Gridless Compressed Sensing for Fully Augmentable Arrays

Direction-of-arrival (DOA) estimation using nonuniform linear arrays is considered. We focus on the so called "fully augmentable arrays" (FAAs) with full set of covariance lags. In FAAs, the number of covariance lags is usually larger than the number of sensors in the array. Thus, with FAAs more sources than the number of sensors can be identified. Existing DOA estimation algorithms for FAAs are based on the assumption of uncorrelated sources. In this paper, based on compressed sensing, we present a DOA estimation algorithm for FAAs without assuming uncorrelated sources. The proposed algorithm is based on the newly introduced gridless SPARse ROW-norm reconstruction (SPARROW) formulation for the joint sparse reconstruction from multiple measurement vectors. By numerical experiments, we show that the proposed algorithm outperforms the existing algorithms in the presence of correlated signals or small number of snapshots. Moreover, using simulations, the behavior of the Cramer-Rao Bound (CRB) for the case of correlated source is demonstrated and it is shown that, when the number of sources is larger than the number of sensors, the CRB for FAAs approaches zero at infinitely large signal-to-noise-ratio (SNR) only if the sources are fully correlated.