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.

中文翻译：

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非均匀噪声中嵌套稀疏圆形阵列通过协方差矩阵完成的欠定 DOA 估计

本文提出了一种基于协方差矩阵完成的算法，用于在存在未知非均匀噪声的情况下使用嵌套稀疏圆形阵列 (NSCA) 进行欠定到达方向 (DOA) 估计。 $N$传感器。所提出的算法提供了一个系统的过程来完成虚拟均匀圆阵列 (UCA) 的协方差矩阵百万美元 传感器（$M > N$）。与 NSCA 的协方差矩阵相比，完整的协方差矩阵能够增加自由度（DOF），并且无噪声以减轻非均匀噪声的影响。完整的协方差矩阵的元素来自三个步骤：（1）来自NSCA协方差矩阵的元素；(2) 由 UCA 的属性生成的元素；(3)基于初始DOA的斜投影算子输出产生的元素。然后使用压缩感知 (CS) 方法基于完整的协方差矩阵估计 DOA，以获得更好的性能。还给出了所提出算法的计算复杂度和CRB。仿真结果表明，所提出的算法在估计精度方面优于最先进的方法。