An electronic device may be provided with wireless circuitry. The wireless circuitry may include one or more antennas and first and second radio-frequency modules. The device may include a conductive housing having dielectric antenna windows. The first module may generate first millimeter wave signals in a first communications band. The antenna may transmit the first signals to external equipment through the dielectric window at a transmit power level. The antenna may receive control signals in the second communications band from the external equipment through the dielectric window. The first and second communications bands may include frequencies greater than 10 GHz. The second module may pass the received control signals to the first module to adjust the transmit power level of the first signals transmitted by the antenna. A duplexer may be interposed between the modules and the antenna for isolating the first and second communications bands.