In this letter, a novel approach to construct virtual array is proposed by exploiting synthetic aperture technology and the concept of difference coarray for sparse arrays. First, we prove that the proposed method can increase the degrees of freedom (DOF) of an arbitrary moving sparse array threefold. Therefore, the maximal number of resolvable sources for direction-of-arrival (DOA) estimation is tripled as well. Furthermore, we prove that the difference coarray of synthetic arrays is a hole-free uniform linear array (ULA) if the difference coarray of original arrays is hole-free. Therefore, for ULA based DOA estimation methods, better performance can be achieved by fully employing all elements in the difference coarray of synthetic arrays. In addition, unlike the dilated nested array method, which enlarges the intersensor spacing of nested arrays threefold to triple DOF, the proposed method does not need to increase array aperture physically. Thus it is more practical to mount a sensor array on a moving platform when taking space limitation into consideration. Simulation results are given to demonstrate the superiority of the proposed method.

中文翻译：

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一种增加移动稀疏阵列自由度的虚拟阵列构造新方法

在这封信中，利用合成孔径技术和稀疏阵列差分共阵列的概念，提出了一种构建虚拟阵列的新方法。首先，我们证明所提出的方法可以将任意移动稀疏阵列的自由度 (DOF) 增加三倍。因此，用于到达方向 (DOA) 估计的可解析源的最大数量也增加了三倍。此外，我们证明如果原始阵列的差分共阵列是无孔的，则合成阵列的差分共阵列是无孔均匀线性阵列（ULA）。因此，对于基于 ULA 的 DOA 估计方法，可以通过充分利用合成阵列差分共阵列中的所有元素来实现更好的性能。另外，不同于膨胀嵌套数组的方法，将嵌套阵列的传感器间距扩大了三倍到三倍自由度，所提出的方法不需要物理增加阵列孔径。因此，考虑到空间限制，将传感器阵列安装在移动平台上更为实用。仿真结果证明了所提出方法的优越性。