Coprime arrays can highly increase degree-of-freedom by operating the second-order virtual signal. However, the corresponding virtual array is discontiguous, and thus most existing direction-of-arrival estimation approaches fail to utilise all received information. To avoid performance loss, the authors intend to convert the discontiguous array into a contiguous one in this Letter and propose two virtual array interpolation algorithms for the coprime array from the perspective of signal reconstruction. By promoting the sparsity of the signal via simplified atomic norm minimisation and enhanced matrix completion, respectively, the two algorithms can effectively reconstruct the signal of the interpolated virtual array in a gridless manner. Simulation results are presented to demonstrate the performance advantage of the two proposed approaches.

中文翻译：

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互质阵列的虚拟阵列插值：信号重建视角

互质阵列可以通过操作二阶虚拟信号来极大地提高自由度。然而，相应的虚拟阵列是不连续的，因此大多数现有的到达方向估计方法无法利用所有接收到的信息。为了避免性能损失，作者打算在本文中将不连续的阵列转换为连续的阵列，并从信号重构的角度提出了两种用于互质阵列的虚拟阵列插值算法。两种算法分别通过简化原子范数最小化和增强矩阵补全来提高信号的稀疏性，可以有效地以无网格方式重构插值虚拟阵列的信号。仿真结果展示了两种方法的性能优势。