Distributed ULAs design with auxiliary elements for unambiguous DOA estimation

Distributed uniform linear arrays (ULAs) extend array aperture but suffer from high sidelobes and angle ambiguity in Direction-of-Arrival (DOA) estimation. To address these fundamental structural flaws, this paper introduces a proactive, design-level framework, termed Auxiliary-Element-based Co-array Completion (AECC), for unambiguous DOA estimation. The core novelty of AECC is the derivation of a closed-form design rule, providing analytical solutions for the theoretical minimum number and optimal positions of auxiliary elements required to fill the holes in the differential co-array. This design guideline facilitates the construction of a continuous virtual ULA, which fundamentally eliminates angle ambiguity and suppresses high sidelobes. By processing the single-snapshot data from the augmented array and performing rank recovery on its covariance matrix, unambiguous DOA estimation is achieved. Extensive simulation results demonstrate that the proposed AECC design rule effectively fills co-array holes, suppresses sidelobes, and mitigates inter-element coupling, showcasing its clear superiority over conventional distributed ULAs.