The scenario of an uplink two-user non-orthogonal multiple access (NOMA) communication system is analytically studied when it operates in the short packet transmission regime. The considered users support mobility and each is equipped with a single antenna, while they directly communicate with a multi-antenna base station. Power-domain NOMA is adopted for the signal transmission as well as the successive interference cancellation approach is performed at the receiver for decoding. The packet error rate (PER) is obtained in simple closed formulae under independent Rayleigh faded channels and for arbitrary user mobility profiles. The practical time variation and correlation of the channels is also considered. Moreover, useful engineering insights are manifested in short transmission time intervals, which define a suitable setup for the forthcoming ultra-reliable and low latency communication systems. Finally, it turns out that the optimal NOMA power allocation can be computed in a straightforward cost-effective basis, capitalizing on the derived PER expressions.
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