Optimal synthesis of circularly symmetric aperture sources with shaped patterns

The problem of the optimal power pattern synthesis of shaped beams by means of circularly symmetric continuous aperture sources is addressed and solved. In particular, a necessary and sufficient existence criterion is provided to test a priori (i.e., without solving the overall synthesis problem) if a non-superdirective continuous aperture source of given size can radiate or not a circularly symmetric power pattern lying in a given arbitrary mask. In the affirmative case, the proposed approach guarantees the achievement of the global optimum by using local optimization techniques, and a number of equivalent aperture distributions are determined in a straightforward fashion. Numerical examples concerning applications of actual interest support the given theory and confirm the effectiveness of the developed approach.