Thinning of 2D and 3D Fractal Antenna Arrays with Bounded and Unbounded Fractal Distribution Functions for Celestial Communications

Fractal antenna arrays are geometry‐based thinned arrays having multiband applications. The major challenge of these arrays is their large number of elements at higher expansion factors. This article presents the thinning of fractal antenna arrays while maintaining an appropriate balance between the side lobe level and beam width by using various quantized fractal distribution functions. A 2D square fractal antenna array and 3DSierpinski gasket antenna array are considered in this article to validate the proposed distribution functions. Nearly one third of the antenna elements are thinned in each successive iteration except in the case of a one‐count distribution function. The proposed technique can simplify practical implementation and exhibits better performance for various parameters such as the side lobe level, side lobe angle, and half power beam width than fully populated fractal antenna arrays.     

基于Weierstrass函数的分形天线阵辐射特性分析

分形天线是分形几何和天线技术交叉的产物,分形概念用于天线阵的工程合成,有助于将等幅度面阵和随机面阵的优点结合起来,将分形的自相似特征用于随机面阵设计有助于控制旁瓣区域的天线方向图。基于维尔斯特拉斯(Weierstrass)广义函数,研究天线阵排列系数函数的连续和不可微分的特性,通过对天线阵的分形电动力学和天线阵可实现性条件的研究分析,给出天线阵合成示例,得到Weierstrass不同尺寸天线阵的辐射特性与分形因子的作用关系。指出雷达天线阵列在结构、频带、副瓣等方面需要进行改进。     

An efficient recursive procedure for evaluating the impedance matrix of linear and planar fractal arrays

The self-similar geometrical properties of fractal arrays are exploited in this paper to develop fast recursive algorithms for efficient evaluation of the associated impedance matrices as well as driving point impedances. The methodology is demonstrated by considering two types of uniformly excited fractal arrays consisting of side-by-side half-wave dipole antenna elements. These examples include a triadic Cantor linear fractal array and a Sierpinski carpet planar fractal array. This class of self-similar antenna arrays become significantly large at higher order stages of growth and utilization of fractal analysis allows the impedance matrix, and hence the driving point impedances, to be obtained much more efficiently than would be possible using conventional analysis techniques.     

Array redundancy for active line arrays

Active imaging arrays are used to image scenes composed of reflectors of transmitted radiation, and in many such applications, line arrays are employed. In this paper, we discuss scanned active line arrays for imaging based on image synthesis. We define the novel concept of array redundancy for active arrays, analogous to the well-known concept of redundancy applied to passive arrays, and we define and give examples of minimum redundancy and reduced redundancy line arrays composed of transmit/receive elements. Such arrays differ from their passive imaging counterparts both in geometry and in element count.     

Fractal antenna engineering: the theory and design of fractalantenna arrays

A fractal is a recursively generated object having a fractional dimension. Many objects, including antennas, can be designed using the recursive nature of a fractal. In this article, we provide a comprehensive overview of recent developments in the field of fractal antenna engineering, with particular emphasis placed on the theory and design of fractal arrays. We introduce some important properties of fractal arrays, including the frequency-independent multi-band characteristics, schemes for realizing low-sidelobe designs, systematic approaches to thinning, and the ability to develop rapid beam-forming algorithms by exploiting the recursive nature of fractals. These arrays have fractional dimensions that are found from the generating subarray used to recursively create the fractal array. Our research is in its infancy, but the results so far are intriguing, and may have future practical applications     

Fractal design of multiband and low side-lobe arrays

Most array factor design techniques are highly dependent on the operating wavelength. In this paper, a novel technique based on fractal structures is described for multiband operation. The analysis is focused in two different approaches: the fractal spatial arrangement of array elements and the fractal design of array factors. Although the patterns of fractal arrays show some interesting similarity properties at several bands, the directivity is not held constant through the bands. Nevertheless, such structures have been shown to be useful for designing low side-lobe arrays with equally weighted current elements. On the other hand, the fractal array factors presented do keep the same shape at several bands because they are designed as self-similar curves. The arrays that would synthesize such patterns present a characteristic power-law current distribution analogous to the spectral distribution of the bandlimited fractal Weierstrass function     

