A generalised nested array (GNA) configuration with large minimum inter-element spacing is attractive to alleviate mutual coupling. In this study, by decomposing and rearranging the sub-arrays of GNA, the authors propose a new nested array configuration named as widened nested array (WNA). The WNA enables to provide the reduced mutual coupling, enhanced degrees of freedom (DOFs), extended array aperture and improved direction of arrival (DOA) estimation performance compared to GNA. The closed-form expressions for sensor positions of WNA are given and the optimal array configuration for largest DOFs is derived. Meanwhile, the authors propose a partial angular compressed sensing(CS) based DOA estimation algorithm for WNA. Specifically, discrete Fourier transform method is first derived for consecutive DOFs of WNA to obtain initial DOA estimates. Subsequently, the initial estimates are utilised to compress the angular range of overcomplete dictionary of the CS algorithm, which is exploited to obtain the fine DOA estimates. Extensive simulation results testify that the proposed algorithm has the same estimation accuracy as CS algorithm with lower complexity.

中文翻译：

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加宽嵌套数组：配置设计，最佳数组和DOA估计算法

具有大的最小元素间间距的广义嵌套阵列（GNA）配置对于减轻相互耦合具有吸引力。在这项研究中，通过分解和重新排列GNA的子数组，作者提出了一种新的嵌套数组配置，称为加宽嵌套数组（WNA）。与GNA相比，WNA可以提供减少的互耦合，增强的自由度（DOF），扩展的阵列孔径和改进的到达方向（DOA）估计性能。给出了WNA传感器位置的闭式表达式，并得出了最大自由度的最佳阵列配置。同时，作者提出了一种基于偏角压缩感知（CS）的WNA DOA估计算法。具体而言，首先针对WNA的连续DOF导出离散傅里叶变换方法，以获得初始DOA估计。随后，利用初始估计值来压缩CS算法的超完备字典的角度范围，并利用该角度范围来获得精细的DOA估计值。大量的仿真结果证明，该算法具有与CS算法相同的估计精度，且复杂度较低。