Sparse covariance fitting for direction of arrival estimation

Abstract

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 l 1 -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 method for direction of arrival estimation of uncorrelated wideband signals

“…In array processing a narrowband signal is usually defined as a signal that meets the condition about the bandwidth to center frequency being less than 1% [16], [17]. Here we extend the narrowband model from [10], [11] to a wideband model and derive a new wideband direction of arrival estimation method which is the novelty of this paper. The received wideband signal is first decomposed into a set of independent narrowband signals using Discrete Fourier Transform (DFT) ( [2], [3]) or narrowband filters ( [6]).…”

“…In order for (10) to be well defined, we need the value of U to be dependent on the variance of the term has correlated entries, it is very difficult to predict the value of U in (11). But using the estimate of the decorrelation…”

A Compact Formulation for the $\ell _{2,1}$ Mixed-Norm Minimization Problem

“…SSR based on an 2,0 mixed-norm approximation has been considered in [38], while a convex relaxation approach based on the 2,1 mixed-norm has been proposed in [37]. DOA estimation based on secondorder signal statistics has been addressed in [42], [43], where a sparse covariance matrix representation is exploited by application of a sparsity prior on the source covariance matrix, leading to an SMV-like sparse minimization problem. In [44]- [46] the authors propose the SPICE method, which is based on weighted covariance matching and constitutes a sparse estimation problem which does not require the assumption of a sparsity prior.…”

A subspace method for array covariance matrix estimation

“…For example, [11] proposes the idea that the eigenvectors of the array covariance matrix have a sparse representation over a dictionary constructed from the steering vectors. In [12,14], it is shown that when the received signals are uncorrelated, the array covariance matrix has a sparse representation over a dictionary constructed using the atoms, i.e. the correlation vectors.…”