2-D Near Field Synthesis of Shaped Beams with Arbitrary Footprints

We propose a new approach to the canonical problem of the synthesis of shaped beams through planar continuous aperture sources. As an important novelty with respect to the state-of-the-art literature, the proposed technique allows enforcing a mask given by an arbitrary lower and upper bound functions on the power generated in the near field zone. In this way, it is possible to realize near field patterns having a well-defined footprint, ripple, and sidelobe level, as well as exhibiting along the azimuth cuts different shapes as entailed by the fulfillment of arbitrary lower and upper bound constraints. This is possible by jointly exploiting a warping strategy for the effective near-field representation followed by an effective 2-D phase retrieval procedure. The advantages of the proposed approach include the capability of a-priori determining the minimum size of the source required to fulfill any assigned power mask and of finding the optimal aperture field distribution by resorting only to Convex Programming and polynomial factorization.