The MMV tail null space property and DOA estimations by tail-[formula omitted] minimization

Abstract

The tail-minimization approach is applied to the joint sparse multiple measurement vector (MMV) model and direction of arrival (DOA) estimations. The mechanism is to estimate the support T of the jointly sparse matrix and minimize the energy in the complement Tc of T during each iteration. An MMV tail-null-space property (MMV-tail-NSP) is derived, which is shown to be necessary and sufficient for the unique solution of the MMV tail minimization problem. The MMV-tail-NSP condition is also shown to be more likely to hold than that of the conventional MMV-NSP for any given MMV basis pursuit problem. Two recovery guarantees and error bound analyses are also derived based on the MMV-robust-tail-NSP condition and merely the MMV-tail-NSP assumption, respectively. Study shows that the MMV tail-minimization approach is among the most effective techniques for the MMV DOA model. In particular, the MMV tail-minimization approach is able to recover signals of rank-enriched sparsity level K0≡[spark(A)−1+rank(X)]/2. In fact, this approach can handle signal recovery of greater sparsity levels than that by others. The advantages of the MMV tail-minimization approach are also reflected in numerous aspects such as handling low signal-to-noise ratio (SNR), limited number of snapshots, and correlated source signals. Results are more accurate with higher resolution as well. It is also capable of detecting the number of sources and estimating DOAs simultaneously. All these characteristics and advantages are fully evidenced by extensive simulation studies.