3D Localization of Near-Field Sources with Symmetric Enhanced Nested Arrays

Sparse arrays can effectively reduce antenna cost and implementation complexity. However, most existing research in sparse array design mainly focuses on far-field scenarios, which cannot be directly applied to near-field (NF) source localization, where the delay term and source incident parameters exhibit a nonlinear relationship. In this paper, employing a symmetric enhanced nested array, a high-precision underdetermined three-dimensional (3D) NF localization method is proposed. Firstly, the symmetry of the array and the fourth-order cumulant are utilized to construct the equivalent virtual far-field (FF) received data. Then, a gridless, sparse, and parametric approach combined with an l1-singular value decomposition-based pairing procedure is employed to obtain estimates of two paired angles. Finally, a one-dimensional (1D) spectral estimator is applied to obtain the estimate of the range parameter. By analyzing the virtual aperture, the optimal parameter configuration for a given number of elements is obtained. As shown by simulation results, the proposed method can handle underdetermined estimation. Compared with the other algorithms, the proposed algorithm achieves significant improvements in both angular and distance accuracy, with enhancements of 65% and 61.7%, respectively.