Fundamentals of spatial and Doppler frequencies in radar STAP

The increasing interest for arbitrary antenna arrays in radar space-time adaptive processing (STAP) creates a need for a thorough understanding of the role of, and dependencies between, spatial and Doppler frequencies and related quantities, especially in the characterization of clutter. We successively introduce "geometrical" and statistical concepts, where we respectively emphasize the 4D direction-Doppler (DD) curve and the 4D power spectral density (PSD) that characterize the (clutter) space-time field. These descriptors, which are flight-configuration dependent, but antenna independent, are fundamental since they can be used to derive the key spectral properties of any antenna, essentially by rotations and projections. These descriptors are related in various ways, mostly because the DD curve is the support of the ridge of the clutter PSD. We also emphasize the surprising benefits of systematically considering the three spatial frequencies that are always present behind the scene, even for the customary linear antenna. A solid, simple, and elegant basis for thinking about STAP for arbitrary measurement configurations and antenna arrays is provided.