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

It was recently shown that low rank Matrix Completion (MC) theory can support the design of new sampling schemes in the context of MIMO radars, enabling significant reduction of the volume of data required for accurate target detection and estimation. Based on the data received, a matrix can be formulated, which can then be used in standard array processing methods for target detection and estimation. For a small number of targets relative to the number of transmission and reception antennas, the aforementioned data matrix is low-rank and thus can be recovered from a small subset of its elements using MC. This allows for a sampling scheme that populates the data matrix in a uniformly sparse fashion. This paper studies the applicability of MC theory on the type of data matrices that arise in colocated MIMO radar systems. In particular, for the case in which uniform linear arrays are considered for transmission and reception, it is shown that the coherence of the data matrix is both asymptotically and approximately optimal with respect to the number of antennas, 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. These results are then generalized to the arbitrary 2-dimensional array case, providing more general but yet easy to use sufficient conditions ensuring low matrix coherence.