A Bayesian Deep Unfolded Network for the Off-Grid Direction-of-Arrival Estimation via a Minimum Hole Array

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.