  In this paper, we study an intelligent reflecting surface (IRS)-assisted
system where a multi-antenna base station (BS) serves a single-antenna user
with the help of a multi-element IRS in the presence of interference generated
by a multi-antenna BS serving its own single-antenna user. The signal and
interference links via the IRS are modeled with Rician fading. To reduce phase
adjustment cost, we adopt quasi-static phase shift design where the phase
shifts do not change with the instantaneous channel state information (CSI). We
investigate two cases of CSI at the BSs, namely, the instantaneous CSI case and
the statistical CSI case, and apply Maximum Ratio Transmission (MRT) based on
the complete CSI and the CSI of the Line-of-sight (LoS) components,
respectively. Different costs on channel estimation and beamforming adjustment
are incurred in the two CSI cases. First, we obtain a tractable expression of
the average rate in the instantaneous CSI case and a tractable expression of
the ergodic rate in the statistical CSI case. We also provide sufficient
conditions for the average rate in the instantaneous CSI case to surpass the
ergodic rate in the statistical CSI case, at any phase shifts. Then, we
maximize the average rate and ergodic rate, both with respect to the phase
shifts, leading to two non-convex optimization problems. For each problem, we
obtain a globally optimal solution under certain system parameters, and propose
an iterative algorithm based on parallel coordinate descent (PCD) to obtain a
stationary point under arbitrary system parameters. Next, in each CSI case, we
provide sufficient conditions under which the optimal quasi-static phase shift
design is beneficial, compared to the system without IRS. Finally, we
numerically verify the analytical results and demonstrate notable gains of the
proposal solutions over existing ones.
