Low-Sidelobe Pattern Synthesis Using Iterative Fourier Techniques Coded in MATLAB [EM Programmer's Notebook]

The iterative Fourier technique for the synthesis of low-sidelobe patterns for linear arrays with uniform element spacing is described. The method uses the property that for a linear array with uniform element spacing, an inverse Fourier transform relationship exists between the array factor and the element excitations. This property is used in an iterative way to derive the array element excitations from the prescribed array factor. A brief outline of the iterative Fourier technique for the synthesis of low-sidelobe patterns for linear arrays will be given. The effectiveness of this method for realizing low-sidelobe sum and difference patterns will be demonstrated for linear arrays equipped with 50 and 80 elements. This demonstration of effectiveness also involves the recovery of the original low-sidelobe patterns, as close as possible, in case of element failures. Included is a program listing of this synthesis method, coded in MATLABtrade. With a few minor modifications/additions, the included MATLAB program can also be used for the design of thinned linear arrays having a periodic element spacing. Since the computational part of the included MATLAB program is coded using vector/matrix operations, this program can easily be extended for the synthesis of low-sidelobe patterns of planar arrays with a periodic element spacing, including pattern recovery in the case of defective elements.     

Phase-only synthesis of minimum peak sidelobe patterns for linearand planar arrays

Minimization of the maximum sidelobe level for a given array geometry by phase-only adjustment of the element excitations is considered. Optimum phases are obtained by using a numerical search procedure to minimize the expression for the pattern sidelobe level with respect to the element phases. Results for both linear and planar arrays of equispaced elements are presented. The data suggests that optimum sidelobe level is a logarithmic function of array size, and optimum patterns have relative efficiencies that are typically somewhat greater than for comparable-amplitude tapered arrays. An analytic synthesis algorithm is presented for use on very large arrays for which the numerical search technique for the minimization of the sidelobe level is computationally impractical. This method produces patterns with characteristics similar to arrays synthesized using the numerical search method, i.e. relatively uniform angular distribution of energy in the sidelobe region, and generally decreasing maximum sidelobe level as the array size is increased     

基于迭代FFT算法的平面阵列交错稀疏布阵方法

交错稀疏阵列天线的设计需要实现“稀疏布阵”和“子阵交错机制”两个关键技术的有机“协同”.提出一种基于改进迭代快速傅里叶变换(Fast Fourier Transformation, FFT)算法的均匀面阵交错稀疏布阵机制.鉴于均匀矩形平面阵列天线激励与方向图存在二维傅里叶变换的关系, 该方法通过对均匀面阵方向图采样的频谱能量分析, 采用交错选取子阵激励的方法, 实现了面阵天线方向图频谱能量的均匀分配, 获得了近似相同方向图的交错子阵设计.在此基础上, 采用迭代FFT算法对交错子阵激励进行迭代循环, 有效降低了交错子阵的峰值旁瓣电平.理论分析与实验仿真证明, 相对于基于循环差集和互补差集的稀疏交错优化方法, 该算法实现的交错稀疏阵列设计具有方向图近似程度更高, 且峰值旁瓣电平更低的优点.     

Thinned arrays using genetic algorithms

Large arrays are difficult to thin in order to obtain low sidelobes. Traditional statistical methods of aperiodic array synthesis fall far short of optimum configurations. Traditional optimization methods are not well suited for optimizing a large number of parameters or discrete parameters. This paper presents how to optimally thin an array using genetic algorithms. The genetic algorithm determines which elements are turned off in a periodic array to yield the lowest maximum relative sidelobe level. Simulation results for 200 element linear arrays and 200 element planar arrays are shown. The arrays are thinned to obtain sidelobe levels of less than -20 dB. The linear arrays are also optimized over both scan angle and bandwidth.<>     

Array pattern distortion and remedies in space-time adaptiveprocessing for airborne radar

