On transmit beamforming in MIMO radar with matrix completion

The paper proposes a matrix completion based colocated MIMO radar (MIMO-MC) approach that employs transmit beamforming. The transmit antennas transmit correlated waveforms to illuminate certain directions. Each receive antenna performs sub-Nyquist sampling of the target returns at uniformly random times, and forwards the samples to a fusion center along with information on the sampling times. Based on the forwarded samples, the fusion center partially fills a matrix, recovers the Nyquist rate samples via matrix completion, and subsequently proceeds with target estimation via standard techniques. The performance of matrix completion depends on the matrix coherence. The paper derives the relations between transmit waveforms and matrix coherence. Specifically, it is shown that, for a rank-1 beamformer, the coherence is optimal, i.e., 1, if and only if the waveforms are unimodular. For a multi-rank beamformer, the coherence of the row space of the data matrix is optimal if the waveform power is constant across each snapshot. Simulation results show that the proposed scheme achieves high resolution with a significantly reduced number of samples.