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.

翻译：摘要：本文提出一种基于相位差的方案，利用均匀平面阵列实现三维视距用户定位，该方案在精确球面波模型下同时适用于近场与远场场景。与先前研究的二维均匀线阵情况不同，三维均匀平面阵列需联合利用两个阵列轴以恢复用户的距离、方位角和天顶角。首先从上行导频中估计相邻天线相位差，再沿阵列轴求和以获取远距离天线单元间的解缠相位差。这些求和相位差可构建多个三方程系统，其解可求得用户距离、方位角与天顶角。我们量化了此类方程系统的数量，给出仅使用三个相位差和的闭式估计器，并提出利用全部可用相位差和的全数据非线性最小二乘估计器。数值结果表明：以闭式估计值初始化的最小二乘估计器能达到克拉美-罗界精度。此外，与依赖超参数调优的现有基线方案不同，所提估计器无需超参数。