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

Abstract

Sparse arrays of only N physical sensors can attain O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) degrees of freedom (DOF), which profits from the O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) length of the central uniform linear array (ULA) segment in their difference coarrays. However, this O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) 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 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) 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.