  Reconfigurable intelligent surfaces (RIS) have drawn considerable attention
recently due to their controllable scattering elements that are able to direct
electromagnetic waves into desirable directions. Although RISs share some
similarities with relays, the two have fundamental differences impacting their
performance. To harness the benefits of both relaying and RISs, a multi-user
communication system is proposed in this paper wherein a relay and an RIS
cooperate to improve performance in terms of energy efficiency. To utilize the
RIS efficiently, the discrete phase shifts of the RIS elements are optimized
along with the beamforming matrices at the transmitter and the relay, targeting
the minimization of the total transmit power subject to a quality-of-service
(QoS) constraint. Then, two suboptimal efficient solutions are proposed for the
resulting discrete and non-convex problem, one based on singular value
decomposition (SVD) and uplink-downlink duality and the other is based on SVD
combined with zero-forcing. Simulations show that the proposed solutions
outperform a system with either a relay or an RIS only, especially when both
are closer to the users than to the base-station.
