Generalized Hole-Filling Strategy for Overlapping Hole-Existing Coprime Arrays for DOA Estimation

The holes in difference coarrays (DCA) of coprime arrays (CA) limit the extension of the aperture thus causing the waste of resources. In this paper, we propose a generalized hole-filling strategy for hole-existing CAs with overlapping subarrays, which allows to extend the aperture completely and achieves a larger hole-free DCA. First, we summarize a generalized CA configuration based on the existing CAs with overlapping subarrays and derive the symmetric relationship between holes and non-consecutive lags in DCA. Then, we propose a hole-free coprime array by arranging a third subarray outside the original configurations, where the first element location is determined by the symmetric relationship. Furthermore, we derive the optimal parameters that produce the largest hole-free DCA with a given number of sensors. Theoretical derivations and simulations are provided to demonstrate that the proposed hole-free coprime configurations overcome the original coprime arrays in terms of uniform degrees of freedom and direction-of-arrival estimation performance.