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Intelligent reflecting surface (IRS) is a promising technology for achievinghigh spectrum efficiency in future wireless networks by leveraging massivelow-cost reflecting elements with each reflecting the incident signal with aproper phase shift. However, prior works on IRS are mainly based on theoptimization of infinite-resolution phase shifters which are practicallyinfeasible due to hardware imperfections. In contrast, we study in this paperan IRS-aided wireless network, where an IRS with only finite-resolution phaseshifter available at each element is deployed to assist in the communicationfrom a multi-antenna access point (AP) to a single-antenna user. We aim tominimize the transmit power at the AP by jointly optimizing the transmitbeamforming at the AP and reflect beamforming at the IRS, subject to thesignal-to-noise ratio (SNR) constraint and practical discrete phase shiftconstraints. We first propose a suboptimal but low-complexity algorithm byexploiting the alternating optimization technique. Then, we reveal that as inthe case with continuous phase shifts, the IRS with discrete phase shifts alsoachieves the squared power gain for asymptotically large number of reflectingelements, despite suffering a performance loss that depends only on theresolution of phase shifters.

Beamforming Optimization for Intelligent Reflecting Surface with Discrete Phase Shifts