Sparse frame DOA estimations via a rank-one correlation model for low SNR and limited snapshots

As a typical problem of sparse frame representations or compressed sensing with frames, direction of arrival (DOA) estimations, via sparse recovery methodologies such as nonlinear optimizations or various greedy algorithms, suffer seriously under severe noisy measurement without proper treatment. In this article, a crucial and effective correlation operation is outlined to mitigate the severe noise effect from the sparse representation point of view. A fast and super resolution method for DOA estimations is therefore established under very low signal-to-noise ratio, and by a sparse recovery technique of null space tuning in the context of compressed sensing and sparse representations. Improvement to the technique using the thresholding difference and alternating grid refinements are also outlined to estimate the source/target numbers dynamically and to improve the precision. Another characteristic is that only a very small number of snapshots are needed in comparison with other techniques. Simulation results demonstrate apparent advantages of the proposed technique over known approaches. The proposed method has the effectiveness at simultaneous high resolution, robustness to noise, and source number estimations. The algorithm is also computationally efficient, which is critical for large array systems and/or mission critical real-time applications.