Some characteristics of frequency measuring FMCW-radar altimeters operating above a rough ground surface

A model for the altimetry signal received from a rough scattering ground surface is postulated and analyzed in the case of a frequency counting FMCW radar altimeter. The general relationships between the altitude bias, noise level and the properties of the rough surface are investigated as well as the influence of smoothing time, signal bandwidth, Doppler bandwidth, and modulation frequency. The coupling between the noise level and the smoothing time is studied for a Gaussian scattering function and saw-tooth modulation. Even smoothing times longer than one modulation cycle are considered. A minimum noise level is obtained for high values of signal bandwidth and modulation frequency. A significant deviation between the noise levels of a zero crossings counter and phase differentiating detector is obtained only for surface roughnesses much smaller than the wavelength corresponding to the frequency excursion.