In this paper, we study information-theoretic limits for simultaneous wireless information and power transfer (SWIPT) systems employing practical nonlinear radio frequency (RF) energy harvesting (EH) receivers (Rxs). In particular, we consider a SWIPT system with one transmitter that broadcasts a common signal to an information decoding (ID) Rx and multiple EH Rxs. Owing to the nonlinearity of the EH Rxs’ circuitry, the efficiency of wireless power transfer depends on the waveform of the transmitted signal. We aim to answer the following fundamental question: What is the optimal input distribution of the transmit signal waveform that maximizes the information transfer rate at the ID Rx conditioned on individual minimum required direct-current (DC) powers to be harvested at the EH Rxs? Specifically, we study the conditional capacity problem of a SWIPT system impaired by additive white Gaussian noise subject to average-power (AP) and peak-power (PP) constraints at the transmitter and nonlinear EH constraints at the EH Rxs. To this end, we develop a novel nonlinear EH model that captures the saturation of the harvested DC power by taking into account not only the forward current of the rectifying diode but also the reverse breakdown current. Then, we derive a novel semi-closed-form expression for the harvested DC power, which simplifies to closed form for low input RF powers. The derived analytical expressions are shown to closely match circuit simulation results. We solve the conditional capacity problem for real- and complex-valued signalling and prove that the optimal input distribution that maximizes the rate-energy (R-E) region is unique and discrete with a finite number of mass points. Furthermore, we show that, for the considered nonlinear EH model and a given AP constraint, the boundary of the R-E region saturates for high PP constraints due to the saturation of the harvested DC power for high input RF powers. In addition, we devise a suboptimal input distribution whose R-E tradeoff performance is close to optimal. All theoretical findings are verified by numerical evaluations.

中文翻译：

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具有多个非线性能量收集接收器的 SWIPT 系统的条件容量和传输信号设计

在本文中，我们研究了采用实用非线性射频 (RF) 能量收集 (EH) 接收器 (Rxs) 的同步无线信息和功率传输 (SWIPT) 系统的信息理论限制。特别地，我们考虑具有一个发送器的 SWIPT 系统，该发送器将公共信号广播到信息解码 (ID) Rx 和多个 EH Rx。由于 EH Rxs 电路的非线性，无线电力传输的效率取决于传输信号的波形。我们的目标是回答以下基本问题：以在 EH Rxs 处收集的各个最小所需直流 (DC) 功率为条件，使 ID Rx 处的信息传输速率最大化的发射信号波形的最佳输入分布是什么？具体来说，我们研究了受加性高斯白噪声影响的 SWIPT 系统的条件容量问题，该噪声受发射机的平均功率 (AP) 和峰值功率 (PP) 约束以及 EH Rxs 的非线性 EH 约束。为此，我们开发了一种新颖的非线性 EH 模型，该模型不仅考虑了整流二极管的正向电流，还考虑了反向击穿电流，从而捕获了收集的直流电源的饱和度。然后，我们推导出一种新的半封闭形式的收集直流功率表达式，它简化为低输入射频功率的封闭形式。导出的分析表达式显示为与电路仿真结果密切匹配。我们解决了实值和复值信号的条件容量问题，并证明了最大化速率能量 (RE) 区域的最佳输入分布是唯一且离散的，具有有限数量的质点。此外，我们表明，对于所考虑的非线性 EH 模型和给定的 AP 约束，由于高输入 RF 功率收集的 DC 功率饱和，RE 区域的边界对于高 PP 约束会饱和。此外，我们设计了一个次优输入分布，其 RE 权衡性能接近最优。所有理论发现都通过数值评估得到验证。由于高输入 RF 功率收集的 DC 功率饱和，因此 RE 区域的边界会因高 PP 限制而饱和。此外，我们设计了一个次优输入分布，其 RE 权衡性能接近最优。所有理论发现都通过数值评估得到验证。由于高输入 RF 功率收集的 DC 功率饱和，因此 RE 区域的边界会因高 PP 限制而饱和。此外，我们设计了一个次优输入分布，其 RE 权衡性能接近最优。所有理论发现都通过数值评估得到验证。