This paper investigates the two-timescale transmission design for reconfigurable intelligent surface (RIS)-aided massive multiple-input multiple-output (MIMO) systems, where the beamforming at the base station (BS) is adapted to the rapidly-changing instantaneous channel state information (CSI), while the passive beamforming at the RIS is adapted to the slowly-changing statistical CSI. Specifically, we first propose a linear minimum mean square error (LMMSE) estimator to obtain the aggregated channel from the users to the BS in each channel coherence interval. Based on the estimated channel, we apply the low-complexity maximal ratio combining (MRC) beamforming at the BS, and then derive the ergodic achievable rate in a closed form expression. To draw design insights, we perform a detailed theoretical analysis departing from the derived ergodic achievable rate. If the BS-RIS channel is Rician distributed, we prove that the transmit power can be scaled proportionally to $1/M$, as the number of BS antennas, $M$, grows to infinity while maintaining a non-zero rate. If the BS-RIS channel is Rayleigh distributed, the transmit power can be scaled either proportionally to $1/\sqrt{M}$ as $M$ grows large, or proportionally to $1/N$ as the number of reflecting elements, $N$, grows large, while still maintaining a non-zero rate. By capitalizing on the derived expression of the data rate under the statistical knowledge of the CSI, we maximize the minimum user rate by designing the passive beamforming at the RIS. Numerical results confirm that, even in the presence of imperfect CSI, the integration of an RIS in massive MIMO systems results in promising performance gains. In addition, the obtained results reveal that it is favorable to place the RIS close to the users rather than close to the BS.
翻译:本文调查了可重新配置智能表面(RIS) 辅助的大规模多投入多输出(MIMO) 系统的双比例传输设计, 基站(BS) 的波束组合适应快速变化的瞬时频道状态信息( CSI), 而RIS 的被动波束变化适应缓慢变化的统计 CSI 。 具体地说, 我们首先提议一个线性最小平均平方差( LMMSE) 估计器, 以便在每个频道一致性间隔中从用户到 BS 的混合频道( BS ) 。 根据估计的频道, 我们应用低兼容度的多投入多输出(MIMO) 最大比率( MRC) 结合在 BS 系统( BRC ) 的组合组合组合组合, 然后以封闭的形式计算出可实现的速率 。 我们进行详细的理论分析, 如果 BS- RIS 频道分布良好, 我们证明传输的电量可以成比例缩成1 m$, 作为BS 的天线, 美元, 美元, 我们的递增多少, 比例 数据 递增 数据在 BIS 中 递增 数据 在不 中, 递增 递增 数据 在不 递增 数据 中, 以 不 递增 一美元 递增 递增 。