  In this paper, we investigate the performance of an RIS-aided wireless
communication system subject to outdated channel state information that may
operate in both the near- and far-field regions. In particular, we take two RIS
deployment strategies into consideration: (i) the centralized deployment, where
all the reflecting elements are installed on a single RIS and (ii) the
distributed deployment, where the same number of reflecting elements are placed
on multiple RISs. For both deployment strategies, we derive accurate
closed-form approximations for the ergodic capacity, and we introduce tight
upper and lower bounds for the ergodic capacity to obtain useful design
insights. From this analysis, we unveil that an increase of the transmit power,
the Rician-K factor, the accuracy of the channel state information and the
number of reflecting elements help improve the system performance. Moreover, we
prove that the centralized RIS-aided deployment may achieve a higher ergodic
capacity as compared with the distributed RIS-aided deployment when the RIS is
located near the base station or near the user. In different setups, on the
other hand, we prove that the distributed deployment outperforms the
centralized deployment. Finally, the analytical results are verified by using
Monte Carlo simulations.
