  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.
