Sparse Recovery for Holographic MIMO Channels: Leveraging the Clustered Sparsity

TL;DR

This work tackles the challenge of estimating HMIMO channels whose dimensionality scales quadratically with the aperture by exploiting clustered sparsity in the wavenumber domain. It introduces a GMM-based von Mises–Fisher (vMF) statistical model to capture both the locations and values of nonzero wavenumber-domain entries, compressing the inference problem to the scatterer count $N_c$. A novel wavenumber-domain EM (WD-EM) algorithm is developed to perform cluster-wise variational inference, with E-step assigning nonzero entries to scatterer clusters and M-step updating cluster parameters and weights, significantly reducing computational complexity. Simulations demonstrate WD-EM’s robustness to observation overhead and SNR, outperforming LS, OMP, and clustering-based baselines while maintaining accuracy at lower RF-chain counts.

Abstract

Envisioned as the next-generation transceiver technology, the holographic multiple-input-multiple-output (HMIMO) garners attention for its superior capabilities of fabricating electromagnetic (EM) waves. However, the densely packed antenna elements significantly increase the dimension of the HMIMO channel matrix, rendering traditional channel estimation methods inefficient. While the dimension curse can be relieved to avoid the proportional increase with the antenna density using the state-of-the-art wavenumber-domain sparse representation, the sparse recovery complexity remains tied to the order of non-zero elements in the sparse channel, which still considerably exceeds the number of scatterers. By modeling the inherent clustered sparsity using a Gaussian mixed model (GMM)-based von Mises-Fisher (vMF) distribution, the to-be-estimated channel characteristics can be compressed to the scatterer level. Upon the sparsity extraction, a novel wavenumber-domain expectation-maximization (WD-EM) algorithm is proposed to implement the cluster-by-cluster variational inference, thus significantly reducing the computational complexity. Simulation results verify the robustness of the proposed scheme across overheads and signal-to-noise ratio (SNR).

Figures (5)

• Figure 1: Observed snapshot of the HMIMO channel on the wavenumber domain.
• Figure 2: Traditional sparse recovery methods estimate all the non-zero entries.
• Figure 3: Our proposed scheme aims to estimate only the GMM-based parameters.
• Figure 5: NMSE versus SNR, with $N_{\rm RF} = 200$.
• Figure 6: NMSE versus $N_{\rm RF}$, with ${\rm SNR} = {\rm 10\ dB}$.