  This paper investigates the system outage performance of a simultaneous
wireless information and power transfer (SWIPT) based two-way
decode-and-forward (DF) relay network, where potential hardware impairments
(HIs) in all transceivers are considered. After harvesting energy and decoding
messages simultaneously via a power splitting scheme, the energy-limited relay
node forwards the decoded information to both terminals. Each terminal combines
the signals from the direct and relaying links via selection combining. We
derive the system outage probability under independent but non-identically
distributed Nakagami-m fading channels. It reveals an overall system ceiling
(OSC) effect, i.e., the system falls in outage if the target rate exceeds an
OSC threshold that is determined by the levels of HIs. Furthermore, we derive
the diversity gain of the considered network. The result reveals that when the
transmission rate is below the OSC threshold, the achieved diversity gain
equals the sum of the shape parameter of the direct link and the smaller shape
parameter of the terminal-to-relay links; otherwise, the diversity gain is
zero. This is different from the amplify-and-forward (AF) strategy, under which
the relaying links have no contribution to the diversity gain. Simulation
results validate the analytical results and reveal that compared with the AF
strategy, the SWIPT based two-way relaying links under the DF strategy are more
robust to HIs and achieve a lower system outage probability.
