Sparse Recovery of Finite Alphabet Signals Using AMP and Its Application in DoA Estimation

This study presents an approximate message passing (AMP)-based method for the reconstruction of sparse signals from multiple measurement vectors. Recently, Ziniel and Schniter have provided a general analysis of the AMP algorithm. They have assumed that the nonzero elements of the sparse signals have Gaussian distribution. This article extends their proposed method to the case that the nonzero elements of sparse vectors are chosen from a discrete finite alphabet. Therefore, the proposed algorithm is called approximate message passing with finite alphabet. Based on this assumption, the passing messages have been derived and the scheduling of the algorithm has been proposed using a three-step strategy. As an application, direction of arrival (DoA) estimation of digitally modulated signals is examined using simulations. The obtained results revealed that the proposed method would improve the DoA estimation accuracy compared to the conventional methods.