Abstract
Coprime arrays can highly increase degree-of-freedom (DOF) by exploiting the equivalent virtual signal. However, since the corresponding virtual array constructed by the coprime array is always a non-uniform linear array (non-ULA), most existing direction-of-arrival (DOA) estimation algorithms fail to utilize all received information and result in performance degradation. To address this issue, we propose a novel interpolation approach for coprime arrays to convert the virtual array into a ULA with which all received information can be efficiently utilized. In this paper, we consider a weighted covariance matrix fitting criterion to formulate a semi-definite programming (SDP) problem with respect to the interpolated virtual signal. After that, we can reconstruct a Hermitian Toeplitz covariance matrix corresponding to the interpolated ULA in a gridless manner, and the number of detectable targets is ulteriorly increased with the reconstructed covariance matrix. The proposed approach is hyperparameter-free so that the tedious process of selecting regularization parameters is avoided. Numerical experiments validate the superiority of the proposed interpolation-based DOA estimation algorithm in terms of DOF characteristic, resolution ability and estimation accuracy compared with several existing techniques.
Highlights
Direction-of-arrival estimation, as an important research branch of array signal processing, has been widely applied in sonar [1], radar [2] and wireless communication [3]
SIMULATION RESULTS we present several numerical experiments to demonstrate the advantages of the proposed interpolationbased DOA estimation algorithm for coprime arrays
We choose a pair of coprime integers M = 3 and N = 5 respectively to deploy the coprime array which consists of M + N − 1 = 7 physical sensors in total, and the sensors are located at {0, 3d, 5d, 6d, 9d, 10d, 12d}
Summary
Direction-of-arrival estimation, as an important research branch of array signal processing, has been widely applied in sonar [1], radar [2] and wireless communication [3]. Whereas the matrix completion-based approaches will generate a performance loss because the partial correlation observation corresponding to the non-uniform segment is retained To address such a problem, the idea of gridless Toeplitz matrix reconstruction [18], [19] is utilized to exploit the potential DOF more recently and it is demonstrated that the reconstructed covariance matrix coincides with the interpolated ULA better. From the perspective of Toeplitz matrix reconstruction in this paper as well, we propose a novel virtual array interpolation-based DOA estimation algorithm for the coprime array. We use ⊗ to stands for the Kronecker product and | · | represents the cardinality of a set
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