Wavenumber-Domain Signal Processing for Holographic MIMO: Foundations, Methods, and Future Directions

Holographic multiple-input multiple-output (H-MIMO) systems represent a paradigm shift in wireless communications by enabling quasi-continuous apertures. Unlike conventional MIMO systems, H-MIMO with subwavelength antenna spacing operates in both far-field and near-field regimes, where classical discrete Fourier transform (DFT) representations fail to sufficiently capture the channel characteristics. To address this challenge, this article provides an overview of the emerging wavenumber-domain signal processing framework. Specifically, by leveraging spatial Fourier plane-wave decomposition to model H-MIMO channels, the wavenumber domain offers a unified and physically consistent basis for characterizing subwavelength-level spatial correlation and spherical wave propagation. This article first introduces the concept of H-MIMO and the wavenumber representation of H-MIMO channels. Next, it elaborates on wavenumber-domain signal processing technologies reported in the literature, including multiplexing, channel estimation, and waveform designs. Finally, it highlights open challenges and outlines future research directions in wavenumber-domain signal processing for next-generation wireless systems.