An FMCW radar sensor system is described having an antenna covered by a radome, a mixer for mixing a frequency-modulated transmission signal with a signal received by the antenna, a device for recording the mixed product of the mixer as a time-dependent signal, a device for calculating the spectrum of the time-dependent signal, and a device for detecting a reflecting coating on the radome, characterized in that the device for detecting the reflecting coating is configured for analyzing the time-dependent signal and for determining the extent of reflection on the radome based on the amplitude of this signal.