Estimating the direction of arrival of spatially spread sources using block-sparse Bayesian learning with an extended dictionary

Estimating the direction of arrival (DOA) of spatially spread sources is a significant challenge in array signal processing. This work introduces an effective method within the sparse Bayesian framework to tackle this issue. A spatially spread source is modeled using a multi-dimensional Slepian signal subspace that expands the dictionary and results in a block-sparse structured solution. By taking advantage of block-sparse Bayesian learning, parameter estimation becomes feasible. A complex Gaussian posterior is derived under a multi-snapshot block-sparse framework with a complex Gaussian prior and varying noise conditions. The hyperparameters are estimated using the expectation-maximization algorithm. Through numerical tests and sea test data evaluations, the proposed method shows superior energy focusing for spatially spread signals. Under limited snapshots and challenging signal-to-noise ratios, the current method can still offer precise DOA determination for spatially spread sources.