On waveform design for MIMO radar with matrix completion

In matrix completion based MIMO radars, the data matrix coherence, and consequently the performance of matrix completion depend on the transmit waveforms. It was recently shown that for uniform linear arrays and orthogonal waveforms, the optimal choice for waveforms are white-noise type functions. This paper deals with the design of optimal transmit waveforms. The design is formulated as an optimization problem on the complex Stiefel manifold, which is a non-convex set, and the optimal waveforms are found via a steepest descent algorithm with nonmonotone line search methods. Numerical results show that for large dimensional data matrices and for a large number of antennas, the objective function converges to its global minimum and the matrix coherence corresponding to the optimal waveforms is asymptotically optimal, thus resulting in very good target estimation performance.