Model-Consistency-Based PRACH Peak Validation Under Large Carrier Frequency Offsets

Large carrier frequency offsets (CFOs) can severely distort the correlation response of the Physical Random Access Channel (PRACH), generating multiple significant peaks even for a single transmitting user equipment (UE), such that CFO-induced pseudo-peaks may exceed the detection threshold and be erroneously identified as valid peaks. This work addresses the problem of peak disambiguation under such conditions by formulating peak selection as a model-consistency validation problem under mismatch. A generalized likelihood ratio test (GLRT) is first formulated to provide a principled statistical validation of each detected candidate peak based on the estimated timing advance (TA) and CFO parameters. While theoretically grounded, this approach is shown to be insufficient under realistic large-CFO conditions, where CFO-induced peak ambiguity is further complicated by multipath-induced model mismatch. To address this limitation, a complementary residual-energy-based criterion is introduced, along with a weighted combination of both metrics, interpreted as a penalized consistency criterion for robust peak selection under model mismatch. The proposed framework enables the selection of a single reliable TA/CFO pair among multiple candidates, improving receiver robustness and reducing spurious updates. Performance is evaluated using precision, recall, and F1-score for both short and long PRACH formats under 3GPP-aligned channel models, including high-CFO and high-Doppler scenarios. Results demonstrate that the proposed weighted strategy generally provides a more robust trade-off than the individual GLRT-only and residual-only criteria.