Uplink NOMA short-packet communications with residual hardware impairments and channel estimation errors

In this paper, we study an uplink non-orthogonal multiple access (NOMA) wireless system with short-packet communications (SPC) in the presence of channel estimation errors and residual transceiver hardware impairments. Two NOMA decoding schemes are considered, namely fixed-order decoding (i.e., mean-power based decoding) and dynamic-order decoding (i.e., instantaneous-power based decoding). We first derive the closed-form exact and asymptotic expressions of the cumulative distribution functions (CDF) of the signal-to-interference-plus-noise ratio (SINR) associated with the two decoding schemes. Based on this, we analyze the average block error-rate (BLER) achieved in the finite block-length regime. Next, we formulate maximum throughput optimization problems with respect to the length of the packet. This problem is shown to be quasi-concave, which facilitates the finding of the optimal block-length via a search algorithm. Analytical comparisons between the NOMA-SPC system and its OMA-SPC counterpart are also performed. Simulation results are provided to validate the analysis.