Non-linear Energy Harvesting Model Research Articles

Achieving Multi-Beam Gain in Intelligent Reflecting Surface Assisted Wireless Energy Transfer

Intelligent reflecting surface (IRS) is a promising technology to boost the efficiency of wireless energy transfer (WET) systems. However, for a multiuser WET system, simultaneous multi-beam energy transmission is generally required to achieve the maximum performance, which may not be implemented by using the IRS having only a single set of coefficients. As a result, it remains unknown how to exploit the IRS to approach such a performance upper bound. To answer this question, we aim to maximize the total harvested energy of a multiuser WET system subject to the user fairness constraints and the non-linear energy harvesting model. We first consider the static IRS beamforming scheme, which shows that the optimal IRS reflection matrix obtained by applying semidefinite relaxation is indeed of high rank in general as the number of energy receivers (ERs) increases, due to which the resulting rank-one solution by applying Gaussian Randomization may lead to significant loss. To achieve the multi-beam gain, we then propose a general time-division based novel framework by exploiting the IRS's dynamic passive beamforming. Moreover, it is able to achieve a good balance between the system performance and complexity by controlling the number of IRS shift patterns. Finally, we also propose a time-division multiple access (TDMA) based passive beamforming design for performance comparison. Simulation results demonstrate the necessity of multi-beam transmission and the superiority of the proposed dynamic IRS beamforming scheme over existing schemes.

Energy Efficiency Optimization for MISO-NOMA SWIPT System with Heterogeneous QoS Requirements

This letter solves the energy efficiency optimization problem for the simultaneous wireless information and power transfer (SWIPT) systems with non-orthogonal multiple access (NOMA), multiple input single output (MISO) and power-splitting structures, where each user may have different individual quality of service (QoS) requirements about information and energy. Nonlinear energy harvesting model is used. Alternate optimization approach is adopted to find the solution, which shows a fast convergence behavior. Simulation results show the proposed scheme has higher energy efficiency than existing dual-layer iteration and throughput maximization methods.

Wireless-powered backscatter communications for smart sustainable cities: A secrecy analysis

Due to its ability to enable self-sustainable communications, wirelessly powered backscatter communication (WP-BackCom) has been deemed a promising technology for supporting smart sustainable cities. We note that the existing works on analyzing the secrecy performance of WP-BackComs have largely ignored the spatial randomness of nodes that is used to model a large-scale network. To fill this gap, this paper evaluates the secrecy outage probability of the large-scale WP-BackComs based on a tractable framework of stochastic geometry (SG). In particular, the imperfect successive interference cancellation (SIC) at each gateway (GW) and eavesdropper (Eve), and the non-linear energy harvesting (EH) model and energy-causality constraint at each backscatter user (BU) are considered. The energy outage probability and secrecy outage probability expressions are derived in the general case at first, then the closed-form expressions are obtained under the special scenario, i.e., the no-noise and the typical propagation loss scenario. Numerical simulations validate the analytical results and examine the impacts of various parameters on the secrecy performance. In particular, there exists an optimal reflection coefficient for secrecy outage probability minimization under certain conditions, and the optimal reflection coefficient increases with the increasing SIC coefficient at GW.

Optimization for IRS-Assisted MIMO-OFDM SWIPT System With Nonlinear EH Model

Simultaneous wireless information and power transfer (SWIPT) has emerged as an appealing solution to prolonging the lifetime of low-power Internet of Things (IoT) networks. Meanwhile, an intelligent reflecting surface (IRS) can reconstruct a favorable wireless propagation environment for IoT terminals to achieve high spectrum and energy efficiencies. To take full advantage of these two technologies, this article studies the optimization of an IRS-assisted multiple-input and multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) SWIPT system with nonlinear energy harvesting (EH) model. In particular, we aim to maximize the achievable data rate by jointly designing the transmit precoding matrices, the IRS matrix, as well as the power splitting (PS) ratio subject to the transmit power and harvested power constraints. Since the formulated problem is highly nonconvex, we develop an alternating optimization (AO)-based algorithm to find a high-quality suboptimal solution. Moreover, we further design a heuristic algorithm based on a two-stage optimization strategy to reduce the computational complexity. Simulation results verify that the proposed AO-based algorithm can significantly improve the achievable data rate compared to conventional benchmarks, and the proposed heuristic low-complexity algorithm can achieve comparable performance to the AO-based algorithm.

