Abstract
Sparse arrays, which can localize multiple sources with less physical sensors, have attracted more attention since they were proposed. However, for optimal performance of sparse arrays, it is usually assumed that the circumstances are ideal. But in practice, the performance of sparse arrays will suffer from the model errors like mutual coupling, gain and phase error, and sensor’s location error, which causes severe performance degradation or even failure of the direction of arrival (DOA) estimation algorithms. In this study, we follow with interest and propose a covariance-based sparse representation method in the presence of gain and phase errors, where a generalized nested array is employed. The proposed strategy not only enhances the degrees of freedom (DOFs) to deal with more sources but also obtains more accurate DOA estimations despite gain and phase errors. The Cramer–Rao bound (CRB) derivation is analyzed to demonstrate the robustness of the method. Finally, numerical examples illustrate the effectiveness of the proposed method from DOA estimation.
Highlights
Superresolution direction finding is a key branch of signal processing, which has received much attention in many fields like radar systems, communication, and navigation [1, 2]
The research of direction of arrival (DOA) estimation has successively gone through three stages: adaptive beamforming, subspace decomposition (such as multiple signal classification (MUSIC) [3], estimation of signal parameters via the rotational invariance technique (ESPRIT) [4], etc.), and subspace fitting (such as maximum-likelihood (ML) algorithm [5], weighted subspace fitting (WSF) algorithm [6], etc.)
In order to verify the DOA estimation performance of the proposed strategy, several numerical simulations are provided
Summary
Superresolution direction finding is a key branch of signal processing, which has received much attention in many fields like radar systems, communication, and navigation [1, 2]. To achieve better estimation performance, the category of sparse reconstruction algorithms, which can be utilized to deal with the coherent sources, was extended to sparse arrays [16,17,18,19]. Another method of taking advantage of difference. To achieve better DOA estimation performance and reduce the adverse effect of gain and phase error, we transfer the DOA estimation into a sparse reconstruction problem with nonnegativity constraint by exploiting a covariance-based sparse representation method. R(·) and I(·) denote the real part and imagery part of a complex number. diag(·), vec(·), and E[·] represent the diagonal matrix operation, vectorization operation, and expectation operation, respectively
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