  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. Using singular
value decomposition (SVD), semidefinite programming (SDP), and function
approximations, we propose different solutions for optimizing the beamforming
matrices at the base-station (BS), the relay, and the phase shifts at the RIS
to minimize the total transmit power subject to quality-of-service (QoS)
constraints. The problem is solved in different cases when the relay operates
in half-duplex and full-duplex modes and when the reflecting elements have
continuous and discrete phase shifts. Simulation results are provided to
compare the performance of the system with and without the RIS or the relay in
both full-duplex and half-duplex modes, under different optimization solutions.
Generally, the results show that the system with full-duplex relay and RIS
cooperation outperforms all the other scenarios, and the contribution of
full-duplex relay is higher than that of the RIS. However, an RIS performs
better than a half-duplex relay when the required QoS is high. The results also
show that increasing the number of RIS reflecting elements improves performance
better in the presence of a relay than in its absence.
