Wireless Communications and Mobile Computing

Volume 2019, Article ID 3519468, 8 pages

https://doi.org/10.1155/2019/3519468

## Distributed Beamforming Design for Nonregenerative Two-Way Relay Networks with Simultaneous Wireless Information and Power Transfer

School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou, Guangdong Province, China

Correspondence should be addressed to Sai Zhao; nc.ude.uhzg@iasoahz

Received 12 April 2019; Revised 2 October 2019; Accepted 29 October 2019; Published 2 December 2019

Academic Editor: Daniele Pinchera

Copyright © 2019 Keyun Liao 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 considers the distributed beamforming design for a simultaneous wireless information and power transfer (SWIPT) in two-way relay network, which consists of two sources, *K* relay nodes and one energy harvesting (EH) node. For such a network, assuming perfect channel state information (CSI) is available, and we study two different beamforming design schemes. As the first scheme, we design the beamformer through minimization of the average mean squared error (MSE) subject to the total transmit power constraint at the relays and the energy harvesting constraint at the EH receiver. Due to the intractable expression of the objective function, an upper bound of MSE is derived via the approximation of the signal-to-noise ratio (SNR). Based on the minimization of this upper bound, this problem can be turned into a convex feasibility semidefinite programming (SDP) and, therefore, can be efficiently solved using interior point method. To reduce the computational complexity, a suboptimal beamforming scheme is proposed in the second scheme, for which the optimization problem could be recast to the form of the Rayleigh–Ritz ratio and a closed-form solution is obtained. Numerical results are provided and analyzed to demonstrate the efficiency of our proposed beamforming schemes.

#### 1. Introduction

Harvesting energy from environment has become a preferred strategy to overcome the key challenge of limited lifetime of devices equipped with battery in wireless networks, e.g., wireless sensor network (WSN) or Bluetooth low-energy mesh (BLE Mesh) network. As an efficient energy harvesting technique, simultaneous wireless information and power transfer (SWIPT) has gained considerable research attention in the academic field [1–6]. The concept of SWIPT was first introduced and a capacity-energy function was first proposed to characterize the fundamental tradeoff between simultaneous energy and information transfer in [1]. Considering SWIPT in multiple-input single-output (MISO) multicasting systems [2], the authors minimize the base station (BS) transmit power by jointly optimizing the beamforming vector at BS and the power splitting parameters of mobile station. In [3], considering a multiple-input multiple-output (MIMO) wireless broadcast scenario, where one receiver harvested energy and another receiver decoded information from the signals sent by a transmitter, two practical schemes, namely, time switching (TS) and power splitting (PS), were proposed. Motivated by the requirement of fifth generation, Xu et al. [4] investigated the cooperative SWIPT NOMA protocol design in single-input single-output (SISO) and multiple-input single-output (MISO). Meanwhile, the security of information transmission also became more and more important. Zhao et al. [5] considered the security of wireless network for SWIPT, which maximize the achievable secrecy rate subject to sum transmit power constraint at relays and energy harvesting (EH) constraint at the EH receiver. Aforementioned papers were investigated under perfect channel state information (CSI). In [6], the MIMO SWIPT system under the condition of imperfect CSI was studied.

Considering its advantage in enhancing spectral efficiency, two-way relay (TWR) network is extensively studied [7–10]. In the TWR network, two source nodes exchanged information through a relay node, and the number of required time slots is reduced from four to two with the aid of analog network coding [7]. In [8], a cooperative relay scheme for distributed amplify-and-forward (AF) relays working under the TWR protocol was considered, and a closed-form solution was obtained. Considering the user fairness, a linear precoding design for relay in multiple-pair two-way MIMO relay systems was investigated [9]. Considering security, cooperative beamforming in cognitive two-way relay networks was studied in [10]. For SWIPT two-way relay channels, the authors of [11–15] considered the relay beamforming design for SWIPT in a nonregenerative TWR network with the objective to maximize the sum rate of TWR. Wen et al. [12] studied the joint source and relay design for MIMO two-way relay networks with SWIPT, which minimized the total mean square error guaranteeing sufficient energy harvested at the sources. The authors of [14, 15] developed a novel distributed energy beamforming scheme for realizing SWIPT in the TWR network, where the former considered two source node exchanged information via an EH relay node and the latter considered multiple-user exchanged messages with the help of an energy-constrained relay node. Considering imperfect CSI and energy efficiency , the robust optimization schemes of MIMO two-way relay networks were considered under the constraint of energy harvesting [16]. In the IoT networks or sensor networks, most of the nodes may have limited volume and limited computation capacity with limited energy supply, some of the relay nodes are providing data communication service, while other idle node(s) could harvest energy to prolong its/their life cycle. That is why we consider multiple relays in two-way transmission, while at the same time, an EH is placed to harvest energy. And to our best knowledge, there is little work on this system model by now.

The main contributions of our paper are summarized as follows:(1)We study the distributed beamforming design in SWIPT-based two-way multiple-relay networks. Differing from [14, 15], we consider the two-way SWIPT system with multiple relays, while only single relay is considered in [14, 15]. Our goal is to minimize the upper bound of average MSE while satisfying the harvested energy requirements of the EH receiver and the total power budgets of the multiple relays.(2)For the case of SWIPT-based two-way multiple-relay networks, the initial problem is a nonconvex problem. Through appropriate mathematical transformation, we could recast the initial problem into the semidefinite programming (SDP) problem. Then, we can obtain a quasi-optimal solution by applying semidefinite relaxation (SDR).(3)To avoid the high computational complexity resulting from solving the SDP problem, we find the suboptimal solution by converting the initial problem into the form of the Rayleigh–Ritz quotient, which is of low complexity.

The rest of this paper is organized as follows: in Section 2, the system model and the problem formulation are illustrated. Section 3 presents our proposed methods to obtain the solutions to the problem of beamforming design. Section 4 constructs complexity analysis of two schemes and provides simulation results. Finally, Section 5 has a conclusion about the paper.

Notations: boldface lowercase and uppercase letters denote vectors and matrices, respectively. The transpose, conjugate, conjugate transpose, Frobenius norm, and trace of matrix **A** are denoted as , and tr(**A**), respectively. vec(**A**) denotes to stack the columns of a matrix **A** into a single vector **a**. denotes the Kronecker product. and denote the maximum and minimum eigenvalues of **A**, respectively. denotes the eigenvector of **A** associating with the maximum eigenvalue. By , we mean that **A** is positive semidefinite. **I** is the identity matrix. denotes the distribution of a circularly symmetric complex Gaussian vector with mean vector 0 and variance 1.

#### 2. System Model

We consider a collaborative network consisting of two source nodes, *K* AF relays using the two-way protocol, and one EH receiver as shown in Figure 1.