Long-distance radio frequency (RF) synchronization through fiber link is attracting more attention in recent years. The repeater becomes increasingly important with the increase of the transmission distance. In this article, we analyze the three main relay methods principally including single-span, signal relay, and cascade connection frequency transmission and compare their frequency instability. The proof-of-concept experiments are also conducted along a 3009.8 km fiber link in the laboratory environment. The system used for comparison is a combination of phase conjugation and phase-locked loop (PLL) designed for long-distance frequency transmission. The best transfer preference can be obtained by using the cascade connection, whose frequency instabilities of $8.8 \times {10^{ - 14}}$ @ 1 s and $8.4 \times {10^{ - 17}}$ @ 10 000 s have been measured for phase-stable RF signal. Our study can be useful for the calibration and comparison of ultra-long-distance atomic clocks.

In this paper, we demonstrate ultrastable radio-frequency (RF) transfer over long-haul optical fiber link. Our stabilized RF transfer technique is based on high-performance dual phase locked loops (dual-PLL) configuration which improves signal to noise ratio (SNR) of the round trip transmitted signals. At the local site, the frequency conversion phase-lock receiver (FCPLR) accomplishes high-quality phase tracking of the RF signal which is transmitted after long distance optical fiber link. The low phase noise signal generated by FCPLR is passively mixed with a local reference signal to realize phase conjugation. Through advisable frequency design, there is no residual RF leakage and nonlinear effect of frequency mixing. Another PLL incorporating a high-quality cleanup oscillator is located at the remote site that favourably improves short-term instability of our transmission system. In our experiment, stabilized 2.4 GHz RF signal transfer over a 1007 km optical fiber link is demonstrated without any electric relay system, and the transmission system achieves a fractional frequency instability of ${8.20\times10^{-14}@1}$ s and ${7.87\times10^{-17}@10000}$ s

To meet the demand of flexible access for high-precision synchronization frequency, we demonstrate multi-node stable radio frequency (RF) dissemination over a long-distance optical fiber. Stable radio frequency signals can be extracted at any node along the optical fiber, not just at the endpoint. The differential mixing structure (DMS) is employed to avoid the frequency harmonic leakage and enhance the precision. The phase-locked loop (PLL) provides frequency reference for the DMS while improving the signal to noise ratio (SNR) of dissemination signal. We measure the frequency instability of multi-node stable frequency dissemination system (MFDS) at different locations along the 2,000 km optical fiber. The measured short-term instability with average time of 1 s are 1.90 × 10⁻¹⁴ @ 500 km, 2.81 × 10⁻¹⁴ @ 1,000 km, 3.46 × 10⁻¹⁴ @ 1,500 km, and 3.84 × 10⁻¹⁴ @ 2,000 km respectively. The long-term instability with average time of 10,000 s are basically the same at any position of the optical fiber, which is about (6.24 ± 0.05) × 10⁻¹⁷. The resulting instability is sufficient for the propagation of precision active hydrogen masers.

To resist the bias drift of the Mach–Zehnder modulator (MZM), we proposed and demonstrated a dither-free bias control method based on the bidirectional proportion integration differentiation (Bi-PID) algorithm. We theoretically analyzed the characteristics of time and frequency signals and made the bias point stable at the null point and quadrature point through optical power feedback and harmonic component feedback, respectively. 726.6 km transmission experiments were conducted to measure the effectiveness of the proposed modulator bias control (MBC) method. The results demonstrated that the stability of the time-sync system with the proposed MBC was better than that of the traditional method in the long-term measurement, whose time deviation (TDEV) was 2.8×10 ^-12 @10 ⁴ s. The frequency stability characterized by Allan deviation (ADEV), reaching 3.1×10 ^-17 @10 ⁴ s, outperformed traditional methods as well.

A convolutional neural network combined with long short-term memory (CNN-LSTM) phase compensation method (PCM) is proposed and demonstrated, where CNN is employed to extract spatial features, and LSTM is used to capture temporal features and realize the long-term predictions of residual phase fluctuations. This is the first-time machine learning (ML) has been used to mitigate the effects of optical path asymmetry caused by temperature variations on radio frequency (RF) transmission systems. The performance is verified by experiments on a unidirectional two-way RF transmission system, in which both the two 259-km-long separate fibers are coupled into one optical cable. The results demonstrate the CNN-LSTM model presents better prediction performance than the other eight previously proposed ML models. When the prediction duration is 40,000 s and the ambient temperature variation range is 14.38 °C, the coefficient of determination (R Squared, R2) between the predicted value and the actual value is higher than 0.99. In addition, compared to the phase locked loop (PLL) PCM, the proposed CNN-LSTM PCM can reduce the root-mean-square (RMS) phase jitter of the received signal from 219 ps to 19.72 ps, and improve the frequency stability of the system at 10,000 s by 84.5%. Overall, the proposed CNN-LSTM PCM can effectively compensate for residual phase fluctuations generated by the optical path asymmetry, providing a potential option for achieving stable RF transmission in telecommunication networks.

In this Letter, we present a fiber-optic radio frequency (RF) transmission scheme based on phase modulation with an interferometric detection structure. A self-developed Michelson interferometer (MI) is used to demodulate the frequency signal via an electrically controlled optical shifter. The two complementary outputs from the interferometer are detected using a balanced detector, which suppresses the common-mode noise of the fiber link. The structure is tested in the laboratory using a frequency transfer system over a 560 km fiber link. Experimental results show that a stable 2.4 GHz frequency transmission with a fractional frequency instability of 3.9 × 10⁻¹⁴ at 1 s and 6.2 × 10⁻¹⁷ at 10,000 s is achieved. Compared with the frequency transmission system based on intensity modulation and direct detection, the frequency instability is improved from 7.3 × 10⁻¹⁴ to 3.9 × 10⁻¹⁴ at 1 s. We believe that the proposed method will be useful for the construction of time-frequency synchronous fiber networks.