Deep unfolded network based on SLIM for direction-of-arrival estimation via nested array

For direction-of-arrival estimation problems, deep learning (DL) has shown excellent performance recently owing to the effectiveness and robustness to complicated cases. However, DL is always requiring massive data and lacks explainable theory, which limits its practical application. Fortunately, deep unfolding is able to overcome the disadvantages of DL and empirically achieves fast convergence. Inspired by that, we construct a deep unfolded network according to the famous Sparse Learning via Iterative Minimization (SLIM), yielding a method called learned-SLIM (LSLIM). LSLIM is able to converge efficiently and inherits the advantages of SLIM, such as low computational complexity, excellent sparsity performance. In addition, nested array is further adopted in LSLIM for high estimation accuracy. Extensive simulations are presented to illustrate the superior of the proposed LSLIM beyond other state-of-the-art algorithms.