Tensor Hierarchical Sparse Recovery for Holographic MIMO Channel Estimation

Holographic MIMO (HMIMO) has emerged as a promising technology for next-generation wireless networks, leveraging densely packed large-scale antenna arrays to capture electromagnetic propagation with unprecedented spatial resolution. In HMIMO systems, achieving accurate channel estimation is crucial to ensuring reliable wireless communications. However, existing estimation methods coming from the 3D von Mises-Fisher (vMF) distribution and the conventional sparse recovery techniques neglect the hierarchical sparsity inherent in the clustered distribution of scatterers. To address this issue, a novel HMIMO channel estimation methodology is proposed, which could reveal a high-dimensional tensor hierarchical sparsity structure of HMIMO channel in the wavenumber domain, where the nonzero supports exhibit in regular columns or rows of the channel tensor. By leveraging this specific structure, a tensor hierarchical orthogonal matching pursuit (THOMP) is proposed, which enables accurate support reconstruction, thereby yielding favorable channel estimation performance. Furthermore, a tensor hierarchical prior information (THPI) is constituted, facilitating a THOMP with prior information (THOMP-P), which is reliable and efficient in counterintuitive scenarios where the THPI fails to accurately indicate the whole supports of the HMIMO channel. Simulation results validate the superior performance of our proposed THOMP-P, particularly in low signal-to-noise ratio scenarios by way of selecting more accurate nonzero supports.