Mutual Coupling Aware Channel Estimation for RIS-Aided Multi-User mmWave Systems

This paper proposes a three-stage uplink channel estimation protocol for reconfigurable intelligent surface (RIS)-aided multi-user (MU) millimeter-wave (mmWave) multiple-input single-output (MISO) systems, where both the base station (BS) and the RIS are equipped with uniform planar arrays (UPAs). The proposed approach explicitly accounts for the mutual coupling (MC) effect, modeled via scattering parameter multiport network theory. In Stage~I, a dimension-reduced subspace-based method is proposed to estimate the common angle of arrival (AoA) at the BS using the received signals across all users. In Stage~II, MC-aware cascaded channel estimation is performed for a typical user. The equivalent measurement vectors for each cascaded path are extracted and the reference column is reconstructed using a compressed sensing (CS)-based approach. By leveraging the structure of the cascaded channel, the reference column is rearranged to estimate the AoA at the RIS, thereby reducing the computational complexity associated with estimating other columns. Additionally, the common angle of departure (AoD) at the RIS is also obtained in this stage, which significantly reduces the pilot overhead for estimating the cascaded channels of other users in Stage~III. The RIS phase shift training matrix is designed to optimize performance in the presence of MC and outperforms random phase scheme. Simulation results validate that the proposed method yields better performance than the MC-unaware and existing approaches in terms of estimation accuracy and pilot efficiency.