An electronic device may have a phased antenna array. An antenna in the array may include a rectangular patch element with diagonal axes. The antenna may have first and second antenna feeds coupled to the patch element along the diagonal axes. The antenna may be rotated at a forty-five degree angle relative to other antennas in the array. The antenna may have one or two layers of parasitic elements overlapping the patch element. For example, the antenna may have a layer of coplanar parasitic patches separated by a gap. The antenna may also have an additional parasitic patch that is located farther from the patch element than the layer of coplanar parasitic patches. The additional parasitic patch may overlap the patch element and the gap in the coplanar parasitic patches. The antenna may exhibit a relatively small footprint and minimal mutual coupling with other antennas in the array.