NR PRACH Detection Probability in the Presence of CFO in Multi-access Environments

This paper presents the miss-detection probability (MDP) for the Physical Random Access Channel (PRACH) of the 3GPP New Radio (NR) specifications focusing on combining of the correlations of the repeated preamble sequences in the presence of a carrier frequency offset (CFO) in multi-access environments. We show that when there is a CFO, coherent combining (CC) of multiple correlations achieves a lower PRACH MDP than using power domain combining (PC) in the low average received signal-to-noise ratio (SNR) region when a large number of cyclic shift (CS) resources are used with high priority. Conversely, we show that the PC achieves a lower PRACH MDP due to the robustness to the CFO in the high average received SNR region. We also show that the required average received SNR at the target PRACH MDP using the CC is reduced by approximately 2.0 dB compared to using the PC when the maximum number of available CS resources is used. Finally, we show that the required average received SNR satisfying the PRACH MDP of $10^{-2}$ is increased by approximately 4.0 dB compared to that at the MDP of $10^{-1}$ when using the maximum number of available CS resources.