3-D Near-Field Source Localization Using Centrosymmetric Cross Array via Cumulant Tensor Reconstruction

In this paper, we address the problem of near-field (NF) source localization and devise an efficient algorithm for two-dimensional (2-D) direction-of-arrival (DOA) and range estimation using a centro-symmetric cross array with low-rank tensor recovery technique. First of all, we create a third-order tensor using the fourth-order cumulants of the array output and recover a low-rank cumulant tensor by solving a generalized tensor nuclear norm minimization problem. By utilizing the recovered cumulant tensor, we derive the closed-form 2-D DOA estimates of the NF sources. Finally, with the estimated DOAs, their ranges are determined via one-dimensional peak search. Compared with the existing NF localization techniques, the proposed method can provide higher 2-D DOA and range estimation accuracy by utilizing the multidimensional information inherent in the cumulants of the array outputs. Furthermore, our algorithm does not involve multidimensional search and parameter pairing. Simulation results illustrate the superiority of the devised solution over several competing techniques.