标题： 学习函数到函数的映射：下一代MIMO系统的傅里叶神经算子 显示英文标题

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

摘要： 下一代多输入多输出（MIMO）系统，以超大规模天线阵列、全息表面、三维架构和柔性天线为特征，即将实现前所未有的数据速率、频谱效率和稳定性。 然而，这些进步给物理层信号处理带来了重大挑战，这些挑战源于复杂的近场传播、连续孔径建模、亚波长天线耦合效应和动态信道条件。 传统的基于模型的方法和深度学习方法在这些新领域固有的巨大计算复杂性和模型不准确性方面常常遇到困难。 本文提出了一种傅里叶神经算子（FNO），作为一种强大且有前景的工具来解决这些挑战。 FNO 在无限维函数空间之间学习函数到函数的映射，使其特别适合于由基于电磁波传播的偏微分方程所描述的复杂物理系统的建模。 我们首先介绍了FNO的基本原理，展示了其无网格特性以及在傅里叶域中高效捕捉全局依赖关系的函数到函数的能力。 此外，我们探讨了FNO在下一代MIMO系统物理层信号处理中的各种应用。 对新型MIMO架构的信道建模和估计的代表性案例研究证明了FNO相比最先进方法的优越性能。 最后，我们讨论了开放性挑战并概述了未来的研究方向，将FNO定位为一种有前景的技术，以发挥下一代MIMO系统的巨大潜力。 显示英文摘要

摘要： 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.