Low-complexity IRS beamforming based on sphere decoding and tabu search

The real-time reconfiguration of intelligent reflecting surface (IRS) is one of the crucial, yet challenging tasks required to exploit the benefits of IRS. In this paper, we study an IRS-aided multiple-input single-output (MISO) wireless network, where a coarsely quantized (few resolution bits) IRS is reconfigured to help the point-to-point communication between a multi-antenna access point (AP) and a single-antenna user. Specifically, the transmit precoders at the AP and the reflecting discrete phase shifters at the IRS are jointly optimized to maximize the signal-to-noise ratio (SNR) at the user. The optimization is studied in two practical wireless propagation environments. First, we consider an environment where the direct AP-user link is in deep fade, which enables the relaxation of the optimization problem such that it can be optimally solved by the proposed sphere-decoder (SD) algorithm. Second, a normal propagation environment for all links is considered, wherein we propose the tabu search (TS) algorithm to solve the joint active and passive beamforming problem with low complexity. The proposed TS algorithm is shown to work well, even in deep-fade AP-user link scenarios. The presented numerical results confirm the validity of our analysis and demonstrate the effectiveness of the proposed schemes over the benchmark schemes on different system setups and propagation environments.