Super-Resolution in Automotive Pulse Radars

In this work we consider a mmWave pulse radar and study the problem of super-resolving the echoes produced by multiple prospective targets. We derive a novel signal model wherein an observed echo is represented in term of a conveniently-structured steering vector and its associated multi-dimensional frequency vector related to the target location; we consider a five-dimensional measurement space, including the delay and Doppler dimensions and the Cartesian axes of a 3-dimensional array. Upon exploiting the atomic norm to harness sparsity in the continuous parameter domain, the unknown frequency vectors and the corresponding atoms are recovered by resorting to the Vandermonde decomposition of a canonical multi-level Toepliz matrix. Conditions for unique resolvability in the noiseless case are provided and discussed; also, a low-complexity formulation of the recovery problem is proposed, wherein the available data samples are conveniently parsed into multiple smaller groups described by the same set of atoms. Finally, numerical results are provided to validate the theoretical analysis and to verify the effect of the additive noise in practical operating scenarios.