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Nature Inspired Antenna Design

Ultrawideband Aperiodic Arrays

(On the left) A portion of a Penrose aperiodic tiling and its corresponding antenna array element locations. (On the right) A wideband planar array design that was generated by optimizing a perturbed Penrose tiling array.




Illustration of the basic inflation process for the Danzer aperiodic set.
(On the left) The three prototiles of the aperiodic set and their edge matching conditions.
(In the middle) The first iteration of the inflation process involves decomposing each prototile into a collection of tiles.
(On the right) The second iteration involves further decomposing each tile based on the rules from the first iteration. Large tilings are formed as this iterative process is repeated.


Selected portion of a Danzer aperiodic tiling.


Illustration of the rapid recursive beamforming algorithm for a two generator polyfractal array.


Radiation patterns for the two components of the interleaved antenna array system. The component array steered to +60\B0 has a minimum interelement spacing of 4.0λ while the component array steered to -30\B0 has a minimum interelement spacing of 8.0λ. The peak side-lobe level of the system is -16.28 dB under these conditions. The right side of the figure illustrates the entire radiation pattern sweep while the left side of the figure shows more detail of the main beam at -30\B0.


Side-lobe level performance of the optimized polyfractal arrays over a range of bandwidth compared to the performance of a periodic linear array. Each polyfractal array was optimized at broadside for simultaneous minimum spacings of 0.5λ and 3.0λ (i.e. fo and 6fo).


   In recent years there has been an increased demand for communication systems with wideband and multifrequency capabilities. Antenna arrays, representing an important component of many communication systems, must be able to keep up with these latest demands. A vast majority of array designs are still based on the conventional periodic element distribution. This type of array has its benefits but it is inherently limited in terms of bandwidth due to the presence of grating lobes at element spacings of one-wavelength or greater. Among the various ways to extend the bandwidth of these arrays are design techniques that involve utilizing non-periodic, or aperiodic, configurations. Our research has shown that judicious selection of the aperiodic configuration can lead to designs with bandwidths much larger than their conventional periodic counterparts.

    Polyfractal arrays and perturbed aperiodic tiling arrays have recently emerged as categories of arrays that can lead to designs with ultrawideband performance. Bandwidths (SLL < -10 dB and no grating lobes) of up to 40:1 have been reported for polyfractal arrays while bandwidths of up to 22:1 have been reported for perturbed aperiodic tiling arrays (see references 1 and 2 below for details).



..: References :..

1 -) Design of Broadband Planar Arrays Based on the Optimization of Aperiodic Tilings
by Thomas G. Spence, and Douglas H. Werner
IEEE Transactions on Antennas and Propagation, Vol. 56, No. 1, January 2008

ABSTRACT: 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 interelement spacing is greater than λ / 2). 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 < -10 dB with no grating lobes) of up to a minimum element spacing of 5 λ . 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 11 λ .




2 -) The Pareto Optimization of Ultrawideband Polyfractal Arrays
by Joshua S. Petko, and Douglas H. Werner
IEEE Transactions on Antennas and Propagation, Vol. 56, No. 1, January 2008

ABSTRACT: The application of global optimization techniques, such as genetic algorithms, to antenna array layouts can provide versatile design methodologies for highly directive, thinned, frequency agile, and shaped-beam antenna systems. However, these methodologies have their limitations when applied to more demanding design scenarios. Global optimizations are not well equipped to handle the large number of parameters used to describe large-N antenna arrays. To overcome this difficulty, a new class of arrays was recently introduced called polyfractal arrays that possess properties well suited for the optimization of large-N arrays. Polyfractal arrays are uniformly excited with an underlying self-similar geometrical structure that leads to aperiodic element layouts. This paper expands on polyfractal array design methodologies by applying a robust Pareto optimization technique with the goal of reducing the peak sidelobe levels at several frequencies specified over a wide bandwidth. A recursive beamforming algorithm and an autopolyploidy based mutation native to polyfractal geometries are used to dramatically accelerate the genetic algorithm optimization process. This paper also demonstrates that the properties of polyfractal arrays can be exploited to create designs that possess no grating lobes and relatively low sidelobe levels over ultrawide bandwidths. The best example discussed in this paper maintains a -15.97 dB peak sidelobe level with no grating lobes from a 0.5 λ , to more than a 20 λ minimum spacing between elements, which corresponds to at least a 40:1 bandwidth for the array.




