  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.
