Controlling Smart Propagation Environments: Long-Term versus Short-Term Phase Shift Optimization

Reconfigurable intelligent surfaces (RISs) have recently gained significant interest as an emerging technology for future wireless networks. This paper studies an RIS-assisted propagation environment, where a single-antenna source transmits data to a single-antenna destination in the presence of a weak direct link. We analyze and compare RIS designs based on long-term and short-term channel statistics in terms of coverage probability and ergodic rate. For the considered optimization designs, closed-form expressions for the coverage probability and ergodic rate are derived. We use numerical simulations to analyze and compare against analytic results in finite samples. Also, we show that the considered optimal phase shift designs outperform several heuristic benchmarks.