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Intelligent reflecting surface (IRS) is a cost-effective solution forachieving high spectrum and energy efficiency in future wireless networks byleveraging massive low-cost passive elements that are able to reflect thesignals with adjustable phase shifts. Prior works on IRS mainly considercontinuous phase shifts at reflecting elements, which are practically difficultto implement due to the hardware limitation. In contrast, we study in thispaper an IRS-aided wireless network, where an IRS with only a finite number ofphase shifts at each element is deployed to assist in the communication from amulti-antenna access point (AP) to multiple single-antenna users. We aim tominimize the transmit power at the AP by jointly optimizing the continuoustransmit precoding at the AP and the discrete reflect phase shifts at the IRS,subject to a given set of minimum signal-to-interference-plus-noise ratio(SINR) constraints at the user receivers. The considered problem is shown to bea mixed-integer non-linear program (MINLP) and thus is difficult to solve ingeneral. To tackle this problem, we first study the single-user case with oneuser assisted by the IRS and propose both optimal and suboptimal algorithms forsolving it. Besides, we analytically show that as compared to the ideal casewith continuous phase shifts, the IRS with discrete phase shifts achieves thesame squared power gain in terms of asymptotically large number of reflectingelements, while a constant proportional power loss is incurred that dependsonly on the number of phase-shift levels. The proposed designs for thesingle-user case are also extended to the general setup with multiple usersamong which some are aided by the IRS. Simulation results verify ourperformance analysis as well as the effectiveness of our proposed designs ascompared to various benchmark schemes.

Beamforming Optimization for Wireless Network Aided by Intelligent Reflecting Surface with Discrete Phase Shifts