WO2022188337A1 - 一种基于解空间裁剪粒子群算法的共形阵方向图综合方法 - Google Patents

一种基于解空间裁剪粒子群算法的共形阵方向图综合方法 Download PDF

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WO2022188337A1
WO2022188337A1 PCT/CN2021/109108 CN2021109108W WO2022188337A1 WO 2022188337 A1 WO2022188337 A1 WO 2022188337A1 CN 2021109108 W CN2021109108 W CN 2021109108W WO 2022188337 A1 WO2022188337 A1 WO 2022188337A1
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array
excitation
array element
conformal
pattern
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宋春毅
王昕�
陈钦
俞鼎柯
席玉章
方文巍
徐志伟
李欢
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Zhejiang University
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    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/50—Systems of measurement based on relative movement of target
    • G01S13/52—Discriminating between fixed and moving objects or between objects moving at different speeds
    • G01S13/522—Discriminating between fixed and moving objects or between objects moving at different speeds using transmissions of interrupted pulse modulated waves
    • G01S13/524—Discriminating between fixed and moving objects or between objects moving at different speeds using transmissions of interrupted pulse modulated waves based upon the phase or frequency shift resulting from movement of objects, with reference to the transmitted signals, e.g. coherent MTi
    • G01S13/526—Discriminating between fixed and moving objects or between objects moving at different speeds using transmissions of interrupted pulse modulated waves based upon the phase or frequency shift resulting from movement of objects, with reference to the transmitted signals, e.g. coherent MTi performing filtering on the whole spectrum without loss of range information, e.g. using delay line cancellers or comb filters
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/03—Details of HF subsystems specially adapted therefor, e.g. common to transmitter and receiver
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G06F17/141—Discrete Fourier transforms
    • G06F17/142—Fast Fourier transforms, e.g. using a Cooley-Tukey type algorithm
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/004—Artificial life, i.e. computing arrangements simulating life
    • G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q21/00—Antenna arrays or systems
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/12—Computing arrangements based on biological models using genetic models
    • G06N3/126—Evolutionary algorithms, e.g. genetic algorithms or genetic programming
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N5/00—Computing arrangements using knowledge-based models
    • G06N5/01—Dynamic search techniques; Heuristics; Dynamic trees; Branch-and-bound
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Definitions

  • the invention relates to the field of array antennas, in particular to a conformal array pattern synthesis method based on a solution space clipping particle swarm algorithm.
  • the conformal array is integrated with the carrier, and the two have the same shape characteristics, which makes the conformal array have many advantages such as large available aperture and wide-angle scanning. Therefore, in recent years, the related technical research on conformal arrays is gradually heating up, but at the same time, the pattern synthesis of conformal arrays faces many challenges. Due to the shape characteristics of conformal arrays, the far-field pattern cannot be decomposed into the product form of the array factor and the pattern of the array elements. Traditional methods such as Chebyshev synthesis and Taylor synthesis are not applicable. The FFT algorithm can only be used to optimize the array. factor, but also face the problem of failure. In addition, the alternate projection method suitable for conformal arrays also has the disadvantage of being prone to local convergence.
  • PSO Particle Swarm Optimization
  • the PSO algorithm is simple, the number of parameters is small, and it is easier to implement.
  • the dimension of the particle vector is the same as the number of parameters to be optimized, when the number of parameters to be optimized is high, the dimension of the solution space is high, the convergence speed of the algorithm becomes slower, and it is easy to fall into local convergence. Therefore, PSO needs to be optimized in a targeted manner.
  • Most of the existing optimizations focus on the improvement of particle update mechanism, the improvement of inertia weight and the integration with other intelligent optimization algorithms.
  • the particle initial value for the basic PSO has not been improved in the aspect of random generation in the solution space.
  • the purpose of the present invention is to not consider the shortage of the optimization solution space in the above-mentioned prior art, and based on the single-objective optimization result of the directional map, make the particles of the PSO algorithm perform a small-scale refined search in the clipped solution space, and improve the initial stage of the basic PSO algorithm.
  • the problem of slow search speed and local convergence caused by random given values can improve the performance of the algorithm, realize the conformal pattern synthesis under the limitation of the dynamic range of the array element excitation, and obtain the conformal array element excitation that satisfies multiple optimization objectives.
  • a conformal array pattern synthesis method based on solution space clipping particle swarm optimization comprising the following steps:
  • the S1 is realized through the following sub-steps:
  • S1.1 Set the optimization goals according to the design indicators, including the normalized far-field pattern peak sidelobe level suppression index SLL, the maximum value of the first null width of the main beam FNMW e , and the desired null position with zero depth
  • c 3 ⁇ 10 8 m/s, which is the speed of electromagnetic wave in vacuum
  • An is the excitation of the nth array element;
  • k is the number of wavelengths, The far-field direction to which the main beam points; is the position vector of the nth array element in the global coordinate system;
  • j represents the imaginary unit;
  • I n is the excitation amplitude of the nth array element
  • ⁇ n is the phase of the nth array element excitation.
  • I pn is the excitation amplitude of the n-th element of the projection array
  • is the array element pattern amplitude of the n-th element of the conformal array in the main beam direction
  • is the magnitude of the array element pattern in the projection array in the direction of the main beam;
  • Each projection array element is represented by a uniform array element centered on it; based on the projection array and uniform array
  • the least squares relationship between the steering vector matrices can be used to obtain the excitation conversion relationship matrix between the projected array and the uniform array:
  • E p is the projection array steering vector matrix
  • E e is the uniform array steering vector matrix
  • c is the transformation matrix that satisfies the least squares relationship
  • S1.11 Perform S1.5-S1.10 iteratively, if the conformal array element excitation meets the dynamic range And the pattern satisfies the peak sidelobe level suppression index, the iteration is terminated, otherwise it runs to the set maximum number of times, and the conformal array element excitation that satisfies the peak sidelobe level suppression index SLL is obtained.
