Sparse arrays can resolve significantly more scatterers or sources than sensor by utilizing the co-array — a virtual array structure consisting of pairwise differences or sums of sensor positions. Although several sparse array configurations have been developed for passive sensing applications, far fewer active array designs exist. In active sensing, the sum co-array is typically more relevant than the difference co-array, especially when the scatterers are fully coherent. This paper proposes a general symmetric array configuration suitable for both active and passive sensing. We first derive necessary and sufficient conditions for the sum and difference co-array of this array to be contiguous. We then study two specific instances based on the Nested array and the Kløve-Mossige basis, respectively. In particular, we establish the relationship between the minimum-redundancy solutions of the two resulting symmetric array configurations, and the previously proposed Concatenated Nested Array (CNA) and Kløve Array (KA). Both the CNA and KA have closed-form expressions for the sensor positions, which means that they can be easily generated for any desired array size. The two array structures also achieve low redundancy, and a contiguous sum and difference co-array, which allows resolving vastly more scatterers or sources than sensors.

中文翻译：

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具有低冗余度和连续和联合阵列的稀疏对称线性阵列

通过利用协同阵列，稀疏阵列可以比传感器分辨更多的散射体或源，这种协同阵列是由成对的差或传感器位置之和组成的虚拟阵列结构。尽管已经为被动感测应用开发了几种稀疏阵列配置，但存在的主动阵列设计要少得多。在主动感应中，总和协同阵列通常比差异协同阵列更相关，尤其是在散射体完全相干的情况下。本文提出了一种适用于主动和被动感应的通用对称阵列配置。我们首先导出必要且充分的条件，以使该数组的和与差协数组连续。然后，我们分别基于嵌套数组和Kløve-Mossige基础研究了两个特定实例。尤其是，我们建立了两个结果对称阵列配置的最小冗余解与先前提出的级联嵌套阵列（CNA）和Kløve阵列（KA）之间的关系。CNA和KA都具有传感器位置的封闭形式的表达式，这意味着可以很容易地为任何所需的数组大小生成它们。这两个阵列结构还实现了低冗余度，以及连续的和差和并列阵列，从而可以解决比传感器更多的散射体或源。