Co-array-based Direction of Arrival (DoA) estimation using Sparse Linear Arrays (SLAs) has recently gained considerable interest in array processing thanks to its capability of providing enhanced degrees of freedom. Although the literature presents a variety of estimators in this context, none of them are proven to be statistically efficient. This work introduces a novel estimator for the co-array-based DoA estimation employing the Weighted Least Squares (WLS) method. An analytical expression for the large sample performance of the proposed estimator is derived. Then, an optimal weighting is obtained so that the asymptotic performance of the proposed WLS estimator coincides with the Cramér-Rao Bound (CRB), thereby ensuring asymptotic statistical efficiency of resulting WLS estimator. This implies that the proposed WLS estimator has a significantly better performance compared to existing methods. Numerical simulations are provided to validate the analytical derivations and corroborate the improved performance.

中文翻译：

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一种用于基于 Co-Array 的 DoA 估计的渐近有效加权最小二乘估计器

使用稀疏线性阵列 (SLA) 的基于协同阵列的到达方向 (DoA) 估计由于其提供增强的自由度的能力，最近在阵列处理中引起了相当大的兴趣。尽管文献在这方面提出了各种估计量，但没有一个被证明在统计上是有效的。这项工作为采用加权最小二乘法 (WLS) 方法的基于协同阵列的 DoA 估计引入了一种新颖的估计器。推导出了所提出的估计器的大样本性能的解析表达式。然后，获得最佳权重，使得所提出的 WLS 估计器的渐近性能与 Cramér-Rao Bound (CRB) 一致，从而确保所得 WLS 估计器的渐近统计效率。这意味着与现有方法相比，所提出的 WLS 估计器具有明显更好的性能。提供了数值模拟来验证分析推导并证实改进的性能。