  • ⁇ in is the lower limit of the search range of the i-th dimension of the particle, is the upper limit of the search range of the i-th dimension
  • X init is the vector formed by the excitation of the conformal array elements obtained by S1
  • the dimension is equal to the number of conformal array elements
  • ⁇ is the solution space clipping factor, which represents the reserved solution space range near the excitation of the conformal array element obtained in S1;
  • sll total is the sum of all the SLL parts higher than the peak sidelobe level suppression index in all sampling point values of the pattern;
  • FNMW and FNMW e are the actual and expected values of the first zero-notch beamwidth; NULL point and the actual and expected values at the zero-sink position; the NULL value and The actual value and the expected value of the zero-sag value;
  • ⁇ 1 , ⁇ 2 , ⁇ 3 are the weight coefficients;
  • ⁇ is the inertia weight coefficient
  • c 1 and c 2 are acceleration factors
  • r 1 and r 2 are random numbers between [0, 1] that satisfy uniform distribution
  • pbest id is the individual optimal value
  • gbest d is the global The optimal value.
  • the velocity of the i-th dimension of the particle in the k-th iteration is the position of the i-th dimension of the particle in the k-th iteration;
  • k is the current iteration number
  • T is the maximum iteration number
  • ⁇ r is the scaling factor of the ⁇ value range
  • ⁇ 0 is the minimum value of the ⁇ value range
  • the conformal array pattern synthesis method based on the solution space clipping particle swarm algorithm of the present invention focuses on the PSO-based conformal array pattern synthesis technology, and focuses on using the low-complexity FFT algorithm to obtain single-objective optimization results, and based on the method As a result, the solution space of the PSO algorithm is trimmed, which effectively improves the convergence speed of the algorithm and avoids the local convergence problem, thereby improving the performance of the PSO algorithm.
  • Form array element incentives are provided.
  • Figure 1 is a schematic diagram of a conformal array model.
  • FIG. 2 is a schematic diagram of the steps of S1 in the embodiment of the present invention.
  • FIG. 3 is an algorithm flowchart of an embodiment of the present invention.
  • FIG. 4 is a comparison diagram of far-field patterns obtained after optimization of the pattern synthesis method and the basic PSO method according to an embodiment of the present invention.
  • FIG. 5 is a comparison diagram of the optimal fitness value obtained after optimization of the pattern synthesis method and the basic PSO method according to the embodiment of the present invention.
  • FIG. 6 is an excitation distribution diagram of a conformal array element that satisfies the multi-objective optimization under the constraint of the dynamic range of the excitation amplitude of the array element obtained by the implementation of the present invention.
  • the conformal array pattern synthesis method based on the solution space clipping particle swarm algorithm of the present invention is shown in Figures 1 to 3, and the method includes the following steps:
  • the conformal array and the uniform array are realized.
  • the array element excitation conversion between the arrays uses the IFFT and FFT methods to quickly calculate and process the pattern, and obtain the conformal array element excitation that satisfies the SLL under the constraint of the dynamic range of the excitation amplitude of the array element; the S1 goes through the following sub-steps accomplish:
  • c 3 ⁇ 10 8 m/s, which is the speed of electromagnetic wave in vacuum
  • An is the excitation of the nth array element;
  • k is the number of wavelengths, The far-field direction to which the main beam points; is the position vector of the nth array element in the global coordinate system;
  • j represents the imaginary unit;
  • I n is the excitation amplitude of the nth array element
  • ⁇ n is the phase of the nth array element excitation.
  • I pn is the excitation amplitude of the n-th element of the projection array
  • is the array element pattern amplitude of the n-th element of the conformal array in the main beam direction
  • is the magnitude of the array element pattern in the projection array in the direction of the main beam;
  • Each projection array element is represented by a uniform array element centered on it; the pattern is the array element excitation matrix and the product of the steering vector matrix, when the far-field patterns of the projected array and the uniform array are equal, the least squares relationship can be established based on the steering vector matrix of the projected array and the uniform array:
  • E p is the projection array steering vector matrix
  • E e is the uniform array steering vector matrix
  • the excitation conversion relationship matrix c between the projection array and the uniform array is obtained based on the variant of the above formula:
  • c is the transformation matrix that satisfies the least squares relationship, represents the conjugate transpose of E e ;
  • S1.6 The array factor is calculated according to the inverse Fourier transform between the uniform array and the array factor, and the product of the array element pattern obtained in S1.2 is the far-field pattern. Compared with the traditional pattern calculation formula , this method uses fast Fourier transform, which has low complexity and fast calculation, and has little influence on the overall calculation amount of the algorithm, making S1 suitable as a pre-step of S2.
  • S1.11 Perform S1.5-S1.10 iteratively, if the conformal array element excitation meets the dynamic range And the pattern satisfies the peak sidelobe level suppression index, the iteration is terminated, otherwise it runs to the set maximum number of times, and the conformal array element excitation that satisfies the peak sidelobe level suppression index SLL is obtained.
  • S2 According to the array element excitation obtained in S1, the solution space of the particle swarm optimization algorithm is cut, and the weight coefficient of nonlinear update is designed to ensure sufficient global search, and the fitness function is designed according to multiple optimization goals, and the conformal array pattern Do further optimization to obtain the conformal array element excitation that satisfies multiple optimization objectives under the constraints of the dynamic range of the excitation amplitude of the array element; the S2 is achieved through the following sub-steps:
  • sll total is the sum of all the SLL parts higher than the peak sidelobe level suppression index in all sampling point values of the pattern
  • FNMW and FNMW e are the actual and expected values of the first zero-notch beamwidth
  • NULL point and the actual and expected values at the zero-sink position the NULL value and The actual value and the expected value of the zero-sag value
  • ⁇ 1 , ⁇ 2 , and ⁇ 3 are weight coefficients, which are used to adjust the search effect.
