Linear optimization of antenna array for radiation pattern defined on a planar surface

In this contribution, the antenna array synthesis for radiation pattern defined on a planar surface is described. This can be required when the electric field r-decay factor effect cannot be neglected, e.g. an antenna array mechanically tilted and a specific pattern defined in terms of cartesian coordinates. Differently from the classical sidelobe level reduction optimization problem, the case in which both a constant power bounded area and a sidelobe suppression region are defined and required to be synthesized is herein addressed. The general nonlinear optimization problem is first presented; then, the derivation of some sub-optimal linear problems based on practical implementation hypothesis is described, with the advantage of a reduced computational complexity. Numerical results validate the effectiveness of the proposed method.