Beamforming Optimization for Intelligent Reflecting Surface with Discrete Phase Shifts

Intelligent reflecting surface (IRS) is a promising technology for achieving high spectrum efficiency in future wireless networks by leveraging massive low-cost reflecting elements with each reflecting the incident signal with a proper phase shift. However, prior works on IRS are mainly based on the optimization of infinite-resolution phase shifters which are practically infeasible due to hardware imperfections. In contrast, we study in this paper an IRS-aided wireless network, where an IRS with only finite-resolution phase shifter available at each element is deployed to assist in the communication from a multi-antenna access point (AP) to a single-antenna user. We aim to minimize the transmit power at the AP by jointly optimizing the transmit beamforming at the AP and reflect beamforming at the IRS, subject to the signal-to-noise ratio (SNR) constraint and practical discrete phase shift constraints. We first propose a suboptimal but low-complexity algorithm by exploiting the alternating optimization technique. Then, we reveal that as in the case with continuous phase shifts, the IRS with discrete phase shifts also achieves the squared power gain for asymptotically large number of reflecting elements, despite suffering a performance loss that depends only on the resolution of phase shifters.