  • ⁇ is the inertia weight coefficient
  • c 1 and c 2 are acceleration factors
  • r 1 and r 2 are random numbers between [0, 1] that satisfy uniform distribution
  • pbest id is the individual optimal value
  • gbest d is the global The optimal value.
  • the velocity of the i-th dimension of the particle in the k-th iteration is the position of the i-th dimension of the particle in the k-th iteration;
  • k is the current number of iterations
  • T is the maximum number of iterations
  • ⁇ r is the scaling factor of the ⁇ value range
  • ⁇ 0 is the minimum value of the ⁇ value range
  • ⁇ r and ⁇ 0 can realize the ⁇ value range. adjust;
  • the maximum number of iterations T is 500 generations. If the iteration reaches the maximum number of iterations, the operation is terminated, otherwise, jump to S2.3; finally, a conformal matrix that satisfies the optimization objective set in S1.1 is obtained Array incentives.
  • Fig. 5 is the curve of the average value of the optimal fitness function value obtained after 20 independent experiments as a function of the iteration here.

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Abstract

本发明公开了一种基于解空间裁剪粒子群算法的共形阵方向图综合方法，该方法首先选取多优化目标中的峰值旁瓣电平指标，设计了基于改进幅相投影法和快速傅里叶变换的迭代过程，完成阵元激励幅度动态范围约束下的方向图单目标综合；并基于上述迭代得到的共形阵阵元激励，进行粒子群算法解空间裁剪，使粒子群进行小范围的精细化搜索，最终实现共形阵方向图的多目标综合，得到满足多个优化目标的共形阵阵元激励。本发明使用低复杂度快速傅里叶变换方法对粒子群算法解空间进行裁剪，降低算法计算量，有效避免了粒子群算法的局部收敛问题，显著提升了粒子群算法解决共形阵方向图多目标综合问题时的算法性能。

Description

一种基于解空间裁剪粒子群算法的共形阵方向图综合方法 技术领域
本发明涉及阵列天线领域，尤其是涉及一种基于解空间裁剪粒子群算法的共形阵方向图综合方法。
背景技术
近年来，雷达系统迅猛发展，使用场景愈加广泛。作为雷达系统电磁收发装置的核心部分，阵列天线备受关注。在不同的使用场景下，针对不同的使用需求，阵列天线需要产生特定的远场方向图。如何通过对阵列天线阵元激励的综合来实现所需阵列方向图一直是研究的热点问题。在工程领域，在实现方向图综合问题时，也会面临诸多限制，阵元激励幅度的动态范围(Dynamic Range Ratio，DRR)就是一个重要的方面，较高的DRR会提高馈电网络的设计难度，增加阵列馈电网络的成本，因此，在综合得到期望阵列方向图的同时，将阵元激励的DRR限制在合理范围内十分重要。
共形阵列与载体相融合，二者具有相同的形状特点，这一特性使共形阵具有可用口径较大，宽角扫描等诸多优点。因此近年来有关共形阵列的相关技术研究也在逐渐升温，但与此同时，共形阵的方向图综合面临许多挑战。共形阵由于其形状特性，远场方向图无法分解为阵因子与阵元方向图的乘积形式，传统方法如切比雪夫综合，泰勒综合方法并不适用，FFT算法由于只能用来优化阵因子，也面临失效的问题。另外，适用于共形阵的交替投影法也具有易陷入局部收敛等缺点。
由于在多参数，非线性目标函数的优化问题上的独特优势，以粒子群优化算法为代表的智能优化算法十分适用于共形阵的方向图综合问题。粒子群优化算法(Particle Swarm Optimization，PSO)由J.Kennedy和R.C.Eberhart等于1995年提出。PSO算法简单，参数数目较少，较为容易实现。但由于粒子向量维度与待优化参数数目相同，因此当待优化参数数目较高时，解空间维度较高，算法收敛速度变慢，并且容易陷入局部收敛。因此，需要针对性地对PSO进行优化。现有的优化多集中于粒子更新机制改进，惯性权重改进以及与其他智能优化算法融合等方面。针对基本PSO的粒子初值在解空间随机生成这一方面的改进并未进行。
发明内容
本发明的目的在于针对上述已有技术并未考虑优化解空间的不足，基于方向图单目标优 化结果，使PSO算法的粒子在裁剪后的解空间作小范围精细化搜索，改善基本PSO算法初值随机给定造成的搜索速度慢和局部收敛等问题，提升算法性能，实现阵元激励动态范围限制下的共形方向图综合，得到满足多个优化目标的共形阵阵元激励
本发明的目的通过如下的技术方案来实现：
一种基于解空间裁剪粒子群算法的共形阵方向图综合方法，包括以下步骤：
S1：将峰值旁瓣电平抑制指标SLL作为唯一指标，基于投影阵列与共形阵列之间的激励转换关系和投影阵列与均匀阵列阵元激励之间的最小二乘关系，实现共形阵列与均匀阵列之间的阵元激励转换，使用IFFT和FFT方法对方向图进行快速计算和处理，得到阵元激励幅度动态范围约束下的满足SLL的共形阵阵元激励；
S2：根据S1得到的阵元激励，进行粒子群算法的解空间裁剪，并设计非线性更新的权重系数，保证充分的全局搜索，根据多个优化目标设计适应度函数，对共形阵方向图做进一步优化，得到阵元激励幅度动态范围约束下的满足多个优化目标的共形阵阵元激励。
进一步地，所述S1通过以下子步骤来实现：
