Design of volumetric antenna arrays based on three-dimensional aperiodic tilings

In this paper, we extend the generation of aperiodic antenna arrays into threedimensions. A certain type of the aperiodic tiling of 3-D space is introduced and spherical arrays of a specified radius are generated based on this tiling. The radiation properties of this type of array are studied and compared to a periodic array with the same aperture size. It is shown that, similar to the planar aperiodic tilings, the 3-D aperiodic tilings exhibit relatively wide bandwidths and are devoid of grating lobes. Also, the excitation current phase of elements can be adjusted to steer the main beam in any given direction, whereas with periodic arrays due to the symmetry, phasing in certain directions will generate grating lobes in the radiation pattern.