  Reconfigurable intelligent surfaces (RISs) consist of many passive elements
of metamaterials whose impedance can be controllable to change the
characteristics of wireless signals impinging on them. Channel estimation is a
critical task when it comes to the control of a large RIS when having a channel
with a large number of multipath components. In this paper, we derive Bayesian
channel estimators for two RIS-assisted massive multiple-input multiple-output
(MIMO) configurations: i) the short-term RIS configuration based on the
instantaneous channel estimates; ii) the long-term RIS configuration based on
the channel statistics. The proposed methods exploit spatial correlation
characteristics at both the base station and the planar RISs, and other
statistical characteristics of multi-specular fading in a mobile environment.
Moreover, a novel heuristic for phase-shift selection at the RISs is developed.
A computationally efficient fixed-point algorithm, which solves the max-min
fairness power control optimally, is proposed. Simulation results demonstrate
that the proposed uplink RIS-aided framework improves the spectral efficiency
of the cell-edge mobile user equipments substantially in comparison to a
conventional single-cell massive MIMO system. The impact of several channel
effects are studied to gain insight about when the channel estimation, i.e.,
the short-term configuration, is preferable in comparison to the long-term RIS
configuration to boost the spectral efficiency.
