Underdetermined DOA Estimation via Covariance Matrix Completion for Nested Sparse Circular Array in Nonuniform Noise

This paper proposes a covariance matrix completion based algorithm for underdetermined direction of arrival (DOA) estimation in the presence of unknown nonuniform noise using nested sparse circular array (NSCA) with only $N$ sensors. The proposed algorithm provides a systematic procedure to complete a covariance matrix for a virtual uniform circular array (UCA) with $M$ sensors ( $M > N$ ). Compared with the covariance matrix of the NSCA, the completed covariance matrix is capable of increasing degrees of freedom (DOFs), and is noise-free to mitigate the effect of nonuniform noise. The elements of the completed covariance matrix are from three steps: (1) elements from covariance matrix of the NSCA; (2) elements generated from the properties of the UCA; (3) elements produced from output of oblique projection operator based on initial DOAs. Then compressive sensing (CS) method is used to estimate DOAs based on the completed covariance matrix for better performance. The computational complexity of the proposed algorithm, and CRB are also given. Simulation results demonstrate that the proposed algorithm outperforms the state-of-the-art methods in estimation accuracy.