Optimization of Peano-Gosper fractile arrays using genetic algorithms to reduce grating lobes during scanning

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.