Space-time adaptive processing (STAP) for airborne early warning radar has been a very active area of research since the late 1980's. An airborne rectangular planar array antenna is usually configured into subarrays and then partial adaptive processing is applied to the outputs of these subarrays. In practice, three kinds of errors are often encountered: the array gain and phase errors existing in each element, the channel gain and phase errors, and the clutter covariance matrix estimation errors due to insufficient secondary data samples. These errors not only degrade the clutter suppression performance, but also cause the adapted array patterns to suffer much distortion (high sidelobes and distorted mainbeams), which may result in the rise of false-alarm probability and make the adaptive monopulse tracking and sidelobe blanketing more difficult. In this paper, the causes of the above three kinds of errors to array pattern distortion are discussed and a novel quadratic soft constraint factored approach is proposed to precisely control the peak sidelobe level of adapted patterns. The soft constraint factor can be determined explicitly according to the peak sidelobe level desired and the known or desired tolerant error standard deviations. Numerical results obtained by using high-fidelity simulated airborne radar clutter data are provided to illustrate the performance of the proposed approach. Although the method is presented for STAP, it can be directly applied to the conventional adaptive beamforming for rectangular planar arrays used to suppress jammers     

基于遗传算法和模拟退火的不等间距稀布阵的设计

副瓣电平在天线阵列的设计中是很重要的指标,已经有很多方法进行这方面的改进。该文在稀布阵概念的基础上,引入了距离微扰,提出不等间距稀布阵的模型,来进一步改善天线阵的副瓣电平,并且利用遗传算法和模拟退火对这种不等间距稀布阵进行了综合设计。给出了200元线阵和4020面阵的优化结果,从仿真结果可以看到天线副瓣电平得到了改善。     

Reflector radiation pattern from planar near-field measurements of array feed

High gain shaped beam antennas for satellite frequency reuse applications are almost exclusively obtained by the use of complex multielement feed arrays to provide pattern control in conjunction with offset reflectors to remove blockage effects. In the design of complex multielement feed arrays for offset reflectors, the element excitations are usually synthesized using the isolated element properties. Proper performance of the array often requires that these theoretical excitations be modified to account for the effects on the feed elements due to the array environment. Near-field planar probing of the fields of the feed array have been found to provide an efficient and accurate method of predicting the secondary performances, including cross polarization and axial ratio. The nearfield measurement technique, moreover, provides an extremely effective method of determining the element performance and for determining the required compensation for desired antenna performance.     

Multiobjective Optimization of Real and Coupled Antenna Array Excitations via Primal-Dual, Interior Point Filter Method From Spherical Mode Expansions

A novel method for the multiobjective optimization of arbitrary planar array excitations is presented. The optimization problem formulation, which inherently takes into account every array element pattern as well as all interelement couplings, is based on matrix-valued functions which are computed from the generalized-scattering-matrix characterization of an array and spherical mode expansions of its radiated field. It allows the maximization of the directive gain subject to a maximum sidelobe level, a maximum crosspolar level and a minimum aperture illumination efficiency, the setting of null-pointing directions and the dynamic range control. To solve the resulting non-linear optimization problem, we have developed a primal-dual interior point method specifically adapted to the presented formulation, which makes use of novel filtering techniques. Numerical examples of arrays of microstrip patches and dielectric resonator antennas covering a wide variety of requirements on these parameters are presented.      

Planar 64 element millimetre wave antenna

A simple 64 element planar array antenna, with H-plane sidelobes below -35 dB at larger angles than 19° from boresight and a gain above 30.4 dBi, is presented for the band 37.0-39.5 GHz. The radiating elements are fed in parallel by a waveguide feed network. The H-plane sidelobe level is reduced by using a combination of arrays, the zero in the element radiation pattern, and amplitude tapering     

Constrained optimization of the performance indices of arbitrary array antennas

The solution to the optimization of performance indices of array antennas such as directive gain, efficiency index, and signal-to-noise ratio, do not provide information regarding the sidelobe region of the radiation pattern. It is shown that, with proper constraints on the sidelobes, a given performance index can be optimized to give a radiation pattern with desired sidelobe levels. As most of the performance indices of an array antenna can be expressed as a ratio of two Hermitian quadratic forms, an eigenvalue method is used for the constrained optimization. This method gives explicit expressions for the excitation vector and constrained values of the performance indices. An iterative technique is used to ensure that the specified field values occur at the sidelobe peak positions. The element excitations obtained by this technique for maximum gain and uniform sidelobe level are similar to these obtained by the Dolph-Chebyshev technique.     

