Active RIS-Aided Massive MIMO With Imperfect CSI and Phase Noise

As a recently proposed reconfigurable intelligent surface (RIS) architecture, active RIS has drawn considerable interest. The important feature of the active RIS is its ability to strengthen the impinging signals to mitigate the multiplicative fading effect inherent in passive RIS-aided systems. Herein, we explore the performance of an active RIS-aided uplink multi-user massive multiple-input multiple-output (MIMO) system, considering the phase noise at the RIS. Furthermore, a two-timescale scheme is utilized, where the base station (BS) beamforming is designed based on the instantaneous aggregated channel state information (CSI), while the statistical CSI is used for designing the phase shifts of the active RIS. In addition, the linear minimum mean square error (LMMSE) estimator is adopted to estimate the aggregated channel, which combines both the cascaded and direct channels. According to the estimated channel, a closed-form expression for the lower bound of achievable rate is derived. Based on the theoretical expressions, the power scaling laws for the considered system are also investigated. Specifically, when each user’s transmit power is proportionally reduced by the quantity of BS antennas M or RIS elements N, we find that the amplified thermal noise causes the lower bound of the achievable rate to approach zero as M or N tends to infinity. Moreover, an optimization approach based on a genetic algorithm (GA) is introduced to obtain the optimal phase shifts for maximizing the achievable rate. Numerical results reveal that the active RIS can greatly enhance the performance of the massive MIMO system compared to its passive counterpart.