Pencil Beams and Flat-Topped Beams with Asymmetric Sidelobes from Circular Arrays [Antenna Designer's Notebook]

Given a circular antenna array, and a requirement for the sidelobes surrounding a pencil beam or flat-topped beam to have a specified φ dependence, it can be advantageous to optimize the array excitations for the best fit between the far field and a pattern synthesized for a continuous circular aperture of the same size.