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This paper investigates the two-timescale transmission design forreconfigurable intelligent surface (RIS)-aided massive multiple-inputmultiple-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 theslowly-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 eachchannel coherence interval. Based on the estimated channel, we apply thelow-complexity maximal ratio combining (MRC) beamforming at the BS, and thenderive the ergodic achievable rate in a closed form expression.  To draw design insights, we perform a detailed theoretical analysis departingfrom the derived ergodic achievable rate. If the BS-RIS channel is Riciandistributed, 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 anon-zero rate.  If the BS-RIS channel is Rayleigh distributed, the transmit power can bescaled either proportionally to $1/\sqrt{M}$ as $M$ grows large, orproportionally 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 thestatistical knowledge of the CSI, we maximize the minimum user rate bydesigning the passive beamforming at the RIS.  Numerical results confirm that, even in the presence of imperfect CSI, theintegration of an RIS in massive MIMO systems results in promising performancegains. In addition, the obtained results reveal that it is favorable to placethe RIS close to the users rather than close to the BS.

Two-Timescale Design for Reconfigurable Intelligent Surface-Aided Massive MIMO Systems with Imperfect CSI