S1.1：根据设计指标设置优化目标，包括归一化远场方向图峰值旁瓣电平抑制指标SLL、主波束第一零陷宽度最大值FNMW e、期望零陷位置
Figure PCTCN2021109108-appb-000001
与零陷深度
Figure PCTCN2021109108-appb-000002
S1.2：设定阵元数N，阵元编号1～N，设定阵元工作中心频率f，计算得到波长λ：
Figure PCTCN2021109108-appb-000003
其中，c＝3×10 8m/s，为真空中电磁波速度；
设定阵元间距为
Figure PCTCN2021109108-appb-000004
以阵列对称中心点所在切线方向为x轴方向，以过该点法线方向为y轴方向，建立全局直角坐标系，并将各阵元在局部坐标系下的方向图函数f(θ)转换为全局坐标系下的方向图函数f n(θ)，计算得到共形阵列远场方向图F(θ)：
Figure PCTCN2021109108-appb-000005
其中：A n为第n个阵元的激励；k为波长数，
Figure PCTCN2021109108-appb-000006
Figure PCTCN2021109108-appb-000007
为主波束指向的远场方向；
Figure PCTCN2021109108-appb-000008
为第n个阵元在全局坐标系下的位置矢量；j表示虚数单位；
S1.3：设定共形阵阵元激励幅度动态范围最大值为drr，将阵元激励A n表示为：
A n＝I n·exp(jα n)            (3)
其中，I n为第n个阵元激励的幅值，α n为第n个阵元激励的相位。计算得到I n的取值范围
Figure PCTCN2021109108-appb-000009
Figure PCTCN2021109108-appb-000010
其中
Figure PCTCN2021109108-appb-000011
为主波束方向在全局坐标系下的位置矢量；
S1.4：在S1.3所确定的幅值范围内，随机初始化共形阵阵元激励；
S1.5：设定主波束方向θ 0＝0°，为全局坐标系y轴方向，在主波束方向上对共形阵列进行投影，得到投影阵列；投影阵列阵元x轴方向坐标与对应共形阵列阵元相等，y轴方向坐标为0；基于近似相等的峰值旁瓣电平关系，投影阵列与共形阵列之间的激励转换关系通过下式计算：
Figure PCTCN2021109108-appb-000012
其中，I pn为投影阵列第n个阵元的激励幅度；|f n(θ 0)|为共形阵列第n个阵元在主波束方向的阵元方向图幅度；|f(θ 0)|为投影阵列中阵元方向图在主波束方向的幅度；
将投影阵列按照更小的间距进行插值，将投影阵列转换为间距更小的均匀阵列，每个投影阵列阵元通过以其为中心的一段均匀阵列阵元来表示；基于投影阵列和均匀阵列的导向矢量矩阵之间存在的最小二乘关系，得到投影阵列与均匀阵列之间的激励转换关系矩阵：
Figure PCTCN2021109108-appb-000013
其中，E p为投影阵列导向矢量矩阵，E e为均匀阵列导向矢量矩阵，c为满足该最小二乘关系的转换矩阵；
S1.6：依照均匀阵列与阵因子之间的逆傅里叶变换计算得到阵因子，与阵元方向图的乘积即为远场方向图；
S1.7：按照峰值旁瓣电平抑制指标SLL，将超出该指标的方向图采样点数值修正为满足指标的数值；
S1.8：将修正后的方向图除以阵元方向图得到阵因子，并采用傅里叶变换得到均匀阵列激励数值；
S1.9：对公式(4)和(5)进行逆运算，得到共形阵阵元激励；
S1.10：根据阵元幅度激励范围
Figure PCTCN2021109108-appb-000014
对共形阵列阵元激励进行修正，使其满足阵元激励幅度动态范围限制；
S1.11：迭代进行S1.5-S1.10，如果共形阵阵元激励满足动态范围
Figure PCTCN2021109108-appb-000015
并且方向图满足峰值旁瓣电平抑制指标，迭代终止，否则运行到设定的最大次数，得到满足峰值旁瓣电平抑制指标SLL的共形阵阵元激励。
进一步地，所述S2通过以下子步骤来实现：
S2.1：基于S1得到的共形阵阵元激励和S1.3得到的阵元激励的幅值范围
Figure PCTCN2021109108-appb-000016
将解空 间进行合理的裁剪，解空间的粒子每一维对应共形阵列中的一个阵元激励，确定第i维的解空间搜索范围如下：
Figure PCTCN2021109108-appb-000017
Figure PCTCN2021109108-appb-000018
其中，
Figure PCTCN2021109108-appb-000019
为粒子第i维搜索范围的下限，
Figure PCTCN2021109108-appb-000020
为第i维搜索范围的上限，X init为S1得到的共形阵阵元激励所组成的向量，维数与共形阵阵元数相等，
Figure PCTCN2021109108-appb-000021
为X init的第i维，σ为解空间裁剪因子，代表在S1得到的共形阵阵元激励附近所保留的解空间范围；
S2.2：在裁剪后的解空间中进行粒子的位置及速度的随机初始化；
S2.3：按照下式计算粒子适应度，更新个体最优值和种群全局最优值
Figure PCTCN2021109108-appb-000022
其中，sll total为方向图所有采样点数值中所有高于峰值旁瓣电平抑制指标SLL部分的加和；FNMW和FNMW e为第一零陷波束宽度的实际值与期望值；NULL point和
Figure PCTCN2021109108-appb-000023
为零陷位置的实际值与期望值；NULL value和
Figure PCTCN2021109108-appb-000024
为零陷数值的实际值与期望值；μ 1、μ 2、μ 3为权重系数；
S2.4：利用下式计算并更新粒子的速度和位置：
Figure PCTCN2021109108-appb-000025
Figure PCTCN2021109108-appb-000026
其中，ω为惯性权重系数；c 1和c 2为加速因子；r 1和r 2为[0，1]之间的满足均匀分布的随机数；pbest id为个体最优值；gbest d为全局最优值。
Figure PCTCN2021109108-appb-000027
在第k次迭代中粒子的第i维的速度，
Figure PCTCN2021109108-appb-000028
为第k次迭代中粒子的第i维的位置；
S2.5：为了在搜索中强调充分的全局搜索，将ω根据下式进行非线性更新：
Figure PCTCN2021109108-appb-000029
其中，k为当前迭代次数，T为最大迭代次数，ω r为ω取值范围的放缩系数，ω 0是ω取值范围的最小值；
