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

TL;DR

This paper introduces a unified HMIMO channel representation in the wavenumber domain, grounded in the Fourier plane-wave series and the Weyl identity, to seamlessly describe near-field and far-field propagation through a distance-independent angular-power spectrum. By replacing the traditional angular (DFT) basis with a Fourier harmonic (FH) wavenumber-domain basis, it addresses power leakage and non-stationarity issues that plague dense, large HMIMO arrays, and accounts for evanescent components where appropriate. The authors show that the wavenumber-domain basis reveals clustered sparsity in both regimes, enabling improved sparse channel estimation and more effective codebook design than conventional methods. They also discuss practical considerations, such as polarization effects and hardware constraints, and propose future research directions that blend EM information theory with HMIMO system design. Overall, the work provides a physically grounded, distance-agnostic framework that could significantly impact HMIMO signal processing and 6G system development. Key mathematical notions include the wavenumber $k=\frac{2\pi}{\lambda}$ and the FH-based basis that represents channels as superpositions of plane waves across wavenumbers, yielding a sparse, interpretable angular power spectrum independent of propagation distance.

Abstract

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.

Figures (5)

• Figure 1: Illustration of the EM signals characterized by different wavenumbers.
• Figure 2: An illustration of the wavenumber-domain representation and the challenges when employing the DFT basis.
• Figure 3: The implementation of the wavenumber-domain basis exposes the sparsity inherent in the HMIMO channel.
• Figure 4: NMSE performance achieved by angular-domain and wavenumber-domain representation versus varying SNR.
• Figure 5: Achievable rate versus distance achieved by the wavenumber-domain basis and DFT basis.