  In this paper, we investigate and reveal the ergodic sum-rate gain (ESG) of
non-orthogonal multiple access (NOMA) over orthogonal multiple access (OMA) in
uplink cellular communication systems. A base station equipped with a
single-antenna, with multiple antennas, and with massive antenna arrays is
considered both in single-cell and multi-cell deployments. In particular, in
single-antenna systems, we identify two types of gains brought about by NOMA:
1) a large-scale near-far gain arising from the distance discrepancy between
the base station and users; 2) a small-scale fading gain originating from the
multipath channel fading. Furthermore, we reveal that the large-scale near-far
gain increases with the normalized cell size, while the small-scale fading gain
is a constant, given by $\gamma$ = 0.57721 nat/s/Hz, in Rayleigh fading
channels. When extending single-antenna NOMA to $M$-antenna NOMA, we prove that
both the large-scale near-far gain and small-scale fading gain achieved by
single-antenna NOMA can be increased by a factor of $M$ for a large number of
users. Moreover, given a massive antenna array at the base station and
considering a fixed ratio between the number of antennas, $M$, and the number
of users, $K$, the ESG of NOMA over OMA increases linearly with both $M$ and
$K$. We then further extend the analysis to a multi-cell scenario. Compared to
the single-cell case, the ESG in multi-cell systems degrades as NOMA faces more
severe inter-cell interference due to the non-orthogonal transmissions.
Besides, we unveil that a large cell size is always beneficial to the ergodic
sum-rate performance of NOMA in both single-cell and multi-cell systems.
Numerical results verify the accuracy of the analytical results derived and
confirm the insights revealed about the ESG of NOMA over OMA in different
scenarios.
