An electronic device comprises a housing having a first side and a second side, a dielectric cover (602) on said second side, and an electrically conductive peripheral structure along edges of said first and second sides. An antenna feed (601) is coupled to a portion (603) of said peripheral structure for using said portion (603) as a radiating antenna element. A conductive member (604, 804) is located on or underneath said dielectric cover (602). The purpose of the conductive member is to enlarge the surface area where the electric field is distributed on to increase the antenna aperture for radiation.