Abstract Sparse arrays, such as nested arrays, are able to resolve more sources than sensors because their difference co-arrays can provide O ( L 2 ) degrees-of-freedom (DOFs) with L physical sensors. Most of the existing nested array direction-finding algorithms apply the spatial smoothing technique to realize this DOFs enhancement. One shortcoming of this type of methods is the efficient co-array aperture is reduced in processing the spatial smoothing, resulting in the DOFs are not fully utilized. In this paper, we propose a new approach using two parallel linear nested arrays to contribute full DOFs for two-dimensional direction-finding. To exploit the entire DOFs, we perform the vectorization of multiple fourth-order cumulant matrices and take the average of their co-array covariance matrices, instead of the spatial smoothing of the vectorization of the data covariance matrix. Based on a well-posed identification analysis, we show that the proposed approach can identify the number of sources approximately three times than the algorithms using the spatial smoothing technique. For example, for a two-level parallel nested array of 2 + 2 sensors in each subarray, the maximum number of sources that can be resolved by the proposed approach is 32, whereas, for most of the existing algorithms, the number reduces to 10.

中文翻译：

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使用具有完整协同阵列孔径扩展的平行嵌套阵列进行二维测向

摘要 稀疏阵列（例如嵌套阵列）能够比传感器解析更多的源，因为它们的差分共阵列可以为 L 个物理传感器提供 O ( L 2 ) 自由度 (DOF)。大多数现有的嵌套阵列测向算法应用空间平滑技术来实现这种自由度增强。这种方法的一个缺点是在处理空间平滑时降低了有效的共阵列孔径，导致自由度没有得到充分利用。在本文中，我们提出了一种使用两个平行线性嵌套阵列为二维测向提供完整自由度的新方法。为了利用整个自由度，我们对多个四阶累积矩阵进行矢量化，并取它们的协阵列协方差矩阵的平均值，而不是数据协方差矩阵矢量化的空间平滑。基于适定识别分析，我们表明所提出的方法可以识别源数量大约是使用空间平滑技术的算法的三倍。例如，对于每个子阵列中 2 + 2 个传感器的两级并行嵌套阵列，所提出的方法可以解决的最大源数为 32，而对于大多数现有算法，数量减少到 10 .