关键词: 波达方向, 四阶累积量, 多项式求根, 平行线阵, 闭式估计

Abstract:

To address the challenges of limited array degrees-of-freedom and noise sensitivity in traditional two-dimensional Direction-of-Arrival （DOA） estimation， this paper proposes a root-finding closed-form estimation algorithm based on a Parallel Fourth-Order Sparse Linear Array （PFOSLA）. First， the signal model for the considered PFOSLA is constructed， and the corresponding fourth-order standard cumulant matrix is analytically derived. Next， a novel matrix transformation method is proposed to convert the original fourth-order standard cumulant matrix into a virtual-element-based fourth-order cumulant matrix， thereby constructing a virtual high-degree-of-freedom array structure. Subsequently， leveraging the noise subspace of this transformed matrix， a polynomial root-finding-based DOA estimation algorithm is developed to achieve efficient two-dimensional angular estimation. Additionally， the computational complexity and the maximum number of resolvable sources are analyzed. Compared with existing methods， the proposed approach significantly increases the number of virtual elements， effectively enhances the number of resolvable sources， and suppresses colored Gaussian noise. Simulation results validate the superiority of the proposed method in terms of signal identifiability， estimation accuracy for two-dimensional DOA， and source resolution probability.

Key words: direction-of-arrival, fourth-order cumulant, polynomial roots finding, parallel liner array, closed-form estimation