Waveform design for MIMO radar with matrix completion

Abstract—It was recently shown that MIMO radars with sparse sensing and matrix completion (MC) can significantly reduce the volume of data required by MIMO radars for accurate target detection and estimation. In MIMO-MC radars, the subsampled target returns are forwarded by the receive antennas to a fusion center, partially filling a matrix, referred to as the data matrix. The data matrix is first completed via MC techniques and then used to estimate the target parameters via standard array processing methods. This paper studies the applicability of MC theory on the data matrix arising in colocated MIMO radars using uniform linear arrays. It is shown that the data matrix coherence, and consequently the performance of MC, is directly related to the transmit waveforms. Among orthogonal waveforms, the optimum choices are those for which, any snapshot across the transmit array has a flat spectrum. The problem of waveform design is formulated as an optimization problem on the complex Stiefel manifold, and is solved via the modified steepest descent method, or the modified Newton algorithm with nonmonotone line search. Although the optimal waveforms are designed for the case of tar-gets falling in the same range bin, sensitivity analysis is conducted to assess the performance degradation when those waveforms are used in scenarios in which the targets fall in different range bins. Index Terms—Complex Stiefel manifold, matrix completion, multiple-input multiple-output (MIMO) radar, waveform design. I