Beamforming Optimization for Intelligent Reflecting Surface with Discrete Phase Shifts

Intelligent reflecting surface (IRS) is a cost-effective solution for achieving high spectrum and energy efficiency in future wireless communication systems by leveraging massive low-cost passive elements that are able to reflect the signals with adjustable phase shifts. Prior works on IRS mostly consider continuous phase shifts at each reflecting element, which however, is practically difficult to realize due to the hardware limitation. In contrast, we study in this paper an IRS-aided wireless network, where an IRS with only a finite number of phase shifts 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 continuous transmit beamforming at the AP and discrete reflect beamforming at the IRS, subject to a given signal-to-noise ratio (SNR) constraint at the user receiver. We first propose a suboptimal and low-complexity solution to the problem by applying the alternating optimization technique. Then, we analytically show that as compared to the ideal case with continuous phase shifts, the IRS with discrete phase shifts achieves the same squared power gain in terms of asymptotically large number of reflecting elements, while a constant performance loss is incurred that depends only on the number of phase-shift levels. Simulation results verify our analytical result as well as the effectiveness of our proposed design as compared to different benchmark schemes.