The design of complex antenna devices is addressed in this work through an instance of the System-by-Design (SbD) paradigm. Towards this end, an approach combining different functional blocks that enable the exploration of the search space, the antenna modeling from the physical viewpoint, and the evaluation of the quality of each trial design is introduced. An innovative algorithm that combines the properties of Orthogonal Arrays (OAs) and of Learning-by-Example tools is proposed to guarantee a reliable modeling of the physical features of the complex antennas of interest. A preliminary numerical validation is presented to assess the advantages and drawbacks of the arising SbD Synthesis strategy.