Generalized coprime structure decomposes the interleaved subarrays in the conventional coprime array by introducing a displacement and the resulting CADiS, i.e. coprime array with displaced subarrays , configuration can enlarge the minimum adjacent spacing between elements to multiples of half-wavelength, which is considerably attractive in alleviating mutual coupling effect. However, the difference co-array that CADiS yields is fractured, which greatly deteriorates direction of arrival (DOA) estimation performance and achievable degrees of freedom of the algorithms based on consecutive co-array, e.g. spatial smoothing technique and Toeplitz matrix method. In this paper, from the mutual coupling effect and difference co-array perspective, we propose an expanded coprime array (ECA) structure by two steps. The first step is to further augment the displacement between the subarrays of CADiS to suppress the mutual coupling effect. The second step is to relocate a proper number of rightmost elements to concatenate the dominant consecutive co-array generated by CADiS to enhance the consecutive difference co-array. Specifically, we provide the closed-form expressions of resulting consecutive difference co-array, the number of relocated elements and their positions. Furthermore, different from the spatial smoothing based methods, we employ Toeplitz matrix property to directly construct the full-rank covariance matrix of the received data from the consecutive co-array with a lower computational cost and present the Toeplitz-MUSIC algorithm to testify the effectiveness and superiority of the proposed ECA structure.

中文翻译：

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用于 DOA 估计的扩展互素阵列：增强连续协阵列并减少互耦

广义互质结构通过引入位移来分解常规互质阵列中的交错子阵列，由此产生的CADiS，即具有位移子阵列的互质阵列，配置可以将元素之间的最小相邻间距扩大到半波长的倍数，这在缓解问题方面具有相当大的吸引力。相互耦合效应。然而，CADiS 产生的差分协同阵列是断裂的，这大大降低了基于连续协同阵列的算法的到达方向（DOA）估计性能和可实现的自由度，例如空间平滑技术和托普利茨矩阵方法。在本文中，我们从互耦效应和差异共阵列的角度出发，提出了一个分两步扩展的互质阵列（ECA）结构。第一步是进一步增大CADiS子阵列之间的位移，以抑制相互耦合效应。第二步是重新定位适当数量的最右边的元素，以连接由 CADiS 生成的占主导地位的连续协同阵列，以增强连续差异协同阵列。具体来说，我们提供了结果连续差分协阵列、重定位元素的数量及其位置的封闭形式表达式。此外，与基于空间平滑的方法不同，我们利用 Toeplitz 矩阵性质，以较低的计算成本直接构造接收到的连续 co-array 数据的满秩协方差矩阵，并提出 Toeplitz-MUSIC 算法来证明其有效性和提议的 ECA 结构的优越性。