Secure MIMO systems with nonlinear energy harvesting using optimal transmit antenna selection over [formula omitted] fading channels

This paper investigates the secrecy performance of multiple-input multiple-output systems with a nonlinear energy harvesting (EH) scheme used at the transmitter to improve energy efficiency and extend the lifetime of energy-constrained systems. Most of the current literature investigates cognitive radio networks with linear EH model. However, in order to realize more realistic scenarios due to hardware constraints, such as the saturation and sensitivity characteristics of the EH components, a nonlinear EH model is examined here and compared with a simpler linear EH scheme. In particular, a practical nonlinear energy harvester model with a source, a destination, an active eavesdropper, and a power beacon is considered under generalized α−μ fading conditions. Here, the eavesdropper can overhear the data transmission messages when the source communicates with the destination using wiretap channels. Furthermore, the source employs all its antennas to combine the radio frequency signals emitted by the power beacon via the maximal ratio combining (MRC) scheme. Moreover, the MRC scheme is used at the destination and eavesdropper to improve the signal’s quality (i.e., at the receiver side). Closed-form expressions for the lower bound and asymptotic security performance are investigated. Next, optimal antenna selection (OAS) scheme and traditional space–time transmission (STT) scheme are compared based on whether the channel state information (CSI) of the wiretap link is available. In addition to deriving the secrecy diversity order and secrecy array gain, asymptotic closed-form analytical expressions for security performance and closed-form analytical expressions for the probability of strictly positive secrecy capacity are also derived for various selection schemes. Finally, numerical results indicate that, compared to the linear EH scheme with just minimal trade-offs, the nonlinear EH scheme represents more realistic and dependable outcomes.

Joint Communication and Trajectory Design for Intelligent Reflecting Surface Empowered UAV SWIPT Networks

Aiming at the limited battery capacity of widely deployed low-power smart devices in the Internet-of-things (IoT), this paper proposes a novel intelligent reflecting surface (IRS) empowered unmanned aerial vehicle (UAV) simultaneous wireless information and power transfer (SWIPT) network framework, in which IRS is used to reconstruct the wireless channel to enhance the wireless energy transmission efficiency and coverage area of the UAV SWIPT networks. In this paper, we formulate an achievable sum-rate maximization problem by jointly optimizing UAV trajectory, successive interference cancellation (SIC) decoding order, UAV transmit power allocation, power splitting (PS) ratio and IRS reflection coefficient while taking account of user non-orthogonal multiple access (NOMA) and a non-linear energy harvesting model. Due to the coupling of optimization variables, this problem is a complex non-convex optimization problem, and it is challenging to solve it directly. We first transform the problem, and then apply the alternating optimization (AO) algorithm framework to divide the transformed problem into four sub-problems to solve it. Specifically, by applying successive convex approximation (SCA), penalty function method and difference-convex (DC) programming, UAV trajectory, SIC decoding order, UAV transmit power allocation, PS ratio and IRS reflection coefficient are alternately optimized until the convergence is achieved. Numerical simulation results verify the effectiveness of our proposed algorithm compared to other algorithms.

Power Minimization in Multi-Antenna Transmitter Aided Bidirectional Tag-to-Device Communications for IoT

Bidirectional device-to-device (D2D) communications with energy-constrained devices hold the potential to revolutionize the low-power communication landscape and provide a means to realize the aim of Internet-of-Things (IoT). In this paper, we aim to explore a communication environment where a multi-antenna transmitter facilitates communication between two users equipped with two different technologies — backscattering and radio frequency based energy harvesting. Under such a setting, we aim to minimize the transmit power over a set of constraints by considering the traditional linear and the more practical nonlinear (sigmoid) energy harvesting model. Henceforth, we propose a novel optimal solution approach, exploiting the geometric interpretation of constraints and interdependency of optimization variables and the performance metric, to solve the formulated non-convex problem for the multi-antenna transmitter case for both the energy harvesting models considered. In addition, we revisit the power minimization problem for the single-antenna transmitter case, solved in our previous work, to demonstrate the applicability of the current solution approach. Furthermore, to establish a fair balance between the performance and the computation-intensive nature of the proposed optimal solution, we present two low complexity sub-optimal solution approaches leveraging the analysis carried out for the single antenna transmitter case. Finally, using the numerical simulations, we assess the performance of our system and present a comparison between the proposed solution approaches by varying some key parameters of our simulation setting.

