An electronic device may include communications circuitry, sensing circuitry, and a set of antennas having first and second feeds for covering different polarizations. The communications circuitry may transmit signals with a first polarization using each of the antennas and may concurrently transmit signals with a second polarization using all but a selected one of the antennas. The sensing circuitry may concurrently transmit sensing signals with the first polarization using one of the antennas and may receive sensing signals with the second polarization using the selected antenna. The sensing signals may include chirp signals generated to include muted periods that correspond to a range of frequencies that overlap frequencies at which the wireless circuitry is subject to radio-frequency interference. This may allow for concurrent wireless communications and sensing operations without interference between the communications circuitry and the sensing circuitry.