Fractional phase measurement of BDS-3 B1C signals via simulated carrier phase observation of Rydberg atom antenna

We propose a five-level atomic scheme incorporating an auxiliary microwave dressing field to achieve sensitivity at the frequency of the BeiDou Navigation Satellite System Phase 3 B1C (BDS-3 B1C) signal, specifically 1.57542 GHz. Carrier phase observation in this frequency band is simulated using the atomic homodyne technique. The contrast ratio and measurement uncertainty of the fractional phase are analyzed, together with the influence of the BDS-3 B1C signal on carrier phase observation. The simulation results show that the fractional phase measurement uncertainty is at the basic sub-radian level for E_\rm B1C ranging from 0.048 V/m to 0.1 V/m, and reaches the high-precision sub-radian level for E_\rm B1C in the range of 0.11 V/m to 0.25 V/m. The distance measurement error coefficient is 0.0014 \textV, with a minimum measurement error of 0.82 cm. In addition, the influence of half-cycle slips on the uncertainty of fractional phase measurements is analyzed.