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

Mu Jia, Hao Sun, Junting Chen, Pooi-Yuen Kam

TL;DR

PR-LRTC addresses the high CSI overhead in pixel-based fluid antenna systems by reconstructing a multi-mode radio map as a 3-way tensor $\boldsymbol{\mathcal{X}} \in \mathbb{R}^{I \times J \times M}$ while enforcing a physics-aware differential prior $\boldsymbol{\mathcal{D}}$ derived from the antenna's EADoF constraints. The method combines data fidelity on sparse measurements with a convex, physics-driven regularizer $\mathcal{R}_{phys}(\mathcal{X}, \mathcal{D})$ and an overlapped low-rank penalty, solved efficiently via ADMM with cycle-consistency and a cyclic difference operator. Key contributions include the explicit differential prior linking inter-mode gains to the geometry, the cycle-consistent projection, and a tractable optimization that yields accurate reconstructions at very low sampling ratios, e.g., 10% with about 4 dB improvement over baselines. This physics-regularized approach enables robust, low-overhead map-based mode management for next-generation FAS, bridging electromagnetic propagation laws with data-driven tensor completion to preserve sharp shadowing edges.

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.

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

TL;DR

PR-LRTC addresses the high CSI overhead in pixel-based fluid antenna systems by reconstructing a multi-mode radio map as a 3-way tensor while enforcing a physics-aware differential prior derived from the antenna's EADoF constraints. The method combines data fidelity on sparse measurements with a convex, physics-driven regularizer and an overlapped low-rank penalty, solved efficiently via ADMM with cycle-consistency and a cyclic difference operator. Key contributions include the explicit differential prior linking inter-mode gains to the geometry, the cycle-consistent projection, and a tractable optimization that yields accurate reconstructions at very low sampling ratios, e.g., 10% with about 4 dB improvement over baselines. This physics-regularized approach enables robust, low-overhead map-based mode management for next-generation FAS, bridging electromagnetic propagation laws with data-driven tensor completion to preserve sharp shadowing edges.

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.
Paper Structure (24 sections, 21 equations, 3 figures, 1 algorithm)

This paper contains 24 sections, 21 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Geometric Environment and Blocking Model
  4. Pixel-Based Reconfigurable Antenna Model
  5. Orthogonal Basis Functions $\{B_k(\phi)\}$
  6. Cyclically Correlated Coding Weights $w_{m,k}$
  7. Received Signal Model
  8. Radio Map Representation and Physical Priors
  9. The Global RSS Tensor ($\mathcal{X}$)
  10. The Physics-Aware Differential Prior ($\mathcal{D}$)
  11. Physics-Regularized Tensor Reconstruction
  12. Problem Formulation
  13. Physics-Aware Regularizer Design
  14. Optimization via ADMM
  15. Primal Update $\mathcal{X}$ (Physics-Data Fusion)
  16. ...and 9 more sections

Figures (3)

  • Figure 1: Pixel-based FAS radio map model. The BS serves users in a cluttered environment. The physical interaction between antenna modes and obstacles induces a structured radio map tensor.
  • Figure 2: Comparison of reconstruction results at 10% sampling ratio. (a) compares the reconstruction details of Mode 0, where the proposed PR-LRTC best preserves the shadowing edges. (b) illustrates the complex 3D structure of the radio map tensor.
  • Figure 3: RMSE (dB) comparison versus sampling ratio.