In this paper, we consider an active reconfigurable intelligent surface (RIS) to assist the multiuser downlink transmission in the presence of practical hardware impairments (HWIs), including the HWIs at the transceivers and the phase noise at the active RIS. The active RIS is deployed to amplify the incident signals to alleviate the multiplicative fading effect, which is a limitation in the conventional passive RIS-aided wireless systems. We aim to maximize the sum rate through jointly designing the transmit beamforming at the base station (BS), the amplification factors and the phase shifts at the active RIS. To tackle this challenging optimization problem effectively, we decouple it into two tractable subproblems. Subsequently, each subproblem is transformed into a second order cone programming problem. The block coordinate descent framework is applied to tackle them, where the transmit beamforming and the reflection coefficients are alternately designed. In addition, another efficient algorithm is presented to reduce the computational complexity. Specifically, by exploiting the majorization-minimization approach, each subproblem is reformulated into a tractable surrogate problem, whose closed-form solutions are obtained by Lagrange dual decomposition approach and element-wise alternating sequential optimization method. Simulation results validate the effectiveness of our developed algorithms, and reveal that the HWIs significantly limit the system performance of active RIS-empowered wireless communications. Furthermore, the active RIS noticeably boosts the sum rate under the same total power budget, compared with the passive RIS.

翻译：暂无翻译