3 -) Interleaved Ultrawideband Antenna Arrays Based on Optimized Polyfractal Tree Structures
by Joshua S. Petko, and Douglas H. Werner
IEEE Transactions on Antennas and Propagation, Vol. 57, Issue 9, September 2009.

ABSTRACT : There is considerable interest in interleaving multiple phased array antennas into a single common aperture system. Current phased array antenna technology is limited to narrowband operation, leading to the appearance of grating lobes and strong mutual coupling effects when they are incorporated into the design of a common aperture system. To overcome this obstacle, a new class of arrays, called polyfractal arrays, has been introduced that possess natural wideband properties well suited for large-scale genetic algorithm optimizations. These arrays also possess recursive beamforming properties and an autopolyploidy-based chromosome expansion that can dramatically accelerate the convergence of a genetic algorithm. In addition, a robust Pareto optimization can be applied to reduce the peak sidelobe levels at several frequencies throughout the intended operating band, leading to ultrawideband antenna array designs. Because of their lack of grating lobes, these polyfractal arrays are ideal building blocks for interleaved antenna array systems. This paper develops these concepts, first creating ultrawideband array designs based on polyfractal geometries and then interleaving these designs into a common aperture system. Several examples of interleaved systems are discussed, with one two-array system possessing a peak sidelobe level of nearly -18 dB with no grating lobes over a 20:1 bandwidth with either of the component array mainbeams steered independently up to 60° from broadside.




4 -) Ultrawideband Aperiodic Antenna Arrays Based on Optimized Raised Power Series Representations
by M. D. Gregory, and Douglas H. Werner
IEEE Transactions on Antennas and Propagation, Vol. 58, Issue 3, pp. 756-764, March 2010.

ABSTRACT : Past research has shown that application of mathematical and geometrical concepts such as fractals, aperiodic tilings, and special polynomials can provide elegant solutions to difficult antenna array design problems. For example, design issues such as beam shaping and control, sidelobe levels, bandwidth and many others have been addressed with such concepts. In this paper, mathematical constructs based on the raised power series (RPS) are utilized to provide easily controlled aperiodicity to a linear array of antenna elements in order to achieve wideband performance. In addition, recursive application of raised power series subarrays and implementation of an optimization technique based on the genetic algorithm is demonstrated to realize impressive ultrawideband performance. The technique introduced here is shown to offer bandwidths of many octaves with excellent sidelobe suppression and no grating lobes. Moreover, the ultrawideband performance for one of the optimized RPS array examples is verified through full-wave simulations which take into account the coupling environment experienced by realistic radiating elements (in this case half-wave dipole antennas for three different operating frequencies).




5 -) Nature-Inspired Design Techniques for Ultra-Wideband Aperiodic Antenna Arrays
M. D. Gregory, J. S. Petko, T. G. Spence and D. H. Werner
IEEE Antennas and Propagation Magazine, Vol. 52, Issue 3, pp. 28 - 45, June 2010.

ABSTRACT : Past research has shown that application of mathematical and geometrical concepts such as fractals, aperiodic tilings, and special polynomials can provide elegant solutions to difficult antenna array design problems. For example, design issues such as beam shaping and control, sidelobe levels, bandwidth and many others have been addressed with such concepts. In this paper, mathematical constructs based on the raised power series (RPS) are utilized to provide easily controlled aperiodicity to a linear array of antenna elements in order to achieve wideband performance. In addition, recursive application of raised power series subarrays and implementation of an optimization technique based on the genetic algorithm is demonstrated to realize impressive ultrawideband performance. The technique introduced here is shown to offer bandwidths of many octaves with excellent sidelobe suppression and no grating lobes. Moreover, the ultrawideband performance for one of the optimized RPS array examples is verified through full-wave simulations which take into account the coupling environment experienced by realistic radiating elements (in this case half-wave dipole antennas for three different operating frequencies).




