Extending Spectral Factorization to the 2-D Mask-Constrained Power Synthesis of Shaped Beams with Arbitrary Footprints

A new method is proposed for the mask-constrained power synthesis of planar sources and exemplified for antenna arrays. In particular, by resorting to recent results achieved in the Phase Retrieval of radiated power patterns exploiting only one measurement surface, we extend the Spectral Factorization method to the case of 2-D shaped beams having arbitrary footprints. The presented method is fast and effective as it avoids exploiting global optimization algorithms, and it also allows identifying the minimum number of array elements (i.e., the minimum source size) required in order to fulfill the 2-D power-pattern mask.