Rate-Splitting Multiple Access in a MISO SWIPT System Assisted by an Intelligent Reflecting Surface

Rate-splitting multiple access (RSMA) and the intelligent reflecting surface (IRS) are novel technologies to improve spectrum and energy efficiencies in multi-antenna networks. In this paper, we investigate a multi-user multiple-input single-output (MISO) simultaneous wireless information and power transfer (SWIPT) system assisted with an IRS and using RSMA. In particular, the IRS assists with data and energy transmission from the base station (BS) to power-splitting (PS) users under a non-linear energy harvesting (EH) model. Our objective is to minimize the transmission power subject to rate and EH requirements at the users. To solve the non-convex problem, we propose a bilevel programming problem in which a genetic algorithm is used to solve the outer optimization problem, and the inner optimization problem is addressed with the semidefinite relaxation (SDR) method. In addition, to study a practical scenario of imperfect channel state information (CSI), we consider a robust beamforming design based on imperfect cascade channels at the BS. Then, we propose a solution based on the S-procedure with the SDR technique. Simulation results show that our proposed RSMA-based scheme provides a significant reduction in transmission power compared to the space-division multiple access (SDMA) and non-orthogonal multiple access (NOMA) methods under perfect and imperfect CSI.

New Results for Pearson Type III Family of Distributions and Application in Wireless Power Transfer

The Pearson type III and the log Pearson type III distributions have been considered in several scientific fields, as in hydrology and seismology. In this article, we present new results for these distributions and we utilize them, for the first time in the literature, to investigate the statistical behavior of wireless power transfer, which can prolong the lifetime of Internet of Things networks, considering the nonlinear relationship between the received and harvested power, which can be precisely modeled by using the logistic function. Specifically, we present new closed-form expressions for the statistical properties of a general form of the Pearson type III and the log Pearson type III distributions and we utilize them to introduce a new member of the Pearson type III family, the logit Pearson type III distribution, through which the logit gamma and the logit exponential distributions are also defined. Moreover, we derive closed-form expressions for the probability density function, the cumulative distribution function and moments of the distributions of the sum, the log sum, and the logit sum of Pearson type III random variables. Furthermore, taking into account that the Pearson type III family of distributions is closely related to the considered nonlinear energy harvesting model the statistical properties of the distribution of the harvested power are derived, for both single input single output and multiple input single output scenarios with or without channel state information at the transmitter.

Energy efficient transceiver design for SWIPT systems with non-orthogonal multiple access and power splitting

This paper studies the energy efficient (EE) optimization for the simultaneous wireless information and power transfer (SWIPT) systems combined with non-orthogonal multiple access for multi-user support. Power splitting at receiver is adopted with nonlinear energy harvesting (EH) model. Our goal is to pursue high EE for information transmission by jointly design the transmit beamforming and power splitting coefficients while satisfying quality of service requirements, such as maximum transmit power budget, minimum data rate, and minimum harvested energy per terminal. The coupling of variables make it the non-convex even with linear EH models, which is difficult to solve. Firstly, after approximating the nonlinear EH model in the optimization objective by linear one, the nonlinear fractional function is transformed into a linear subtractive form with two groups of coupled variables. After transformations, the original problem is approximately solved in an alternate way. Through the iterative procedure, semi-definite relaxation and arithmetic–geometric mean inequality are adopted to deal with the non-convex constraints. Simulation results reveal that our proposed method has a faster convergence speed and a higher energy efficiency than the benchmarks.

