Codebook-Based IRS System: Impact of Channel Estimation Errors and Pilot Power Adaptation on Codeword Selection and Data Rate

The codebook-based scheme for intelligent reflecting surfaces (IRSs) decouples the training and control signaling overheads from the number of IRS elements by selecting the IRS reflection pattern from a pre-specified codebook. We analyze the performance of a training scheme that exploits a novel trade-off between the powers allocated for selection pilots, which are used to select the reflection pattern, and the demodulation pilot, which is used for estimating the channel for demodulation. We develop a selection-aware linear minimum mean-square error estimator of the effective channel gain of the selected reflection pattern. When the direct link is blocked, we derive an elegant closed-form expression for the beamforming gain. When the direct link is present, which requires a different analysis, we derive a novel upper bound and insightful asymptotic expressions for the beamforming gain. We then present a novel expression for the achievable rate that accounts for the impact of noisy channel estimates on both selection of the reflection pattern and demodulation of data. We optimize the pilot and data powers and the codebook size. Our approach yields a significantly better rate than conventional schemes, and establishes the advantages of allocating substantially different powers to the selection and demodulation pilots and data.