  Cell-Free Massive multiple-input multiple-output (MIMO) and reconfigurable
intelligent surface (RIS) are two promising technologies for application to
beyond-5G networks. This paper considers Cell-Free Massive MIMO systems with
the assistance of an RIS for enhancing the system performance under the
presence of spatial correlation among the engineered scattering elements of the
RIS. Distributed maximum-ratio processing is considered at the access points
(APs). We introduce an aggregated channel estimation approach that provides
sufficient information for data processing with the main benefit of reducing
the overhead required for channel estimation. The considered system is studied
by using asymptotic analysis which lets the number of APs and/or the number of
RIS elements grow large. A lower bound for the channel capacity is obtained for
a finite number of APs and engineered scattering elements of the RIS, and
closed-form expressions for the uplink and downlink ergodic net throughput are
formulated in terms of only the channel statistics. Based on the obtained
analytical frameworks, we unveil the impact of channel correlation, the number
of RIS elements, and the pilot contamination on the net throughput of each
user. In addition, a simple control scheme for optimizing the configuration of
the engineered scattering elements of the RIS is proposed, which is shown to
increase the channel estimation quality, and, hence, the system performance.
Numerical results demonstrate the effectiveness of the proposed system design
and performance analysis. In particular, the performance benefits of using RISs
in Cell-Free Massive MIMO systems are confirmed, especially if the direct links
between the APs and the users are of insufficient quality with high
probability.
