A Novel Demodulation and Selection Pilot Power Trade-Off for Codebook-Based IRS with Imperfect Channel Estimates

The codebook-based scheme for intelligent reflecting surfaces (IRSs) provides flexibility in controlling the training overhead. In it, the reflection pattern with the largest received signal strength is selected from a pre-specified codebook and configured at the IRS. We analyze 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 to estimate the channel for demodulation. We develop a novel selection-aware estimator of the beamforming gain of the selected reflection pattern. We derive a tight bound for the achievable rate and an elegant closed-form expression for the beamforming gain. These account for the impact of imperfect channel estimates on the selection of the reflection pattern and the coherent demodulation of the data symbols. The proposed scheme achieves a higher rate than conventional schemes by allocating substantially different powers to the selection and demodulation pilots and data symbols.