Subspace-Based Localization of Far-Field and Near-Field Signals Without Eigendecomposition

Abstract

We propose a new subspace-based localization of far-field (FF) and near-field (NF) narrowband signals (LOFNS) without eigendecomposition impinging on a symmetrical uniform linear array, where the oblique projection operator is utilized to isolate the NF signals from the FF ones, and the procedures of computationally burdensome eigendecomposition are not required in the estimation of the NF and FF location parameters and the computation of oblique projection operator. As a measure against the impact of finite array data, an alternating iterative scheme is presented to improve the estimation accuracy of the oblique projection operator and, hence, that of the NF location parameters, where the “saturation behavior” encountered in most of localization methods is overcome. Furthermore, the statistical analysis of the proposed LOFNS is studied, and the asymptotic mean-squared-error expressions of the estimation errors are derived for the FF and NF location parameters. Finally, the effectiveness and the theoretical analysis of the proposed LOFNS are substantiated through numerical examples, and the simulation results demonstrate that the LOFNS provides remarkable and satisfactory estimation performance for both the NF and FF signals compared with some existing localization methods even with eigendecomposition.