Channel Estimation for Flexible Intelligent Metasurfaces: From Model-Based Approaches to Neural Operators

2025-07-31

AI Summary

In flexible intelligent metasurface (FIM)-assisted millimeter-wave communications, accurately acquiring channel state information (CSI) under continuous, high-dimensional deformation spaces remains challenging. To address this, we propose the Hierarchical Fourier Neural Operator (H-FNO), the first neural operator framework tailored for FIM channel modeling. H-FNO enables end-to-end learning of nonlinear, continuous channel mappings from discrete measurements, exhibiting mesh independence, multi-scale feature capture, and physical interpretability. By integrating model-driven priors—including interpolation kernels and sparse recovery—and constructing global convolutional operators in the Fourier domain, H-FNO significantly improves estimation accuracy and pilot efficiency. It faithfully reconstructs nonlinear channel responses across continuous deformations and implicitly learns anisotropic spatial filtering characteristics intrinsic to the FIM’s geometric structure.

Technology Category

• Machine Learning: Multimodal Learning
• Search and Optimization: Sampling/Simulation-based Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Flexible intelligent metasurfaces (FIMs) offer a new solution for wireless communications by introducing morphological degrees of freedom, dynamically morphing their three-dimensional shape to ensure multipath signals interfere constructively. However, realizing the desired performance gains in FIM systems is critically dependent on acquiring accurate channel state information across a continuous and high-dimensional deformation space. Therefore, this paper investigates this fundamental channel estimation problem for FIM assisted millimeter-wave communication systems. First, we develop model-based frameworks that structure the problem as either function approximation using interpolation and kernel methods or as a sparse signal recovery problem that leverages the inherent angular sparsity of millimeter-wave channels. To further advance the estimation capability beyond explicit assumptions in model-based channel estimation frameworks, we propose a deep learning-based framework using a Fourier neural operator (FNO). By parameterizing a global convolution operator in the Fourier domain, we design an efficient FNO architecture to learn the continuous operator that maps FIM shapes to channel responses with mesh-independent properties. Furthermore, we exploit a hierarchical FNO (H-FNO) architecture to efficiently capture the multi-scale features across a hierarchy of spatial resolutions. Numerical results demonstrate that the proposed H-FNO significantly outperforms the model-based benchmarks in estimation accuracy and pilot efficiency. In particular, the interpretability analysis show that the proposed H-FNO learns an anisotropic spatial filter adapted to the physical geometry of FIM and is capable of accurately reconstructing the non-linear channel response across the continuous deformation space.

Problem

• Estimating channel state in flexible intelligent metasurfaces for millimeter-wave communication
• Developing model-based and deep learning frameworks for accurate channel estimation
• Enhancing estimation accuracy and pilot efficiency with hierarchical Fourier neural operators

Innovation

• Model-based frameworks for channel estimation
• Fourier neural operator for learning mappings
• Hierarchical FNO for multi-scale feature capture