Element Failure Correction for a Large Monopulse Phased Array Antenna With Active Amplitude Weighting

Recently a new method is introduced to synthesize low sidelobe patterns for planar array antennas with a periodic element arrangement. The method makes use of the property that for a planar array with periodic spacing of the elements, 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. The same method is also able to partially compensate the degradation of the sidelobe and gain performance of array patterns due to element failures. Numerical examples of array-failure correction using this method are given for ultralow sidelobe sum and difference patterns of a 5800-element circular array where the failed elements are randomly dispersed across the aperture. The tapers in this array are created exclusively by active weighting in the transmit/receive (T/R) modules using variable gain control.     

Synthesis of Low and Equal-Ripple Sidelobe Patterns in Time-Modulated Circular Antenna Arrays

In this paper, the time modulation technique is applied into circular antenna arrays with uniform amplitude excitations for the synthesis of ultra-low sidelobe and equal-ripple radiation patterns. The differential evolution (DE) algorithm is adopted to optimize the excitation phases and the switch-on time intervals of each element of the time-modulated circular array (TMCA). Several low-sidelobe patterns synthesized from TMCAs were compared to those of the conventional circular arrays. Numerical results show that the TMCA can be successfully used for the synthesis of low SLLs even if the amplitude excitations are uniform. Supported in part by the Natural Science Foundation of China under Grant No. 60571023, the New Century Excellent Talent Program in China (Grant No. NCET-06-0809), and in part by the 111 project of China (Grant No. B07046).     

Evolutionary optimization for pattern synthesis and reduction of mutual coupling of linear antenna arrays

Optimal design of antenna arrays to minimize the mutual coupling effects in the geometrical arrangements of the linear antenna array (LAA) and circular antenna array (CAA) is dealt with in this work. Two different cases are considered to reduce the effect of LAA and CAA: Case‐1 in which the current excitations of the antenna array are considered to get the optimal radiation pattern of two geometry called LAA and CAA and Case‐2 in which inter‐element spacing and current excitations are both optimized for LAA geometry. A cost function that involves the mutual coupling factor as an optimization factor is developed to reduce the side lobe level (SLL), which takes mutual coupling effects into consideration. Excitation values and inter‐elemental spacing are optimized using particle swarm optimization (PSO). In LAA, for 8‐, 12‐, 16‐element arrays, SLLs are reduced by ?15.52, ?16.71, and ?17.78 dB in Case‐1. For the same sets of element arrays, SLLs were reduced by ?17.35, ?19.71, and ?20.26 dB in Case‐2. In CAA, the current excitations of the antenna array are optimized. For 8‐, 12‐, and 16‐ element arrays, SLLs are reduced to ?7.405, ?10.52, and ?9.43 dB, respectively. The arrays coded with the help of MATLAB based computation and the results obtained by MATLAB are validated by using CST.     

Fractile arrays: a new class of tiled arrays with fractal boundaries

In this paper, a new class of antenna arrays are introduced, which we call fractile arrays. A fractile array is defined as any array with a fractal boundary contour that tiles the plane without gaps or overlaps. It will be shown that the unique geometrical features of fractiles may be exploited in order to make available a family of deterministic arrays that offer several highly desirable performance advantages over their conventional periodic planar array counterparts. Most notably, fractile arrays have no grating lobes even when the minimum spacing between elements is increased to at least one-wavelength. This has led to the development of a new design methodology for modular broadband low-sidelobe arrays that is based on fractal tilings. Several examples of fractile arrays will be considered including Peano-Gosper, terdragon, 6-terdragon, and fudgeflake arrays. Efficient iterative procedures for calculating the radiation patterns of these fractile arrays to arbitrary stage of growth P are also introduced in this paper.     

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.     

