  In this paper, we propose a robust design framework for IRS-aided
communication systems in the presence of user location uncertainty. By jointly
designing the transmit beamforming vector at the BS and phase shifts at the
IRS, we aim to minimize the transmit power subject to the worse-case quality of
service (QoS) constraint, i.e., ensuring the user rate is above a threshold for
all possible user location error realizations. With unit-modulus, this problem
is not convex. The location uncertainty in the QoS constraint further increases
the difficulty of solving this problem. By utilizing techniques of Taylor
expansion, S-Procedure and semidefinite relaxation (SDP), we transform this
problem into a sequence of semidefinite programming (SDP) sub-problems.
Simulation results show that the proposed robust algorithm substantially
outperforms the non-robust algorithm proposed in the literature, in terms of
probability of reaching the required QoS target.
