Abstract:This letter 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 include a classical Fraunhofer near-field case and absolute 3D position RMSE in meters, and show near-CRB performance when the closed-form initialization is reliable. Moreover, unlike state-of-the-art baseline schemes, whose performance depends on well-tuned hyperparameters, the proposed estimators are hyperparameter-free.
From: Nikola Zlatanov [view email]
[v1]
Wed, 1 Apr 2026 10:40:36 UTC (141 KB)
[v2]
Sat, 5 Sep 2026 20:38:17 UTC (151 KB)
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