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This paper provides a theoretical framework for understanding the performanceof reconfigurable intelligent surface (RIS)-aided massive multiple-inputmultiple-output (MIMO) with zero-forcing (ZF) detectors under imperfect channelstate information (CSI). We first propose a low-overhead minimum mean squareerror (MMSE) channel estimator, and then derive and analyze closed-formexpressions for the uplink achievable rate. Our analytical results demonstratethat: $1)$ regardless of the RIS phase shift design, the rate of all usersscales at least on the order of$\mathcal{O}\left(\log_2\left(MN\right)\right)$, where $M$ and $N$ are thenumbers of antennas and reflecting elements, respectively; $2)$ by aligning theRIS phase shifts to one user, the rate of this user can at most scale on theorder of $\mathcal{O}\left(\log_2\left(MN^2\right)\right)$; $3)$ either $M$ orthe transmit power can be reduced inversely proportional to $N$, whilemaintaining a given rate. Furthermore, we propose two low-complexitymajorization-minimization (MM)-based algorithms to optimize the sum user rateand the minimum user rate, respectively, where closed-form solutions areobtained in each iteration. Finally, simulation results validate all derivedanalytical results. Our simulation results also show that the maximum sum ratecan be closely approached by simply aligning the RIS phase shifts to anarbitrary user.

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