# Two-Way Multi-Antenna Relaying with Simultaneous Wireless Information and Power Transfer
## 1 Introduction  
Recently, simultaneous wireless information and power transfer (SWIPT) has gained great interest due to its capability to deal with the energy scarcity in energy-constrained wireless networks [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]. In the seminal works [1; 2], the fundamental trade-off between information and power transfer in different point-to-point wireless channels was studied. On the other hand, two practical receiver designs for SWIPT, namely power splitting (PS) and time switching (TS), were firstly presented in [3; 4]. Specifically, the PS-based receiver spits the received radio-frequency signal into two streams of different power for harvesting energy and decoding information, whereas the TS-based receiver switches over time between those two operations. The SWIPT has been adopted later in more complicated communication scenarios, including the broadband wireless system [5], the cellular network [6], the interference channel [7; 8], and the relay channel [9; 10]. This paper focuses on the last scenario. Many works in the literature (e.g., [11; 12; 13; 14; 15]) have been devoted to two-way multi-antenna relaying (without SWIPT) as this approach can not only extend communication range but also improve spectral efficiency. In a basic two-way multi-antenna relay network (see Figure 1), an intermediate relay node equipped with multiple antennas is used to assist two end nodes in exchanging their information. Nevertheless, application of SWIPT to this kind of network is still in its infancy [16; 17; 18]. In [16], the SWIPT-based beamforming design for a multi-antenna relay was considered to maximize the sum rate of its two-way relay network. In [17], the authors presented a three-phase two-way relay network where an energy-constrained multi-antenna relay node harvests energy from a pair of single-antenna source nodes, and presented an optimal power allocation solution. In [18], an optimal joint sourceand relay beamforming scheme for two-way multi-antenna relay networks with SWIPT was proposed based on the principle of singular value decomposition. Depending on the nature and complexity of relays, relaying schemes can be classified into two main categories: non-regenerative relaying and regenerative relaying [19]. Non-regenerative relaying generally implies that the relays only amplify their received signals before retransmitting them. Then, it is often referred to as amplify-and-forward (AF) relaying in the literature. Note that all existing works on two-way multi-antenna relaying with SWIPT (i.e., [16; 17; 18]) are non-regenerative. On the other hand, regenerative relaying requires the relays to change the waveforms and/or the data contents by performing some processing in the digital domain. An example is the decode-and-forward (DF) relay, which receives the data from its immediate predecessor, decodes, re-encodes, and finally retransmits it. To the best of our knowledge, regenerative relaying has not yet been considered in the SWIPT-based two-way multi-antenna relay networks. In this paper, we consider a two-way relay network in which two single-antenna end nodes communicate with each other through a multi-antenna relay node that is energy constrained. This relay node harvests energy from the two end nodes and use the harvested energy for forwarding their information. Based on two half-duplex relaying protocols, called power splitting-based relaying (PSR) and time switching-based relaying (TSR) [9], for separate energy harvesting and information processing at the relay node, six multiple-antenna relaying schemes, namely PS-AF, PS-DF, PS-DF with space-time coding (PS-DF-STC), TS-AF, TS-DF, and TS-DF-STC, are designed for the considered network. In the DF-oriented design, network coding (NC) [20] is applied to the end nodes' information that is decoded at the relay node. Moreover, by having multiple antennas at the relay node, STC [21] is used in the PS-DF-STC and TS-DF-STC schemes with the aim of achieving a better end-to-end decoding performance.