Flat-top power patterns of arbitrary footprint produced by arrays of arbitrary planar geometry

This paper presents a novel technique for synthesis of flat-top power patterns with desired footprints, generated by array elements positioned on an arbitrary planar geometry. Traditionally, this problem had been considered as a protracted complex nonlinear optimization problem specially when the number of array elements is large for obtaining a desired and detailed pattern. Using the formulation of patterns generated by circular apertures the problem is converted to a collocation problem which not only reduces the number of unknowns but also generalizes the method to any arbitrary planar aperture. Derivation of the closed form formulae specially for the the nonlinear problem simplifies implementation of the method.