Methods of operating a transceiver including an antenna having a plurality of antenna feed elements are presented. The methods include defining a plurality of antenna gain constraint values gk associated with K geographic constraint points within a geographic region, iteratively generating M antenna feed element weights wM that result in antenna response values fK at the K geographic constraint points based on the corresponding antenna gain constraint values gK, forming an antenna beam from the antenna to the geographic region using the antenna feed element weights wM, and communicating information over the antenna beam. Related transceivers, satellites, and satellite gateways are also disclosed.