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Intelligent reflecting surfaces (IRSs) are regarded as a key enabler of greenwireless communication, due to their capability of customizing favorablewireless propagation environments. In this paper, we investigate resourceallocation for IRS-assisted green multiuser multiple-input single-output (MISO)systems. To minimize the total transmit power, both the beamforming vectors atthe access point (AP) and the phase shifts at multiple IRSs are jointlyoptimized, while taking into account the minimum required quality-of-service(QoS) of multiple users. First, two novel algorithms, namely a penalty-basedalternating minimization (AltMin) algorithm and an inner approximation (IA)algorithm, are developed to tackle the non-convexity of the formulatedoptimization problem when perfect channel state information (CSI) is available.Unlike existing designs that cannot ensure convergence, the proposedpenalty-based AltMin and IA algorithms are guaranteed to converge to astationary point and a Karush-Kuhn-Tucker (KKT) solution of the design problem,respectively. Second, the impact of imperfect knowledge of the CSI of thechannels between the AP and the users is investigated. To this end, anon-convex robust optimization problem is formulated and the penalty-basedAltMin algorithm is extended to obtain a stationary solution. Simulationresults reveal a key trade-off between the speed of convergence and theachievable total transmit power for the two proposed algorithms. In addition,we show that the proposed algorithms can significantly reduce the totaltransmit power at the AP compared to various baseline schemes and that theoptimal numbers of transmit antennas and IRS reflecting elements, whichminimize the total power consumption of the considered system, are finite.

IRS-Assisted Green Communication Systems: Provable Convergence and Robust Optimization