Fourth-Order Cumulant Based 3-D Near-Field Underdetermined Parameter Estimation With Exact Spatial Propagation Model

Based on the exact spherical wavefront model, an under-determined estimation method for three-dimensional (3-D) parameters of near-field (NF) sources using L-shaped nested arrays is proposed, referred to as the cumulant algorithm. This algorithm leverages the temporal-spatial domain cumulants of NF sources by constructing virtual data through delayed fourth-order cumulant (FOC) calculations of the original received data. Subsequently, a spatial-spectrum-based subspace method is applied for 3-D NF localization, which involves a 3-D spectral search procedure. Additionally, the maximum number of identifiable NF sources of the proposed algorithm is analyzed. Simulation results demonstrate that, based on the exact spherical wavefront model, the proposed algorithm can achieve underdetermined 3-D parameter estimation of NF sources without any matching process, and it performs better in localization than existing methods.