Two-Time Scale RIS Phase Error and Channel Estimation Method for RIS-Aided Systems

This letter addresses channel estimation for reconfigurable intelligent surface (RIS)-aided systems under hardware impairments, RIS phase offsets (POs). We propose a low-complexity PO estimator that averages downlink (DL) pilot responses across frequency, then reuses the DL phase to align uplink pilots at the user without extra training. Using only base station-RIS power inferred from DL, we develop a weighted least-squares cascaded-channel estimator. We also quantify PO impact on representative LS-based and two-timescale schemes. Simulations show robust PO compensation, sizable normalized mean square error reductions, and achievable-rate gains with limited pilots.