Dictionary optimization for DOA approximation in a single snapshot

In the Direction of Arrival approximation, Compressed Sensing algorithm will fail to identify correct atoms due to high cumulative coherence of the redundant dictionary (manifold matrix). For insufficient number of samples, especially for a single snapshot, less statistical information aggravates such adverse effects. In this paper, we utilize the observed signal to construct a weighted matrix which can reduce the cross cumulative coherence of the redundant dictionary. And then, we develop a constructive algorithm combing with the weighted matrix to estimate Direction of Arrival. The simulation results prove our algorithm can effectively reduce the signal deviation caused by high coherence of dictionary, specifically in the circumstance of closely spatial sources.