Nonuniformly spaced linear and planar array antennas for sidelobe reduction

The material discussed can be divided into two parts. In the first part, an iteration method is presented for calculating the distances between the elements of a symmetrical nonuniformly spaced linear array antenna for sidelobe reduction. The amplitude of the excitation is assumed to be constant. The iteration method is applied to linear array consisting of 24 elements. After a few iterations, the sidelobe-to-mainlobe power ratio was reduced to over 22 dB from its value of 13.2 dB for uniform array spacing. In the second part, several symmetrical nonuniformly spaced planar array antennas have been designed, using the nonuniform linear array spacings of part one. The planar arrays include square-shaped and circular structures, with the number of elements ranging from 284 to 576. The iteration method discussed can be applied to linear arrays with any number of elements to obtain nonuniform grid spacings for sidelobe reduction. A number of planar grid structures can be constructed using the nonuniform linear grids. The nonuniform linear and planar arrays utilize fewer radiating elements and result in desirable sidelobe structures.     

宽带相控阵天线延迟线分析

采用频率无关移相器的相控阵天线的波束指向会随频率发生变化,实时延迟线是提高宽带相控阵天线波束指向精度的重要方法。分析了子阵级采用延迟线,单元级使用移相器的宽带相控阵天线副辫特性,发现当工作频率改变时,由于阵列存在周期相位误差导致天线副瓣电平抬高。针对此问题,提出单元级精细延迟线方案,消除周期相位误差对天线副瓣的影响。仿真结果表明,这种方法在扩展相控阵天线带宽的同时,明显改善了天线的副瓣特性。     

共享孔径同心圆阵稀疏交错优化布阵方法

同心圆阵列天线具有波束对称、360°方位角扫描、抗干扰能力强等优点，被广泛应用于星载、机载、舰载雷达及飞机声呐等领域。在天线孔径有限的情况下，如何进一步提高同心圆阵的孔径利用率，通过孔径的空分复用，设计出子阵稀疏交错分布的多功能同心圆阵列天线，具有较大的研究价值。利用均匀同心圆阵列天线激励与方向图函数存在二维傅里叶-贝塞尔变换关系，基于二维三次插值和密度加权，提出了一种同心圆阵稀疏交错优化布阵的方法。该方法通过对均匀同心圆阵列天线方向图采样值的频谱能量进行分析，采用三次插值的方法，实现了同心圆天线阵列方向图函数到同心圆阵元激励能量的映射转换；基于密度加权的原理，对排序后归一化阵元激励的奇偶交错选取，使得稀疏交错子阵方向图频谱能量均分匹配，实现了同心圆阵的稀疏交错优化布阵设计。仿真结果表明，该方法得到的交错子阵天线具有峰值旁瓣电平低、主瓣宽度窄且方向图性能近似程度高的优点，有效解决了同心圆阵列天线稀疏交错优化布阵的设计难题，实现了两子阵交错的共享孔径多功能同心圆阵列天线设计。     

六边形平面阵旁瓣电平优化的遗传算法

首先对遗传算法作了改良,精心设计了适应函数,使遗传算法可以快速收敛。然后用改进的遗传算法降低天线单元正三角形排列的六边形平面阵的最大旁瓣电平,结果表明通过对激励幅度的优化,六边形平面阵的辐射特性可以获得很大的改善,天线阵的最大旁瓣电平比均匀激励的降低了约11dB。良好的计算结果表明遗传算法是目前求解此类问题的有效方法。     

Further discrete optimizations for continuous aperture illuminations

Two applications of an iterative procedure to establish a means of optimizing theoretical low sidelobe antenna patterns are discussed. Examples described consider discrete element linear array antennas where the parameters involved in the optimization process are coefficients ordinarily associated with continuous aperture illuminations. One application uses the iterative procedure to control far-out sidelobe levels of the far-field pattern to establish array element excitations appropriate for low sidelobe behavior throughout the entire visible region of space. The other application uses the procedure to establish beam port amplitude weightings at a minimum number of beam ports in a multibeam feed network also suitable for low sidelobe antenna pattern behavior.     

