Design of a Multi-User Wireless Information and Power Transfer System Employing Either Active IRS or AF Relay

In this paper, we optimize a Wireless Information and Power Transfer (WIPT) system including multiple pairs of users, where transmitters employ a single-antenna to transmit their information and power to their receivers with the help of one multiple-antenna Amplify-and-Forward (AF) relay or an active Intelligent Reflecting Surface (IRS). We propose a joint Time Switching (TS) scheme in which transmitters, receivers, and the relay/IRS are either in their energy or information transmission/reception modes. The transmitted multi-carrier unmodulated and modulated waveforms are used for Energy Harvesting (EH) and Information Decoding (ID) modes, respectively. In order to design an optimal fair system, we maximize the minimum rate of all pairs for both relay and IRS systems through a unified framework. This framework allows us to simultaneously design energy waveforms, find optimal relay/IRS amplification/reflection matrices, allocate powers for information waveforms, and allocate time durations for various phases. This problem turns out to be non-convex. Thus, we propose an iterative algorithm by using the Minorization-Maximization (MM) technique, which efficiently converges to the optimized solution, i.e., stationary point of the problem (under mild conditions). Numerical examples show that the proposed method improves the performance of the multi-pair WIPT relay/IRS system under various setups.