# Wireless Energy Harvesting Two-Way Relay Networks with Hardware Impairments
## 1 Introduction  
Energy harvesting (EH) has recently attracted enormous attention from researchers as a promising supplemental technology in prolonging the lifetime of a wireless network, especially in wireless sensor networks [1], cognitive radio networks [2], etc. With energy harvesting technique, the energy can be captured through solar power [3], strongly coupled magnetic resonances [4] or radio-frequency (RF) signals in ambient environments [5]. Since RF signals carry energy as well as information, the integration of RF energy harvesting capabilities into wireless communication systems provides a possibility of simultaneous wireless information and power transfer (SWIPT) [6]. The pioneer work of initial work on SWIPT is discussed in [7], which considers an ideal receiver design that is able to simultaneously observe and extract power from the same received signal. However, as discussed in [8], this such an ideal receiver does not hold exist in practice. For practical implementation, the study in [8] also introduces two realizable receiver architectures design: time switching (TS) and power splitting (PS). Cooperative relay network [9; 10] is a common application scenario of SWIPT. In relay networks, the relay expenditures additional resources for relaying, which might result a decreased lifetime for energy-constrained relay networks. A handful of research efforts have explored SWIPT for one-way relay (OWR) and two-way relay (TWR) networks. In [11], [PERSON] et al. analyze TS and PS protocols for one-way amplify-and-forward (AF) relay networks, and derive analytical expressions for the outage probability and the ergodic capacity. [PERSON] et al. [12] study the optimal power splitting design tomaximize the cooperative capacity of OWR networks with AF and decode-and-forward (DF) protocols. The work in [13] investigates the impact of SWIPT on the performance of one source-destination, multiple-relay cooperative networks and derive a closed-form expression of the outage probability. With relay selection, the a closed-form expression of the outage probability has been derived and verified over independent Nakagami-\(m\) fading channels in [14] for a dual-hop wireless powered cooperative system. For two-way relaying AF networks with the PS protocol, [PERSON] et al. [15] analytically derive the exact expressions, tight upper and lower bounds on the outage probability and the ergodic capacity. In [16], resource allocation of the PS and time phases ratios for the PS-based SWIPT and that of the TS and time phases ratios for the TS-based SWIPT are studied to minimize the system outage probability in TWR networks. The above research works contribute in the area of assuming that the transceiver and receiver hardware of all nodes is perfect. In practice, however, the hardware of a wireless node undergo several kinds of impairments such as phase noise, I/Q imbalance, high power amplifier non-linearities, etc. [17; 18]. There are several works have investigated the effect of hardware impairments (HI) in relay networks, which are illustrated next. In [19], the authors quantify the impact of HI on dual-hop AF and DF relaying networks and derive the outage probability subject to Nakagami-\(m\) fading. [PERSON] et al. [20] analyze the impact of HI at the relay in an AF-TWR configuration, and deduce a closed-form expression for the outage probability (OP) and symbol-error rates (SERs). In [21], the impact of HI on spectrum underlay cognitive multiple-relay networks is studied. [PERSON] et al. [22] study the joint source/relay precoding design for a practical MIMO two-way AF relaying system that suffers from HI. Recently, there emerges a few recent works concentrating on analyzing analyzed the impact of HI on energy harvesting enabled relay networks. [PERSON] et al. [23] consider the joint impacts of EH and HI on multiple-relay one-way networks, and analyze the OP under two relay selection protocols.