Stochastic Geometry Based Performance Study for Wireless-Powered Backscatter Communications

Wirelessly powered backscatter communication (WP-BackCom) enables battery-free Internet of Things (IoT) nodes to passively modulate and backscatter information on the energy signals transmitted by power beacons (PBs) and to harvest energy for realizing energy self-sustainability. It has been deemed a promising solution for the large-scale deployment of IoT nodes. In this paper, we exploit stochastic geometry (SG) to develop a tractable framework to evaluate the successful transmission probability in WP-BackCom while considering the imperfect successive interference cancellation (SIC) at each gateway (GW) and the non-linear energy harvesting (EH) model and energy-causality constraint at each backscatter user (BU). The successful transmission probability is defined as the probability for the event that not only the BU can harvest sufficient power from PBs for sustaining its operation but also the backscattered information can be successfully decoded by the GW. We derive the active probability into a closed form and then obtain the successful transmission probability based on the random spectrum access (RSA) policy. The closed-form expression for the successful transmission probability is derived under three special cases. We also devise a closed-form expression for the sub-optimal reflection coefficient to obtain a sub-optimal successful transmission probability. The analysis reveals that the sub-optimal reflection coefficient increases with the SIC coefficient. Numerical simulations validate the correctness of the above theoretical derivations and examine the impacts of various parameters on the successful transmission probability.

Joint Optimization of Trajectory, Task Offloading, and CPU Control in UAV-Assisted Wireless Powered Fog Computing Networks

This paper studies a rotary-wing unmanned aerial vehicle (UAV)-assisted wireless powered fog computing network, where a UAV serves as both a mobile wireless energy source and a mobile fog server to provide charging and computing services to a group of ground sensors. The UAV first broadcasts radio frequency (RF) signals to charge the sensors, and then the sensors use the harvested energy to complete their tasks by local computing and fog computing, where the partial offloading policy is employed. In order to achieve green communication system design, an optimization problem is formulated to minimize the UAV’s energy consumption by jointly optimizing the UAV’s trajectory, the task offloading allocation and computing resource allocation, where the piecewise nonlinear energy harvesting (EH) model, the charging requirements of sensors and velocity constraints of UAV are taken into account together. To solve the non-convex problem, an iterative method is designed based on the successive convex approximation (SCA) theory. Simulation results show that our presented scheme converges within a few iterations, by using which the UAV’s energy consumption can be greatly reduced compared to benchmark schemes. It is also observed that the harvested energy by the linear EH model have obvious bias compared to that obtained by the nonlinear EH model. And in the case of nonlinear EH model, as circuit saturation threshold increases, the UAV moves closer to the sensors such that their tasks can be completed, which may result in a higher energy consumption of the UAV. Besides, the velocity variation of UAV is relatively small by introducing the velocity constraint, which avoids drastic steering of the UAV in our considered scenario.

RIS-Empowered Non-Linear Energy Harvesting Communications Over Nakagami-m Channels

We propose novel reconfigurable-intelligent-surface (RIS)-based energy harvesting (EH) systems with linear EH (L-EH) and non-linear EH (NL-EH) models where channels are exposed to Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> fading. We also compare two RIS-based EH systems in terms of RIS locations, namely RIS-EH and RIS-information processing (RIS-IP). In the RIS-EH, RIS increases the amount of harvested energy, while in the RIS-IP, RIS is utilized to improve the information processing link. Closed-formed expressions of throughput, outage probability, and average harvested power are derived and confirmed via simulation. The L-EH model overestimates system performance, while the NL-EH model provides a realistic interpretation of EH system design.

Joint Subcarrier and Transmission Power Allocation in OFDMA-Based WPT System for Mobile-Edge Computing in IoT Environment

Mobile-edge computing (MEC) is expected to play an important role in the next-generation of Internet-of-Things (IoT) services with artificial intelligence (AI) by providing the sustainable computation capability of resource-constrained IoT devices. Since the finite battery lifetime has been a longstanding challenge of the MEC system for IoT services, the wireless power transfer (WPT) technology has been recently developed for the MEC system in order to support the perpetual operation of IoT devices. In this article, we introduce two resource allocation problems for OFDMA-based WPT-MEC systems: 1) a max–min energy fairness (MMEF) problem and 2) a power sum maximization (PSM) problem. These problems ensure high-performance computations for AI-based applications, where the network reliability and the tremendous power consumption may be required. Moreover, we incorporate a logarithmic nonlinear energy harvesting (EH) model into our formulated problems, which lead to nonconvex mixed-integer nonlinear programming (MINLP) problems. In order to resolve these NP-hard problems, we convert the proposed problems into their equivalent convex forms by applying the continuous relaxation method. The near-optimal solutions are thereby obtained in closed-form expressions by leveraging the Lagrangian duality method for each relaxed problem. Numerical results are presented to validate the merits of the proposed algorithms of MMEF&PSM over the alternative benchmark algorithm and provide significant insights on the effects of the key system parameters, including the number of IoT devices and power transmission subcarriers.

