  In this paper, we investigate the system outage probability of a simultaneous
wireless information and power transfer (SWIPT) based two-way
amplify-and-forward (AF) relay network considering transceiver hardware
impairments (HIs), where the energy-constrained relay node processes the
received signals based on a power splitting protocol and the two terminals
employ a selection combining (SC) scheme to exploit the signals from the direct
and relaying links. Assuming independent but non-identically distributed
Nakagami-m fading channels, we derive the system outage probability in a
closed-form, which enables us to identify two crucial ceiling effects on the
system outage probability caused by HIs in the high data rate regions, i.e.,
relay cooperation ceiling (RCC) and overall system ceiling (OSC). Specifically,
the RCC prevents the relaying link from participating in cooperative
communications, while the OSC leaves the overall system in outage. Furthermore,
we derive the achievable diversity gain of the considered network, which shows
that the diversity gain equals either the shape parameter of the direct link or
zero. Computer simulations are provided to validate the correctness of our
analytical results, and study the effects of various system parameters on the
system outage performance and the optimal power splitting ratio, as well as the
energy efficiency.
