Harnessing Holes for Spatial Smoothing with Applications in Automotive Radar

Abstract

This paper studies spatial smoothing using sparse arrays in single-snapshot Direction of Arrival (DOA) estimation. We consider the application of automotive MIMO radar, which traditionally synthesizes a large uniform virtual array by appropriate waveform and physical array design. We explore deliberately introducing holes into this virtual array to leverage resolution gains provided by the increased aperture. The presence of these holes requires re-thinking DOA estimation, as conventional algorithms may no longer be easily applicable and alternative techniques, such as array interpolation, may be computationally expensive. Consequently, we study sparse array geometries that permit the direct application of spatial smoothing. We show that a sparse array geometry is amenable to spatial smoothing if it can be decomposed into the sum set of two subsets of suitable cardinality. Furthermore, we demonstrate that many such decompositions may exist - not all of them yielding equal identifiability or aperture. We derive necessary and sufficient conditions to guarantee identifiability of a given number of targets, which gives insight into choosing desirable decompositions for spatial smoothing. This provides uniform recovery guarantees and enables estimating DOAs at increased resolution and reduced computational complexity.