A fully deterministic procedure for the synthesis of sparse antenna arrays radiating shaped beams is presented. The developed algorithm is based on a compressive sensing technique which, starting from an array with a very dense grid of elements, iteratively solves a minimization problem aimed at producing a sparse array with a strongly reduced number of elements. However, such technique solves a field synthesis problem. So, the constraints of the optimization problem are suitably modified during the iterations, in order to solve a power pattern synthesis problem. Numerical examples are provided, that show the improvements that can be achieved in terms of reduction of the number of radiating elements.
