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Channel Estimation for Holographic MIMO: Wavenumber-Domain Sparsity Inspired Approaches

Yuqing Guo, Yuanbin Chen, Ying Wang

TL;DR

The paper tackles sparse channel estimation for holographic MIMO (HMIMO) by shifting to a wavenumber-domain representation based on Fourier plane-wave harmonics. It designs a wavenumber-domain sparsifying basis and formulates the HMIMO channel estimation as a compressed sensing problem solvable by the proposed WD-OMP algorithm, with a channel model $oldsymbol{H}=oldsymbol{\\Psi}_R \boldsymbol{H}_a \boldsymbol{\\Psi}^H_S$ and $oldsymbol{H}_a=\mathrm{diag}(\\bm{\\sigma}_R)\mathbf{W}\mathrm{diag}(\\bm{\\sigma}_S)$, where $\\mathbf{W}$ is Gaussian and the angular power is captured via VMF-based spectral factors. The WD-OMP method jointly selects wavenumber-domain index pairs and solves a small LS problem to update coefficients, reconstructing the HMIMO channel efficiently. Simulation results demonstrate strong NMSE performance and robustness to antenna spacing, especially when spacings are well below half a wavelength, outperforming angular-domain sparsity methods and other CS baselines. The approach offers a practical path to accurate CSI for HMIMO systems with large apertures and dense element grids, reducing estimation overhead while maintaining high accuracy.

Abstract

This paper investigates the sparse channel estimation for holographic multiple-input multiple-output (HMIMO) systems. Given that the wavenumber-domain representation is based on a series of Fourier harmonics that are in essence a series of orthogonal basis functions, a novel wavenumber-domain sparsifying basis is designed to expose the sparsity inherent in HMIMO channels. Furthermore, by harnessing the beneficial sparsity in the wavenumber domain, the sparse estimation of HMIMO channels is structured as a compressed sensing problem, which can be efficiently solved by our proposed wavenumber-domain orthogonal matching pursuit (WD-OMP) algorithm. Finally, numerical results demonstrate that the proposed wavenumber-domain sparsifying basis maintains its detection accuracy regardless of the number of antenna elements and antenna spacing. Additionally, in the case of antenna spacing being much less than half a wavelength, the wavenumber-domain approach remains highly accurate in identifying the significant angular power of HMIMO channels.

Channel Estimation for Holographic MIMO: Wavenumber-Domain Sparsity Inspired Approaches

TL;DR

The paper tackles sparse channel estimation for holographic MIMO (HMIMO) by shifting to a wavenumber-domain representation based on Fourier plane-wave harmonics. It designs a wavenumber-domain sparsifying basis and formulates the HMIMO channel estimation as a compressed sensing problem solvable by the proposed WD-OMP algorithm, with a channel model and , where is Gaussian and the angular power is captured via VMF-based spectral factors. The WD-OMP method jointly selects wavenumber-domain index pairs and solves a small LS problem to update coefficients, reconstructing the HMIMO channel efficiently. Simulation results demonstrate strong NMSE performance and robustness to antenna spacing, especially when spacings are well below half a wavelength, outperforming angular-domain sparsity methods and other CS baselines. The approach offers a practical path to accurate CSI for HMIMO systems with large apertures and dense element grids, reducing estimation overhead while maintaining high accuracy.

Abstract

This paper investigates the sparse channel estimation for holographic multiple-input multiple-output (HMIMO) systems. Given that the wavenumber-domain representation is based on a series of Fourier harmonics that are in essence a series of orthogonal basis functions, a novel wavenumber-domain sparsifying basis is designed to expose the sparsity inherent in HMIMO channels. Furthermore, by harnessing the beneficial sparsity in the wavenumber domain, the sparse estimation of HMIMO channels is structured as a compressed sensing problem, which can be efficiently solved by our proposed wavenumber-domain orthogonal matching pursuit (WD-OMP) algorithm. Finally, numerical results demonstrate that the proposed wavenumber-domain sparsifying basis maintains its detection accuracy regardless of the number of antenna elements and antenna spacing. Additionally, in the case of antenna spacing being much less than half a wavelength, the wavenumber-domain approach remains highly accurate in identifying the significant angular power of HMIMO channels.
Paper Structure (7 sections, 20 equations, 2 figures, 1 algorithm)

This paper contains 7 sections, 20 equations, 2 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Fourier-Harmonic-Based Channel Representation
  4. Sparse Representation of the HMIMO Channel
  5. Sparse HMIMO Chanel Estimation
  6. Simulation Results
  7. Conclusion

Figures (2)

  • Figure 1: Variances ${\sigma}^2_R(l_x,l_y)$ and $\sigma^2_S(m_x,m_y)$ structured in the wavenumber domain. The parameters are $L_{R,x}=L_{R,y}=L_{S,x}=L_{S,y}=32.25\lambda$, $N_c=4$, and $\alpha_{R,i}=\alpha_{S,i}=140$. $\theta_{R,i}$ and $\theta_{S,i}$ are randomly sampled within $[0^\circ,90^{\circ}]$. $\phi_{R,i}$ and $\phi_{S,i}$ are randomly sampled within $[0^\circ,360^{\circ}]$.
  • Figure 2: (a) NMSE performance versus SNR. (b) NMSE performance versus the pilot length $P$. (c) NMSE performance versus antenna spacing $\delta$.