Physics-Aware Tensor Reconstruction for Radio Maps in Pixel-Based Fluid Antenna Systems

TL;DR

This paper introduces a physics-regularized tensor completion method for reconstructing high-fidelity radio maps in fluid antenna systems, significantly reducing measurement overhead while preserving shadowing details.

Contribution

It proposes a novel PR-LRTC framework that integrates environmental physics with low-rank tensor modeling for accurate radio map reconstruction from sparse data.

Findings

Achieves 4 dB gain over baselines at 10% sampling ratio

Preserves sharp shadowing edges effectively

Provides a robust, physics-compliant reconstruction method

Abstract

The deployment of pixel-based antennas and fluid antenna systems (FAS) is hindered by prohibitive channel state information (CSI) acquisition overhead. While radio maps enable proactive mode selection, reconstructing high-fidelity maps from sparse measurements is challenging. Existing physics-agnostic or data-driven methods often fail to recover fine-grained shadowing details under extreme sparsity. We propose a Physics-Regularized Low-Rank Tensor Completion (PR-LRTC) framework for radio map reconstruction. By modeling the signal field as a three-way tensor, we integrate environmental low-rankness with deterministic antenna physics. Specifically, we leverage Effective Aerial Degrees-of-Freedom (EADoF) theory to derive a differential gain topology map as a physical prior for regularization. The resulting optimization problem is solved via an efficient Alternating Direction Method of Multipliers (ADMM)-based algorithm. Simulations show that PR-LRTC achieves a 4 dB gain over baselines at a 10% sampling ratio. It effectively preserves sharp shadowing edges, providing a robust, physics-compliant solution for low-overhead beam management.