  In this paper, we investigate the intelligent reflecting surface
(IRS)/reconfigurable intelligent surface (RIS)-aided integrated sensing and
communication (ISAC) system based on sensing mutual information (MI).
Specifically, the base station (BS) perceives the sensing target via the
reflected sensing signal by the IRS, while communicating with the users
simultaneously. Our aim is to maximize the sensing MI, subject to the quality
of service (QoS) constraints for all communication users, the transmit power
constraint at the BS, and the unit-modulus constraint on the IRS's passive
reflection. We solve this problem under two cases: one simplified case assuming
a line-of-sight (LoS) channel between the BS and IRS and no clutter
interference to sensing, and the other generalized case considering the Rician
fading channel of the BS-IRS link and the presence of clutter interference to
sensing. For the first case, we show that the dedicated sensing beamformer
cannot enhance the sensing MI if the BS-user direct links are blocked, and
develop a low-complexity iterative algorithm to jointly optimize the BS and IRS
active/passive beamformers. In contrast, for the second case, we propose an
alternative iterative algorithm, which can also be applied to the first case,
to solve the beamforming design problem under the general setup. Numerical
results are provided to validate the performance of the proposed algorithms, as
compared to various benchmark schemes.
