A signal processing device includes: an acquisition unit configured to acquire phase information of a reception signal of each of plural virtual antennas generated based on a combination of plural transmission antennas and plural reception antennas; a first calculation unit configured to calculate, based on the phase information, at least one first phase difference between the plural transmission antennas in an outward path along which a transmission wave transmitted from the plural transmission antenna reaches a target; a second calculation unit configured to calculate, based on the phase information, at least one second phase difference between the plural reception antennas in a return path along which a reflected wave reflected by the target reaches the plural reception antennas; and a determination unit configured to determine, based on the first phase difference and the second phase difference, whether the outward path and the return path match each other.