  Reconfigurable Intelligent Surfaces (RIS) are planar structures connected to
electronic circuitry, which can be employed to steer the electromagnetic
signals in a controlled manner. Through this, the signal quality and the
effective data rate can be substantially improved. While the benefits of
RIS-assisted wireless communications have been investigated for various
scenarios, some aspects of the network design, such as coverage, optimal
placement of RIS, etc., often require complex optimization and numerical
simulations, since the achievable effective rate is difficult to predict. This
problem becomes even more difficult in the presence of phase estimation errors
or location uncertainty, which can lead to substantial performance degradation
if neglected. Considering randomly distributed receivers within a ring-shaped
RIS-assisted wireless network, this paper mainly investigates the effective
rate by taking into account the above-mentioned impairments. Furthermore, exact
closed-form expressions for the effective rate are derived in terms of Meijer's
$G$-function, which (i) reveals that the location and phase estimation
uncertainty should be well considered in the deployment of RIS in wireless
networks; and (ii) facilitates future network design and performance
prediction.
