  We consider a wireless communication system, where a transmitting source is
assisted by both a reconfigurable intelligent reflecting surface (IRS) and a
decode-and-forward half-duplex relay (hybrid IRS-relay scheme) to communicate
with a destination receiver. All devices are equipped with multiple antennas,
and transmissions occur in two stages. In stage 1, the source splits the
transmit message into two sub-messages, transmitted to the destination and the
relay, respectively, using block diagonalization to avoid interference. Both
transmissions will benefit from the IRS. In stage 2, the relay re-encodes the
received sub-message and forwards it (still through the IRS) to the
destination. We optimize power allocations, beamformers, and configurations of
the IRS in both stages, in order to maximize the achievable rate at the
destination. We compare the proposed hybrid approach with other schemes
(with/without relay and IRS), and confirm that high data rate is achieved for
the hybrid scheme in case of optimal IRS configurations.
