Robust Downlink Beamforming for Multiuser MISO SWIPT Systems ⋆

In this paper, we studies robust downlink beamforming for a multiuser multiple-input single-output (MISO) simultaneous wireless information and power transfer (SWIPT) system when only imperfect knowledge of the channel state information (CSI) is available at the transmitter. Specifically, we exploit two different models to describe CSI errors: a) deterministic bounded and b) stochastic random. For the deterministic bounded error model, the worst-case based robust beamforming is designed to minimize the total transmit power while guaranteeing the signal-to-interference-and-noise ratio constraints at information receivers and energy harvesting constraints at the energy receivers. The optimization problem of interest is non-convex and hard to solve. With the aid of S-procedure and semidefinite relax (SDR) techniques, we finally transform the considered non-convex problem into a semidefinite program (SDP) problem, which is convex and can be solved efficiently by using standard interior-point methods. On the other hand, considering the stochastic random CSI errors and following the chance constrained approach, we modify our design objective to minimize the total transmit power subject to probabilistic quality of service constraints of each receivers. The aforementioned probabilistic constraints have no closed-form expression and are non-convex in general. We turn this non-convex optimization problem into a SDP problem by utilizing the Bernstein-type inequality together with SDR. Finally, numerical results are provided to corroborate the robustness and effectiveness of the proposed methods.