A Tiling Method for Sub-Arrayed Spherical Conformal Phased Array Antennas Based on Maximum 3-D Space Entropy Model

Spherical conformal phased array antennas (SCPAAs) offer exceptional wide-angle scanning capabilities, yet their high cost and intricate design present significant barriers to large-scale and widespread application. In response, this article introduces a tiling method for sub-arrayed SCPAAs, guided by a maximum 3-D space entropy model (M3D-SEM). By introducing the concept of 3-D space entropy for SCPAAs, the tiling problem can be transformed into a subarray partition for the full array, avoiding the issue of changeable radiation aperture of SCPAAs at different scanning angles. Then, the tiling topology formed by two-element tiles for sub-arrayed SCPAAs is binary coded and optimized by convex integer optimization programming based on M3D-SEM. The desired polarized array pattern synthesis is further finished by the convex optimization based on the optimized tiling layout for a sub-arrayed SCPAA. Two numerical examples with real simulated element patterns are provided to demonstrate the effectiveness of the suggested method. The results indicate that within the hemispherical beam coverage, the optimized sub-arrayed SCPAA with half of its transmit/receive (T/R) channels reduced, exhibits directivities only 1.1–1.9 dB lower compared with the original SCPAA. Moreover, the optimized sub-arrayed SCPAA also exhibits superior scanning performance when compared with other arrays with the same number of channels.