The present disclosure relates to a radar apparatus and a method for processing a signal using a radar apparatus, and more particularly, to an apparatus and a method for receiving and processing reception signals having different polarization characteristics using one array antenna. Specifically, the present disclosure provides a radar apparatus including: a long-range transmission antenna unit including one or more long-range transmission array antennae which transmit a first polarized transmission signal; a short-range transmission antenna unit including one or more short-range transmission array antennae which transmit a second polarized transmission signal; a complex array antenna unit which includes one or more complex array antennae receiving a first polarized reception signal and a second polarized reception signal which are received by reflecting the first polarized transmission signal and the second polarized transmission signal from a target; and a signal processing unit which detects the target using the first polarized reception signal and the second polarized reception signal, in which the first polarized reception signal has a cross polarization characteristic with respect to the second polarized reception signal, and a radar signal processing method.