  Active reconfigurable intelligent surface (RIS) has attracted significant
attention as a recently proposed RIS architecture. Owing to its capability to
amplify the incident signals, active RIS can mitigate the multiplicative fading
effect inherent in the passive RIS-aided system. In this paper, we consider an
active RIS-aided uplink multi-user massive multiple-input multiple-output
(MIMO) system in the presence of phase noise at the active RIS. Specifically,
we employ a two-timescale scheme, where the beamforming at the base station
(BS) is adjusted based on the instantaneous aggregated channel state
information (CSI) and the statistical CSI serves as the basis for designing the
phase shifts at the active RIS, so that the feedback overhead and computational
complexity can be significantly reduced. The aggregated channel composed of the
cascaded and direct channels is estimated by utilizing the linear minimum mean
square error (LMMSE) technique. Based on the estimated channel, we derive the
analytical closed-form expression of a lower bound of the achievable rate. The
power scaling laws in the active RIS-aided system are investigated based on the
theoretical expressions. When the transmit power of each user is scaled down by
the number of BS antennas M or reflecting elements N, we find that the thermal
noise will cause the lower bound of the achievable rate to approach zero, as
the number of M or N increases to infinity. Moreover, an optimization approach
based on genetic algorithms (GA) is introduced to tackle the phase shift
optimization problem. Numerical results reveal that the active RIS can greatly
enhance the performance of the considered system under various settings.
