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

TL;DR

This paper introduces a phase-difference-based 3D user localization method using a planar array, effective in both near- and far-field scenarios, with estimators that are hyperparameter-free and achieve near-optimal accuracy.

Contribution

It develops a novel 3D localization scheme leveraging summed phase differences in planar arrays, extending beyond 2D linear arrays, and provides estimators that are hyperparameter-free and CRB-achieving.

Findings

The least-squares estimator achieves Cramér-Rao bound accuracy.

The proposed estimators outperform state-of-the-art schemes in accuracy and robustness.

The method is applicable to both near-field and far-field regimes.

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 Cram\'er--Rao bound accuracy. Moreover, unlike state-of-the-art baseline schemes, whose performance depends on well-tuned hyperparameters, the proposed estimators are hyperparameter-free.