PRACH Detection Probability in the Presence of Strong Phase Noise for NR Uplink in Sub-THz Bands

This paper presents the miss detection probability (MDP) for the physical random access channel (PRACH) in the 3GPP New Radio (NR) uplink in the presence of strong phase noise (PN) in the sub-Terahertz (THz) bands. The PRACH is a physical channel that a set of user equipment (UE) first transmits in the uplink for initial access. Hence, it is needed to achieve a low PRACH MDP under a low received signal-to-noise ratio (SNR) condition. The impact of PN that is induced in local oscillators in base station and UE transceivers in the sub-THz bands is larger than that in the millimeter-wave bands. Therefore, it is important to investigate the impact of strong PN on the PRACH detection probability in the sub-THz bands. Link-level simulation results show that the Wiener PN component in a subTHz PN model fluctuates quickly over the PRACH preamble duration. Accordingly, the strong PN in the sub-THz bands comprising the Wiener PN and uncorrelated Gaussian PN is reduced when taking the correlation over the PRACH preamble sequence duration with a 139 -chip length. We show that the degradation in the PRACH MDP due to the strong PN is slight when the power spectral density (PSD) at a 0-Hz frequency offset in the Wiener PN is -25 ~ dBc/Hz and the PSD in the Gaussian PN is lower than approximately -93 dBc/Hz.