S2.6：如果迭代达到最大次数，则运算终止，否则跳转到S2.3；最终得到满足S1.1设置的优化目标的共形阵阵元激励。
本发明的有益效果如下：
本发明的基于解空间裁剪粒子群算法的共形阵方向图综合方法，聚焦研究基于PSO的共形阵列方向图综合技术，着眼于使用低复杂度的FFT算法得到单目标优化结果，并基于该结果对PSO算法的解空间进行裁剪，有效提升了算法的收敛速度并且避免了局部收敛问题，从而提升了PSO算法性能，能够实现共形阵列的多目标方向图优化，得到满足多优化目标的共形阵阵元激励。
附图说明
图1是共形阵列模型示意图。
图2是本发明实施例S1步骤的示意图。
图3是本发明实施例的算法流程图。
图4是本发明实施例的方向图综合方法、基本PSO方法优化后得到的远场方向图对比图。
图5是本发明实施例的方向图综合方法、基本PSO方法优化后得到的最优适应度值对比图。
图6是本发明实施得到的阵元激励幅度动态范围约束下的满足多目标优化的共形阵阵元激励分布图。
具体实施方式
下面根据附图和优选实施例详细描述本发明，本发明的目的和效果将变得更加明白，以下结合附图和实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。
本发明的基于解空间裁剪粒子群算法的共形阵方向图综合方法，如图1～图3所示，该方法包括以下步骤：
S1：将峰值旁瓣电平抑制指标SLL作为唯一指标，基于投影阵列与共形阵列之间的激励转换关系和投影阵列与均匀阵列阵元激励之间的最小二乘关系，实现共形阵列与均匀阵列之间的阵元激励转换，使用IFFT和FFT方法对方向图进行快速计算和处理，得到阵元激励幅度动态范围约束下的满足SLL的共形阵阵元激励；所述S1通过以下子步骤实现：
S1.1：根据设计指标设置优化目标，优化目标包括归一化远场方向图峰值旁瓣电平抑制指标SLL＝-35dB、主波束第一零陷宽度最大值FNMW e＝10°，期望零陷位置
Figure PCTCN2021109108-appb-000030
Figure PCTCN2021109108-appb-000031
与零陷深度
Figure PCTCN2021109108-appb-000032
S1.2：设定阵元数N＝41，阵元编号1～41，设定阵元工作中心频率f，计算得到波长λ：
Figure PCTCN2021109108-appb-000033
其中，c＝3×10 8m/s，为真空中电磁波速度；
设定阵元间距为
Figure PCTCN2021109108-appb-000034
以阵列对称中心点所在切线方向为x轴方向，以过该点法线方向为y轴方向，建立全局直角坐标系，并将各阵元在局部坐标系下的方向图函数f(θ)转换为全局坐标系下的方向图函数f n(θ)，对于本实施例，f n(θ)＝f(θ)*cos(θ)。计算得到共形阵列远场方向图F(θ)：
Figure PCTCN2021109108-appb-000035
其中：A n为第n个阵元的激励；k为波长数，
Figure PCTCN2021109108-appb-000036
Figure PCTCN2021109108-appb-000037
为主波束指向的远场方向；
Figure PCTCN2021109108-appb-000038
为第n个阵元在全局坐标系下的位置矢量；j表示虚数单位；
S1.3：设定共形阵阵元激励幅度动态范围最大值为drr＝5，将阵元激励A n表示为：
A n＝I n·exp(jα n)             (3)
其中，I n为第n个阵元激励的幅值，α n为第n个阵元激励的相位。计算得到I n的取值范围
Figure PCTCN2021109108-appb-000039
Figure PCTCN2021109108-appb-000040
其中
Figure PCTCN2021109108-appb-000041
为主波束方向在全局坐标系下的位置矢量，α n的计算公式可以使阵列远场方向图的指向满足主波束方向；
S1.4：在S1.3所确定的幅值范围内，随机初始化共形阵阵元激励；
S1.5：设定主波束方向θ 0＝0°，为全局坐标系y轴方向，在主波束方向上对共形阵列进行投影，得到投影阵列；如附图2所示，投影阵列阵元x轴方向坐标与对应共形阵列阵元相等，y轴方向坐标为0；基于近似相等的峰值旁瓣电平关系，投影阵列与共形阵列之间的激励转换关系通过下式计算：
Figure PCTCN2021109108-appb-000042
其中，I pn为投影阵列第n个阵元的激励幅度；|f n(θ 0)|为共形阵列第n个阵元在主波束方向的阵元方向图幅度；|f(θ 0)|为投影阵列中阵元方向图在主波束方向的幅度；
将投影阵列按照更小的间距进行插值，将投影阵列转换为间距更小的均匀阵列，每个投影阵列阵元通过以其为中心的一段均匀阵列阵元来表示；方向图为阵元激励矩阵和导向矢量矩阵的乘积，当投影阵列与均匀阵列的远场方向图相等时，基于投影阵列和均匀阵列的导向矢量矩阵可建立最小二乘关系：
Figure PCTCN2021109108-appb-000043
其中，E p为投影阵列导向矢量矩阵，E e为均匀阵列导向矢量矩阵，基于上式的变式得到投影阵列与均匀阵列之间的激励转换关系矩阵c：
Figure PCTCN2021109108-appb-000044
其中，c即为为满足该最小二乘关系的转换矩阵，
Figure PCTCN2021109108-appb-000045
代表E e的共轭转置；
S1.6：依照均匀阵列与阵因子之间的逆傅里叶变换计算得到阵因子，与S1.2得到的阵元方向图的乘积即为远场方向图，相较于传统方向图计算公式，该方法使用快速傅里叶变换，复杂度低，计算较快，对算法整体计算量影响较小，使S1适合作为S2前置步骤。
S1.7：按照峰值旁瓣电平抑制指标SLL，将超出该指标的方向图采样点数值修正为满足指标的数值，即将方向图的旁瓣抑制在SLL以下；
S1.8：将修正后的方向图除以阵元方向图得到阵因子，并采用傅里叶变换得到均匀阵列激励数值；
S1.9：对公式(4)和(6)进行逆运算，得到共形阵阵元激励；
S1.10：根据阵元幅度激励范围
Figure PCTCN2021109108-appb-000046
对共形阵列阵元激励进行修正，使其满足阵元激励幅度动态范围限制；
S1.11：迭代进行S1.5-S1.10，如果共形阵阵元激励满足动态范围
Figure PCTCN2021109108-appb-000047
并且方向图满足峰值旁瓣电平抑制指标，迭代终止，否则运行到设定的最大次数，得到满足峰值旁瓣电平抑制指标SLL的共形阵阵元激励。
