Optimization of peano-gosper fractile arrays using genetic algorithms to reduce grating lobes during scanning

Abstract

A new class of modular broadband low-sidelobe arrays has been recently introduced that are based on the theory of fractile (fractal tile) geometry. In this paper, the radiation properties of the Peano-Gosper fractile array are compared to those of the conventional square and hexagonal arrays. It is demonstrated that the Peano-Gosper array has the same desirable grating lobe conditions as the hexagonal array, while achieving a much lower overall sidelobe level. When a Peano-Gosper fractile array with minimum element spacing of one wavelength is scanned, grating lobes occur. It will be shown that a genetic algorithm can perturb the element locations of the Peano-Gosper fractile array in order to reduce side lobe levels to an acceptable level. The genetic algorithm implements the two-point crossover technique along with mutations. The genetically optimized stage 1 Peano-Gosper curve with perturbed element locations can be used to create higher order stage arrays, which allows the highly desirable recursive property to be preserved. The genetically optimized Peano-Gosper fractile array remains relatively broadband.

Modular broadband planar arrays based on generalized Peano-Gosper curves

“…Once convergence was reached, the best design from the GA was used as the seed for a Nelder-Mead local optimizer. The number of parameters to be optimized in a PG array corresponds to the number of interior elements along its generator curve [3]. In the case of arrays based on the N=13 generator, there are 12 perturbation locations that are to be optimized.…”

“…One way to circumvent this limitation is via a perturbation technique that alters the fixed interior lattice of the PGFA. The technique is based on perturbing the interior elements along the stage-1 PG curve and using these element locations to generate higher-order stages of the PGFA (analogous to the conventional iterative PGFA generation process) [3]. Combining this with an optimization algorithm has lead to perturbed PGFA designs with enhanced scanning capabilities over at least a 2:1 bandwidth, while preserving several of the other beneficial properties.…”

“…Recently, new generalized versions of Peano-Gosper space-filling curves were discovered [3], [4]. These new curves have several properties in common with the conventional PG curve, including a single path without any branches, a path that falls on an equilateral triangular lattice, and iterative construction using an initiator and generator.…”

“…For example, the generator of the conventional PG curve contains seven equi-length segments and accordingly, its high-order curves can be subdivided into seven identical curves of the previous stage. The new curves offer alternate degrees of modularity, ranging from 13 up to infinity [3], [4]. Additionally, since these curves possess larger generators, they offer more design variables that can be varied when combined with the array perturbation technique.…”