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This article proposes a new algorithm for finding the angles of arrival of multiple uncorrelated sources impinging on a uniform linear array of sensors. The method is based on sparse signal representation and does not require either the knowledge of the number of the sources or a previous initialization. The proposed technique considers a covariance matrix model based on overcomplete basis representation and tries to fit the unknown signal powers to the sample covariance matrix. Sparsity is enforced by means of a l1-norm penalty. The final problem is reduced to an objective function with a non-negative constraint that can be solved efficiently using the LARS/homotopy algorithm. The method described herein is able to provide high resolution with a low computational burden. It proceeds in an iterative fashion solving at each iteration a small linear system of equations until a stopping condition is fulfilled. The proposed stopping criterion is based on the residual spectrum and arises in a natural way when the LARS/homotopy is applied to the considered objective function.

Sparse covariance fitting for direction of arrival estimation