S2：根据S1得到的阵元激励，进行粒子群算法的解空间裁剪，并设计非线性更新的权重系数，保证充分的全局搜索，根据多个优化目标设计适应度函数，对共形阵方向图做进一步优化，得到阵元激励幅度动态范围约束下的满足多个优化目标的共形阵阵元激励；所述S2通过以下子步骤实现：
S2.1：基于S1得到的共形阵阵元激励和S1.3得到的阵元激励的幅值范围
Figure PCTCN2021109108-appb-000048
将解空间进行合理的裁剪，解空间的粒子每一维对应共形阵列中的一个阵元激励，确定第i维的解空间搜索范围如下：
Figure PCTCN2021109108-appb-000049
Figure PCTCN2021109108-appb-000050
其中，
Figure PCTCN2021109108-appb-000051
为粒子第i维搜索范围的下限，
Figure PCTCN2021109108-appb-000052
为第i维搜索范围的上限，X init为S1得到的共形阵阵元激励所组成的向量，维数与共形阵阵元数相等，
Figure PCTCN2021109108-appb-000053
为X init的第i维，σ为解空间裁剪 因子，代表在S1得到的共形阵阵元激励附近所保留的解空间范围。该式从整体上确定了阵元激励幅度动态范围
Figure PCTCN2021109108-appb-000054
约束下的粒子搜索的解空间范围；
S2.2：在裁剪后的解空间中进行粒子的位置及速度的随机初始化；
S2.3：按照下式计算粒子适应度，更新个体最优值和种群全局最优值：
Figure PCTCN2021109108-appb-000055
其中，sll total为方向图所有采样点数值中所有高于峰值旁瓣电平抑制指标SLL部分的加和；FNMW和FNMW e为第一零陷波束宽度的实际值与期望值；NULL point和
Figure PCTCN2021109108-appb-000056
为零陷位置的实际值与期望值；NULL value和
Figure PCTCN2021109108-appb-000057
为零陷数值的实际值与期望值；μ 1、μ 2、μ 3为权重系数，用于调节搜索效果，对于本实施例，μ 1＝0.1，μ 2＝0.5，μ 3＝0.4；
S2.4：利用下式计算并更新粒子的速度和位置
Figure PCTCN2021109108-appb-000058
Figure PCTCN2021109108-appb-000059
其中，ω为惯性权重系数；c 1和c 2为加速因子；r 1和r 2为[0，1]之间的满足均匀分布的随机数；pbest id为个体最优值；gbest d为全局最优值。
Figure PCTCN2021109108-appb-000060
在第k次迭代中粒子的第i维的速度，
Figure PCTCN2021109108-appb-000061
为第k次迭代中粒子的第i维的位置；
S2.5：由于已经对解空间进行了裁剪，因此粒子的搜索特点为小范围的精细搜索，较为强调解空间中的全局搜索。ω为调节全局搜索与局部搜索的权重系数，将ω根据下式进行非线性更新：
Figure PCTCN2021109108-appb-000062
其中，k为当前迭代次数，T为最大迭代次数，ω r为ω取值范围的放缩系数，ω 0是ω取值范围的最小值，ω r和ω 0可以实现对ω取值范围的调节；
S2.6：对于本实施例，最大迭代次数T为500代，如果迭代达到最大迭代次数，则运算终止，否则跳转到S2.3；最终得到满足S1.1设置的优化目标的共形阵阵元激励。
图4和图5所展示的是，当共形阵阵元激励幅度动态范围动态drr＝5，阵列方向图按照S1.1设置时，本发明的共形阵方向图综合方法、基本PSO算法优化后得到的远场方向图和最优适应度值对比图。从图4可以看出，本发明的方向图综合方法与基本PSO算法相比，可以将峰值旁瓣电平成功抑制在-35dB以下，第一零陷主波束宽度限制在10°以内，并在期望的 位置生成期望的零陷深度。图5是20次独立实验后得到的最优适应度函数值的平均值随迭代此处变化的曲线，该曲线表明本发明的方向图综合方法可以搜索到更好的最优适应度值，即优化效果更好。图6是共形阵阵元激励分布，可以看出阵元激励范围是[0.2，1]，满足阵元激励幅度动态范围限制drr＝5。
本领域普通技术人员可以理解，以上所述仅为发明的优选实例而已，并不用于限制发明，尽管参照前述实例对发明进行了详细的说明，对于本领域的技术人员来说，其依然可以对前述各实例记载的技术方案进行修改，或者对其中部分技术特征进行等同替换。凡在发明的精神和原则之内，所做的修改、等同替换等均应包含在发明的保护范围之内。

Claims (2)

  1. 一种基于解空间裁剪粒子群算法的共形阵方向图综合方法，其特征在于，包括以下步骤：
    S1：将峰值旁瓣电平抑制指标SLL作为唯一指标，基于投影阵列与共形阵列之间的激励转换关系和投影阵列与均匀阵列阵元激励之间的最小二乘关系，实现共形阵列与均匀阵列之间的阵元激励转换，使用IFFT和FFT方法对方向图进行快速计算和处理，得到阵元激励幅度动态范围约束下的满足SLL的共形阵阵元激励；
    S2：根据S1得到的阵元激励，进行粒子群算法的解空间裁剪，并设计非线性更新的权重系数，保证充分的全局搜索，根据多个优化目标设计适应度函数，对共形阵方向图做进一步优化，得到阵元激励幅度动态范围约束下的满足多个优化目标的共形阵阵元激励；
    所述S1通过以下子步骤来实现：
    S1.1：根据设计指标设置优化目标，包括归一化远场方向图峰值旁瓣电平抑制指标SLL、主波束第一零陷宽度最大值FNMW e、期望零陷位置
    Figure PCTCN2021109108-appb-100001
    与零陷深度
    Figure PCTCN2021109108-appb-100002
    S1.2：设定阵元数N，阵元编号1～N，设定阵元工作中心频率f，计算得到波长λ：
    Figure PCTCN2021109108-appb-100003
    其中，c＝3×10 8m/s，为真空中电磁波速度；
    设定阵元间距为
    Figure PCTCN2021109108-appb-100004
    以阵列对称中心点所在切线方向为x轴方向，以过该点法线方向为y轴方向，建立全局直角坐标系，并将各阵元在局部坐标系下的方向图函数f(θ)转换为全局坐标系下的方向图函数f n(θ)，计算得到共形阵列远场方向图F(θ)：
    Figure PCTCN2021109108-appb-100005
    其中：A n为第n个阵元的激励；k为波长数，
    Figure PCTCN2021109108-appb-100006
