  In this paper, we study an active IRS-aided simultaneous wireless information
and power transfer (SWIPT) system. Specifically, an active IRS is deployed to
assist a multi-antenna access point (AP) to convey information and energy
simultaneously to multiple single-antenna information users (IUs) and energy
users (EUs). Two joint transmit and reflect beamforming optimization problems
are investigated with different practical objectives. The first problem
maximizes the weighted sum-power harvested by the EUs subject to individual
signal-to-interference-plus-noise ratio (SINR) constraints at the IUs, while
the second problem maximizes the weighted sum-rate of the IUs subject to
individual energy harvesting (EH) constraints at the EUs. The optimization
problems are non-convex and difficult to solve optimally. To tackle these two
problems, we first rigorously prove that dedicated energy beams are not
required for their corresponding semidefinite relaxation (SDR) reformulations
and the SDR is tight for the first problem, thus greatly simplifying the AP
precoding design. Then, by capitalizing on the techniques of alternating
optimization (AO), SDR, and successive convex approximation (SCA),
computationally efficient algorithms are developed to obtain suboptimal
solutions of the resulting optimization problems. Simulation results
demonstrate that, given the same total system power budget, significant
performance gains in terms of operating range of wireless power transfer (WPT),
total harvested energy, as well as achievable rate can be obtained by our
proposed designs over benchmark schemes (especially the one adopting a passive
IRS). Moreover, it is advisable to deploy an active IRS in the proximity of the
users for the effective operation of WPT/SWIPT.
