An electronic device may have a first phased antenna array that radiates through a display and a second phased antenna array that radiates through a rear wall. The first array may include a front-facing dielectric resonator antenna and the second array may include a rear-facing dielectric resonator antenna. The front and rear-facing antennas may share a dielectric resonating element. Feed probe(s) may excite a first volume of the dielectric resonating element to radiate through the display and may excite a second volume of the dielectric resonating element to radiate through the rear wall. The dielectric resonating element may have a geometry that helps to isolate the front-facing dielectric resonator antenna from the rear-facing dielectric resonator antenna. The first and second arrays may collectively cover an entire sphere around the device while occupying a minimal amount of volume within the device.