Application of Aperiodic 'Einstein' Monotile in Limited Field of View Phased Arrays

The discovery of the 'Einstein' monotile represents one of the most significant advancements in geometry in 2023. Research based on this monotile has been initiated across various fields. This paper introduces a limited field-of-view (LFOV) phased array based on the 'Einstein' monotile (Hat polykite) to address grating lobes. The proposed phased array demonstrates reduced implementation complexity compared to aperiodic phased arrays constructed from periodic or conditionally aperiodic tiles. It also exhibits increased engineering practicality compared to aperiodic phased arrays made from non-'Einstein' aperiodic tiles, particularly in assembly with loadbearing lattice structures. Two examples of Hat polykite-based phased arrays are presented in this paper. In Example A, a phased array is introduced where each subarray consists of a single antenna element. The proposed phased array is optimized to achieve a maximum grating lobe level (MGL) of-15 dB. In Example B, a subarray based on the Hat polykite comprises 8 antenna elements. The optimized phased array achieves an aperture efficiency of 90% and maintains a flat grating lobe level within a beam scanning range of 18°.