    为主波束指向的远场方向；
    Figure PCTCN2021109108-appb-100007
    为第n个阵元在全局坐标系下的位置矢量；j表示虚数单位；
    S1.3：设定共形阵阵元激励幅度动态范围最大值为drr，将阵元激励A n表示为：
    A n＝I n·exp(jα n)  (3)
    其中，I n为第n个阵元激励的幅值，α n为第n个阵元激励的相位；计算得到I n的取值范围
    Figure PCTCN2021109108-appb-100008
    其中
    Figure PCTCN2021109108-appb-100009
    为主波束方向在全局坐标系下的位置矢量；
    S1.4：在S1.3所确定的幅值范围内，随机初始化共形阵阵元激励；
    S1.5：设定主波束方向θ 0＝0°，为全局坐标系y轴方向，在主波束方向上对共形阵列进行投影，得到投影阵列；投影阵列阵元x轴方向坐标与对应共形阵列阵元相等，y轴方向坐标为0；基于近似相等的峰值旁瓣电平关系，投影阵列与共形阵列之间的激励转换关系通过下式计算：
    Figure PCTCN2021109108-appb-100010
    其中，I pn为投影阵列第n个阵元的激励幅度；|f n(θ 0)|为共形阵列第n个阵元在主波束方向的阵元方向图幅度；|f(θ 0)|为投影阵列中阵元方向图在主波束方向的幅度；
    将投影阵列按照更小的间距进行插值，将投影阵列转换为间距更小的均匀阵列，每个投影阵列阵元通过以其为中心的一段均匀阵列阵元来表示；基于投影阵列和均匀阵列的导向矢量矩阵之间存在的最小二乘关系，得到投影阵列与均匀阵列之间的激励转换关系矩阵：
    Figure PCTCN2021109108-appb-100011
    其中，E p为投影阵列导向矢量矩阵，E e为均匀阵列导向矢量矩阵，c为满足该最小二乘关系的转换矩阵；
    S1.6：依照均匀阵列与阵因子之间的逆傅里叶变换计算得到阵因子，与阵元方向图的乘积即为远场方向图；
    S1.7：按照峰值旁瓣电平抑制指标SLL，将超出该指标的方向图采样点数值修正为满足指标的数值；
    S1.8：将修正后的方向图除以阵元方向图得到阵因子，并采用傅里叶变换得到均匀阵列激励数值；
    S1.9：对公式(4)和(5)进行逆运算，得到共形阵阵元激励；
    S1.10：根据阵元幅度激励范围
    Figure PCTCN2021109108-appb-100012
    对共形阵列阵元激励进行修正，使其满足阵元激励幅度动态范围限制；
    S1.11：迭代进行S1.5-S1.10，如果共形阵阵元激励满足动态范围
    Figure PCTCN2021109108-appb-100013
    并且方向图满足峰值旁瓣电平抑制指标，迭代终止，否则运行到设定的最大次数，得到满足峰值旁瓣电平抑制指标SLL的共形阵阵元激励。
  2. 根据权利要求1所述的基于解空间裁剪粒子群算法的共形阵方向图综合方法，其特征在于，所述S2通过以下子步骤来实现：
    S2.1：基于S1得到的共形阵阵元激励和S1.3得到的阵元激励的幅值范围
    Figure PCTCN2021109108-appb-100014
    将解空 间进行合理的裁剪，解空间的粒子每一维对应共形阵列中的一个阵元激励，确定第i维的解空间搜索范围如下：
    Figure PCTCN2021109108-appb-100015
    Figure PCTCN2021109108-appb-100016
    其中，
    Figure PCTCN2021109108-appb-100017
    为粒子第i维搜索范围的下限，
    Figure PCTCN2021109108-appb-100018
    为第i维搜索范围的上限，X init为S1得到的共形阵阵元激励所组成的向量，维数与共形阵阵元数相等，
    Figure PCTCN2021109108-appb-100019
    为X init的第i维，σ为解空间裁剪因子，代表在S1得到的共形阵阵元激励附近所保留的解空间范围；
    S2.2：在裁剪后的解空间中进行粒子的位置及速度的随机初始化；
    S2.3：按照下式计算粒子适应度，更新个体最优值和种群全局最优值
    Figure PCTCN2021109108-appb-100020
    其中，sll total为方向图所有采样点数值中所有高于峰值旁瓣电平抑制指标SLL部分的加和；FNMW和FNMW e为第一零陷波束宽度的实际值与期望值；NULL point和
    Figure PCTCN2021109108-appb-100021
    为零陷位置的实际值与期望值；NULL value和
    Figure PCTCN2021109108-appb-100022
    为零陷数值的实际值与期望值；μ 1、μ 2、μ 3为权重系数；
    S2.4：利用下式计算并更新粒子的速度和位置：
    Figure PCTCN2021109108-appb-100023
    Figure PCTCN2021109108-appb-100024
    其中，ω为惯性权重系数；c 1和c 2为加速因子；r 1和r 2为[0，1]之间的满足均匀分布的随机数；pbest id为个体最优值；gbest d为全局最优值；
    Figure PCTCN2021109108-appb-100025
    在第k次迭代中粒子的第i维的速度，
    Figure PCTCN2021109108-appb-100026
    为第k次迭代中粒子的第i维的位置；
    S2.5：为了在搜索中强调充分的全局搜索，将ω根据下式进行非线性更新：
    Figure PCTCN2021109108-appb-100027
    其中，k为当前迭代次数，T为最大迭代次数，ω r为ω取值范围的放缩系数，ω 0是ω取值范围的最小值；
    S2.6：如果迭代达到最大次数，则运算终止，否则跳转到S2.3；最终得到满足S1.1设置的优化目标的共形阵阵元激励。
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Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116192206A (zh) * 2023-03-03 2023-05-30 电子科技大学 基于广义回归神经网络的大规模共形阵实时波束综合方法
