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：本文研究在存在实际硬件损伤（HWIs）条件下，利用有源可重构智能表面（RIS）辅助多用户下行链路传输，其中包含收发端的硬件损伤以及有源RIS处的相位噪声。部署有源RIS旨在放大入射信号以缓解传统无源RIS辅助无线系统中的乘性衰落效应。我们通过联合设计基站（BS）的发射波束赋形、有源RIS的放大因子和相位偏移，以最大化总和速率。为有效解决这一具有挑战性的优化问题，我们将其分解为两个易于处理的子问题。随后，每个子问题被转化为二阶锥规划问题。采用块坐标下降框架进行求解，其中发射波束赋形与反射系数交替设计。此外，提出另一种高效算法以降低计算复杂度：具体地，通过利用Majorization-Minimization方法，每个子问题被重新表述为一个易处理的代理问题，其闭式解通过拉格朗日对偶分解方法和逐元素交替序列优化方法获得。仿真结果验证了所提算法的有效性，并揭示了硬件损伤显著限制了有源RIS赋能无线通信的系统性能。此外，在相同总功率预算下，与无源RIS相比，有源RIS显著提升了总和速率。