Is RIS-Aided Massive MIMO Promising with ZF Detectors and Imperfect CSI?

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 $\mathcal{O}\left(\log2\left(MN\right)\right)$, 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 $\mathcal{O}\left(\log2\left(MN^{2\right)\right)$;} $3)$ 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.