  Smart and reconfigurable wireless communication environments can be
established by exploiting well-designed intelligent reflecting surfaces (IRSs)
to shape the communication channels. In this paper, we investigate how multiple
IRSs affect the performance of multi-user full-duplex communication systems
under hardware impairment at each node, wherein the base station (BS) and the
uplink users are subject to maximum transmission power constraints. Firstly,
the uplink-downlink system weighted sum-rate (SWSR) is derived which serves as
a system performance metric. Then, we formulate the resource allocation design
for the maximization of SWSR as an optimization problem which jointly optimizes
the beamforming and the combining vectors at the BS, the transmit powers of the
uplink users, and the phase shifts of multiple IRSs. Since the SWSR
optimization problem is non-convex, an efficient iterative alternating approach
is proposed to obtain a suboptimal solution for the design problem considered
and its complexity is also discussed. In particular, we firstly reformulate the
main problem into an equivalent weighted minimum mean-square-error form and
then transform it into several convex sub-problems which can be analytically
solved for given phase shifts. Then, the IRSs phases are optimized via a
gradient ascent-based algorithm. Finally, numerical results are presented to
clarify how multiple IRSs enhance the performance metric under hardware
impairment.
