Application of Aperiodic “Einstein” Monotile in Phased Arrays With Limited Beam Scanning Range

Abstract

The discovery of the ‘Einstein’ monotile represents one of the most significant advancements in geometry in 2023, prompting research across multiple disciplines. This paper proposes a phased array with a limited beam scanning range based on the ‘Einstein’ monotile (Hat polykite), characterized by low grating lobe levels and high aperture efficiency. The proposed phased array reduces implementation complexity compared to periodic subarrays and enhances engineering practicality relative to other aperiodic tiles, particularly in load-bearing lattice configurations. Two examples of Hat polykite-based phased arrays are presented in this paper. Example A presents a sparse phased array, where each element is embedded within a Hat polykite, optimized for a maximum grating lobe level of −15 dB. Example B features a subarray comprising eight antenna elements based on the Hat polykite. This configuration achieves 90% aperture efficiency while keeping the maximum grating lobe level below −14 dB within an ±18° main beam scanning range.

Keywords

• ‘Einstein’ monotile
• aperiodic tiling
• grating lobe suppression
• limited beam scanning range
• phased array