Learning Function-to-Function Mappings: A Fourier Neural Operator for Next-Generation MIMO Systems

2025-10-06

AI Summary

Next-generation massive MIMO systems face fundamental physical-layer challenges—including near-field propagation, continuous-aperture modeling, sub-wavelength antenna coupling, and dynamic channel variations—where conventional model-driven and data-driven approaches suffer from high computational complexity, limited accuracy, and poor generalization. Method: This paper pioneers the integration of Fourier Neural Operators (FNOs) into MIMO channel modeling and estimation, establishing an end-to-end function-to-function mapping framework that enables efficient, physics-consistent surrogate modeling of electromagnetic wave propagation governed by partial differential equations. The approach is mesh-free, captures global dependencies, and requires no discretization assumptions or predefined channel statistics. Contribution/Results: Experiments demonstrate significant improvements over state-of-the-art methods in prediction accuracy, cross-scenario generalization, and inference efficiency, validating FNO’s effectiveness and scalability for complex electromagnetic environments.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Next-generation multiple-input multiple-output (MIMO) systems, characterized by extremely large-scale arrays, holographic surfaces, three-dimensional architectures, and flexible antennas, are poised to deliver unprecedented data rates, spectral efficiency and stability. However, these advancements introduce significant challenges for physical layer signal processing, stemming from complex near-field propagation, continuous aperture modeling, sub-wavelength antenna coupling effects, and dynamic channel conditions. Conventional model-based and deep learning approaches often struggle with the immense computational complexity and model inaccuracies inherent in these new regimes. This article proposes a Fourier neural operator (FNO) as a powerful and promising tool to address these challenges. The FNO learns function-to-function mappings between infinite-dimensional function spaces, making them exceptionally well-suited for modeling complex physical systems governed by partial differential equations based on electromagnetic wave propagation. We first present the fundamental principles of FNO, demonstrating its mesh-free nature and function-to-function ability to efficiently capture global dependencies in the Fourier domain. Furthermore, we explore a range of applications of FNO in physical-layer signal processing for next-generation MIMO systems. Representative case studies on channel modeling and estimation for novel MIMO architectures demonstrate the superior performance of FNO compared to state-of-the-art methods. Finally, we discuss open challenges and outline future research directions, positioning FNO as a promising technology for enabling the enormous potential of next-generation MIMO systems.

Problem

• Modeling complex near-field propagation in large-scale MIMO systems
• Addressing computational complexity in dynamic channel conditions
• Learning function mappings for electromagnetic wave propagation systems

Innovation

• Fourier neural operator learns function-to-function mappings
• Mesh-free approach captures global Fourier domain dependencies
• Models electromagnetic wave propagation via partial differential equations