Low-Complexity optimization for Direction-of-Arrival Estimation via Approximate Message Passing

Abstract

Sparsity-inducing techniques have been introduced into direction of arrival (DOA) estimation and achieved a great success in performance. However the computational complexity of the conventional sparsity-inducing techniques is prohibitively high and thus prevents such methods from application. In this paper, we propose a low-complexity DOA estimation algorithm based on approximate message passing (AMP). Derived from the loopy belief propagation, AMP is a fast algorithm to obtain the posterior distribution of the signal. The proposed algorithm combines the AMP with expectation maximization (EM) technique to adaptively learn the hyper-parameters in the Gaussian priori of the signal. Closed-form update rule of signal prior variance is derived using fix-point method, an estimator of sources number and an empirical update rule for noise variance are also derived. Compared with the state-of-the-art algorithms, the proposed algorithm reduces the computational complexity by several orders of magnitude, while obtaining comparable performance of DOA estimation. Numerical simulation demonstrates the advantages of the proposed algorithm.