CN116315736A (zh) * 2023-03-17 2023-06-23 电子科技大学 基于二重粒子群算法的共形阵列同时发射多波束动态组阵方法
CN116842846A (zh) * 2023-07-14 2023-10-03 云南师范大学 一种基于改进的do算法的阵列天线方向图综合设计方法
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US12431634B2 (en) 2021-03-08 2025-09-30 Zhejiang University Method for generate array element excitation of a conformal array based on an iterative algorithm
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CN115688585B (zh) * 2022-10-31 2026-02-27 西安交通大学 一种基于遗传算法的核反应堆系统分析程序参数自动优化方法
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104393414A (zh) * 2014-11-21 2015-03-04 西安电子科技大学 基于时间调制共形相控阵列的快速方向图综合方法
CN106126836A (zh) * 2016-06-28 2016-11-16 西安电子科技大学 基于加权法向回归法的阵列天线方向图拟合方法
CN109813967A (zh) * 2017-11-21 2019-05-28 深圳市通用测试系统有限公司 一种阵列天线方向图的测量方法、设备、系统以及计算机可读存储介质
CN113033080A (zh) * 2021-03-08 2021-06-25 浙江大学 一种基于解空间裁剪粒子群算法的共形阵方向图综合方法

Family Cites Families (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5347287A (en) * 1991-04-19 1994-09-13 Hughes Missile Systems Company Conformal phased array antenna
US9395718B1 (en) * 2005-06-03 2016-07-19 Sciperio, Inc. Optimization of unique antenna and RF systems for specific substrates
US9843103B2 (en) * 2014-03-26 2017-12-12 Elwha Llc Methods and apparatus for controlling a surface scattering antenna array
US9912055B2 (en) * 2014-07-10 2018-03-06 The Boeing Company Method and apparatus for modifying a reconfiguration algorithm for an antenna system
KR101877141B1 (ko) * 2016-12-08 2018-07-10 한국항공우주연구원 안테나 패턴 합성 장치 및 방법
CN106886656B (zh) * 2017-03-15 2020-12-25 南京航空航天大学 一种三维阵列天线方向图旁瓣抑制方法
CN107657070B (zh) * 2017-07-31 2021-05-25 西安电子科技大学 基于遗传算法频率分集共形阵列波束的解耦合方法及天线
US11303040B2 (en) * 2019-05-08 2022-04-12 The Government Of The United States Of America, As Represented By The Secretary Of The Navy Conformal phased arrays
CN112100811A (zh) * 2020-08-13 2020-12-18 西北工业大学 一种基于自适应风驱动优化算法的天线阵方向图综合方法

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104393414A (zh) * 2014-11-21 2015-03-04 西安电子科技大学 基于时间调制共形相控阵列的快速方向图综合方法
CN106126836A (zh) * 2016-06-28 2016-11-16 西安电子科技大学 基于加权法向回归法的阵列天线方向图拟合方法
CN109813967A (zh) * 2017-11-21 2019-05-28 深圳市通用测试系统有限公司 一种阵列天线方向图的测量方法、设备、系统以及计算机可读存储介质
CN113033080A (zh) * 2021-03-08 2021-06-25 浙江大学 一种基于解空间裁剪粒子群算法的共形阵方向图综合方法

Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116192206A (zh) * 2023-03-03 2023-05-30 电子科技大学 基于广义回归神经网络的大规模共形阵实时波束综合方法
CN116192206B (zh) * 2023-03-03 2023-09-12 电子科技大学 基于广义回归神经网络的大规模共形阵实时波束综合方法
CN116315736A (zh) * 2023-03-17 2023-06-23 电子科技大学 基于二重粒子群算法的共形阵列同时发射多波束动态组阵方法
CN116842846A (zh) * 2023-07-14 2023-10-03 云南师范大学 一种基于改进的do算法的阵列天线方向图综合设计方法
CN116842846B (zh) * 2023-07-14 2024-03-08 云南师范大学 一种基于改进的do算法的阵列天线方向图综合设计方法
CN117852371A (zh) * 2023-12-25 2024-04-09 西安电子科技大学 高效的共形阵列天线方向图综合方法
CN119783532A (zh) * 2024-12-25 2025-04-08 云南师范大学 基于改进鹈鹕优化算法的稀布阵列天线设计方法

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