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