Synthesis of Optimal Sum and Difference Patterns from Time Modulated Hexagonal Planar Arrays

An efficient array synthesis technique is developed for the design of optimal monopulse antennas in time modulated planar arrays with triangular lattices and hexagonal boundaries. Major emphasis is laid on the realization of low sidelobe array patterns from uniform amplitude excitations, and the inherent sideband radiations in time modulated arrays are suppressed to a sufficient low level. The synthesis technique implements the differential evolution strategy (DES) as the optimization tool, and a fast computation method based on 2D Fast Fourier Transform (FFT) is employed to speed up the optimization. Numerical results show that with the aid of the time modulation technique, the sum, difference, and double-difference patterns are obtainable from an array with fixed uniform amplitude excitations, thus demonstrating the effectiveness and validity of the proposed technique.     

Mutual coupling and sidelobe tapers in phase-only antenna synthesisfor linear and planar arrays

A method of obtaining the lowest possible peak sidelobe levels, given a specified sidelobe envelope, by phase-only variation of the generator phases is presented. A generalization of earlier work by the authors, this technique involves the optimization of a piecewise differentiable objective function using the method of steepest descent to obtain desired generator phases, given prescribed excitation magnitudes. The method has been applied to both linear and planar arrays of radiators, with single-mode mutual coupling effects included to provide realistic data. Values for the various array performance indices are presented, and results indicate that introduction of sidelobe taper improves the array gain while raising the peak sidelobe level somewhat. Inclusion of mutual coupling effects alters the required phases for optimum patterns but does not significantly affect the performance indices of the array     

A procedure for synthesizing a specified sidelobe topography usingan arbitrary array

A simple method to arrive at an optimum set of array excitations to achieve a specified radiation pattern is presented. An auxiliary function is formulated, based on the envelope of the required sidelobe structure and the array factor, in the sidelobe region. This function is minimized, subject to the main lobe constraints and the null steering constraints, to determine the excitations. An iterative procedure is used to generate the desired pattern, with the additional constraints like sidelobe level, symmetric excitation, and so on. The method has been successfully applied to synthesize linear arrays and circular arc arrays and to generate symmetric as well as asymmetric patterns     

Element pattern of an axial dipole in a cylindrical phased array, Part I: Theory

Cylindrical array antennas are attractive for applications requiring uniform360degazimuthal pattern performance. For very low sidelobe or precise angle measurement designs, an accurate knowledge of the mutually coupled element pattern becomes important. A modal solution is presented for an element pattern in a periodic array of axial dipole radiators placed coaxially over a circular cylindrical ground. This solution avoids the problems associated with asymptotic appproaches and displays a number of advantages: 1) it is exact, subject only to truncation errors; 2) it is uniformly valid in all spatial regions for both rectangular and, with a simple modification, for triangular isosceles lattice configurations; and 3) it provides absolute gain information. The analysis is presented along with numerical results for representative parameter values, selected to illustrate the various trade-offs. Comparison with published data employing the asymptotic approach and with planar array results is given.     

Out-of-Band Response of Antenna Arrays

The response of antenna arrays to out-of-band frequencies has been analyzed using the effective-aperture approach. An average value of effective aperture can be obtained by averaging the incidence angle and the polarization of the incidence field. Far-field patterns have also been calculated by treating the array element excitations as random variables. The randomness in the element excitations causes a decrease in directivity and an increase in sidelobe level. Out-of-band measurements on a slotted-waveguide array confirm these trends.