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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[lambda], to more than a 20[lambda] minimum spacing between elements, which corresponds to at least a 40:1 bandwidth for the array. Index Terms--Antenna array, autopolyploidy, fractal, fractal-random, genetic algorithm (GA), large-N, Pareto, polyfractal, polyploidy, strength Pareto evolutionary algorithm (SPEA), ultrawideband (UWB).

There has been considerable recent interest in techniques for the optimization of large-N antenna arrays. Unfortunately, the successful development of such techniques has been hindered by the large number of independent parameters that must be optimized and the complexity of the calculations needed for the electromagnetic evaluation of large-N arrays. One promising new design methodology for large-N arrays which has recently been introduced is based on properties of a subset of fractal-random arrays called polyfractal arrays. Polyfractal arrays have many embedded self-similar structures, thereby allowing very large and seemingly complex array layouts to be described with only a small set of independent parameters. In addition, by effectively utilizing the self-similarity of polyfractal arrays, a considerable reduction can be achieved in the amount of time required to evaluate the radiation patterns of large-N arrays. This paper introduces a type of nature-based design process that applies a specially formulated genetic algorithm (GA) technique to evolve optimal polyfractal array layouts. The most unique aspect of this optimization technique is a new autopolyploidy-based chromosome expansion that maximizes the efficiency of the GAs. Simple polyfractal geometries are used in the initial stage or first epoch of the optimization because the number of independent parameters is small and the computation times are relatively fast. After the optimization converges for the first epoch, more complicated descriptions of these polyfractal arrays are introduced to provide additional independent parameters for the optimizer as it progresses through later epochs of evolution. This process has been shown to be very effective in creating optimized large-N arrays, the largest example considered here being a 1616-element linear array with a -24.30-dB sidelobe level and a 0.056[degrees] half-power beamwidth. Index Terms--Autopolyploidy, fractal arrays, fractal-random arrays, genetic algorithms (GAs), large-N arrays, polyfractal arrays, polyploidy.

Recently, in order to successfully combine the positive attributes of both periodic and random arrays into one design, a novel class of arrays, known as fractal-random arrays, has been introduced. In addition, several researchers have successfully used genetic algorithms, robust global optimization techniques based on natural selection, to find solutions to complex array layout problems. This paper introduces a type of nature-based design process that applies a specially formulated genetic algorithm to evolve optimal layouts of an important subset of fractal-random arrays, which we call polyfractal arrays. Also, this paper discusses how the underlying self-similar properties of polyfractal arrays can be exploited to increase the speed of the associated array factor calculations. This speed increase dramatically reduces the time required for the genetic algorithm to converge thereby making it possible to effectively evolve optimal array configurations which are much larger than has been previously possible. Moreover, the fractal-random properties of these polyfractal arrays are shown to provide substantially wider bandwidth performance than their conventional counterparts. Finally, several design examples of genetically optimized linear polyfractal arrays with narrow beamwidths, improved sidelobe suppression and wide bandwidths are presented. Index Terms--Broadband arrays, fractal-random arrays, fractals, genetic algorithms, nature-based antenna design.

This paper introduces a design methodology for miniature multiband as well as reconfigurable (i.e., tunable) antennas that exploits the self-similar branching structure of three-dimensional (3-D) fractal trees. Several fundamental relationships, useful for design purposes, are established between the geometrical structure of the fractal tree antenna and its corresponding radiation characteristics. In particular, it will be shown that the density and elevation angle of the branches play a key role in the effective design of miniature 3-D fractal tree antennas. Several design examples are considered where fractal trees are used as end-loads in order to miniaturize conventional dipole or monopole antennas. Multiband and reconfigurable versions of these miniature antennas are also proposed, where either reactive LC traps or RF switches are strategically placed throughout the branches and/or along the trunk of the trees. Included among these designs is a miniature reconfigurable dipole antenna that achieves a 57% size reduction for the center frequency of the lowest intended band of operation and has a tunable bandwidth of nearly 70%. Index Terms--Fractal antennas, fractal tree antennas, miniature anennas, reconfigurable antennas.