Irregular Subarray Tiling via Rotational Symmetry

To reduce the cost of an
$n\times n$
polarimetric phased array antenna, an innovative subarray tiling technology is proposed based on a geometrical property called rotational symmetry. This property requires the tiling solution to remain unchanged after a series of rotations, and hence, a consistent scanning performance in multiple beam directions is guaranteed. By considering the rotation as the reordering of the array elements, an improved Algorithm X is proposed, which is computationally efficient to find the rotational symmetric exact tiling solutions (RSETS). Due to a compressed scale of the RSETS and a faster dimension reduction of the dictionary matrix, it is convenient to obtain an RSETS with the scanning performance approximated that of the optimal solution. A 12 × 12 X-band dual-polarized microstrip patch array antenna is simulated for the verification of the proposed method under mutual coupling effects. A desired scanning performance is accomplished on both copolarization and cross-polarization patterns of multiple beam directions, which is better than 99.75% of exact tiling solutions.