Wireless Communications and Mobile Computing

Volume 2018, Article ID 7906957, 8 pages

https://doi.org/10.1155/2018/7906957

## Power-Splitting Scheme for Nonlinear Energy Harvesting AF Relaying with Direct Link

^{1}School of Management, Xi’an Polytechnic University, Xi’an, China^{2}Army Academy of Border and Coastal Defence, Department of Information and Arms, Xi’an, China

Correspondence should be addressed to Liqin Shi; moc.621@niqiltcennoc

Received 3 May 2018; Revised 6 June 2018; Accepted 10 June 2018; Published 2 July 2018

Academic Editor: Fuhui Zhou

Copyright © 2018 Xiaobo Bai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Simultaneous wireless information and power transfer (SWIPT) is a promising technique to prolong the lifetime of energy-constrained relay systems. Most previous works optimize power-splitting (PS) scheme based on a linear or a simple two-piecewise linear energy harvesting (EH) model, while the employed EH model may not characterize the properties of practical EH harvesters well. This leads to a mismatch between the existing PS scheme and the practical EH harvester available for relay systems. Motivated by this, this paper is devoted to the design of PS scheme in a nonlinear EH amplify-and-forward energy-constrained relay system in the presence of a direct link between the source and the destination. In particular, we formulate an optimization problem to maximize the system capacity according to the instantaneous channel state information, subject to a nonlinear EH model based on the logistic function. The objective function of the formulated problem is proven to be unimodal and there is no closed-form expression for the optimal PS ratio due to the complexity of logistic function. In order to reduce overhead cost of optimizing PS ratio, a simpler nonlinear EH model based on the inverse proportional function is employed to replace the nonlinear EH model based on the logistic function and we further derive the closed-form expression for the optimal PS ratio. Simulation results reveal that a higher system capacity can be achieved when the PS scheme is optimized based on nonlinear EH models instead of the linear EH model, and that there is only a marginal difference between the capacity under the two optimal PS schemes optimized for two different nonlinear EH models.

#### 1. Introduction

The aim of Internet of Things (IoT) is to enable people and things to be connected anytime, anyplace, with anything and anyone, ideally using any path/network and any service [1]. It allows massive IoT devices such as low-power wireless sensors to access the wireless communication networks and communicate with each other. The limited lifetime of IoT devices is a fundamental problem for implementing IoT deployment. Motivated by this, simultaneous wireless information and power transfer (SWIPT) is proposed and devoted to the solution of this problem. On the other hand, relaying technology is highly beneficial in wireless communications in terms of the communication range, the energy efficiency, and the system capacity [2, 3]. However, when the relaying technology is employed in IoT networks, the IoT devices are unwilling to be a relay in order to avoid the extra energy consumption since these devices usually have limited battery capacity. Thus, integrating SWIPT and relaying is a viable option to strike a tradeoff between information processing and power supply and gains much attention recently [4–6]. In this field, the design of energy harvesting (EH) scheme, which instructs the relay either to switch the received radio frequency (RF) signal in the time domain or to split the received RF signal in the power domain to provide signal processing and power transfer, is one of the most important issues.

Until now, there have been many reports [4–14] regarding how to design an appropriate EH scheme for SWIPT based relay systems. The works [4, 7] studied the effects of power-splitting (PS) ratio and time-switching (TS) ratio on the amplify-and-forward (AF) and decode-and-forward (DF) relay systems by deriving the expressions for outage probability and ergodic capacity. In [8], both the PS ratio and TS ratio were optimized to maximize the system transmission rate in DF relay systems, where the relay has a certain amount of remaining energy. By combining both TS and PS, a hybrid scheme was proposed and further optimized in [9]. The authors of [10] designed two optimal PS schemes with full and partial channel state information (CSI) to minimize the system outage probability in an AF relay system. Assuming the availability of source-destination link, the optimal PS ratio was designed and the diversity gains for the relay and the destination were analyzed [11]. By means of the stochastic geometry, the authors proposed a dynamic PS scheme in a DF relay system with a random number of transmitter-receiver pairs and investigated its outage probability [12]. Recognizing the advantages of nonorthogonal multiple access (NOMA) in spectrum efficiency, a novel cooperative SWIPT-NOMA system was integrated [13], and an optimal PS scheme was further proposed [14].

