Sparse Spatial Smoothing: Reduced Complexity and Improved Beamforming Gain via Sparse Sub-Arrays

This paper addresses the problem of single snapshot Direction-of-Arrival (DOA) estimation, which is of great importance in a wide-range of applications including automotive radar. A popular approach to achieving high angular resolution when only one temporal snapshot is available is via subspace methods using spatial smoothing. This involves leveraging spatial shift-invariance in the antenna array geometry—typically a uniform linear array (ULA)—to rearrange the single snapshot measurement vector into a spatially smoothed matrix that reveals the signal subspace of interest. However, conventional approaches using spatially shifted ULA sub-arrays can lead to a prohibitively high computational complexity due to the large dimensions of the resulting spatially smoothed matrix. Hence, we propose to instead employ judiciously designed sparse sub-arrays, such as nested arrays, to reduce the computational complexity of spatial smoothing while retaining the aperture and identifiability of conventional ULA-based approaches. Interestingly, this idea also suggests a novel beamforming method which linearly combines multiple spatially smoothed matrices corresponding to different sets of shifts of the sparse (nested) sub-array. This so-called shift-domain beamforming method is demonstrated to boost the effective SNR, and thereby resolution, in a desired angular region of interest, enabling single snapshot low-complexity DOA estimation with identifiability guarantees.