Exploiting convexity in array antenna synthesis problems

Many efforts have been done in recent years to solve array antenna synthesis problems in a way as effective as possible. Stochastic optimization schemes have been widely applied, but useful mathematical properties of the problem, which may be useful in the synthesis process, have been neglected in many cases of interest. In this communication we show that in a number of array antenna synthesis problems proposed in the literature global optimizations are not required at all, as the problem is indeed convex with respect to all the available degrees of freedom. Then, with reference to very recent results proposed in the literature, we show how a proper exploitation of the convexity, both with respect to a part of the unknowns and derived from the exploitation of useful radiated field representations also allows to achieve design solutions significantly better than existing ones. Finally, some challenging synthesis problems which still need attention (and possibly new solutions) are discussed.