Unified Far-Field and Near-Field in Holographic MIMO: A Wavenumber-Domain Perspective

This article conceives a unified representation for near-field and far-field holographic multiple-input multiple-output (HMIMO) channels, addressing a practical design dilemma: "Why does the angular-domain representation no longer function effectively?" To answer this question, we pivot from the angular domain to the wavenumber domain and present a succinct overview of its underlying philosophy. In re-examining the Fourier plane-wave series expansion that recasts spherical propagation waves into a series of plane waves represented by Fourier harmonics, we characterize the HMIMO channel employing these Fourier harmonics having different wavenumbers. This approach, referred to as the wavenumebr-domain representation, facilitates a unified view across the far-field and the near-field. Furthermore, the limitations of the DFT basis are demonstrated when identifying the sparsity inherent to the HMIMO channel, motivating the development of a wavenumber-domain basis as an alternative. We then present some preliminary applications of the proposed wavenumber-domain basis in signal processing across both the far-field and near-field, along with several prospects for future HMIMO system designs based on the wavenumber domain.