Phase-Modulation-Based Stable Radio Frequency Transmission via 125 km Fiber Optic Link

This paper proposes a stable radio frequency (RF) transfer scheme based on phase modulation. The passive compensation method is used to compensate the phase variations. The use of only one mixer reduces the power consumption during the frequency mixing process. By utilizing a phase modulator, the issue of bias drifting, encountered in RF transmission systems with intensity modulation method, is eliminated. A single-mode fiber (SMF) serves as a dispersive medium for phase modulation-to-intensity modulation (PM-to-IM) conversion. Our passive compensation system with phase modulation has the characteristics of robustness and low insertion loss at the modulation module. The RF signal with frequency of 2.4 GHz is transferred via a 125 km fiber optic link. The measured standard Allan deviation (ADEV) of our transmission system is 3.66 × <inline-formula><tex-math notation="LaTeX">$10^{-13}$</tex-math></inline-formula> at 1 s and 2.26 × <inline-formula><tex-math notation="LaTeX">$10^{-16}$</tex-math></inline-formula> at 10000 s, which is better than that of the reference atomic clock. The proposed system will be useful for further applications such as in square kilometer arrays and remote clock comparison.

to the advantages of good magnetic shielding ability, an optical fiber is considered a potential transmission medium for RF transmission. Under actual conditions, changes of surrounding environment will deteriorate the instability of a transferred signal. Hence, phase noise correction is necessary to improve the signal transmission stability. Up to now, several research groups have proposed solutions for a stable RF transfer over fiber. These solutions are based on round-trip transmission of the signal and obtaining the phase variations. In one of the group of methods, the optical (electrical) delay line, phase shifter, or voltage-controlled oscillator (VCO) are actively adjusted [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]. Typically, the tunable ranges of the mentioned compensation components are limited. The compensation bandwidth of the feedback loop is limited to frequencies less than the inverse optical-propagation round-trip time of the fiber optic link [27]. Compared to the active compensation method, a passive compensation method has been proposed and demonstrated [28], [29], [30], [31], [32], [33]. There are no tunable devices in this scheme, and it has limitless compensation range and high compensation speed. Consequently, the passive compensation system has shown its superiority compared to the actively compensation method.
However, there is a critical issue in the RF signal transfer system which is the modulation process. Most of these systems adopt intensity modulation method. Meantime, a timedependent DC bias control signal is indispensable to control phase shift of the transmitted optical signal [34]. This results in the RF signal transmission system complex and expensive. Moreover, it would introduce the issue of bias drifting. We intend to pave the way for economical and robust solutions for stable RF transfer.
Herein, we propose a stable RF transfer scheme by using the passive compensation method. First, only one frequency mixer is adopted to accomplish phase conjugation. Second, the phase-modulation method is used, and the single-mode fiber (SMF) helps us to accomplish phase modulation-to-intensity modulation (PM-to-IM) conversion. Consequently, the issue of bias drifting during the modulation process is canceled. Compared with the intensity modulation method, the insertion loss during the modulation is lower. Finally, our system does not require any active feedback device, making it more robust. A verification experiment is conducted over a 125 km fiber optic link. The standard Allan deviation (ADEV) of our transmission system is 3.66 × 10 −13 at 1 s and 2.26 × 10 −16 at 10000 s. This is superior to the frequency instability of the referenced atomic clock, which is 1.2 × 10 −11 at 1 s and 2.7 × 10 −13 at 10000 s. Thus, our system is capable of transferring a reference signal with minimal stability degradation [35].
II. PRINCIPLE Fig. 1 illustrates the RF transmission system, which is based on electro-optic phase modulation. At the local site (LS), two signal generators are referenced to a cesium clock. Signal V 1 can be expressed as: The signal V 1 is phase modulated onto the optical signal and transferred to the remote site (RS) via SMF. To recover the RF signal, the PM-to-IM conversion is realized by using the dispersive fiber. After transmission via the fiber link, the signal detected by the photo detector (PD) can be written as: where ϕ f iber is the phase changes caused by the fiber optic link. Subsequently, signal V 2 is phase modulated on the optical signal and transferred to LS. At the LS, we obtain the signal V 3 , expressed as: The signal V 3 goes through a divide-by-2 component, and the 1.2 GHz signal is filtered out, At the LS, the output of the other RF signal generator (RF 2) is where ξ is a constant phase difference. After mixing with V 5 , signal V 4 is frequency up converted into 2.4 GHz: The signal V 6 is phase conjugated with V 2 in terms of the phase fluctuation caused by the fiber link. After transmitting via the same fiber link, the phase fluctuation is canceled. This is under the well known assumption that the signal experiences the same phase change in bidirectional fiber optic links [32]. At the RS, the detected signal V 7 becomes Consequently, the outputted 2.4 GHz signal V 7 at the RS is phase coherent with the target signal V 1 . A reference signal transmission is accomplished using our passive phase compensation method, which is based on phase modulation.

