  This paper investigates the reconfigurable reflecting surface (RIS)-aided
multiple-input-single-output (MISO) systems with imperfect channel state
information (CSI), where RIS-related channels are modeled by Rician fading.
Considering the overhead and complexity in practical systems, we employ the
low-complexity maximum ratio combining (MRC) beamforming at the base station
(BS), and configure the phase shifts of the RIS based on long-term statistical
CSI. Specifically, we first estimate the overall channel matrix based on the
linear minimum mean square error (LMMSE) estimator, and evaluate the
performance of MSE and normalized MSE (NMSE). Then, with the estimated channel,
we derive the closed-form expressions of the ergodic rate. The derived
expressions show that with Rician RIS-related channels, the rate can maintain
at a non-zero value when the transmit power is scaled down proportionally to
$1/M$ or $1/N^2$, where $M$ and $N$ are the number of antennas and reflecting
elements, respectively. However, if all the RIS-related channels are fully
Rayleigh, the transmit power of each user can only be scaled down
proportionally to $1/\sqrt{M}$ or $1/N$. Finally, numerical results verify the
promising benefits from the RIS to traditional MISO systems.
