Synthesis of Transmitarrays via Convex Relaxation

A mathematical approach for the phase-only synthesis of transmitarray antennas based on iterative convex optimization is presented. Using semidefinite relaxation techniques, the proposed framework is suitable for a wide range of beam shaping applications. The synthesis of a pencil-beam pattern with reduced sidelobe levels and limited gain loss is illustrated. The pattern distortion due to the quantization of the optimal phase distribution is investigated to provide realistic design guidelines.