# Low-Frequency Communication Based on Rydberg-Atom Receiver
## 4 Results and Discussion
Therefore, it is essential to analyze the demodulated signal waveforms and SNR variations under different emission voltages to ensure reliable data transmission and reception. Figure 5 illustrates the waveforms of the demodulated PRBS signal received by the Rydberg atom under three modulation modes at emission voltages of 8 V, 4 V, and 1 V. At an emission voltage of 8 V, the demodulated signals for BPSK, OOK, and 2 FSK accurately reflected the characteristics of the original signals, indicating an adequate SNR for effective demodulation. When the emission voltage was reduced to 4 V, the demodulated signals for BPSK and OOK exhibited significant noise interference, while the 2 FSK signal demonstrated superior noise resistance. At an emission voltage of 1 V, demodulation of all signal types became infeasible, indicating that the noise level exceeded the threshold required for reliable signal recovery. In low-frequency communication, the application of nonlinear noise processing techniques is essential. Furthermore, the presence of nonlinear amplification circuits in low-frequency signal transmission systems requires modulation schemes with a constant envelope to mitigate the impact of nonlinearity on the signal. Additionally, due to the high-power output of the transmitter, it is critical to prevent high-voltage transient issues between the transmitter and the antenna, requiring the transmitted signal to exhibit continuous phase characteristics. Moreover, as the signal propagates through the marine channel, it undergoes significant distortion in both amplitude and phase. In this study, three modulation methods--OOK, BPSK, and 2 FSK--were evaluated. OOK does not maintain a constant signal envelope during transmission, and BPSK lacks continuous phase during transmission. Consequently, 2 FSK has become a widely used modulation technique in low-frequency communication  
Figure 4: Spectrum for different modulation modes. (**a**) the OOK signal bandwidth ranged from 98 kHz to 102 kHz (\(f_{c}\pm f_{b}\)); (**b**) the BPSK signal bandwidth ranged from 98 kHz to 102 kHz (\(f_{c}\pm f_{b}\)); (**c**) the 2 FSK signal bandwidth ranged from 88 kHz to 112 kHz (\(1/f_{2}-f_{1}\mid+2f_{b}\)). As shown in Figure 6, the SNR of the three received signals is compared as a function of the emission voltage. At relatively high emission voltages (6 to 10 V), the SNR of the three received signals remains stable, showing no significant variation as the emission voltage decreases. Furthermore, the SNR of the three received signals is nearly identical at the same emission voltage, maintaining a level of approximately 22 dB. As the emission voltage decreases below 6 V, the SNR of all three received signals exhibits a noticeable decline. However, at the same emission voltage, the SNR of 2 FSK consistently surpasses that of the other two methods, demonstrating its superiority in low-frequency communication. This enhanced noise resilience is attributed to the inherent properties of 2 FSK and the unique characteristics of Rydberg atom sensors. Unlike BPSK and OOK, which rely on phase or amplitude modulation, 2 FSK employs two distinct frequencies to represent binary states. This frequency diversity enables 2 FSK to spread the signal over a wider bandwidth, inherently reducing the impact of narrowband noise. Additionally, the separation of signal components in the frequency domain provides a natural form of error correction, as the receiver can more easily distinguish between the two frequencies, even in noisy environments. This mechanism is particularly effective at lower emission voltages, where the SNR is more critical. Rydberg atoms, with their large polarizabilities and transition dipole moments, exhibit high sensitivity to electric fields, enabling efficient detection of low-frequency signals. The use of two distinct frequencies in 2 FSK enables Rydberg atoms to better distinguish between signal states, even in noisy environments, thereby enhancing the system's overall noise resilience.