Conditional Capacity and Transmit Signal Design for SWIPT Systems with Multiple Nonlinear Energy Harvesting Receivers
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In this paper, we study information-theoretic limits for simultaneous wireless information and power transfer (SWIPT) systems employing practical nonlinear radio frequency 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 randomly deployed 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. We adopt a circuit-based nonlinear EH model and derive a novel closed-form expression for the harvested DC power, which is shown to closely match circuit simulation results. We solve the conditional capacity problem for both real- and complex-valued transmissions and show that unlike for the conventional linear EH model, there exists a rate-energy (R-E) tradeoff for the considered nonlinear EH model. We prove that the optimal input distribution that maximizes the R-E region is unique and discrete with a finite number of mass points. We devise a suboptimal distribution whose R-E performance is close to optimal. Furthermore, we prove that the R-E tradeoff curve for the considered problem with multiple EH Rxs can be completely characterized by solving the same problem for each EH Rx separately. All theoretical findings are verified by numerical evaluations.
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