Electronic devices may be provided that contain wireless communications circuitry. The wireless communications circuitry may include radio-frequency transceiver circuitry and antenna structures. An electronic device may include a display mounted within a housing. A peripheral conductive member may run around the edges of the display and housing. Dielectric-filled gaps may divide the peripheral conductive member into individual segments. A ground plane may be formed within the housing from conductive housing structures, printed circuit boards, and other conductive elements. The ground plane and the segments of the peripheral conductive member may form antennas in upper and lower portions of the housing. The radio-frequency transceiver circuitry may implement receiver diversity using both the upper and lower antennas. The lower antenna may be used in transmitting signals. The upper antenna may be tuned using a tunable matching circuit.