Near-Field Source Localization in 3-D Using Two Parallel Centrally Symmetric Unfold Coprime Array

Most near-field (NF) localization algorithms cannot deal with the underdetermined case, while those which can are computationally expensive due to employment of fourth-order cumulants. In this work, a low-complexity solution is provided for underdetermined three-dimensional (3-D) NF localization, by employing second-order statistics with a tailored array configuration named two parallel centrally symmetric unfold coprime (TPSC) array. Its implementation can be divided into three stages. Firstly, the proposed algorithm constructs two cross-correlation matrices based on the received array data, which eliminates the non-linear range-related information of NF signals. Secondly, covariance and vectorization operations are applied to these two cross-correlation matrices to form a virtual array with extended aperture. Finally, the two-dimensional (2-D) angle parameters are estimated by the sparse and parametric approach (SPA) and a phase retrieval operation, and then the one-dimensional (1-D) range parameter is achieved by the multiple signal classification (MUSIC) algorithm. One specific feature is that the estimated angle and range parameters are matched automatically. An analysis of the properties of the TPSC array is provided, and an optimal parameter configuration is derived, given that the total number of array elements is fixed. Simulation results demonstrate that the designed TPSC array can achieve underdetermined 3-D NF localization, and deliver enhanced estimation capabilities, surpassing those of established algorithms.