Performance Analysis of Dual-Hop AF Relaying with Non-Linear/Linear Energy Harvesting.

Massive device-to-device communication nodes and Internet of Things (IoT) devices are expected to be crucial components in next-generation wireless networks. However, the energy constraint of these nodes presents a challenge since the energy of the batteries is limited. Motivated by this, radio frequency energy harvesting (EH) has been developed as an efficient strategy to overcome the energy constraint of IoT devices and sensor networks. In this paper, a wireless-powered dual-hop amplify-and-forward relaying system, in the absence of a direct link between the source (S) and the destination (D), is considered. It is assumed that a dedicated power beacon (PB) transmits an energy-bearing signal from which the power-constrained S and relay (R) harvest energy. Theoretical derivations of bit error probability, outage probability, and throughput expressions are performed for both linear and non-linear energy harvesting models. Moreover, the theoretical results provided for different system parameters are validated via Monte Carlo simulations. The obtained results reveal the difference between the realistic non-linear EH model and the conventional linear EH model, which overestimates the system performance at high levels of harvested energy. Thus, it leads to misunderstanding the real performance of the EH systems. However, at low levels of harvested energy, both models behave similarly and provide realistic results.

Throughput Maximization for IRS-Aided MIMO FD-WPCN With Non-Linear EH Model

This paper studies an intelligent reflecting surface (IRS)-aided multiple-input-multiple-output (MIMO) full-duplex (FD) wireless-powered communication network (WPCN), where a hybrid access point (HAP) operating in FD broadcasts energy signals to multiple devices for their energy harvesting (EH) in the downlink (DL) and meanwhile receives information signals from devices in the uplink (UL) with the help of an IRS. Taking into account the practical finite self-interference (SI) and the non-linear EH model, we formulate the weighted sum throughput maximization optimization problem by jointly optimizing DL/UL time allocation, precoding matrices at devices, transmit covariance matrices at the HAP, and phase shifts at the IRS. Since the resulting optimization problem is non-convex, there are no standard methods to solve it optimally in general. To tackle this challenge, we first propose an element-wise (EW) based algorithm, where each IRS phase shift is alternately optimized in an iterative manner. To reduce the computational complexity, a minimum mean-square error (MMSE) based algorithm is proposed, where we transform the original problem into an equivalent form based on the MMSE method, which facilities the design of an efficient iterative algorithm. In particular, the IRS phase shift optimization problem is recast as an second-order cone program (SOCP), where all the IRS phase shifts are simultaneously optimized. For comparison, we also study two suboptimal IRS beamforming configurations in simulations, namely partially dynamic IRS beamforming (PDBF) and static IRS beamforming (SBF), which strike a balance between the system performance and practical complexity.

Mutual Information Maximization for SWIPT AF MIMO Relay Systems With Non-Linear EH Models and Imperfect Channel State Information

In this paper, we investigate a two-hop simultaneous wireless information and power transfer (SWIPT) amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay communication system with an energy-limited relay node. The relay node harvests energy based on the radio-frequency (RF) signal transmitted from the source node through the time-switching (TS) protocol and fully uses the harvested energy to precode and forward the information to the destination node. The non-linear energy harvesting models are considered at the relay node. With the consideration of the channel estimation error, the joint optimization of the TS factor, source and relay precoding matrices is proposed with robustness against the channel state information (CSI) mismatch to maximize the mutual information (MI) between the source and destination nodes. The optimal structure for the source and relay precoding matrices is derived to simplify the transceiver optimization problem. Numerical simulations show that the system performance provided by the proposed algorithms with robustness is better than the non-robust algorithm.

