Manifold Optimization-Based Channel Estimation for RIS-Assisted MmWave MIMO-OFDM Systems.

This paper proposes a manifold optimization-based tensor recovery algorithm for channel estimation (MO-TRACE) in reconfigurable intelligent surface (RIS)-assisted millimeter wave (mmWave) MIMO-OFDM systems. Specifically, considering the inherent sparse scattering characteristics of mmWave channels, the multidimensional cascaded channel in the angular-delay domain is represented by a sparse and low-rank tensor, and we formulate the channel estimation problem as a sparse and low-rank tensor recovery problem. Then, we use the canonical polyadic (CP) decomposition technique to decompose the tensor into multiple factor matrices, where the factor matrices are related to the channel parameters. To account for the sparse factor matrices, we add the sparse regularization terms of the factor matrices to the optimization objective, which can also reduce the number of nonzero columns in factor matrices, i.e., the rank of the tensor. As the concatenation of multiple factor matrices can be seen as a point on a product manifold, we apply MO algorithms to search for the optimal sparse point with enhanced convergence speed. The proposed MO-TRACE algorithm provides a more precise description of channels and ensures that the iteration point always remains within the feasible domain, thereby enhancing solution accuracy. Simulation results validate the superiority of the proposed MO-TRACE in terms of estimation accuracy.