These works [4–14] were based on a linear EH model, in which the RF-to-direct current (DC) power conversion efficiency is a fixed constant and independent of the input power of the energy harvester. As pointed out by [15–17], the practical energy harvester operates in a nonlinear mode and the linear EH model may not characterize the properties of practical EH harvesters well. Further, the optimal PS schemes based on the linear EH model may not be optimal for the practical scenario. As a result, the existing schemes based on a linear EH model may need to be redesigned to avoid the mismatch caused by the resource allocation under the linear EH model, and ever-increasing attention has been paid into the study of nonlinear EH model in wireless communications (see [18–30] and references therein). References [18–25] introduced the nonlinear EH model into the wireless powered communication networks, the SWIPT-NOMA system, and the cognitive radio networks with SWIPT, where the resource allocation scheme, including the transmit power of the transmitter, and the PS/TS ratio, is concentrated. The studies revealed that a higher system capacity could be achieved by designing the EH scheme based on the nonlinear EH model instead of the conventional linear one. Apart from the aforementioned networks, the researchers have also studied the design of EH scheme in nonlinear EH relay systems [26–30]. For example, the authors of [26, 27] focused on the design of PS scheme for nonlinear EH two-way relay systems. Since the low complexity of hardware is very vital to energy-constrained relay systems, the researches on one-way relay systems have attracted a lot of interests [28–30]. In particular, the works [28, 29] derived the outage probability of a PS enabled nonlinear EH relay system. Considering the perfect/imperfect CSI at the relay, an optimal PS scheme was developed to minimize the outage probability [30] in an AF nonlinear EH relay system. These aforementioned works have laid the foundation for the design of EH scheme in one-way relay systems. After careful analysis of the existing works [28–30], it can be found that a simple two-piecewise linear EH model was employed, and that the employed two-piecewise linear model cannot provide sufficient precision compared with the existing nonlinear EH models based on the logistic function and the inverse proportional function. Therefore, there still remains a large gap to be filled regarding the design of EH scheme for nonlinear EH one-way relay systems.

Motivated by this observation, this paper is devoted to the design of PS schemes for an AF relay system with direct link in terms of system capacity, where the nonlinear EH models proposed in [16, 18] are used to characterize the properties of practical EH circuits. Our contributions are as follows.(i)We optimize the PS scheme to maximize the system capacity under the nonlinear EH model based on a logistic function. We prove that the objective function is unimodal and the optimal solution is obtained by the golden section search method.(ii)Employing the nonlinear EH model based on an inverse proportional function instead of the logistic function, a closed-form expression for the optimal PS ratio is derived to maximize the system capacity. Compared with the PS scheme optimized for the nonlinear EH model based on the logistic function, the PS scheme optimized for the nonlinear EH model based on the inverse proportional enjoys a lower computational complexity with the near-optimal performance.

It is worth pointing out that energy efficiency (EE) is also an important performance metric. Since the EE is defined as the ratio of system capacity to power consumption [31], the optimization of EE is equivalent to the optimization of system capacity for a fixed transmit power. Thus, our derived optimal solution of this paper is the same as the optimal solution to maximize EE. If the transmit power is adjustable and smaller than a maximum power transmit, we should optimize both PS ratio and transmit power simultaneously. In this case, the solution to maximize EE is different from the derived results of this paper, while how to obtain the optimal PS ratio and optimal transmit power is beyond the scope of this paper.

#### 2. System Model and Working Flow

As shown in Figure 1, we consider a SWIPT based AF relay system, composed of a source node , an energy-constrained relay node , and a destination node . To be general, we assume that there exists a direct link between the source and the destination. All nodes operate in a half-duplex mode and are equipped with single antenna. It is assumed that both the source and the destination are equipped with fixed power supply, and that both “harvest-then-forward” scheme and the PS scheme are employed to encourage the relay to be cooperative with the source’s transmission. Let and denote the channel coefficients between and in a quasistatic fading model. Let denote the transmit power of the source. All the channel state information (CSI) is available at the relay in order to investigate the system performance limits of the PS scheme. Moreover, we ignore the processing energy required by the transmit/receive circuitry at the relay [4–14].