Hierarchically Structured Matrix Recovery-Based Channel Estimation for RIS-Aided Communications

Reconfigurable intelligent surface (RIS) has emerged as a promising technology for improving capacity and extending coverage of wireless networks. In this letter, we consider RIS-aided millimeter wave (mmWave) multiple-input and multiple-output (MIMO) communications, where acquiring accurate channel state information is challenging due to the high dimensionality of channels. To achieve efficient channel estimation, fully exploiting the structures of the channels is crucial. To this end, we formulate the channel estimation as a hierarchically structured matrix recovery problem, and design a low-complexity message passing algorithm to solve it, leveraging the unitary approximate message passing. Simulation results demonstrate the superiority of the proposed algorithm with performance close to the oracle bound.