SSB-Based Time/Frequency Synchronization and Noise Estimation Evaluation Report

This report presents a systematic Monte Carlo evaluation of three tightly coupled receiver functions in 5G NR downlink: SSB-based frame synchronization via PSS matched filtering, fine carrier frequency offset (CFO) estimation using PSS–SSS differential phase, and noise power estimation from known SSB sequences. Three correlator lengths (64, 128, 256 taps) are compared under AWGN and 3GPP TDL-A/C fading channels, with multipath (fD = 0) and Doppler (fD = 300 Hz) effects evaluated independently. Two CFO estimators—coherent phasor-sum and angle-averaging—are benchmarked against the Cramér–Rao Lower Bound (CRLB), while three noise variance estimators are compared against the Kay (1993) CRLB with DC subcarrier exclusion. Key findings: (i) the 256-tap correlator detects 12.1 dB below the PDSCH operating point under AWGN and eliminates the multipath-induced error floor observed with the 128-tap; (ii) the coherent CFO estimator achieves near-CRLB performance under both AWGN and static fading, with no irreducible floor—Doppler (fD = 300 Hz) is identified as the dominant impairment, introducing a ~134 Hz floor that remains 3.9× below the worst-case oscillator tolerance at 3.5 GHz; (iii) the PSS–SSS complex differential noise estimator achieves RMSE = 0.09 under AWGN (CRLB = 0.089) and 0.14–0.18 under static fading. Detailed arithmetic complexity analysis is provided at the MAC, CORDIC, and FPGA resource level for each module. All evaluations use 10,000 Monte Carlo frames with 3GPP-compliant coupled oscillator impairments.