A base station antenna (BSA) system includes a radio-frequency (RF) generator having a plurality of power-amplifying circuits therein, and an antenna, which includes a plurality of columns of radiating elements. These radiating elements are electrically coupled by RF signal routing to a corresponding plurality of ports of the antenna that receive a corresponding plurality of RF input signals. These RF input signals have respective amplitudes and phases that support the concurrent generation of three spaced-apart RF beams by the antenna and are derived from respective RF signals generated by the plurality of power-amplifying circuits. The RF input signals including: (i) a first RF input signal defined by at least two linearly superposed RF signals of equivalent frequency having unequal combinations of amplitude and phase weighting, and (ii) a second RF input signal defined by at least two linearly superposed RF signals of equivalent frequency having unequal combinations of amplitude and phase weighting.