Sparse arrays, which can localize multiple sources with less physical sensors, have attracted more attention since they were proposed. However, for optimal performance of sparse arrays, it is usually assumed that the circumstances are ideal. But in practice, the performance of sparse arrays will suffer from the model errors like mutual coupling, gain and phase error, and sensor’s location error, which causes severe performance degradation or even failure of the direction of arrival (DOA) estimation algorithms. In this study, we follow with interest and propose a covariance-based sparse representation method in the presence of gain and phase errors, where a generalized nested array is employed. The proposed strategy not only enhances the degrees of freedom (DOFs) to deal with more sources but also obtains more accurate DOA estimations despite gain and phase errors. The Cramer–Rao bound (CRB) derivation is analyzed to demonstrate the robustness of the method. Finally, numerical examples illustrate the effectiveness of the proposed method from DOA estimation.

中文翻译：

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广义嵌套阵列基于增益和相位误差校准的基于稀疏度的DOA估计

自提出以来，稀疏阵列可以用较少的物理传感器来定位多个源，因此备受关注。但是，对于稀疏阵列的最佳性能，通常假定情况是理想的。但是在实践中，稀疏阵列的性能将受到模型误差（例如互耦，增益和相位误差以及传感器的位置误差）的影响，这会导致严重的性能下降甚至到达方向（DOA）估计算法失败。在这项研究中，我们感兴趣地遵循并提出了在存在增益和相位误差的情况下基于协方差的稀疏表示方法，其中采用了广义嵌套数组。所提出的策略不仅提高了自由度（DOF）以处理更多的信号源，而且尽管有增益和相位误差，但仍能获得更准确的DOA估计。对Cramer-Rao界（CRB）推导进行了分析，以证明该方法的鲁棒性。最后，数值算例说明了从DOA估计中提出的方法的有效性。