Abstract
In this paper, we reformulate the gridless direction of arrival (DoA) estimation problem in a novel reweighted covariance fitting (CF) method. The proposed method promotes joint sparsity among different snapshots by means of nonconvex Schatten-p quasi-norm penalty. Furthermore, for more tractable and scalable optimization problem, we apply the unified surrogate for Schatten-p quasi-norm with two-factor matrix norms. Then, a locally convergent iterative reweighted minimization method is derived and solved efficiently via a semidefinite program using the optimization toolbox. Finally, numerical simulations are carried out in the background of unknown nonuniform noise and under the consideration of coprime array (CPA) structure. The results illustrate the superiority of the proposed method in terms of resolution, robustness against nonuniform noise, and correlations of sources, in addition to its applicability in a limited number of snapshots.
Highlights
direction of arrival (DoA) estimation is a major task in array signal processing
Gridless covariance fitting (CF) is preferable in the presence of a nonuniform noise background, in this paper we develop a new gridless sparse method for DoA estimation based on recently developed gridless CF methods
By exploiting the positive semidefinite (PSD) and Toeplitz structure of the parameterized data covariance matrix, a gridless CF criterion is formulated in an efficient joint sparsity optimization problem
Summary
DoA estimation is a major task in array signal processing. It has wide applications in radar, sonar, wireless communications, underwater acoustics, and seismology [1,2,3]. The nonuniform noise is a challenging problem in sparse estimation methods, where the sample covariance matrix is no longer low-rank To eliminate this problem the recent research studies get rid of noise in two major methods, the first one is by using linear transform primarily and solving noise-free optimization problem as in [30, 31]. Despite the convexity of the preliminary gridless optimization models, it has been shown that the estimation performance of such convex relaxation will degrade in the presence of measurement noise or when some assumptions are violated (e.g., spatial sources separation limit and signals correlation). Due to the one-to-one relation between frequency and direction information, we look forward to achieve a better gridless DoA estimation using Schatten-p quasi-norm penalty
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