A transmitter or receiver can include a phased array antenna system in which multiple characteristics of a transmitted or received beam can be controlled electronically. For example, in embodiments that include a transmitter, dual outputs of N signal modifiers can be connected to orthogonal inputs of N dual-orthogonally polarized antenna elements. Each signal modifier can modify the amplitude and phase of a communications signal in two parallel signal paths to produce two signal components each of which is an amplitude-modified/phase-shifted version of the communication signal. Multiple characteristics of the combined beam can be simultaneously controlled by setting the amplitude and/or phase-shift parameter values in the dual signal paths in the signal modifiers to combined values that individually affect each of the multiple characteristics of the combined beam.