Mutual Coupling in Holographic MIMO: Physical Modeling and Information-Theoretic Analysis

TL;DR

This work develops a physically grounded framework for holographic MIMO that jointly models correlation and mutual coupling through continuous multiport impedance kernels and Fourier-based channel representations. It shows that transmit coupling acts as a physical precoder that can whiten or color the wavenumber response, enabling DOF augmentation and altered eigenvalue polarization depending on antenna patterns and losses. The paper derives both a punctiform and a physical-antenna coupling theory, introduces a composite MIMO channel with coupling, and analyzes ergodic capacity in low- and high-SNR regimes, highlighting where coupling improves performance and how to design patterns to match the fading spectrum. Practically, these results suggest reconfigurable antenna patterns can adapt to SNR conditions to maximize spatial dimensions and capacity within a fixed aperture, with implications for metasurface and tightly coupled antenna designs.

Abstract

This paper presents a comprehensive framework for holographic multiantenna communication, a paradigm that integrates both wide apertures and closely spaced antennas relative to the wavelength. The presented framework is physically grounded, enabling information-theoretic analyses that inherently incorporate correlation and mutual coupling among the antennas. This establishes the combined effects of correlation and coupling on the information-theoretic performance limits across SNR levels. Additionally, it reveals that, by suitably selecting the individual antenna patterns, mutual coupling can be harnessed to either reinforce or counter spatial correlations as appropriate for specific SNRs, thereby improving the performance.

Figures (7)

• Figure 1: Multiantenna circuit model. Each transmit antenna is driven by an ideal zero-impedance current source, which is the Norton equivalent of a source with an infinite impedance in parallel. In turn, each receive antenna is connected to an infinite-impedance voltmeter, such that no current is drawn from antennas.
• Figure 2: Mutual coupling between spatially causal antennas centered at ${\boldsymbol{{\sf s}}}$ and ${\boldsymbol{{\sf r}}}$. Top: the coupling between punctiform antennas takes the form of a spherical wave from ${\boldsymbol{{\sf s}}}$ to ${\boldsymbol{{\sf r}}}$. Bottom: physical antennas with arbitrary responses, ${\sf a}_\text{t}(\bm{\cdot})$; the coupling arises from the superposition of spherical waves emitted from points ${\boldsymbol{{\sf p}}}$ on the transmitting antenna's skin and received at points ${\boldsymbol{{\sf q}}}$ on the receiving antenna's skin.
• Figure 3: Normalized sorted eigenvalues of the transmit correlation matrix in an isotropic channel. UPA with uncoupled antennas spaced by $\lambda/2$ and aperture $20 \lambda$. The solid line indicates the exact channel in \ref{['corr_exact']}, circles denote its Fourier approximation in \ref{['tx_corr']}.
• Figure 4: Normalized sorted eigenvalues of the transmit correlation matrix under isotropic scattering. UPA with omnidirectional antennas ($\rho = 0.01$) spaced by $\lambda/2$ and aperture $20 \lambda$. The solid line is for the exact channel in \ref{['numerical_inv']}, circles for its Fourier approximation in \ref{['tx_corr_coupled']}.
• Figure 5: Having the reciprocal of the antenna power pattern counter or match the fading spectrum causes coupling to reduce or enhance antenna correlation, respectively. This is because fading maps to the channel via convolution in \ref{['spectrum_HC']}, whereas coupling acts as a deconvolution through the reciprocal of the pattern. For a fixed antenna count, reducing correlation appears to expand the antenna spacing, hence the aperture, while increasing correlation is interchangeable with compressing the antenna spacing, hence the aperture.