Robust downlink beamforming and power splitting design in multiuser MISO SWIPT system

In this paper, we consider robust transmit strategy for a multiuser MISO broadcast system with simultaneous wireless information and power transmission (SWIPT), under the assumption of imperfect channel state information at the transmitter (CSIT), where each user is equipped with a power splitter and can harvest power and decode information at the same time. To optimally design the robust transmit beamforming (BF) and power splitting (PS), our design objective is to minimize the total transmit power of the base station (BS) subject to individual energy harvesting (EH) constraint and signal-to-interference-plus-noise-ratio (SINR) constraint at each user. The original problem is non-convex and can be optimally solved by reformulating it into a two-stage problem. First, by fixing the PS factors of each receive antenna, we derive the equivalent conditions of SINR constraint and EH constraint, and then convert the original problem into a relaxed semidefinite programming (SDP) problem by applying the semidefinite relaxation (SDR) technique, which can be solved efficiently by standard interior-point algorithm. Second, the optimal PS factors design problem are solved by a one/M-dimension search over the minimum target of the transmit power. Interestingly, we have shown that the SDR is tight. Simulation results have shown to validate the robustness and effectiveness of the proposed algorithm.