Beamforming design based on energy harvesting proportional fairness in a simultaneous wireless information and power transfer system

Abstract

In this paper, we propose a beamforming design based on energy harvesting proportional fairness to overcome the unbalance of energy harvesting in a simultaneous wireless information and power transfer system. We aim at achieving the energy harvesting proportional fairness while guaranteeing the signal to interference plus noise ratio constraints at the information receivers and total power constraint at the transmitter by optimizing the beamforming vectors. This optimization problem is of non-convex and hence difficult to solve. In order to solve it, in this paper, we first use the semi-definite relaxation technique as a tool to transform it into a semi-definite program problem, and then propose an iterative algorithm based on bisection method to obtain the optimal beamforming vectors. Besides, we also extend our result to a robust case where the transmitter only knows a part of the channel state information and the bound of channel errors, and propose an iterative algorithm based on worst-case method to obtain the corresponding beamforming vectors. Finally, the simulation results show that the proposed algorithms can achieve both the energy harvesting proportional fairness and global optimum.