Element spacing optimization for 2 by 2 arrays

This paper presents a spacing optimization procedure for 2 by 2 steerable arrays. The optimization goal is to obtain narrowest steering beams without grating lobes for all steering angles in two dimensions. The radiation pattern of a single antenna, element pattern, is used for setting a limit of steering angles. Expressions for the array factor are derived and used with an element pattern to obtain the largest element spacing without grating lobes. This gives narrowest steering beams. Microstrip patch antennas are used as a case study in this paper. The half power beamwidth and the dimensions of Microstrip patch antennas need to be considered in the design. The result shows that the largest element spacing without grating lobes for a half-wave by half-wave patch antenna is 1.29 wavelength.