Manifold Optimization Based Channel Estimation Algorithm for Semi-Passive RIS Assisted System

This paper addresses the issue of rank acquisition in channel estimation for a semi-passive reconfigurable intelligent surface (RIS) assisted communication system and proposes a channel estimation algorithm based on manifold optimization (CEMO). Specifically, by exploring the spatial structure and low-rank characteristics of channels, we design a practical transmission scheme to formulate the channel between RIS and transmitter as a low-rank tensor completion problem with tubal missing entries. To simplify the acquisition of tensor rank, we apply a tensor singular value decomposition (T-SVD)-based tensor completion algorithm to solve the low-rank tensor completion problem. The core of the T-SVD-based tensor completion algorithm is to acquire the inherent basis representation of observed data, which can be conducted on the complex t-Grassmiann manifold, and thus we can apply Manifold Optimization (MO) to realize it. Compared with the two benchmark methods, the proposed algorithm achieves higher estimation accuracy and lower computational complexity when the observation ratio reaches a certain level.