Analysis and Optimization of an Intelligent Reflecting Surface-Assisted System With Interference

In this article, 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. To the best of our knowledge, this is the first work that considers optimal quasi-static phase shift design for an IRS-assisted system in the presence of interference.