DOA Estimation of Coherent Sources With Sparse Arrays via Toeplitz Matrix Reconstruction

In recent years, sparse arrays have made considerable strides in resolving uncorrelated sources. However, the ubiquitous coherent sources across various emerging applications pose unique challenges for direction-of-arrival (DOA) estimation with sparse arrays. In this work, based on insight into the structure of the source covariance matrix, we first propose an effective strategy to achieve decorrelation by partitioning the diagonal and off-diagonal elements in the source covariance matrix. Then, we introduce two Toeplitz matrix reconstruction programs tailored for DOA estimation with sparse arrays. On one hand, we directly implement the decorrelation operation on the covariance matrix of sparse arrays, and further construct a Toeplitz matrix reconstruction program via virtual array interpolation for enhanced DOA estimation. On the other hand, we relate the sparse array to the hypothetical uniform linear array (ULA) through the compressed matrix, and perform decorrelation operation on the covariance matrix of the hypothetical ULA. Following this, a Toeplitz matrix reconstruction program via physical array interpolation is formulated for DOA estimation. Unlike the prevailing decorrelation techniques, the proposed algorithms can precisely estimate coherent sources without losing degrees of freedom and array aperture. Moreover, the Cramér-Rao bound pertinent to this problem is derived. Numerical simulations demonstrate that the proposed algorithms outperform their competitors in estimating coherent sources.