An overview of fractal antenna engineering research

Recent efforts by several researchers around the world to combine fractal geometry with electromagnetic theory have led to a plethora of new and innovative antenna designs. In this report, we provide a comprehensive overview of recent developments in the rapidly growing field of fractal antenna engineering. Fractal antenna engineering research has been primarily focused in two areas: the first deals with the analysis and design of fractal antenna elements, and the second concerns the application of fractal concepts to the design of antenna arrays. Fractals have no characteristic size, and are generally composed of many copies of themselves at different scales. These unique properties of fractals have been exploited in order to develop a new class of antenna-element designs that are multi-band and/or compact in size. On the other hand, fractal arrays are a subset of thinned arrays, and have been shown to possess several highly desirable properties, including multi-band performance, low sidelobe levels, and the ability to develop rapid beamforming algorithms based on the recursive nature of fractals. Fractal elements and arrays are also ideal candidates for use in reconfigurable systems. Finally, we provide a brief summary of recent work in the related area of fractal frequency-selective surfaces.     

New Elements Concentrated Planar Fractal Antenna Arrays for Celestial Surveillance and Wireless Communications

This research introduces three new fractal array configurations that have superior performance over the well‐known Sierpinski fractal array. These arrays are based on the fractal shapes Dragon, Twig, and a new shape which will be called Flap fractal. Their superiority comes from the low side lobe level and/or the wide angle between the main lobe and the side lobes, which improves the signal‐to‐intersymbol interference and signal‐to‐noise ratio. Their performance is compared to the known array configurations: uniform, random, and Sierpinski fractal arrays.     

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.     

分形天线的IFS实现与特性分析

分形最基本的特征就是自相似特性与分数维，可以很好的用于设计天线。文章讲述了用IFS(迭代函数系统)实现分形天线的过程。并对一些典型的分形天线及分形天线阵列的特性进行了分析。     

Synthesis of fractal patterns from concentric-ring arrays

A technique has been developed for the synthesis of fractal radiation patterns from concentric-ring arrays. A family of functions known as generalised Weierstrass functions, have been shown to play a key role in the theory of fractal radiation pattern synthesis. The authors examine the self-similarity relation of the array patterns     

基于矩量法的分形环八木天线的特性分析

八木天线是一种常用的天线形式.本文将Minkowski分形环应用于八木天线设计中,利用分形结构的空间填充特性来减小天线的横向尺寸,从而实现天线小型化设计.设计了工作于880～960MHz的6元二阶Minkowski分形环八木天线,以矩量法为核心对设计天线进行数值分析,将线天线模拟为细带线模型,天线表面采用三角单元进行剖分,RwG基函数作为电流展开函数.同方环八木天线进行了比较,在驻波特性、辐射特性相似情况下,分形环八木天线的尺寸缩减了29.8%.     

基于分形的低副瓣天线阵列研究

通过对Cantor集线阵及其补集、同心圆环分形阵的阵列因子方向图特性的分析,指出大间距的分形阵列方向图具有高副瓣的缺点,提出了通过分形阵列阵元的锥削密度加权和少量大间距单元幅度加权相结合的方法来抑制副瓣,改善分形阵的方向图性能,给出了两种具有分形特点的高效率、低副瓣阵列形式和实际测试结果,为分形天线阵列的工程化应用提供了思路。     

Dual band FSS with fractal elements

Experimental and computed results of a frequency selective surface (FSS) based on a certain type of fractal element are presented. The fractal element is a two iteration Sierpinski gasket dipole. Owing to the dual band behaviour of the two iteration Sierpinski gasket dipole, two stopbands are exhibited within the operating frequency band. This behaviour is obtained by arraying one simple element in a single layer frequency selective surface (FSS)     

