Airborne radar ice sounding is challenged by surface clutter masking the depth signal of interest. Surface clutter may even be prohibitive for potential space-based ice sounding radars. To some extent the radar antenna suppresses the surface clutter, and a multi-phase-center antenna in combination with coherent signal processing techniques can improve the suppression, in particular if the direction of arrival (DOA) of the clutter signal is estimated accurately. This paper deals with data-driven DOA estimation. By using P-band data from the ice shelf in Antarctica it is demonstrated that a varying penetration depth influences the DOA.