POPT: Physics-Informed Deep Learning for Phase-Only Positioning in Distributed MIMO

Abstract

This article develops a physics-informed deep learning framework for single-snapshot 3D phase-only positioning in narrowband phase-coherent distributed multiple-input multiple-output (D-MIMO) networks under two-ray propagation. Unlike prior phase-coherent D-MIMO localization methods that largely assume line-of-sight (LoS)-only channels, we consider a LoS path and a specular ground reflection. Since the narrowband single-snapshot observation cannot resolve these components in delay, their coherent superposition induces structured perturbations in the carrier phase measurements. To address this, we develop a Gaussian process (GP)-based model that learns the quasi-periodic phase distortion caused by ground reflection from carrier phase measurements collected at a small number of training locations and uses it to generate high-quality synthetic samples. Building on these samples, we propose the Phase-Only Positioning Transformer (POPT), an encoder-only transformer that captures inter-antenna point (AP) phase relationships without solving the highly non-convex maximum-likelihood (ML) problem underlying model-based estimators. We also derive the fundamental position error bound (PEB) and develop maximum-likelihood estimation (MLE) for the considered multipath phase-only D-MIMO positioning problem. Numerical results show that, with only 50 GP training locations, the proposed method achieves near-PEB accuracy. The analytical MLE is highly sensitive to relative permittivity mismatch, whereas the proposed method mitigates this dependence by learning the phase perturbation directly from measurement data. Compared with MLE, the proposed approach also reduces floating-point operation (FLOP) complexity and inference time by about 1.7 and 3.6 orders of magnitude, respectively.