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.
In this paper, we present a hybrid optimization framework for gridless sparse Direction of Arrival (DoA) estimation under the consideration of heteroscedastic noise scenarios. The key idea of the proposed framework is to combine global and local minima search techniques that offer a sparser optimizer with boosted immunity to noise variation. In particular, we enforce sparsity by means of reformulating the Atomic Norm Minimization (ANM) problem through applying the nonconvex Schatten-p quasi-norm (0<p<1) relaxation. In addition, to enhance the adaptability of the relaxed ANM in more practical noise scenarios, it is combined with a covariance fitting (CF) criterion resulting in a locally convergent reweighted iterative approach. This combination forms a hybrid optimization framework and offers the advantages of both optimization approaches while balancing their drawbacks. Numerical simulations are performed taking into account the configuration of co-prime array (CPA). The simulations have demonstrated that the proposed method can maintain a high estimation resolution even in heteroscedastic noise environments, a low number of snapshots, and correlated sources.
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