  This paper investigates the passive beamforming and deployment design for an
intelligent reflecting surface (IRS) aided full-duplex (FD) wireless system,
where an FD access point (AP) communicates with an uplink (UL) user and a
downlink (DL) user simultaneously over the same time-frequency dimension with
the help of IRS. Under this setup, we consider three deployment cases: 1) two
distributed IRSs placed near the UL user and DL user, respectively; 2) one
centralized IRS placed near the DL user; 3) one centralized IRS placed near the
UL user. In each case, we aim to minimize the weighted sum transmit power
consumption of the AP and UL user by jointly optimizing their transmit power
and the passive reflection coefficients at the IRS (or IRSs), subject to the UL
and DL users' rate constraints and the uni-modulus constraints on the IRS
reflection coefficients. First, we analyze the minimum transmit power required
in the IRS-aided FD system under each deployment scheme, and compare it with
that of the corresponding half-duplex (HD) system. We show that the FD system
outperforms its HD counterpart for all IRS deployment schemes, while the
distributed deployment further outperforms the other two centralized deployment
schemes. Next, we transform the challenging power minimization problem into an
equivalent but more tractable form and propose an efficient algorithm to solve
it based on the block coordinate descent (BCD) method. Finally, numerical
results are presented to validate our analysis as well as the efficacy of the
proposed passive beamforming design.
