Calibrating nested sensor arrays for DOA estimation utilizing continuous multiplication operator

Abstract Recently proposed nested array can increase the number degrees of freedom (DOFs) greatly in comparison with uniform linear array, enabling us to extend it to tackle the problem of direction of arrival (DOA) estimation in the presence of gain-phase errors. By exploiting continuous multiplication operator and an auxiliary source, the gain-phase error matrix is efficiently estimated under the assumption that part of sensors are well calibrated. After compensating the gain-phase errors, a full-rank virtual covariance matrix is obtained by subvector division and the DOAs are successfully obtained via the ESPRIT technique. The proposed algorithm is a general one, and can be easily applied to coprime array and other mainstream DOA solving techniques (such as MUSIC and sparsity-based approaches). The performance analysis and Cramer-Rao Bound for DOA estimation with partly calibrated nested array are given and the effectiveness of the proposed algorithm is verified by numerical simulations.

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