The orthogonal method for the geometry synthesis of a linearantenna array

The orthogonal method for geometry synthesis of a linear antenna array is presented. We start from an initial array, and we perturb the element positions by using an iterative procedure and applying the orthogonal method. Applications for arrays with uniform excitation give patterns with the desired sidelobe level     

A multi-objective approach in the linear antenna array design

We show that linear antenna array design can be modeled as a multi-objective optimization problem. A genetic algorithm is proposed for the solution of this problem. This genetic algorithm efficiently computes the trade-off curve between main beam width and side lobe level for linear antenna arrays with uniform and non-uniform separations. For uniform separation, the proposed algorithm is validated against the Chebyshev method for the cases of 6-, 8-, 10-, and 12-element linear arrays. Simulation results for non-uniform spacing with uniform and non-uniform excitations applied across the array indicate that the trade-off curve between main beam width and side lobe level for uniform spacing arrays can be improved by introducing non-uniform spacing.     

Phase-locked injection laser arrays with variable stripe spacing

A phase-locked injection laser array is described which utilizes variations in spacing of identical lasing elements to vary the coupling between them. In general, phase-locked arrays have been fabricated as periodic structures with uniform coupling, although arrays with different element sizes have been described. An important advantage of the variable spacing array (VSA) structure over those designs is that the fundamental array mode can be readily matched to a uniform pumping profile across the entire array aperture. This allows the variable spacing arrays to be optimized for high-power operation. A coupled-mode analysis indicates that excellent matching of fundamental array mode to a uniform gain distribution can be obtained. However, for some array geometries the operation of array modes other than conventional 0 and 180° phase shift modes is enhanced. Variable spacing arrays have exhibited phase-locked behavior to CW outputs as high as 80 mW (7 elements) and single longitudinal mode operation to powers > 50 mW. Observation of the array emission patterns confirms the results of the coupled-mode analysis.     

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     

Optimal virtual element patterns for adaptive arrays

A major problem in the use of small arrays is the perturbation in the element patterns due to mutual coupling and diffraction effects. The element patterns differ from each other and need to be corrected in order to obtain an array pattern that is close to the desired one. A matrix method can be used to correct the element patterns by modifying the original input/output weights to corresponding weights for corrected elements and vice versa. In this paper the main goal of the array correction is the maximal identity of the element patterns. In addition to identical element patterns the corrected array is characterized by uniform element spacing, which can be chosen to differ significantly from the element spacing in the real array making the corrected array more like a pure virtual array. For the array correction the linear least square error method has been used. To show the applicability of the virtual array, this method is applied to a typical beam scan case, and also over a frequency band.     

一种基于迭代FFT算法的直线稀疏阵列优化方法

介绍了一种基于迭代快速傅里叶变换(FFT)算法的优化方法来实现直线稀疏阵列的峰值旁瓣电平最优化,分析并给出了该方法的详细优化步骤.利用阵列因子与阵元激励之间存在的傅里叶变换关系,对不同的初始随机阵元激励分别作迭代循环,便可以得到最优的阵元分布.在迭代过程中,根据稀疏率将阵元激励按幅度大小置1置0来完成阵列稀疏.通过对仿真结果进行分析,证明了该方法的快速性、有效性和稳健性.     

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.<>     

Edge effects in finite arrays of uniform slits on a ground plane

The results obtained by modeling a linear array as an infinite periodic structure can be used for the analysis of finite arrays as the zero-order approximation of a perturbation technique. This idea is utilized to investigate the edge effects in two arrays of uniform slits fed by parallel-plate waveguides terminated on a ground plane. It is shown that the realized gain pattern of an element depends substantially upon its position in the array. This is true particularly for the deep resonance notches in the patterns which are present for certain element spacings. When the array is excited with uniform magnitude and linear phase, the aperture voltages are the superposition of a term, corresponding to the infinite array model, plus another correction term (a "spatial transient") representing the edge effect. The influence of this term is particularly relevant when the array is scanned at endfire. In such a case, the method introduced here allows the prediction of the element terminal admittances and the array pattern, while according to the infinite array model no radiation would be permitted.     

