Multiple-Fold Redundancy Arrays With Robust Difference Coarrays: Fundamental and Analytical Design Method

Sparse arrays of only $N$ physical sensors can attain $O(N^{2})$ degrees of freedom (DOF), which profits from the $O(N^{2})$ length of the central uniform linear array (ULA) segment in their difference coarrays. However, this $O(N^{2})$ ULA segment of such configurations (e.g., minimum-/low-redundancy arrays (MRAs/LRAs), nested arrays, and coprime arrays as well as their variations) is inevitably susceptible to sensor failures, which is a crucial issue concerning array robustness (or system reliability) in practical applications. In this article, we present a novel sparse array geometry, named multiple-fold redundancy array (MFRA), by exploiting element redundancies in the difference coarray. The MFRA is not only more robust to sensor failures than the conventional minimum-/low-redundancy, nested, and coprime arrays but also can enjoy up to $O(N^{2})$ DOF as these conventional arrays do. To efficiently construct MFRAs with desirable characteristics (including multiple-fold redundancy, satisfactory DOF, and hole-free difference coarray), a systematic design method is developed. Based on this method, some analytical structure patterns are derived for closed-form geometric construction. Several important properties of MFRAs are proved theoretically, and numerical examples are presented to demonstrate their characteristics and superior performances.