Matrix Completion in Colocated MIMO Radar: Recoverability, Bounds&Theoretical Guarantees

It was recently shown that low rank matrix completion theory can be employed for designing new sampling schemes in the context of MIMO radars, which can lead to the reduction of the high volume of data typically required for accurate target detection and estimation. Employing random samplers at each reception antenna, a partially observed version of the received data matrix is formulated at the fusion center, which, under certain conditions, can be recovered using convex optimization. This paper presents the theoretical analysis regarding the performance of matrix completion in colocated MIMO radar systems, exploiting the particular structure of the data matrix. Both Uniform Linear Arrays (ULAs) and arbitrary 2-dimensional arrays are considered for transmission and reception. Especially for the ULA case, under some mild assumptions on the directions of arrival of the targets, it is explicitly shown that the coherence of the data matrix is both asymptotically and approximately optimal with respect to the number of antennas of the arrays involved and further, the data matrix is recoverable using a subset of its entries with minimal cardinality. Sufficient conditions guaranteeing low matrix coherence and consequently satisfactory matrix completion performance are also presented, including the arbitrary 2-dimensional array case. Index Terms Matrix Completion, Subspace Coherence, Strong Incoherence Property, Colocated MIMO Radar, Array Processing