Directions of arrival estimation by learning sparse dictionaries for sparse spatial spectra

A major limitation of most methods exploiting sparse signal or spectral models for the purpose of estimating directions-of-arrival stems from the fixed model dictionary that is formed by array response vectors over a discrete search grid of possible directions. In general, the array responses to actual DoAs will most likely not be members of such a dictionary. In this work, the sparse spectral signal model with uncertainty of linearized dictionary parameter mismatch is considered, and the dictionary matrix is reformulated into a multiplication of a fixed base dictionary and a sparse matrix. Based on this double-sparsity model, an alternating dictionary learning-sparse spectral model fitting approach is proposed to reduce the estimation errors of DoAs and their powers. Group-sparsity estimator and Lasso-based Least Squares are utilized in the formulation of the associated optimization problem. The performance of the proposed methods are demonstrated by numerical simulations.