An effective approach for the optimal focusing of array fields subject to arbitrary upper bounds

A new approach to the optimal focusing of array fields subject to arbitrary upper bounds is presented. The approach formulates the problem as the minimization of a linear function in a convex set. Unlike other approaches, this one guarantees the achievement of the global optimum by using local optimization techniques and can, moreover, deal with any convex constraint on the unknowns, such as near field constraints. Optimization is performed by two ad hoc developed solution algorithms, which exploit the geometrical characteristics of the problem at hand, thus leading to extremely effective and computationally efficient numerical codes. An extensive numerical analysis has been performed in all cases of linear, planar, and circular arc arrays. The enhanced performance of the proposed technique with respect to the solution algorithms available in the literature fully confirms the effectiveness of the approach.