A unified framework for coarray hole-filling in distributed nested arrays

Distributed nested arrays (DNAs) enable high-resolution direction-of-arrival (DOA) estimation; however, their large baselines introduce coarray holes, leading to severe angular ambiguities. To address this problem, this paper presents a unified coarray hole-filling framework applicable to arbitrary baseline configurations. The proposed approach consists of two complementary solutions based on the baseline-to-aperture ratio L. For large baselines ($$L \ge 5$$), a closed-form solution is derived that yields the minimum number and optimal placement of auxiliary elements. For the more challenging short-baseline regime ($$L < 5$$), where the discrete nature of the coarray causes complex interference, an efficient search algorithm, termed the Deterministic Search Framework for Hole-Filling (DSF-HF), is proposed. This algorithm solves the problem in its fundamental discrete form, with the search accelerated by an Integrity Preservation Constraint (IPC) that prevents conflicts in the reconstructed virtual array. The framework unifies both solutions, as the closed-form result is shown to be an exact special case of the general search algorithm. Simulation results verify the effectiveness of the proposed framework, demonstrating its capability to construct a contiguous, hole-free virtual array for any baseline, thereby enabling reliable high-resolution DOA estimation.