An electronic device may be provided antennas and control circuitry. The antennas may be arranged in an array of unit cells. Each unit cell may include a first antenna that conveys signals in a first frequency band higher than 10 GHz and a second antenna that conveys radio-frequency signals in a second frequency band higher than the first frequency band. A first of the unit cells may be provided with a first set of antennas that transmits radio-frequency signals in a third frequency band higher than the second frequency band. A second of the antenna unit cells may be provided with a second set of antennas that receives the radio-frequency signals after being reflected off of external objects. The control circuitry may perform spatial ranging operations by processing the transmitted and received signals in the second frequency band.