Robust Sparse Arrays with Multiple-Fold Redundant Difference Coarrays

Spares arrays can attain $O(N^{2})$ degrees of freedom (DOF) usingonly $N$ physical sensors, which profits from the $O(N^{2})$ length of the central uniform linear array (ULA) segment in their difference coarray (DCA). To obtain the optimal DOF performance, the single-fold redundant DCA (that is, each element of DCA occurs as only once as possible) is persistently pursued in array design. Such a criterion inevitably leads this ${O}(N^{2})$ ULA segment susceptible to sensor failures, which is a crucial issue concerning array/DCA robustness (or system reliability) in practical applications. That is quite serious for minimum/low-redundancy, nested, and coprime configurations as well as their variations. This paper introduces a novel sparse array geometry, named multiple-fold redundancy array (MFRA), exploiting element redundancies of the DCA. The MFRA is more robust to sensor failures than the aforementioned sparse arrays, for which the concepts of quasi-essentialness and reliability is introduced. Several numerical examples are presented to demonstrate the MFRA's robustness to sensor failures.