Insights into Cumulative Impact of Channel Estimation Errors on RIS Phase-Shift Configuration and Data Demodulation

In a reconfigurable intelligent surface (RIS)-aided downlink, channel estimation errors due to noise during training lead to a sub-optimal RIS phase-shift configuration. This degrades the RIS beamforming gain. Furthermore, the errors lead to an imperfect estimate of the degraded beamforming gain itself. We analyze the cumulative impact of these errors on the achievable rate. We present two innovations that make our analysis tractable and insightful. First, we present a novel approximation for the effective downlink channel gain in the presence of estimation errors. Second, we prove that the central limit theorem applies to the effective downlink channel gain even in the presence of estimation errors and correlated cascaded channels due to closely-spaced RIS elements. Our analysis leads to insightful closed-form expressions for the optimal pilot and data powers that maximize the rate. The optimal power allocation achieves a significantly higher rate than the conventional approach that assigns equal power to pilots and data.