Low-Complexity Near-Field Angle–Range Localization for XL-MIMO Communications

Abstract

For near-field angle–range localization in extremely large-scale multiple-input multiple-output (XL-MIMO) systems, many existing estimators for <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>-antenna arrays suffer from the prohibitive complexity of grid search or <inline-formula> <tex-math notation="LaTeX">$M \times M$ </tex-math></inline-formula> covariance/projector operations. This letter proposes the Scalable Progressive Angle–Range Estimator (SPARE) for localizing <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> users with a uniform planar antenna array (UPA). SPARE first estimates the angles using the centrosymmetric correlations of the UPA, then estimates the ranges via local phase differences using the previously estimated angles, and finally performs the exact spherical-wave refinement. The leading-order complexity of SPARE scales linearly with <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>. Simulations demonstrate near-Cramér-Rao bound (CRB) accuracy and low complexity.