An antenna module that includes an antenna substrate, a plurality of three-dimensional (3-D) antenna cells on a first surface of the antenna substrate, a plurality of packaged circuitry on a second surface of the antenna substrate, and a plurality of supporting balls mounted on the second surface of the antenna substrate. The plurality of packaged circuitry includes a plurality of radio-frequency (RF) chips on the second surface of the antenna substrate. Each of the plurality of 3-D antenna cells comprises a raised antenna patch with a plurality of projections and a plurality of supporting legs, where at least a relief cut is provided between one of the plurality of projections and one of the plurality of supporting legs.