  This paper investigates a multiuser downlink communication system with
coexisting intelligent reflecting surface (IRS) and classical half-duplex
decode-and-forward (DF) relay. In this system, the IRS and the DF relay
interact with each other and assist transmission simultaneously. In particular,
active beamforming at the base station (BS) and at the DF relay, and passive
beamforming at the IRS, are jointly designed to maximize the sum-rate of all
users. The sum-rate maximization problem is nonconvex due to the coupled
beamforming vectors. We propose an alternating optimization (AO) based
algorithm to tackle this complex co-design problem. Numerical validation and
discussion on the superiority of the coexistence system and the tradeoffs
therein are presented.
