中文摘要：

针对无线携能通信系统中存在能量获取不均衡的问题，提出了一种基于能量获取比例公平的波束成形设计方案。该方案在满足信息接收者的信干噪比以及发送端的最大发送功率等约束条件的基础上，通过优化波束矢量实现能量获取的比例公平。此设计在数学上是一个很难直接求解的非凸优化问题。为此，本文首先利用半定松弛技术将其转换为半定规划问题，然后结合二分法提出了可以获得最优波束矢量的迭代算法。此外，在发送端仅知道部分信道状态信息且知道信道误差范围的情况下，采用最差性能最优的方法对原优化问题进行了鲁棒波束成形设计，并提出了相应的迭代算法。仿真结果表明所提算法均可实现能量获取的比例公平且性能达到全局最优。

英文摘要：

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 di？cult 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.