Gridless Wideband DOA Estimation Using Group-Sparse Weighted Atomic Norm Minimization

Wideband direction-of-arrival (DOA) estimation is a fundamental problem in array signal processing, with broad applications in acoustic localization and related areas. This paper introduces a weighted multi-frequency framework formulated as a semi-definite program to achieve gridless estimation. The proposed approach couples the non-convex sparsity-promoting objectives of multiple subbands via convex constraints, thereby enhancing group sparsity and enabling effective information fusion across frequencies. The formulation demonstrates robustness against aliasing and the associated collision effect, while maintaining favorable convergence properties. In addition, detailed algorithmic implementations are developed for practical noisy environments, and the feasibility of achieving underdetermined DOA estimation is further investigated. Simulation results validate the theoretical analysis and confirm the superior performance of the proposed method.