Analytical array polynomial method for linear antenna arrays with phase-only control

A new analytical synthesis technique is developed for the phase-only control of linear antenna arrays and is based on the Schelkunoff's unit circle. The array factor is formulated as an array polynomial in the complex z-plane and as a product of corresponding subpolynomials such that their roots are located on the unit circle. A constraint is derived such that the expansion of the subpolynomials yields current excitations with unity magnitudes. In general, the constraint of phase-only control forces some element excitations to be zero for an arbitrary number of array elements. The subpolynomial with the largest degree is used to synthesize the main beam characteristics. The null steering for interference suppression is obtained by using only one subpolynomial to steer only one null. The results verify the developed analytical solution to synthesize the prescribed patterns using the phase shifters of the linear antenna arrays.     

Model-based synthesis of shaped-beam patterns with the minimum number of elements: a state-space method

Conventional antenna array synthesis methods can give good performance for uniform spaced antenna arrays within desired performance bounds. However, due to the restriction of uniform antenna element spacing, a lot of elements are required. Because of the above-mentioned drawback, in this paper, a new approach is presented to synthesise uniform spaced antenna array using the minimum number of elements. This approach introduces the state-space model to represent the desired discrete array pattern that is sampled uniformly from ?1 to 1 corresponding to 0–180°, then uses the desired sampled array pattern directly to construct the forward–backward data matrix that is introduced to estimate the model parameters, from which the locations and excitations of the new antenna elements can be extracted. The appropriate roots that are located on the unit circle are selected to obtain new radiation pattern. Simulation results show the viability for both shaped-beam and pencil-beam designs.     

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.     

On the empirical optimization of antenna arrays

Empirical optimization is an algorithm for the optimization of antenna array performance under realistic conditions, accounting for the effects of mutual coupling and scattering between the elements of the array and the nearby environment. The algorithm can synthesize optimum element spacings and optimum element excitations. It is applicable to arrays of various element types having arbitrary configurations, including phased arrays, conformal arrays and nonuniformly spaced arrays. The method is based on measured or calculated element-pattern data, and proceeds in an iterative fashion to the optimum design. A novel method is presented in which the admittance matrix representing an antenna array, consisting of both active and passive elements, is extracted from the array's element-pattern data. The admittance-matrix formulation incorporated into the empirical optimization algorithm enables optimization of the location of both passive and active elements. The methods also provide data for a linear approximation of coupling as a function of (nonuniform) element locations, and for calculation of element scan impedances. Computational and experimental results are presented that demonstrate the rapid convergence and effectiveness of empirical optimization in achieving realistic antenna array performance optimization.     

Antenna designer's notebook-effects of a missing element on Taylorarray patterns

It is well known that the sidelobe level of a tapered low-sidelobe array is degraded by a missing or failed element and that the effect is strongest (worst) when the outage (missing element) is at or near the center of the array. To illustrate this quantitatively, the effects of one missing center element in various tapered linear arrays is shown     

迭代投影的平顶方向图综合算法

针对现有的平顶波束综合形成算法计算量较大的问题,提出了一种迭代求解平顶波束的快速形成算法。该算法首先设置方向图参数、迭代条件,然后利用方向图与阵元加权系数的变换关系设计投影算法并通过二阶差分运算确定过渡带,最后结合蝶形计算方法快速迭代逼近理想的平顶方向图。实验结果表明,该算法相比凸优化算法运算效率较高,并且可修复阵元失效后的平顶方向图。算法运算次数随着副瓣阈值、主瓣宽度和零陷深度等参数的变化而变化。     

Cosine pattern synthesis for single and multiple main beamuniformly spaced linear arrays

The method of cosine pattern synthesis for single- and multiple-main-beam equispaced linear arrays is introduced. The cosine pattern function is characterized by the position of the main beam in the &thetas;-domain and its half-power beamwidth. The Fourier series and Woodward-Lawson methods are applied to the special cases of single- or multiple-main-beam cosine pattern synthesis. The patterns produced by application of these classical shaped-beam synthesis methods can then be used as initial patterns for iterative and perturbational techniques. Examples are presented and discussed, including the use of multiple-main-beam cosine pattern synthesis to design a high-power, high-frequency, ground-based transmitter for the creation of an array of `wireless' ionospheric dipoles