Wireless Energy Transfer Beamforming With Löwner-John Ellipsoidal Approximation

Abstract

The physical layer beamforming design of downlink wireless energy transfer (WET) is investigated. To minimize the power of WET with respect to the terminals’ quality of service requirements, the physical beamforming design is modeled as a non-convex quadratically constrained quadratic program (QCQP) problem. A two-step method to solve the QCQP is proposed. First, the QCQP is tightened into an ellipsoidal approximation problem with the aid of a Lowner-John ellipsoid, by solving a semidefinite program (SDP). Second, due to the approximation problem’s ellipsoidal nature, it is solved as another SDP. The proposed method is compared using numerical results to the conventional semidefinite relaxation (SDR) approach. It is demonstrated that for equivalent computing time cost, the proposed method usefully improves the energy efficiency of the downlink WET compared with SDR.