We consider a wireless powered two-way relaying system consisting of two energy constrained single antenna sources and one multi-antenna relay with constant power supply. The time division protocol is adopted, where the relay first acts as the energy source and employs energy beamforming to charge the two sources, and then switches its role as a relay to help forward the information to the sources. To maintain user fairness, we aim to maximize the minimum rate of two sources, by jointly optimizing the energy beamforming vector, time splitting factor and relay transformation matrix. To further reduce the complexity of the optimal algorithm, we propose an alternating optimization method, where closed-form expressions for the energy beamforming and time splitting factor are obtained. To gain more insights, we propose a simple suboptimal design and analyze the outage probability and the average rate when the relay applies simple energy beamforming and transformation matrix. The analysis shows that the system can achieve a diversity order of N3\frac {N}{3} for a system with a relay of NN antennas. Numerical results show that the performance of the proposed low-complexity alternating optimization method approaches the optimal algorithm over the entire SNR range, but has a significantly low complexity, and the proposed suboptimal design can also achieves a decent performance especially in small NN regime.

中文翻译：

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无线供电多天线双向中继系统的优化与分析


我们考虑一种无线供电的双向中继系统，由两个能量受限的单天线源和一个具有恒定电源的多天线中继组成。采用时分协议，其中中继首先充当能量源，并利用能量波束成形为两个源充电，然后切换其作为中继的角色以帮助将信息转发到源。为了保持用户公平性，我们的目标是通过联合优化能量波束成形向量、时间分割因子和中继变换矩阵来最大化两个源的最小速率。为了进一步降低最优算法的复杂度，我们提出了一种交替优化方法，其中获得了能量波束形成和时间分割因子的封闭式表达式。为了获得更多见解，我们提出了一种简单的次优设计，并分析了继电器应用简单能量波束形成和变换矩阵时的中断概率和平均率。分析表明，对于具有 NN 个天线中继的系统，系统可以实现 N3\frac {N}{3} 的分集阶数。数值结果表明，所提出的低复杂度交替优化方法的性能在整个SNR范围内接近最优算法，但复杂度明显较低，并且所提出的次优设计也可以实现不错的性能，特别是在小型NN体系中。