Wireless Communications and Mobile Computing

Volume 2018, Article ID 1802063, 9 pages

https://doi.org/10.1155/2018/1802063

## Dynamic Power Splitting Strategy for SWIPT Based Two-Way Multiplicative AF Relay Networks with Nonlinear Energy Harvesting Model

^{1}Shaanxi Key Laboratory of Information Communication Network and Security, Xi’an University of Posts and Telecommunications, Xi’an, China^{2}Integrated Service Networks Lab of Xidian University, Xi’an, China

Correspondence should be addressed to Yinghui Ye; moc.621@hyytcennoc

Received 8 March 2018; Accepted 7 May 2018; Published 11 June 2018

Academic Editor: Wolfgang H. Gerstacker

Copyright © 2018 Tianci Wang 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

This paper investigates an energy-constrained two-way multiplicative amplify-and-forward (AF) relay network, where a practical nonlinear energy harvesting (NLEH) model is equipped at the relay to realize simultaneous wireless information and power transfer (SWIPT). We focus on the design of dynamic power splitting (DPS) strategy, in which the PS ratio is able to adjust itself according to the instantaneous channel state information (CSI). Specifically, we first formulate an optimization problem to maximize the outage throughput, subject to the NLEH. Since this formulated problem is nonconvex and difficult to solve, we further transfer it into an equivalent problem and develop a Dinkelbach iterative method to obtain the corresponding solution. Numerical results are given to verify the quick convergence of the proposed iterative method and show the superior outage throughput of the designed DPS strategy by comparing with two peer strategies designed for the linear energy harvesting (LEH) model.

#### 1. Introduction

Internet of things (IoT) devices are usually powered by batteries with limited energy storage capacity, leading to a key constraint of the performance of energy-constrained wireless networks [1, 2]. To address this problem, simultaneous wireless information and power transfer (SWIPT) has been recently proposed as a promising solution to prolong the lifetime of energy-constrained wireless networks, where the wireless signal is either switched in the time domain or split in the power domain to provide signal transmission and power transfer using the same wireless carrier, i.e., time switching (TS) strategy and power splitting (PS) strategy. Accordingly, SWIPT is applicable in energy-constrained networks for striking a balance between information and energy [3–5].

Relaying techniques, including one-way relay networks (OWRNs) and two-way relay networks (TWRNs), are highly beneficial in wireless communications to overcome shadowing effects, to increase the communication range, to improve the energy efficiency, and to increase the achievable throughput [6]. Of particular interest is the two-step (or three-step) TWRNs, in which one node shares its data with the other node via an intermediate relay. The system configuration may arise in many practical scenarios, e.g., data exchange between sensor nodes and the data through an immediate relay in IoT networks [7, 8]. However, in fact, the relay nodes may have limited battery capacity and thus rely on some external resources to charge in order to remain active. Further, due to the random positions of relay nodes, consistent power supply may be unavailable for energy-constrained relay nodes, leading to possible power outages. As a result, the aforementioned two promising techniques, SWIPT and two-step (or three-step) TWRNs, can be integrated to balance between information and energy [9].

Up to now, several works have been reported regarding this issue [10–15]. Authors of [10, 11] introduced decode-and-forward (DF) and amplify-and-forward (AF) into PS strategy based SWIPT with two-step TWRNs, respectively. Reference [12] studied the optimal PS strategy to maximize the energy efficiency. Since the circuitry design of three-step is simpler than that of two-step, [13] studied the bounds performance for PS based SWIPT with three-step DF-TWRNs in terms of outage probability. Different from [13], the authors of [14] studied the PS based three-step multiplicative AF-TWRNs, due to the advantage of three-step multiplicative TWRNs in outage probability and investigated the corresponding outage performance with a static PS strategy, where the PS ratio is determined by statistic channel state information (CSI). This results in a room for improving by making full use of the instantaneous CSI. Due to this reason, the dynamic PS (DPS) strategy was further developed [15]. It was shown that the outage performance can be improved by employing the DPS strategy.

However, the above works discussed [10–15] were based on the assumption of a linear energy harvesting (LEH) model, which was shown to be inaccurate and not capable of capturing the nonlinear behaviour of RF energy harvesting (RF-EH) circuits [16]. As a result, those existing strategies based on the LEH model lead to significant performance loss in a real scenario owing to the mismatching between linear and nonlinear EH (NLEH) model. Even though several works [16–27] have been reported regarding the applications of the NLEH model for wireless communications, most of them (see [16–24]) focused on the wireless powered communication (WPC) networks and point-to-point/cognitive radio networks with SWIPT. Apart from the aforementioned networks, the applications of a NLEH model have also been studied to the OWRNs [25–27]. In [25, 26], the authors investigated the outage performance of a NLEH relaying network with a PS strategy. Considering the perfect/imperfect CSI at the relay, the optimal PS strategy was developed in terms of outage performance [27]. However, there is no work in the existing literature studying the TWRNs with a NLEH harvester. This motivates our work.

In this paper, we study a DPS strategy for three-step multiplicative AF-TWRNs, where the relay is equipped with a NLEH harvester (this work extends the recent work [15] into the NLEH) to realize the SWIPT. To incentivize the relay to cooperate with the source, the harvest-then-forward scheme is adopted, i.e., the relay only uses the harvested energy from the source’s signal to assist its transmissions. In order to investigate the upper bound outage throughput of the considered network, we assume that CSI is available. Our contributions are as follows.

We formulate an optimization problem to maximize the outage throughput by adjusting the PS ratio according to the instantaneous CSI. The optimization problem is equivalent to maximize worse end-to-end signal-to-noise ratio (SNR), which is nonconvex and difficult to solve. On this basis, we reformulate it as a fractional programming problem and employ the Dinkelbach method to derive a DPS strategy. The simulation results show, compared with the existing strategies, the proposed DPS strategy achieves a larger outage throughput.

The rest of this paper is organized as follows. In Section 2, we introduce the system model. In Section 3, we formulate an optimization problem to maximize outage throughput and design an iterative method to obtain the optimal solution. Section 4 provides simulation results to verify our work. Finally, Section 5 concludes the paper.

#### 2. System Model

##### 2.1. Multiplicative AF-TWRNs

We consider a NLEH multiplicative AF-TWRNs, where an energy-constrained relay coordinates the two-way communications for two terminals (i.e., node 1 and node 2) exchanging information by adopting the harvest-then-forward scheme, as shown in Figure 1. All nodes are equipped with one antenna due to the limited space (since the main focus of this work is on the novel dynamic power splitting (DPS) scheme design subject to the nonlinear model, for analytical tractability, we consider the single antenna AF relay networks). We ignore the direct transmission between two terminals due to the heavy fading [15]. For successful information exchange between the two nodes, we consider the following assumptions [14, 15]:(i)The total transmission time block is divided into three consecutive equal time slots, as shown in Figure 2. First, node 1 sends the signal to . And then, node 2 sends the signal to . Finally, the relay broadcasts the multiplied signal to nodes ( = 1 or 2) using the harvested energy.(ii)The path-loss model is distance-dependent with a rate of , where is the path-loss exponent and is the distance between node and relay . Let denote the complex channel coefficients from the relay to the destination node , respectively. Each link is independent with frequency nonselective Rayleigh block fading. Further, CSI is available in order to investigate the upper bound outage performance.(iii)The processing energy required by the transmit/receive circuitry at the relay is ignored since it is very small compared with the transmit energy.