An antenna system includes an array of antenna elements, each element including: one or more first terminals and second terminals that receive a vertically polarized wireless signal and a horizontally polarized wireless signal, respectively, at a radio frequency; a first signal combining circuit and a second signal combining circuit that combine the horizontally polarized wireless signal and the horizontally polarized wireless signal to obtain a combined vertically polarized signal and a combined horizontally polarized signal, respectively; a first frequency converting circuit and a second frequency converting circuit that convert the combined vertically polarized signal and the combined horizontally polarized signal to a baseband vertically polarized signal and a baseband horizontally polarized signal, respectively, at a frequency different from the radio frequency; a baseband processing circuit that combines the baseband vertically polarized signal and the baseband horizontally polarized signal after a 90° phase shift to obtain an LHCP or RHCP signal.