process, the beam in the center of the beam shaping interval is shaped by the fast attenuation fundamental beam, and the beams on both sides of the beam shaping interval except for the center are shaped by the Taylor fundamental beam. Then, the fundamental beams of each beam pointing participating in the beam shaping are linearly weighted and summed to obtain the final composite pattern. The fast attenuation fundamental beam is: E D,i (θ)=(ψ(θ)·α D ·b i )K(θ) T α D ＝α T ·α M In the formula, E D,i (θ) is the radiation pattern of the fast attenuation fundamental beam; ψ(θ) is the steering vector; α D β represents the amplitude premodulation of the rapidly attenuating fundamental beam; · represents element-wise multiplication between vectors; i For the compensation phase modulation of the i-th beam; K(θ) is the transmitted beam of each array element; θ is the elevation angle; Where, α D =α T ·α M In the formula, α T For window function; α M α is the initial amplitude pre-modulation amount for rapidly attenuating the fundamental beam. M The objective function is obtained by solving for the objective function, which is: In the formula, ε v Let [θ] be the weight of the v-th optimization interval. vmax ,θ vmin ] represents the range of the v-th interval, θ e The angle at which the beam points; The conjugate of the elements of ψ(θ) is indicated.

2. The anti-UAV radar beamforming method based on hybrid basis beam synthesis according to claim 1, characterized in that, A genetic algorithm with real-number encoding is used to solve for the optimal weighting coefficients, thereby decoupling the actual amplitude modulation and phase modulation of each array element and obtaining the final radiation pattern.

3. The anti-UAV radar beamforming method based on hybrid basis beam synthesis according to claim 1, characterized in that, The final synthesis pattern is as follows: E a (θ)=W×E s (i) In=[in -I ,In -I+1 ,…,In i ,…In I ] Where W is the weighting coefficient, i∈[-I,I], and i represents the i-th fundamental beam; E s (θ) is the fundamental beam pattern matrix; CH l To select parameters for the fundamental beam group, CH l =diag(ch l,-I ,…,ch l,i ,…,ch l,I ), α l E represents the amplitude pre-modulation amount of the l-th base beam group in the L-group base beam group participating in beamforming; l (θ) represents the beam pattern of the l-th base beam group; CH l The value can be 0 or 1, where 1 means it participates in shaping and 0 means it does not participate in shaping.

4. The anti-UAV radar beamforming method based on hybrid basis beam synthesis according to claim 3, characterized in that, The fitness function used to solve for the optimal weighting coefficients is: Among them, [θ f_min ,θ f_max ]、[θ c_min ,θ c_max ] are the shaping intervals for the flat-top region and the cosecant fourth power region, respectively, k p k y These are the weights for the flat-top region and the cosecant fourth power region, respectively, E r (θ) represents the desired radiation pattern.

5. The anti-UAV radar beamforming method based on hybrid basis beam synthesis according to claim 1, characterized in that, The method for selecting the central part is as follows: starting from the midpoint of the shaping interval, expand continuously to both sides with a predetermined step size. During the expansion process, observe the sidelobe level of the fast attenuation fundamental beam. When the sidelobe on any side of the fast attenuation fundamental beam rises, the expansion degree corresponding to the previous step size is the interval occupied by the central part.

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