Statistical Channel Estimation for Holographic MIMO Exploiting the Clustered Sparsity

This paper investigates the statistical channel state information (S-CSI) estimation for holographic multiple-input-multiple-output (HMIMO) systems. Instead of acquiring S-CSI based on instantaneous channel state information (I-CSI), we directly estimate S-CSI by leveraging its clustered sparsity. Specifically, the inherent clustered sparsity of HMIMO S-CSI is characterized by von Mises–Fisher (vMF) distribution, given arbitrary number, position and angular spread of scatterers. The number of parameters to be estimated can be compressed to the order of scatterers' quantities from the order of degrees of freedom (DoFs) of the array. Then, a novel wavenumber-domain expectation-maximization (WD-EM) algorithm is proposed to implement cluster-by-cluster variational inference, which significantly reduces the computational complexity. Finally, simulation results validate the robustness of the proposed scheme with respect to pilot overhead and signal-to-noise ratio (SNR).