  In this paper, a novel cooperative non-orthogonal multiple access (NOMA)
system is proposed, where one near user is employed as decode-and-forward (DF)
relaying switching between full-duplex (FD) and half-duplex (HD) mode to help a
far user. Two representative cooperative relaying scenarios are investigated
insightfully. The \emph{first scenario} is that no direct link exists between
the base station (BS) and far user. The \emph{second scenario} is that the
direct link exists between the BS and far user. To characterize the performance
of potential gains brought by FD NOMA in two considered scenarios, three
performance metrics outage probability, ergodic rate and energy efficiency are
discussed. More particularly, we derive new closed-form expressions for both
exact and asymptotic outage probabilities as well as delay-limited throughput
for two NOMA users. Based on the derived results, the diversity orders achieved
by users are obtained. We confirm that the use of direct link overcomes zero
diversity order of far NOMA user inherent to FD relaying. Additionally, we
derive new closed-form expressions for asymptotic ergodic rates. Based on
these, the high signal-to-noise radio (SNR) slopes of two users for FD NOMA are
obtained. Simulation results demonstrate that: 1) FD NOMA is superior to HD
NOMA in terms of outage probability and ergodic sum rate in the low SNR region;
and 2) In delay-limited transmission mode, FD NOMA has higher energy efficiency
than HD NOMA in the low SNR region; However, in delay-tolerant transmission
mode, the system energy efficiency of HD NOMA exceeds FD NOMA in the high SNR
region.
