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We study information-theoretic limits for simultaneous wireless informationand power transfer (SWIPT) systems employing nonlinear radio frequency (RF)energy harvesting (EH) receivers (Rxs). In particular, we consider a SWIPTsystem with one transmitter that broadcasts a common signal to an informationdecoding (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 ofthe transmitted signal. We aim to answer the following fundamental question:What is the optimal input distribution of the transmit signal waveform thatmaximizes the information transfer rate at the ID Rx conditioned on individualminimum required direct-current (DC) powers to be harvested at the EH Rxs?Specifically, we study the conditional capacity problem of a SWIPT systemimpaired by additive white Gaussian noise subject to average-power (AP) andpeak power (PP) constraints at the transmitter and nonlinear EH constraints atthe EH Rxs. To this end, we develop a novel nonlinear EH model that capturesthe saturation of the harvested DC power by taking into account the reversebreakdown current of the rectifying diode. We derive a novel semiclosed-formexpression for the harvested DC power, which simplifies to closed form for lowinput RF powers. The derived analytical expressions are shown to closely matchcircuit simulation results. We solve the conditional capacity problem for real-and complex-valued signalling and prove that the optimal input distributionthat maximizes the rate-energy (R-E) region is unique and discrete with afinite number of mass points. Furthermore, we show that the boundary of the R-Eregion saturates for high PP constraints due to the saturation of the harvestedDC power for high input RF powers. In addition, we devise a suboptimal inputdistribution whose R-E tradeoff performance is close to optimal.

Conditional Capacity and Transmit Signal Design for SWIPT Systems with Multiple Nonlinear Energy Harvesting Receivers