An angle-of-arrival antenna system uses two orthogonal arrays of patch antenna elements to measure the angle of arrival of a wireless signal irrespective of its polarization. Each antenna element has an antenna patch located over a corresponding ground patch. A shorting wall directly electrically connects one edge of the antenna patch to a corresponding edge of the underlying ground patch. The edge of the ground patch is also directly connected to a system ground plane. No other edges of the ground patch are connected to the system ground plane. The shorting wall acts as an impedance that isolates the ground patch from the system ground plane, and therefore improves isolation between the antenna elements. The antenna system may be constructed using conventional circuit-board fabrication techniques by implementing each shorting wall as an array of plated through-holes or slots.