An efficient algorithm is presented to reduce the number of antenna elements for a complex-excitation and pattern reconfigurable planar array. The approach alternately iterates between two procedures. One procedure involves a multiple measurement vectors (MMV) sparse recovery process for minimizing the number of antenna elements and finding multiple sets of complex-valued excitations for multiple different patterns. The other procedure is a local optimization for the real-valued positions of the elements. Results from a set of numerical experiments are presented to assess its performance in terms of the computational efficiency and the ability to reduce the number of antenna elements while maintaining array pattern characteristics. An alternating iterative algorithm for planar sparse array synthesis is presented.A sparse processing technique is used to minimize the number of antenna element.A local optimization is performed for refining the real-valued element positions.