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This paper studies a multiuser multiple-input single-output (MISO) broadcast simultaneous wireless information and power transfer (SWIPT) system, where a multi-antenna access point (AP) sends wireless information and energy simultaneously via spatial multiplexing to multiple single-antenna receivers each of which implements information decoding (ID) or energy harvesting (EH). We aim to maximize the weighted sum-power transferred to all EH receivers subject to given minimum signal-to-interference-and-noise ratio (SINR) constraints at different ID receivers. In particular, we consider two types of ID receivers (referred to as Type I and Type II, respectively) without or with the capability of cancelling the interference from (a priori known) energy signals. For each type of ID receivers, we formulate the joint information and energy transmit beamforming design as a nonconvex quadratically constrained quadratic program (QCQP). First, we obtain the globally optimal solutions for our formulated QCQPs by applying an optimization technique so-called semidefinite relaxation (SDR). It is shown via SDR that under the condition of independently distributed user channels, no dedicated energy beam is used for the case of Type I ID receivers to achieve the optimal solution; while for the case of Type II ID receivers, employing no more than one energy beam is optimal. Next, we establish a new form of the celebrated uplink-downlink duality for our studied downlink beamforming problems, and thereby develop alternative algorithms to obtain the same optimal solutions as by SDR. Finally, numerical results are provided to evaluate the performance of proposed optimal beamforming designs for MISO SWIPT systems.
Xu et al. (Fri,) studied this question.