This paper provides a theoretical framework for understanding the performance of reconfigurable intelligent surface (RIS)-aided massive multiple-input multiple-output (MIMO) with zero-forcing (ZF) detectors under imperfect channel state information (CSI). We first propose a low-overhead minimum mean square error (MMSE) channel estimator, and then derive and analyze closed-form expressions for the uplink achievable rate. Our analytical results demonstrate that: $1)$ regardless of the RIS phase shift design, the rate of all users scales at least on the order of $\mathcal{O}\left(\log_2\left(MN\right)\right)$, where $M$ and $N$ are the numbers of antennas and reflecting elements, respectively; $2)$ by aligning the RIS phase shifts to one user, the rate of this user can at most scale on the order of $\mathcal{O}\left(\log_2\left(MN^2\right)\right)$; $3)$ either $M$ or the transmit power can be reduced inversely proportional to $N$, while maintaining a given rate. Furthermore, we propose two low-complexity majorization-minimization (MM)-based algorithms to optimize the sum user rate and the minimum user rate, respectively, where closed-form solutions are obtained in each iteration. Finally, simulation results validate all derived analytical results. Our simulation results also show that the maximum sum rate can be closely approached by simply aligning the RIS phase shifts to an arbitrary user.

翻译：本文提供了一个理论框架, 用于理解可重新配置智能表面(RIS) 的性能。 在不完善的频道状态信息( CSI) 下, 以零强制检测器( ZF) 进行大规模多投入多输出( MIMO ) 。 我们首先提出一个低超版最小平均平方差( MMSE) 频道估计器, 然后为上行可实现的速率计算和分析封闭式表达式。 我们的分析结果显示: 1美元, 不论RIS 阶段转换设计, 所有用户的比值至少以$mathcal{O_ left( log_ 2\ left) (MN\right) 顺序排列; 3美元或2美元, 简略分析率( MON\right)\right) 为美元, 其中美元是天线和反映元素的数量; 2美元, 通过将RINS 阶段的比值调整, 这个用户的比值最多可以按 $=2 leglegal- relift (log_right) ralalalalalalalalationalal) exalationaltial dalization 比率, 我们所有的比值表示一个最接近的比值。