  Reconfigurable Intelligent Surfaces (RISs) have been recently considered as
an energy-efficient solution for future wireless networks due to their fast and
low-power configuration, which has increased potential in enabling massive
connectivity and low-latency communications. Accurate and low-overhead channel
estimation in RIS-based systems is one of the most critical challenges due to
the usually large number of RIS unit elements and their distinctive hardware
constraints. In this paper, we focus on the uplink of a RIS-empowered
multi-user Multiple Input Single Output (MISO) uplink communication systems and
propose a channel estimation framework based on the parallel factor
decomposition to unfold the resulting cascaded channel model. We present two
iterative estimation algorithms for the channels between the base station and
RIS, as well as the channels between RIS and users. One is based on alternating
least squares (ALS), while the other uses vector approximate message passing to
iteratively reconstruct two unknown channels from the estimated vectors. To
theoretically assess the performance of the ALS-based algorithm, we derived its
estimation Cram\'er-Rao Bound (CRB). We also discuss the downlink achievable
sum rate computation with estimated channels and different precoding schemes
for the base station. Our extensive simulation results show that our algorithms
outperform benchmark schemes and that the ALS technique achieves the CRB. It is
also demonstrated that the sum rate using the estimated channels always reach
that of perfect channels under various settings, thus, verifying the
effectiveness and robustness of the proposed estimation algorithms.
