  In this work, a non-orthogonal multiple access (NOMA) based transmission
between two sources and two end-users is examined over independent
non-identically distributed (i.n.i.d.) slow Nakagami-$m$ fading channels, where
a single relay using decode-and-forward (DF) protocol is selected out of a set
of full-duplex/half-duplex (FD/HD) multiple relays in accordance with the
quality of service criterion. Two relay selection (RS) strategies, selecting a
relay to maximize data rate of user 1 at selected relay and selecting a relay
out of a set of relays providing service quality for user 1 to maximize data
rate of user 2, are analyzed. Additionally, not only perfect successive
interference cancellation (pSIC) but also imperfect SIC (ipSIC) is considered.
The exact and asymptotic outage probability (OP) expressions are derived and
validated via Monte Carlo simulation technique. Unlike existing works, our
expressions are unique and valid for all cases such as FD and HD together with
pSIC and ipSIC, i.e. expressions are not given separately but in a single
compact form. Effect of each component such as pSIC, ipSIC, and
self-interference (SI) for FD transmission on error floor of OP is
demonstrated. Moreover, the optimum relay location is illustrated for a plenty
of scenarios consisting of combination of different power allocations, data
rates, pSIC/ipSIC, and total transmitted powers.
