Tensor Modalization-Based Holographic MIMO Channel Estimation

To capture the essence of electromagnetic propagation in arbitrary scattering, the holographic MIMO (HMIMO) channel is usually modeled by a Fourier plane-wave series expansion. HMIMO channel estimation, whose mathematical formulation is significantly varied, reminiscent of conventional sparse recovery solutions may result in unprecedented challenges. In this letter, we propose a tensor modalized channel estimation approach for efficient holographic communications. Specially, Fourier plane wave-based channel is formulated as a 2-mode tensor by jointly employing the physical dimensions of the transmitter and the receiver, enabling the extraction of high-dimensional electromagnetic characteristics. The channel estimation problem is further modeled as a 3-mode sparse tensor reconstruction issue by exploiting spatial characteristics of wireless channels, wherein an additional tensor dimension is added for the information union of various channel slices. Tensor compressive sampling matching pursuit (TCoSaMP) is elaborated based on a multiple selection mechanism, with theoretical guarantees derived from the perspective of a high-dimensional tensor. Furthermore, detailed complexity analysis demonstrates the efficiency of TCoSaMP. Simulation results validate that the proposed method offers improvements in both accuracy and computational efficiency.