6 -) Generalized Space-Filling Gosper Curves and Their Application to the Design of Wideband Modular Planar Antenna Arrays
by T. G. Spence and D. H. Werner
IEEE Transactions on Antennas and Propagation, Vol. 58, No. 12, December 2010

ABSTRACT: The Peano-Gosper space-filling curve provides an excellent framework for designing planar antenna array distributions with modular architectures and suppressed sidelobes over a relatively wide bandwidth. The curve consists of a self-avoiding path that intersects a triangular lattice and its construction is based on the iterative application of a generating curve. There exist a number of other recently discovered curves, coined generalized Gosper curves, that possess properties similar to those of the Peano-Gosper curve but are based on larger and more complex generating curves. In this paper these generalized curves will be examined as the framework for antenna array layouts. It will be shown that arrays based on these curves have a number of excellent characteristics while offering modular array configurations and sizes that are not inherent to Peano-Gosper arrays. Moreover, when combined with a simple recursive-perturbation technique, the element distributions of these arrays can be efficiently adjusted to generate designs with bandwidths that far exceed that of standard periodic- and triangular-lattice arrays. The efficacy of this technique will be demonstrated through design examples, including one that has more than a 10:1 bandwidth. Full-wave simulations of a wideband patch array will also be used to investigate the effects of mutual coupling on these array distributions.




7 -) Analysis and Design Optimization of Robust Aperiodic Micro-UAV Swarm-Based Antenna Arrays
by F. Namin, J. S. Petko and D. H. Werner
IEEE Transactions on Antennas and Propagation, Vol. 60, No. 5, May 2012

ABSTRACT: Micro-UAV swarm-based antenna arrays provide a novel solution for high-risk radar imaging applications. These apertures lack a single point of failure by distributing their resources and sensors across multiple platforms. However, turbulence and positional errors provide a challenging operational environment when it comes to the implementation of these systems. Turbulence can limit the aperture's ability to coherently resolve a target and cause aircrafts to collide in midair if the formation is too tightly packed with closely spaced elements. This paper introduces several techniques that can reduce the effects of turbulence on the system. First, a phase compensation algorithm is presented that can eliminate the effects of turbulence on the main beam of the array. In addition, sparse antenna apertures can be used to create flight formations that reduce the probability of midair collisions. Traditional periodic apertures are insufficient because these arrays display grating lobes at wide interelement spacings. Therefore, two aperiodic array optimization methodologies are discussed that produce sparse array configurations suitable for micro-UAV formations. These sparse arrays exhibit low peak side-lobe levels without the presence of grating lobes over wide interelement spacings. By combining phase compensation with optimized sparse aircraft formations, one can achieve high radiation pattern resolution in a micro-UAV based radar imaging application.




8 -) Design of Ultra-Wideband, Aperiodic Antenna Arrays With the CMA Evolutionary Strategy
by Philip J. Gorman, Micah D. Gregory, and Douglas H. Werner
IEEE Transactions on Antennas and Propagation, Special Issue on Innovative Phased Array Antennas Based on Non-regular Lattices and Overlapped Subarrays, Vol. 62, No. 4, pp. 1663-1672, April 2014. (invited paper)

ABSTRACT: Recently, the covariance matrix adaption evolutionary strategy (CMA-ES) has received attention for outperforming conventional global optimization techniques such as the genetic algorithm (GA) or particle swarm optimization (PSO), often used in electromagnetic designs. Here, CMA-ES is first applied to the design of ultra-wideband aperiodic arrays using realistic spiral radiating elements. To improve the axial ratio of the array, optimization was extended to incorporate a mechanical rotation of each spiral element. This novel strategy of optimizing both the location and rotation of each element provides noticeable improvement in both the axial ratio and sidelobe level performance.
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9 -) A Review of High Performance Ultra-Wideband Antenna Array Layout Design
by Douglas H. Werner, Micah D. Gregory, and Pinguan L. Werner
Proceedings of The 8th European Conference on Antennas and Propagation (EuCAP), The Hague, The Netherlands, 6-11 April 2014.


ABSTRACT: An overview of many of the new and powerful methods for generating ultra-wideband array layouts is given, focusing mainly on the contributions of the Computational Electromagnetics and Antennas Research Lab (CEARL) at Penn State. Evolutionary strategies and optimization algorithms are used exclusively with most of these design techniques, allowing for easy creation of arrays of various sizes and properties. These ultra-wideband array design methods span multiple dimensions, ranging from simple linear arrays to planar and volumetric types. A selection of design methods will be covered here along with example arrays, their performance, and suggested applications.

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