Sparse arrays can resolve more source direction-of-arrivals (DOAs) than sensors in array processing. This property is achieved with DOA estimators based on the difference coarray. However, sensor failures on sparse arrays could make these DOA estimators inapplicable. In the literature, array processing under sensor failures can be coped with array diagnosis. The failed sensors are detected first in array diagnosis, and the data on these detected failed sensors are removed next. However, errors in detecting the failure patterns degrade the performance. This letter presents coarray combinations for sparse arrays under sensor failures. In converting array data from the physical array to the difference coarray, coarray combination matrices (CCMs) aim to preserve the structures of the difference coarray under sensor failures. This condition corresponds to a system of equations with the CCMs. With prior knowledge about the failure patterns, a convex optimization problem is cast for this system of equations. The optimal CCM is pre-computed with closed-form expressions, avoids array diagnosis, and applies to coarray-based DOA estimators. Furthermore, numerical examples demonstrate that the proposed method reduces the errors in DOA estimation in comparison with other methods where the data on the detected failed sensors are removed.

中文翻译：

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最优 Coarray 组合对稀疏阵列上的传感器故障具有鲁棒性

与阵列处理中的传感器相比，稀疏阵列可以解决更多的源到达方向 (DOA)。这个属性是通过基于差分协列的 DOA 估计器来实现的。然而，稀疏阵列上的传感器故障可能使这些 DOA 估计器不适用。在文献中，传感器故障下的阵列处理可以应对阵列诊断。在阵列诊断中首先检测到故障传感器，然后删除这些检测到的故障传感器的数据。但是，检测故障模式中的错误会降低性能。这封信介绍了传感器故障下稀疏阵列的 coarray 组合。在将阵列数据从物理阵列转换为差分协同阵列时，协同阵列组合矩阵 (CCM) 旨在在传感器故障时保留差分协同阵列的结构。此条件对应于具有 CCM 的方程组。借助有关故障模式的先验知识，可以为该方程组提出凸优化问题。最优 CCM 是用闭式表达式预先计算的，避免了阵列诊断，并适用于基于 coarray 的 DOA 估计器。此外，数值示例表明，与删除检测到的故障传感器数据的其他方法相比，所提出的方法减少了 DOA 估计中的误差。