Analysis of bone X-rays using morphological fractals

The authors have applied mathematical morphology for fractal analysis on bone X-ray images. The digitized gray level image is treated as a three-dimensional surface whose fractal dimension is calculated by performing a series of dilations on this surface and plotting the area of the resulting set of surfaces against the size of the structuring element. This approach has the added advantage of encoding structural information via the use of a structuring element. The algorithm has been applied to several bone radiographs, and the results demonstrate that the fractal dimension using mathematical morphology gives a robust texture measure of trabecular bone structures.     

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.     

Design of Broadband Planar Arrays Based on the Optimization of Aperiodic Tilings

Antenna arrays based on aperiodic tilings have been shown to exhibit low sidelobe levels and modest bandwidths over which grating lobes are suppressed. In addition, compared to conventional periodic arrays, these arrays are naturally thinned (i.e., mean inter element spacing is greater than ). The generation of these arrays involves placing array elements at the locations of the vertices of an aperiodic tiling. To obtain a realizable design, the entire array is then scaled and truncated to achieve a desired minimum element spacing and aperture size. This paper demonstrates that it is possible to greatly extend the bandwidth of these arrays by incorporating a simple perturbation scheme into the basic array generation process. The implementation of this perturbation scheme is straightforward and it lends itself well to being combined with an optimization technique such as the genetic algorithm. It is successfully used to generate arrays that have large bandwidths (peak sidelobe level dB with no grating lobes) of up to a minimum element spacing of . Moreover, the flexibility of this technique will be further demonstrated by introducing a slight variation of the basic scheme that is capable of generating arrays with extremely wide bandwidths. An example will be presented for an array design that has a bandwidth corresponding to a minimum element spacing of up to .     

Preliminary Investigations of a Low-Cost Ultrawideband Array Concept

A design concept is presented that achieves ultra wideband (UWB) array performance with significantly fewer elements than the traditional approach of using a single wideband antenna element type to fully populate the array. Starting from a conventional 8:1 bandwidth array design of a given aperture size, an array of equivalent aperture and bandwidth is created using scaled elements of three different sizes. This wavelength-scaled equivalent array has fewer than 18% of the original element count, i.e., roughly 6-times fewer elements, a similar reduction in weight, and most importantly, a significant reduction in electronics required to feed the array. If proven viable, array architectures of this type could make UWB arrays significantly more cost effective. In this preliminary numerical study, rigorous full-wave simulation tools are used to test the performance of small but informative wavelength-scaled array configurations of flared-notch radiators for the single-polarization case.      

Corner-fed microstrip antenna element and arrays for dual-polarization operation

A systematic study on the dual-polarized corner-fed microstrip antenna element and arrays with thin single-layer structure is presented. The impedance matrices and S-parameters of the element and arrays are investigated by the proposed extended multiport network method (EMNM). The co- and cross-polarization patterns are also analyzed. It is shown that this kind of antenna element has an isolation about 10 dB higher than that of a conventional edge-fed square patch. A series of new dual-polarized arrays of corner-fed patches have been designed and analyzed based on the EMNM. The experimental results of five arrays indicate that these arrays achieve an isolation of 27/spl sim/38 dB with a maximum of higher than 28/spl sim/58 dB and cross-polarization level of lower than -23/spl sim/ -30 at boresight, which are substantially better than those of similar dual-polarized arrays of edge-fed patches. All theoretical results are in good agreement with experimental ones.     

利用3/2 维分形方形的频率选择表面的特性研究

：以方形结构FSS 为基础,利用3/2 维分形方法,设计了一种新型的频率选择表面,利用CST 进行仿真,并将结果与Y 分形结构进行对比,对其特性进行分析。结果表明：新型频率选择表面有多个频带,且具有较好的传输特性、角度稳定度和频率稳定度,可实现天线多频复用的应用。