Beamforming Optimization for Intelligent Reflecting Surface-Aided SWIPT IoT Networks Relying on Discrete Phase Shifts

Intelligent reflecting surface (IRS) is capable of constructing the favorable wireless propagation environment by leveraging massive low-cost reconfigurable reflect array elements. In this article, we investigate the IRS-aided multiple-input-multiple-output (MIMO) simultaneous wireless information and power transfer (SWIPT) for Internet-of-Things (IoT) networks, where the active base station (BS) transmits beamforming and the passive IRS reflection coefficients are jointly optimized for maximizing the minimum signal-to-interference-plus-noise ratio (SINR) among all information decoders (IDs), while maintaining the minimum total harvested energy at all energy receivers (ERs). Moreover, the IRS with practical discrete phase shifts is considered, and thereby the max-min SINR problem becomes an NP-hard combinatorial optimization problem with a strong coupling among optimization variables. To explore the insights and generality of this max-min design, both the single-ID single-ER (SISE) scenario and the multiple-IDs multiple-ERs (MIME) scenario are studied. In the SISE scenario, the classical combinatorial optimization techniques, namely, the special ordered set of type 1 (SOS1) and the reformulation-linearization (RL) technique, are applied to overcome the difficulty of this max-min design imposed by discrete optimization variables. Then, the optimal branch-and-bound algorithm and suboptimal alternating optimization algorithm are, respectively, proposed. We further extend the idea of alternating optimization to the MIME scenario. Moreover, to reduce the iteration complexity, a two-stage scheme is considered aiming to separately optimize the BS transmit beamforming and the IRS reflection coefficients. Finally, numerical simulations demonstrate the superior performance of the proposed algorithms over the benchmarks in both the two scenarios.