For direction-of-arrival (DOA) estimation problems in a sparse domain, sparse Bayesian learning (SBL) is highly favored by researchers owing to its excellent estimation performance. However, traditional SBL-based methods always assign Gaussian priors to parameters to be solved, leading to moderate sparse signal recovery (SSR) effects. The reason is Gaussian priors play a similar role to $l_2$ regularization in sparsity constraint. Therefore, numerous methods are developed by adopting hierarchical priors that are used to perform better than Gaussian priors. However, these methods are in straitened circumstances when multiple measurement vector (MMV) data are adopted. On this basis, a block-sparse SBL method (named BSBL) is developed to handle DOA estimation problems in MMV models. The novelty of BSBL is the combination of hierarchical priors and block-sparse model originating from MMV data. Therefore, on the one hand, BSBL transfers the MMV model to a block-sparse model by vectorization so that Bayesian learning is directly performed, regardless of the prior independent assumption of different measurement vectors and the inconvenience caused by the solution of matrix form. On the other hand, BSBL inherited the advantage of hierarchical priors for better SSR ability. Despite the benefit, BSBL still has the disadvantage of relatively large computation complexity caused by high dimensional matrix operations. In view of this, two operations are implemented for low complexity. One is reducing the matrix dimension of BSBL by approximation, generating a method named BSBL-APPR, and the other is embedding the generalized approximate message passing (GAMB) technique into BSBL so as to decompose matrix operations into vector or scale operations, named BSBL-GAMP. Moreover, BSBL is able to suppress temporal correlation and handle wideband sources easily. Extensive simulation results are presented to prove the superiority of BSBL over other state-of-the-art algorithms.

The direction-of-arrival (DOA) estimation of wideband signals, based on sparse signal reconstruction, has recently been proposed, owing to its unique high-resolution performance. As a typical tool of sparse signal reconstruction, sparse Bayesian learning (SBL) enhances little sparsity in most works, leading to a non-robust local fitting. To significantly enhance sparsity, we proposed a novel hierarchical Bayesian prior framework, and deduced a novel iterative approach. It was discovered that the iterative approach had a lower computational complexity than the majority of current state-of-the-art algorithms. Besides, the proposed approach achieves a high angular estimation accuracy and sparsity performance, by utilizing the joint sparsity of the multiple measurement vector (MMV) models. Moreover, the approach stabilizes the estimated values between different frequencies or snapshots, so as to obtain a flat spatial spectrum. Extensive simulation results are presented, to demonstrate the superior performance of our method.

As an important research focus in radar detection and localization, direction-of-arrival (DOA) estimation has advanced significantly owing to deep learning techniques with powerful fitting and classifying abilities in recent years. However, deep learning inevitably requires substantial data to ensure learning and generalization abilities and lacks reasonable interpretability. Recently, a deep unfolding technique has attracted widespread concern due to the more explainable perspective and weaker data dependency. More importantly, it has been proven that deep unfolding enables convergence acceleration when applied to iterative algorithms. On this basis, we rigorously deduce an iterative sparse Bayesian learning (SBL) algorithm and construct a Bayesian deep unfolded network in a one-to-one correspondence. Moreover, the common but intractable off-grid errors, caused by grid mismatch, are directly considered in the signal model and computed in the iterative process. In addition, minimum hole array, little considered in deep unfolding, is adopted to further improve estimation performance owing to the maximized array degrees of freedom (DOFs). Extensive simulation results are presented to illustrate the superiority of the proposed method beyond other state-of-the-art methods.