An electronic device and antenna system for generation of millimeter-wave frequency radiation. The antenna system has first conductive structure, a second conductive structure, and an antenna comprising a first antenna element configured to excite a first electric field having a first polarization, and a second antenna element configured to excite a second electric field having a second polarization. The first antenna element and the second antenna element extend in an antenna plane. An anisotropic dielectric volume is partially enclosed by the antenna, the first conductive structure, and the second conductive structure. A first surface of the dielectric volume is open to the exterior of the antenna system. The dielectric volume allows the first and second electric fields to propagate, within the dielectric volume, from the antenna at least partially towards the first conductive structure, and to radiate from the first surface to the exterior.