Energy-Balancing Resource Allocation for Wireless Cooperative IoT Networks With SWIPT

In this article, orthogonal frequency-division multiplexing (OFDM)-based downlink simultaneous wireless information and power transfer (SWIPT) is considered in the Internet of Things (IoT) wireless interference network, where one hybrid access point (HAP) performs both wireless power transfer (WPT) and wireless information transfer (WIT) to energy harvesting (EH) and information decoding (ID) nodes while multiple coexisting energy access points (EAPs) carry energy to EH nodes. As the transmission methodology for interference avoidance, we improve and refine the subcarrier separation (SS), which allocates the dedicated energy subcarrier set orthogonal to the information subcarrier set. Based on the modified SS, to enhance the harvested energy while minimizing the number of dedicated energy subcarriers, we design the cooperative WPT with transmit diversity and adopt the time-division multiple access scheme for multiple EH nodes. The optimal joint subcarrier, node, and power allocation problem is formulated based on the proposed transmission strategies to maximize the achievable sum rate for given energy requirement with a practical nonlinear EH model for low-power IoT nodes. However, it is difficult to obtain the global optimal solution due to the nonconvexity of the problem, so we investigate the cooperative resource allocation scheme. First, to solve the subcarrier allocation and node selection jointly, two basic methods for maximizing energy and minimizing rate loss are designed, and the additional scheme considering both energy requirement and rate-loss minimization is proposed by introducing a weighting factor for balancing the total transmit power into WPT and WIT. Then, the optimal power allocation on the allocated subcarriers and selected nodes is performed with the split transmit power. Simulation results show that the proposed schemes achieve superior rate–energy (R-E) region to conventional schemes. Our study provides useful insights on how to transmit signals for improving performance in IoT interference networks with SWIPT.

Coverage Performance of UAV-Assisted SWIPT Networks With Directional Antennas

This article studies the coverage performance of unmanned aerial vehicle (UAV)-assisted simultaneous wireless information and power transfer (SWIPT) networks under the nonlinear and linear energy harvesting (EH) models in the rich scattering scenarios, including smart farming and smart ranching, where the None-Line-of-Sight (NLoS) links are the dominate component of the wireless channel. Multiple UAVs are equipped with directional antennas to transfer information and energy to ground users (GUs). Power splitting (PS) or time switching (TS) architecture is employed at GUs. In order to evaluate the system performance in fading channels, the information and energy coverage probabilities of the system are discussed, and by using the stochastic geometry approach and the approximate scaling method, the general and lower bound explicit expressions of the coverage probabilities are derived. Numerical results show that the coverage performance of PS-based systems is superior to that of TS-based systems. Moreover, although the linear EH model yields better results than the nonlinear one, as the linear EH model is too ideal, its yielded results may mismatch practical EH circuits, and the ones yielded by the nonlinear EH model is much closer to practice, as the nonlinear EH model is based on real data measurement. Additionally, the nonlinear EH model has a relatively small effect on the harvested energy coverage probability, and the linear EH model introduces greater bias for the TS-based system than that for PS-based one.

Age of information and energy efficiency of amplify‐and‐forward relay‐assisted Internet of Things with nonlinear energy harvesting and imperfect channel state information over Nakagami‐ fading channels

AbstractThe emergence of the fifth generation of communication networks (5G) has paved the way for the fast development of Internet of Things (IoT) as well as many real‐time and mission‐critical applications. Because the status update required to be as timely as possible, a new metric termed as age of information (AoI) was born with the ability of capturing the timeliness. However, in practical implementation the sensor is energy constrained and transmits very low‐power signals, which yield high AoI so that the received status update can be stale or even outdated. To overcome this problem, this work proposes an IoT system model by integrating energy harvesting (EH), amplify‐and‐forward (AF) relay cooperation, and short packet communication (SPC) techniques. In the proposed scheme, the relay that is connected to fixed power grid, transfers energy radio frequency signals to charge the sensor and assists forwarding status update by using time switching scheme. The employment of SPC overcomes the freshness loss caused by relay cooperation and EH. Then, this work investigates the AoI and energy efficiency of the proposed scheme under finite block length communications over Nakagami‐ fading channels by specially considering channel state information (CSI) and nonlinear EH model. Under these practical constraints, the tractable AF relay transmission model and the end‐to‐end approximated signal‐to‐noise ratio are found. The end‐to‐end block error probability of finite block length transmission is derived, too. Third, under the simultaneous consideration of nonlinear EH and outdated CSI, the statistical descriptions of the time duration for the sensor fully charging its battery are derived as well as the ones of the time intervals of update packet delivery. As a result, the average AoI is achieved with closed‐form expression and the tradeoff model of AoI to energy efficiency is established by simultaneously exploiting outdated CSIs and nonlinearity of EH circuit. The presented numerical analysis exploits the impact of the outdated CSIs and nonlinear EH model and gives the insights of such model.