Mobile Information Systems

Volume 2017 (2017), Article ID 1760187, 17 pages

https://doi.org/10.1155/2017/1760187

## Massive MIMO Relay Systems with Multipair Wireless Information and Power Transfer

^{1}Shandong Jiaotong University, Jinan 250357, China^{2}Department of Electronics Engineering, Inha University, Incheon 22212, Republic of Korea^{3}Department of Information and Communication Engineering, Inha University, Incheon 22212, Republic of Korea

Correspondence should be addressed to Kyung Sup Kwak; rk.ca.ahni@kawksk

Received 25 November 2016; Accepted 5 February 2017; Published 26 February 2017

Academic Editor: Jeongyeup Paek

Copyright © 2017 Hongwu Liu 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 destination-aided simultaneous wireless information and power transfer (SWIPT) for a decode-and-forward relay network, in which massive multiple-input multiple-output antennas are deployed at relay to assist communications among multiple source-destination pairs. During relaying, energy signals are emitted from multiple destinations when multiple sources are sending their information signals to relay. With power splitting and unlimited antennas at relay, asymptotic expression of harvested energy is derived. The analysis reveals that asymptotic harvested energy is independent of fast fading effect of wireless channels; meanwhile transmission powers of each source and destination can be scaled down inversely proportional to the number of relay antennas. To significantly reduce energy leakage interference and multipair interference, zero-forcing processing and maximum-ratio combing/maximum-ratio transmission are employed at relay. Fundamental trade-off between harvested energy and achievable sum rate is quantified. It is shown that asymptotic sum rate is neither convex nor concave with respect to power splitting and destination transmission power. Thus, a one-dimensional embedded bisection algorithm is proposed to jointly determine the optimal power splitting and destination transmission power. It shows that destination-aided SWIPT are beneficial for harvesting energy and increasing sum rate. The significant sum rate improvements of the proposed schemes are verified by numerical results.

#### 1. Introduction

Recently, simultaneous wireless information and power transfer (SWIPT) have been envisioned for wireless relay networks [1–3]. The focuses on SWIPT for relay networks mainly include two relaying protocols, that is, time switching (TS) relaying and power splitting (PS) relaying [1]. In TS relaying, a relay harvests energy from a source-emitted RF signal and forwards source signal in a time-division manner. In PS relaying, a relay extracts energy for forwarding from its received source signal with PS operation. Generally, PS relaying can increase its spectrum efficiency by reducing the consumed time slots compared to that of TS relaying. In attempting to effectively utilize available time slots, SWIPT schemes with destination-aided energy flow (EF) have emerged [2–4]. In [2], the destination-aided EF was proposed for TS relaying protocol. In [3], an autonomous multiple-input multiple-output (MIMO) relay employing PS-based energy receiver was investigated with destination-aided EF. For cognitive relay systems, the authors in [4] proposed sending EFs from destination to energy-constrained relay.

In the above mentioned destination-aided EF transmission schemes [2, 3], only a single source-destination pair was considered. However, the demands for relay-assisted SWIPT with multiple source-destination pairs have emerged. For instance, authors in [5] proposed several power allocation schemes for a relay network, where multiple source-destination pairs communicate with each other via a common energy harvesting relay. In [6], the outage performances of SWIPT in large-scale networks with/without relay were analyzed, where multiple receivers harvest energy using PS technique. By employing multiple energy harvesting relays to assist multipair communications, the authors in [7] proposed distributed PS for SWIPT by using game theory. In [8], multiple relays were applied to assist communications from multiple base stations to multiple cell-edge users and PS-based energy receivers were deployed at multiple relays. For wireless power transfer enabled collaborative mobile clouds, cellular data distributing among multiple mobile users was investigated in [9]. It has shown that the energy-constrained relays need to harvest energy from ambient radio-frequency (RF) signals to support multipair communications in future dense heterogeneous networks [6–10].

One challenge in relay-assisted SWIPT is a limited amount of harvested energy. Due to path-loss and inefficient RF-to-DC conversion, only a small fraction of energy emitted by a source can be harvested at relay. In order to harvest energy efficiently, smart antennas were employed in SWIPT systems (see [11] and references therein). In [12], TS and PS receivers were proposed for SWIPT in MIMO broadcasting channels. A low-complexity antenna switching for MIMO relay networks with SWIPT was investigated in [13]. Moreover, multiple antennas were deployed at relay to harvest energy from EF emitted by a single destination [3]. Although MIMO techniques have improved SWIPT performance to a certain extent, harvesting enough energy cannot be guaranteed by a limited number of antennas.

