On waveform conditions in MIMO radars using matrix completion

It was recently shown that MIMO radars with matrix completion (MIMO-MC radars) can achieve the performance of MIMO radars but with significantly fewer samples. The matrix completion performance depends on the coherence of the matrix. In MIMO-MC radars and for the scenario in which the targets fall in the same range bin, the coherence of the received data matrix is asymptotically optimal, i.e., 1, when the transmit waveforms have flat spatial spectrum. In this paper, we study the performance of such waveforms when used to estimate targets that fall in different range bins. We show that, if such optimal waveforms are additionally designed to have good correlation properties, the matrix coherence is slightly larger than 1 but bounded by 2 as long as the maximal range delay is of the order of the pulse duration. Thus, in such cases the MC performance degrades only slightly.