The idea of Integrated Sensing and Communication (ISAC) offers a promising
solution to the problem of spectrum congestion in future wireless networks.
This paper studies the integration of intelligent reflective surfaces (IRS)
with ISAC systems to improve the performance of radar and communication
services. Specifically, an IRS-assisted ISAC system is investigated where a
multi-antenna base station (BS) performs multi-target detection and multi-user
communication. A low complexity and efficient joint optimization of transmit
beamforming at the BS and reflective beamforming at the IRS is proposed. This
is done by jointly optimizing the BS beamformers and IRS reflection
coefficients to minimize the Frobenius distance between the covariance matrices
of the transmitted signal and the desired radar beam pattern. This optimization
aims to satisfy the signal-to-interference-and-noise ratio (SINR) constraints
of the communication users, the total transmit power limit at the BS, and the
unit modulus constraints of the IRS reflection coefficients. To address the
resulting complex non-convex optimization problem, an efficient alternating
optimization (AO) algorithm combining fractional programming (FP),
semi-definite programming (SDP), and second order cone programming (SOCP)
methods is proposed. Furthermore, we propose robust beamforming optimization
for IRS-ISAC systems by adapting the proposed optimization algorithm to the IRS
channel uncertainties that may exist in practical systems. Using advanced tools
from convex optimization theory, the constraints containing uncertainty are
transformed to their equivalent linear matrix inequalities (LMIs) to account
for the channels' uncertainty radius. The results presented quantify the
benefits of IRS-ISAC systems under various conditions and demonstrate the
effectiveness of the proposed algorithm