  This paper considers an active reconfigurable intelligent surface (RIS)-aided
communication system, where an M-antenna base station (BS) transmits data
symbols to a single-antenna user via an N-element active RIS. We use
two-timescale channel state information (CSI) in our system, so that the
channel estimation overhead and feedback overhead can be decreased
dramatically. A closed-form approximate expression of the achievable rate (AR)
is derived and the phase shift at the active RIS is optimized. In addition, we
compare the performance of the active RIS system with that of the passive RIS
system. The conclusion shows that the active RIS system achieves a lager AR
than the passive RIS system.
