  Recently, ultra-reliable and low-latency communications (URLLC) using
short-packets has been proposed to fulfill the stringent requirements regarding
reliability and latency of emerging applications in 5G and beyond networks. In
addition, multiple-input multiple-output non-orthogonal multiple access (MIMO
NOMA) is a potential candidate to improve the spectral efficiency, reliability,
latency, and connectivity of wireless systems. In this paper, we investigate
short-packet communications (SPC) in a multiuser downlink MIMO NOMA system over
Nakagami-m fading, and propose two antenna-user selection methods considering
two clusters of users having different priority levels. In contrast to the
widely-used long data-packet assumption, the SPC analysis requires the redesign
of the communication protocols and novel performance metrics. Given this
context, we analyze the SPC performance of MIMO NOMA systems using the average
block error rate (BLER) and minimum blocklength, instead of the conventional
metrics such as ergodic capacity and outage capacity. More specifically, to
characterize the system performance regarding SPC, asymptotic (in the high
signal-to-noise ratio regime) and approximate closed-form expressions of the
average BLER at the users are derived. Based on the asymptotic behavior of the
average BLER, an analysis of the diversity order, minimum blocklength, and
optimal power allocation is carried out. The achieved results show that MIMO
NOMA can serve multiple users simultaneously using a smaller blocklength
compared with MIMO OMA, thus demonstrating the benefits of MIMO NOMA for SPC in
minimizing the transmission latency. Furthermore, our results indicate that the
proposed methods not only improve the BLER performance but also guarantee full
diversity gains for the respective users.
