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.Comment: 19 pages, 7 figures, under review in Transactions on Signal
Processing (2013