  We consider a multiuser multiple-input single-output interference channel
where the receivers are characterized by both quality-of-service (QoS) and
radio-frequency (RF) energy harvesting (EH) constraints. We consider the power
splitting RF-EH technique where each receiver divides the received signal into
two parts a) for information decoding and b) for battery charging. The minimum
required power that supports both the QoS and the RF-EH constraints is
formulated as an optimization problem that incorporates the transmitted power
and the beamforming design at each transmitter as well as the power splitting
ratio at each receiver. We consider both the cases of fixed beamforming and
when the beamforming design is incorporated into the optimization problem. For
fixed beamforming we study three standard beamforming schemes, the zero-forcing
(ZF), the regularized zero-forcing (RZF) and the maximum ratio transmission
(MRT); a hybrid scheme, MRT-ZF, comprised of a linear combination of MRT and ZF
beamforming is also examined. The optimal solution for ZF beamforming is
derived in closed-form, while optimization algorithms based on second-order
cone programming are developed for MRT, RZF and MRT-ZF beamforming to solve the
problem. In addition, the joint-optimization of beamforming and power
allocation is studied using semidefinite programming (SDP) with the aid of rank
relaxation.
