Underdetermined 3-D Parameter Estimation of Near-field Sources with Exact Spherical Wavefront Model

To realize three-dimensional (3-D) underdetermined parameter estimation for near-field (NF) sources by L-shaped nested arrays, two NF localization methods based on the exact spherical wavefront model are proposed, including the cumulant-based method and the covariance-based method, which utilizes the temporal-spatial domain cumulants and correlations of NF sources, respectively. The cumulant algorithm constructs virtual received data through delayed fourth-order cumulant calculations of the original received data, while the covariance algorithm involves delayed autocovariance and delayed cross-covariance calculations. Subsequently, spatial-spectrum based subspace method is applied to both cumulant-based and covariance-based 3-D NF localization, where the former requires a 3-D spectral search procedure and the latter involves a one-dimensional and a two-dimensional spatial spectrum estimator to obtain the 3-D parameters. Furthermore, the computational complexity, the maximum number of identifiable NF sources and performance analysis of two proposed algorithms are provided. Simulation results demonstrate that the two proposed algorithms can achieve underdetermined 3-D parameter estimation for NF sources without any matching processes procedure. While the covariance algorithm has lower computational complexity, the cumulant algorithm performs better in parameter estimation.