3D User Localization for Planar Arrays in LoS Near- and Far-Fields via Summed Phase Differences

2026-04-01

AI Summary

This work addresses the joint near-field and far-field localization problem for three-dimensional line-of-sight users equipped with a uniform planar array, which requires simultaneous estimation of range, azimuth, and elevation angles. The paper presents the first extension of the phase-difference summation method to 3D uniform planar arrays: adjacent antenna phase differences are estimated from uplink pilots and cumulatively summed along array axes to obtain unwrapped phase differences between widely spaced antennas, thereby constructing a multidimensional system of equations. A closed-form analytical initializer combined with a nonlinear least squares estimator is proposed, requiring no hyperparameter tuning and enabling seamless near–far field localization under a unified spherical wavefront model. Initialized by the closed-form solution, the estimator approaches the Cramér–Rao bound with high accuracy and robust performance.

Abstract

This paper presents a phase-difference-based scheme for three-dimensional (3D) line-of-sight (LoS) user localization using a uniform planar array (UPA), applicable to both near-field and far-field regimes under the exact spherical-wave model. Unlike the previously studied two-dimensional (2D) uniform linear array (ULA) case, the 3D UPA case requires jointly exploiting the two array axes in order to recover the user's range, azimuth, and zenith angle. Adjacent-antenna phase-differences are first estimated from uplink pilots and then summed along the array axes to obtain unwrapped phase-differences between widely separated antenna elements. These summed phase-differences enable the construction of multiple three-equation systems whose solutions yield the user's range, azimuth, and zenith angle. We quantify the number of such equation systems, provide a representative closed-form estimator that uses only three phase-difference sums, and propose an all-data nonlinear least-squares estimator that exploits all available sums. Numerical results show that the least-squares estimator, when initialized by the closed-form estimate, achieves Cramér--Rao bound accuracy. Moreover, unlike state-of-the-art baseline schemes, whose performance depends on well-tuned hyperparameters, the proposed estimators are hyperparameter-free.

Problem

• 3D localization
• uniform planar array
• near-field
• far-field
• phase differences

Innovation

• phase-difference summation
• 3D localization
• uniform planar array
• near-field and far-field
• hyperparameter-free estimation