Beamforming Optimization for Intelligent Reflecting Surface-Aided MISO Communication Systems

Abstract

This article considers an intelligent reflecting surface (IRS)-assisted point-to-point multiple-input single-output communication system. An IRS implemented by configurable phase shifters is used to assist the transmission from an access point (AP) equipped with multiple antennas to a user having a single antenna. We aim to jointly optimize the transmit beamforming at the AP and the reflect beamforming at the IRS to maximize the spectral efficiency of the system. The considered joint optimization problem can be decoupled into the transmit and reflect beamforming design problems by applying the maximum-ratio transmission strategy. The former has a closed-form expression, whereas the latter requires solving a nonconvex optimization problem. A known solution based on manifold optimization (MO) is proposed to solve the reflect beamforming design problem. Although the MO-based algorithm achieves higher spectral efficiency than the conventional semidefinite relaxation approach, it incurs high time complexity. On this basis, we address this issue by proposing a computationally efficient gradient projection (GP)-based algorithm for the reflect beamforming design problem. When low-resolution (e.g., 1–2 bits) phase shifters are adopted, we leverage an innovative probability learning technique on the basis of the cross-entropy (CE) framework to alleviate the performance loss caused by the use of low-resolution phase shifters. Simulation results demonstrate that the proposed GP-based algorithm nearly obtains the same spectral efficiency as the state-of-the-art MO-based algorithm at a low complexity. However, the running time is significantly reduced. When low-resolution phase shifters are employed, the proposed CE-based algorithm outperforms the test algorithms in terms of spectral and energy efficiency in various system configurations.