  Reconfigurable intelligent surface (RIS) has recently gained significant
interest as an emerging technology for future wireless networks thanks to its
potential for improving the coverage probability in challenging propagation
environments. This paper studies an RIS-assisted propagation environment, where
a source transmits data to a 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, we derive closed-form expressions for the
coverage probability and ergodic rate, which explicitly unveil the impact of
both the propagation environment and the RIS on the system performance. Besides
the optimization of the RIS phase profile, we formulate an RIS placement
optimization problem with the aim of maximizing the coverage probability by
relying only on partial channel state information. An efficient algorithm is
proposed based on the gradient ascent method. Simulation results are
illustrated in order to corroborate the analytical framework and findings. The
proposed RIS phase profile is shown to outperform several heuristic benchmarks
in terms of outage probability and ergodic rate. In addition, the proposed RIS
placement strategy provides an extra degree of freedom that remarkably improves
system performance.
