A Sparse Linear Array Approach in Automotive Radars Using Matrix Completion

We consider an automotive radar using a sparse linear array (SLA) in the context of multi-input multi-output (MIMO) radar. The key problem in SLA is the selection of the locations of the array elements so that the peak sidelobe level of the virtual SLA beampattern is low. Prior approaches have focused on optimal sparse array design, or use of interpolation techniques for filling the holes in the synthesized SLA before applying digital beamforming for angle finding. In this paper, different from previous efforts, we use matrix completion to complete the corresponding virtual uniform linear array (ULA) before estimating the target angle. In particular, we show that for a small number of targets within the same range-Doppler cell, the Hankel matrix constructed by subarrays of the virtual ULA is low-rank, and thus under certain conditions, can be completed based on the SLA measurements. We derive the coherence properties of the Hankel matrix so that the matrix can be competed via nuclear norm minimization methods. We also demonstrate via examples the effect of various SLA topologies on the identifiability of the Hankel matrix.