Recently, massive MIMO techniques were applied to improve wireless transmission capacity by exploiting its large array gain [14, 15]. A review of massive MIMO can be found in [16]. By employing linear signal processing [17], massive MIMO techniques have obtained increased signal-to-interference-plus-noise ratio (SINR) and power efficiency, which makes massive MIMO suitable to be deployed in practical SWIPT prototypes [18]. In [19], massive MIMO antennas were employed at a hybrid data-and-energy access point such that the minimum data rate among user nodes can be maximized whenever the number of antennas at the access point grows without bound. In [20], the authors proposed a low-complexity antenna partitioning algorithm for SWIPT systems with massive MIMO. Subjecting to a minimum harvested energy constraint, interference can be mitigated and throughput can be maximized [20]. Note that all the above mentioned works on SWIPT with massive MIMO were constrained in single-hop communications systems. To the best of our knowledge, only a few works have been conducted for multipair massive MIMO relay networks with SWIPT; for example, the authors in [21] proposed TS and PS relaying protocols for multiway amplify-and-forward (AF) relay networks, where information sharing among multiple users was aided by a massive MIMO relay.

In this paper, we propose a two-phase relaying protocol with destination-aided EFs for a decode-and-forward (DF) relay network, where multiple source-destination pairs communicate via a massive MIMO relay [10]. Different from the work of [7], where synchronization among multiple relays is required, we consider only a single relay with massive MIMO antennas and destination-aided EFs. This model has many interests, for example, in environmental sensor networks, Internet of things, and future dense heterogeneous networks, where interuser communications can be realized with the aid of an energy-constrained relay [3–10]. The main contributions of this paper can be summarized as follows:(i)The important performance metrics including asymptotic harvested energy and asymptotic achievable rate are derived for the case in which the number of relay antennas grows without bound.(ii)We show that destination-aided EFs are beneficial for boosting energy harvesting and, hence, the achievable sum rate can be improved significantly with the aid of destination-aided EFs. The optimal destination transmission power that maximizes the achievable sum rate is derived in closed-form. The optimal PS factor that maximizes the achievable sum rate is derived in closed-form.(iii)We also show that by using zero-forcing (ZF) processing and maximum-ratio combing/maximum-ratio transmission (MRC/MRT) at relay, energy leakage interference (ELI) and multipair interference (MI) can be cancelled completely as the number of relay antennas grows without bound. When the number of relay antennas is large, transmission powers of each source and each destination can be scaled inversely proportional to the number of relay antennas.(iv)We show that asymptotic sum rate is neither convex nor concave with respect to PS and destination transmission power, such that conventional convex optimization methods cannot be applied. We propose a one-dimensional embedded bisection (EB) algorithm to jointly determine the optimal PS and destination transmission power, so that the sum rate can be improved significantly.

The rest of this paper is organized as follows. Section 2 describes the system model and presents ZF processing and MRC/MRT processing. Section 3 presents the asymptotic analysis of system performance. The one-dimensional EB algorithm is also presented in Section 3. Section 4 presents numerical results and discusses the system performance of the proposed schemes. Finally, Section 5 summarizes the contributions of this study.

*Notation*. The superscripts , , and represent the transpose, conjugate, and conjugate-transpose, respectively. and stand for the expectation and variance operations, respectively. denotes the complex space and stands for the circularly symmetric complex Gaussian distribution with zero mean and variance matrix . Unless otherwise stated, vectors and matrices are, respectively, represented by bold lowercase and uppercase letters. is the identity matrix, is the zero matrix, and is the zero matrix. denotes trace operation of a matrix .

#### 2. System Model

A block diagram of the considered multipair massive MIMO DF relay network is depicted in Figure 1, where single-antenna equipped sources () transmit their information signals to single-antenna equipped destinations () via an -antenna equipped wireless-powered massive MIMO relay (R). Without loss of generality, we assume that is larger than in this paper. We also assume that a direct link between the source and destination of each pair does not exist due to large path-loss or obstacles. All nodes work in half-duplex mode. Moreover, noises at relay’s information detecting (ID) receiver and destinations’ receivers are modeled as complex zero-mean additive noises, while noise power at relay’s energy harvesting (EH) receiver is assumed to be small, so that it is neglected.