Joint Transmit and Reflective Beamforming Design for Active IRS-Aided SWIPT Systems

To further improve the performance of passive intelligent reflecting surface (IRS)-assisted communication systems and mitigate the serious path loss due to "double-fading" of IRS-assisted links, an active IRS-aided simultaneous wireless information and power transfer (SWIPT) system is investigated. This paper jointly optimizes the transmit beamforming at the base station (BS) and the phase shifts at the active IRS in order to maximize the power collected by the energy harvesting receiver under both perfect and imperfect channel state information (CSI) states, subject to the signal-to-interference-noise ratio constraint of the information decoding receiver, and the power constraints of the BS/IRS. Under perfect CSI, the alternating optimization algorithm is utilized for obtaining the transmit beamforming at the BS and the phase shifts at the active IRS. For each subproblem, we first transform non-convex objective function and constraints into convex ones by performing a first-order Taylor expansion. Then, each subproblem is solved by using the interior point method. Given that obtaining perfect CSI is impractical, two robust beamforming designs are proposed for imperfect CSI case. Under the bounded CSI error model, we first transform the non-convex optimization problem into two semidefinite programming subproblems, and then solve each subproblem based on S-procedure and sequential rank-one constraint relaxation (SROCR) techniques. Under the stochastic CSI error model, the alternating optimization method is applied in an iterative manner based on Bernstein-type inequality and SROCR technique. Simulation results show that both robust and non-robust schemes for active IRS-assisted SWIPT systems can achieve extremely superior performance over conventional passive IRS-assisted systems under the same overall power budget.