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 peakpower (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 semiclosed-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

Radio frequency energy harvesting presents a viable solution for prolonging the lifetime of wireless communication devices. In this paper, we study downlink multi-user scheduling for a time-slotted system with simultaneous wireless information and power transfer. In particular, in each time slot, a single user is scheduled to receive information, while the remaining users opportunistically harvest the ambient radio frequency energy. We devise novel online scheduling schemes in which the tradeoff between the users' ergodic rates and their average amount of harvested energy can be controlled. In particular, we modify the well-known maximum signal-to-noise ratio (SNR) and maximum normalized-SNR (N-SNR) schedulers by scheduling the user whose SNR/N-SNR has a certain ascending order (selection order) rather than the maximum one. We refer to these new schemes as order-based SNR/N-SNR scheduling and show that the lower the selection order, the higher the average amount of harvested energy in the system at the expense of a reduced ergodic sum rate. The order-based N-SNR scheduling scheme provides proportional fairness among the users in terms of both the ergodic achievable rate and the average harvested energy. Furthermore, we propose an order-based equal throughput (ET) fair scheduler, which schedules the user having the minimum moving average throughput out of the users whose N-SNR orders fall into a given set of allowed orders. We show that this scheme provides the users with proportionally fair average harvested energies. In this context, we also derive feasibility conditions for achieving ET with the orderbased ET scheduler. Using the theory of order statistics, the average per-user harvested energy and ergodic achievable rate of all proposed scheduling schemes are analyzed and obtained in closed form for independent and non-identically distributed Rayleigh, Ricean, Nakagami-m, and Weibull fading channels.Our closed-form analytical results are corroborated by simulations. Index TermsWireless information and power transfer, RF energy harvesting, multi-user scheduling, fairness.

In this paper, we consider a wireless powered communication system, where an energy harvesting (EH) node harvests energy from a radio frequency (RF) signal broadcasted by an access point (AP) in the downlink (DL). The node stores the harvested energy in an energy buffer and uses the stored energy to transmit data to the AP in the uplink (UL). We investigate two simple online transmission policies for the EH node, namely a best-effort policy and an on-off policy, which do not require knowledge of the EH profile nor of the UL channel state information. In particular, for both policies, the EH node transmits in each time slot with a constant desired power if sufficient energy is available in its energy buffer. Otherwise, the node transmits with the maximum possible power in the best-effort policy and remains silent in the on-off policy in order to preserve its energy for future use. For both policies, we use the theory of discrete-time continuous-state Markov chains to analyze the limiting distribution of the stored energy for finite-and infinite-size energy buffers. We provide this limiting distribution in closed form for a Nakagami-m fading DL channel, i.e., for a Gamma distributed EH process and analyze the outage probability for a Nakagami-m fading UL channel. The analytical results derived in this paper are not limited to EH via RF WPT but are applicable for any independent and identically distributed EH process, originating from e.g. solar and wind energy. Our results reveal that, for low-to-medium outage probabilities, the best-effort policy is superior to the on-off policy and the optimal constant UL transmit power of the EH node that minimizes the outage probability is always less than the average harvested power but increases with the capacity of the energy buffer. The opposite behaviour is observed for high outage probabilities, where turning off the transmission in case of insufficient stored energy results in an improved outage performance compared to always transmitting with best effort. Furthermore, we show that despite the low-complexity of the proposed online policies, their minimum outage probability is near-optimal and closely approaches the outage probability of the optimal offline power allocation policy.

In this paper, we design a resource allocation algorithm for multiuser simultaneous wireless information and power transfer systems for a realistic non-linear energy harvesting (EH) model. In particular, the algorithm design is formulated as a nonconvex optimization problem for the maximization of the longterm average total harvested power at EH receivers subject to quality of service requirements for information decoding receivers. To obtain a tractable solution, we transform the corresponding non-convex sum-of-ratios objective function into an equivalent objective function in parametric subtractive form. This leads to a computationally efficient iterative resource allocation algorithm. Numerical results reveal a significant performance gain that can be achieved if the resource allocation algorithm design is based on the non-linear EH model instead of the traditional linear model.

In this paper, we study information-theoretic limits for simultaneous wireless information and power transfer (SWIPT) systems employing a practical nonlinear radio frequency (RF) energy harvesting (EH) receiver. In particular, we consider a three-node system with one transmitter that broadcasts a common signal to separated information decoding (ID) and EH receivers. Owing to the nonlinearity of the EH receiver circuit, the efficiency of wireless power transfer depends significantly on the waveform of the transmitted signal. In this paper, we aim to answer the following fundamental question: What is the optimal input distribution of the transmit waveform that maximizes the rate of the ID receiver for a given required harvested power at the EH receiver? In particular, we study the capacity of a SWIPT system impaired by additive white Gaussian noise (AWGN) under average-power (AP) and peak-power (PP) constraints at the transmitter and an EH constraint at the EH receiver. Using Hermite polynomial bases, we prove that the optimal capacityachieving input distribution that maximizes the rate-energy region is unique and discrete with a finite number of mass points. Furthermore, we show that the optimal input distribution for the same problem without PP constraint is discrete whenever the EH constraint is active and continuous zero-mean Gaussian, otherwise. Our numerical results show that the rate-energy region is enlarged for a larger PP constraint and that the rate loss of the considered SWIPT system compared to the AWGN channel without EH receiver is reduced by increasing the AP budget.