CFO-Robust Detection for 5G PRACH under Fading Channels: Analytical Modeling and Performance Evaluation

TL;DR

This work develops a comprehensive analytical framework for robust PRACH preamble detection in 5G NR under CFO and fading. It derives PDP statistics for flat Rayleigh channels for both coherent and power combining across independent and identical repetition channels, and presents closed-form or numerically tractable thresholds and detection probabilities. A CFO-aware detector is proposed that leverages PDP correlations, including a practical peak-selection algorithm to control false alarms while preserving detection performance. Numerical results reveal when PC or CC is advantageous and demonstrate significant gains from the CFO-aware detector, with implications for more spectral-efficient PRACH configurations in dense 5G deployments.

Abstract

The Physical Random Access Channel (PRACH) is essential for initial access and synchronization in both 5G and future 6G networks; however, its detection is highly sensitive to impairments such as high user density, large carrier frequency offset (CFO), and fast fading. Although prior studies have examined PRACH detection, they are often restricted to specific scenarios or lack a comprehensive analytical characterization of performance. We introduce a unified analytical framework that characterizes the statistical distribution of the received power delay profile (PDP) under flat Rayleigh fading and supports both coherent combining (CC) and power combining (PC) repetition strategies. For each strategy, we derive optimal threshold expressions and closed-form detection probabilities. Furthermore, we analyze two key cases depending on the coherence time: identical and independent channel realizations per repetition. Secondly, we exploit the correlation induced by CFO across cyclic shifts to design a novel low-complexity detector that exploits PDP dependencies. Numerical results indicate that PC outperforms CC when repetitions experience independent channels, while CC can be preferable under identical realizations in limited settings. On the other hand, the proposed CFO-aware detector delivers improved robustness under severe CFO conditions.

Figures (11)

• Figure 1: The $g$-th device PRACH transmitter.
• Figure 2: Full frequency domain representation of the PRACH receiver.
• Figure 3: Format C0 PDP with $\epsilon=0.3$ and $u_{0}=51$ without noise and channel.
• Figure 4: Detection probability comparison of combining techniques for format B1 with $n^{(\mathrm{ant})}=1$ and $n^{(\mathrm{inter})}=0$.
• Figure 5: Detection probability comparison between formats B1 and B2 for different number of receive antennas, SNR of -20 dB, and $n^{(\mathrm{inter})}=0$.