  Intelligent reflecting surfaces (IRSs) have received much attention recently
and are envisioned to promote 6G communication networks. In this paper, for
wireless communications aided by IRS units, we formulate optimization problems
for power control under quality of service (QoS) and max-min fair QoS under
three kinds of traffic patterns from a base station (BS) to mobile users (MUs):
unicast, broadcast, and multicast. The optimizations are achieved by jointly
designing the transmit beamforming of the BS and the phase shift matrix of the
IRS. For power control under QoS, existing IRS studies in the literature
address only the unicast setting, whereas no IRS work has considered max-min
fair QoS. Furthermore, we extend our above optimization studies to the novel
settings of multi-antenna mobile users or/and multiple intelligent reflecting
surfaces. For all the above optimizations, we provide detailed analyses to
propose efficient algorithms. To summarize, our paper presents a comprehensive
study of optimization problems involving power control, QoS, and fairness in
wireless networks enhanced by IRSs.
