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Intelligent reflecting surfaces (IRSs) have received considerable attention from the wireless communications research community recently. In particular, as low-cost passive devices, IRSs enable the control of the wireless propagation environment, which is not possible in conventional wireless networks. To take full advantage of such IRS-assisted communication systems, both the beamformer at the access point (AP) and the phase shifts at the IRS need to be optimally designed. However, thus far, the optimal design is not well understood. In this paper, a point-to-point IRS-assisted multiple-input single-output (MISO) communication system is investigated. The beamformer at the AP and the IRS phase shifts are jointly optimized to maximize the spectral efficiency. Two efficient algorithms exploiting fixed point iteration and manifold optimization techniques, respectively, are developed for solving the resulting non-convex optimization problem. The proposed algorithms not only achieve a higher spectral efficiency but also lead to a lower computational complexity than the state-of-the-art approach. Simulation results reveal that deploying large-scale IRSs in wireless systems is more efficient than increasing the antenna array size at the AP for enhancing both the spectral and the energy efficiency.

Wireless communications via intelligent reflecting surfaces (IRSs) has received considerable attention from both academia and industry. In particular, IRSs are able to create favorable wireless propagation environments with typically lowcost passive devices. While various IRS-aided wireless communication systems have been investigated in the literature, thus far, the optimal design of such systems is not well understood. In this paper, IRS-assisted single-user multiple-input single-output (MISO) communication is investigated. To maximize the spectral efficiency, a branch-and-bound (BnB) algorithm is proposed to obtain globally optimal solutions for both the active and passive beamformers at the access point (AP) and the IRS, respectively. Simulation results confirm the effectiveness of deploying IRSs in wireless systems. Furthermore, by taking the proposed optimal BnB algorithm as the performance benchmark, the optimality of existing design algorithms is investigated.