Energy beamforming has emerged as a promising technique for enhancing the energy transfer efficiency of radio-frequency (RF) enabled wireless power transfer (WPT). However, the performance of conventional energy beamforming may seriously degrade due to the non-linear RF to direct current (DC) conversion at energy receivers (ERs). To tackle this issue, this letter proposes a new time-division energy beamforming scheme, in which different energy beamforming matrices (of high ranks in general) are time shared to exploit the “convex-concave” shape of the RF-DC power relation at ERs. In particular, we maximize the minimum harvested DC energy among all ERs, by jointly optimizing the energy beamforming matrices and the corresponding time allocation subject to a given charging time duration (e.g., a second). To solve the formulated non-convex min-DC-energy maximization problem, we propose an efficient solution by using the techniques of alternating optimization and successive convex approximation (SCA). Numerical results show that the proposed time-division energy beamforming design indeed outperforms the conventional multi-beam and time-division-multiple-access (TDMA)-based energy transmissions.

中文翻译：

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用于具有非线性能量收集的多用户无线电力传输的时分能量波束成形

能量波束成形已成为一种很有前途的技术，可用于提高启用射频 (RF) 的无线电力传输 (WPT) 的能量传输效率。然而，由于能量接收器 (ER) 处的非线性 RF 到直流 (DC) 转换，传统能量波束成形的性能可能会严重降低。为了解决这个问题，这封信提出了一种新的时分能量波束形成方案，其中不同的能量波束形成矩阵（通常是高秩）是时间共享的，以利用 RF-DC 功率关系的“凸凹”形状急诊室。特别是，我们通过联合优化能量波束成形矩阵和在给定充电持续时间（例如，一秒）下的相应时间分配来最大化所有 ER 中收集的最小直流能量。为了解决公式化的非凸最小直流能量最大化问题，我们通过使用交替优化和连续凸逼近 (SCA) 技术提出了一种有效的解决方案。数值结果表明，所提出的时分能量波束成形设计确实优于传统的基于多波束和时分多址 (TDMA) 的能量传输。