Antenna systems and related methods are disclosed. An antenna system includes an antenna controller configured to operably couple to an array of electromagnetic (EM) scattering elements. The controller is configured to determine a performance parameter of the antenna system for a plurality of different combinations of different spatial holographic phases and effective mode indices having different modulation patterns corresponding thereto, and select one of the modulation patterns based on the performance parameter corresponding thereto. A method includes storing data indicating a modulation pattern determined based on a spatial holographic phase and an effective mode index for each of a plurality of different main beam angles from the antenna, and controlling the antenna to operate with a main beam pointed in each of the plurality of different main beam angles by controlling the antenna to operate in each modulation pattern corresponding to the plurality of main beam angles.