# Low-Frequency Communication Based on Rydberg-Atom Receiver
## 4 Results and Discussion  
In this study, three distinct modulation techniques were employed: 2 FSK, OOK, and BPSK. The typical waveforms of the three modulation techniques are illustrated in Figure 3a. In 2 FSK, two distinct frequencies are used to represent the binary states of a digital signal, typically denoted as '1' and '0'. The transition between these frequencies is instantaneous, and the frequency remains constant for the duration of each bit interval, thereby encoding the binary information in the frequency domain. OOK is characterized by the transmission of a continuous wave (CW) signal during the '1' state and the absence of the signal during the '0' state. This method is highly susceptible to noise and requires a relatively high SNR for reliable detection. In BPSK, two phases, typically separated by 180 degrees, are used to represent the two binary digits. The phase transition is binary, and the phase state remains constant throughout each bit interval, encoding the digital information in the phase domain. The pseudo-random binary sequence (PRBS) signal, as recommended by the International Telecommunication Union (ITU), was used for low-frequency communication tests. As shown in Figure 3b, PRBS signals are generated using a deterministic linear feedback shift register (LFSR) process, which emulates the properties of randomness. The generation of PRBS involves a sequence of binary states produced by feeding the output of the shift register back through a series of taps, which are predefined by a characteristic polynomial. This polynomial determines the length of the shift register and the period of the resulting sequence, ensuring high predictability and repeatability while maintaining statistical properties similar to random sequences. The generation polynomial used in this work is \(1+x^{6}+x^{7}\). The spectrum of the signal received by Rydberg atoms under the three modulation modes--2 FSK, OOK, and BPSK--was obtained to enable precise demodulation and cal  
Figure 3: (**a**) Waveforms of 2 FSK, OOK, and BPSK signals. In 2 FSK, the carrier signal’s frequency is modulated to represent two binary states, with distinct frequencies corresponding to ‘1’ and ‘0’. OOK is an amplitude modulation technique in which the presence of the carrier signal represents a binary ‘1’, and its absence represents a binary ‘0’. BPSK is characterized by phase modulation of the carrier signal to represent two distinct binary states, typically 0 and 1. (**b**) The generation process of the Pseudo-Random Binary Sequence (PRBS). The generation polynomial used in this work is \(1+x^{6}+x^{7}\), and the total number of bits in one period is 127.  
culation of communication parameters, such as the SNR and bit error rate (BER). A data rate (\(f_{b}\)) of 2 Kbps, a communication distance of 15 cm, and an emission voltage of 20 V were used in the test. The spectra are shown in Figure 4. In the experiment, the carrier frequency \(f_{c}\) of OOK and BPSK was 100 kHz, while the two-carrier frequency \(f_{1}\) and \(f_{2}\) of 2 FSK were 90 kHz and 110 kHz. From the spectrum it can be concluded that the OOK signal bandwidth ranged from 98 kHz to 102 kHz (\(f_{c}\pm f_{b}\)), the BPSK signal bandwidth ranged from 98 kHz to 102 kHz (\(f_{c}\pm f_{b}\)), and the 2 FSK signal bandwidth ranged from 88 kHz to 112 kHz (\(1/f_{2}-f_{1}\mid+2f_{b}\)). The analysis indicates that the bandwidth of the filters used in the demodulation process should be nearly identical for OOK and BPSK signals. Among the modulation schemes considered, 2 FSK exhibits the largest bandwidth occupancy at equivalent data rates due to its inherent frequency deviation properties, which require a broader frequency spectrum to distinguish between the two frequency components encoding binary information. In practical communication applications, reliable transmission and successful demodulation require the received signals to achieve a certain strength and maintain a high SNR.