Some facts and challenges in array antenna synthesis

Antennas synthesis is one of the canonical problem in applied electromagnetism. Many efforts have been done in recent years to solve the problem in convenient and accurate way. In this framework, global optimization based procedures have been widely applied. On the other side, the diffused enthusiasm for these 'physically inspired' global optimization techniques has induced to neglect, in a number of cases, some characteristics of the problem which may be useful in the synthesis process. With reference to the synthesis of array antennas, we first show that in a number of problems proposed in the literature global optimisation is not required at all, as the problem is indeed convex with respect to all the available degrees of freedom. Then, we also show that a proper exploitation of convexity with respect to a part of the unknowns (when available) allows to achieve design solutions significantly better than those available in the literature. Finally, some challenging synthesis problems which still need attention (and possibly new solution approaches) are briefly introduced.