  This work analyzes the performance of a downlink multi-user multiple-input
multiple-output (MU-MIMO) non-orthogonal multiple access (NOMA) communications
system. To reduce hardware complexity and exploit antenna diversity, we
consider a transmit antenna selection (TAS) scheme and equal-gain combining
(EGC) receivers. Further, we consider Weibull-distributed fading channels to
account for non-linearities of the propagation medium and to cover, as special
cases, important fading scenarios such as Rayleigh and exponential models.
Performance metrics such as the outage probability (OP) and the average bit
error rate (ABER) are derived in an exact manner. An asymptotic analysis for
the OP and for the ABER is also carried out. Moreover, we obtain exact
expressions for the probability density function (PDF) and the cumulative
distribution function (CDF) of the end-to-end signal-to-noise ratio (SNR).
Interestingly, our results indicate that, except for the first user (nearest
user), in a high-SNR regime the ABER achieves a performance floor that depends
solely on the user's power allocation coefficient and on the type of
modulation, and not on the channel statistics or the amount of transmit and
receive antennas. To the best of the authors' knowledge, no performance
analyses have been reported in the literature for the considered scenario. The
validity of all our expressions is confirmed via Monte-Carlo simulations.
