Phase-only control of antenna sum and shaped patterns through null perturbation

Satisfactory sum or shaped antenna radiation patterns can often be synthesized by modifying just the phase distribution of an initial excitation by an arbitrary amplitude distribution. As examples, we calculate linear and circular apertures with uniform, Taylor, or cosine-section amplitude distributions, affording symmetric sum patterns with low sidelobe levels or symmetric shaped patterns with low ripple and sidelobe levels; linear aperture distributions, affording patterns with low sidelobe levels on one side of the beam; and planar arrays, with uniform or cosine-section amplitude distributions affording φ-symmetric or elongated-oval footprints