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

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.