III. RESULTS OF THE PM-TO-IM SYSTEM
As mentioned previously, the signal recovery technique presented in this paper is accomplished by PM-to-IM conversion in a dispersive fiber (SMF). As for the optical fiber used in our experiment, the typical value of the dispersion parameter is 17 ps/(nm · km). In this section, we discuss and provide experimental verification of the signal power response in our RF transfer system. Under the condition of a low signal modulation, the first-order harmonic of the optical signal after detected is as follows: where m is the modulation index, ω RF is the angular frequency of the phase modulated signal, and β 2 and L is the secondorder dispersion coefficient and length of the fiber optic link, respectively. (8) is a well-known formula used to calculate the frequency response of a phase-modulation-based frequency transfer system with a dispersive fiber optic link under the linear modulation assumption [36]. Thus, the power of the detected RF signal will have the following proportional relationship:  where D is the dispersion coefficient of the optical fiber, λ 0 is the center wavelength of the optical signal, and c is speed of light in vacuum. We employ a vector network analyzer (VNA) to test the normalized power response (NPR) in a 19.4 km SMF as a function of the modulation frequency. There is no amplification equipment in the system. The uncertainty that affects the test results is reduced as much as possible. Fig. 2(a) shows the experimental principle. The electro-optic phase modulator utilized in this experiment is manufactured by EOSPACE, and the PD model is Optilab LR-30-M. The output frequency of the VNA (Agilent 8722ES) is set to vary from 50 MHz to 25 GHz. The wavelength of the optical signal is 1550.00 nm. Fig.  2(b) shows the experimental result and theoretical calculation results when using three different wavelengths in our system (1549.32 nm, 1550.12 nm and 1550.92 nm). It can be seen that the theoretical curves of the three different wavelengths almost overlap. The maximal difference is 0.02 dB@6.1 GHz, which could be marked after the graph is zoomed in. Though  Fig. 2(b) is representative for our PM-to-IM system when the wavelength spacing is 0.8 nm. The RF frequency of the peak point of the NPR is 14.7 GHz. (9) is used to calculate the NPR in a 125 km SMF for a 2.4 GHz modulation RF frequency. It corresponds to the NPR of the 6.1 GHz modulation frequency in the transmission system with a 19.4 km SMF. As shown in Fig. 2(b), the NPR of the 6.1 GHz modulation frequency is −30.6 dB. In our 2.4 GHz signal transmission system, the power of electrical signal injected into phase modulator is 10 dBm. The electric signal after photo detector is amplified and the power is increased to 11 dBm, which is sufficient for re-modulation (V 2 ) or input power of the divide-by-2 device (V 3 ). Consequently, the power response is sufficient for our stable 2.4 GHz signal transmission system.

IV. EXPERIMENTAL SETUP AND RF TRANSFER RESULTS
In the experiment, the 10 MHz signals generated by a cesium clock (OSA 3235B) are injected into the reference signal interfaces of two signal generators (Agilent E8257D, ROHDE & SCHWARZ SMBV100 A). In our experiment, the two different signal generators synchronized to the clock inevitably introduce some phase errors. It could be improved by utilizing phaselocked dielectric oscillators with high consistency of phase with the clock. The length of the ITU G.652 fiber optic link is 125 km and the loss is 26 dB. DWDM is utilized to couple optical signals with different wavelengths, and the effect of backscattering is efficiently suppressed. The optical wavelengths used in our system are 1550.92 nm, 1550.12 nm and 1549.32 nm. In our experiment, the power of each optical signal injected into the fiber link is appropriately tuned to be 0 dBm. The RF power at each modulator is 10 dBm. The optical power injected into PD is tuned to be about −1 dBm, which is the output of EDFA. In our experiment, a signal analyzer (ROHDE & SCHWARZ, FSV30) is used to measure signal-to-noise ratio(SNR) of the transmitted signal [37]. The SNR of 2.4 GHz signal is 54 dB (@RBW 3 MHz) after transmitted along the 125 km fiber link. And the SNR of the 2.4 GHz RF signal is 65 dB(@RBW 3 MHz) before transmission. The residual stability of the proposed RF transmission system is tested by comparing the phase of signal V 7 with signal V 1 . The root-mean-square phase jitter of the stable 2.4 GHz signal at the RS is 0.005 rd. Fig. 3 shows the ADEV of the atomic clock (1.2 × 10 −11 at 1 s and 2.7 × 10 −13 at 10000 s) provided by the vendor. The standard ADEV of the free running one-way signal is 3.40 × 10 −10 at 1 s and 1.38 × 10 −11 at 10000 s. After compensated, it reaches 3.66 × 10 −13 at 1 s and 2.26 × 10 −16 at 10000 s.
The ADEV characterizes the time domain stability of the signal, as presented in our previous conference paper [38]. In this paper, the frequency domain properties are supplemented. The phase noise power spectral density(PSD) can be obtained by utilizing the Fourier transform of phase fluctuation data. Fig. 4 shows the phase noise PSD of the free running 2.4 GHz signal and the 125 km compensated fiber optic link, where the original signal sampling rate is 1 Hz. The fiber noise is rejected by ∼7 orders of magnitude near the 0.5 Hz Fourier frequency for the compensated link which is compared to the free running signal.
The noise suppression near the low Fourier frequency area (f ≤ 10 −3 Hz) is ∼3 orders of magnitude.
We add Table I to show the results of a comparison of the technical indicators related to our experiment with typical technical indicators of the current frequency transmission over fiber. Clearly, our experimental result is comparable with those obtained by other research groups. Although the transfer stability is not as high as the existing results, our technique has certain advantages over other stable RF transfer techniques. Our technique aims at stable RF signal transmission with high robustness. Only one mixer is adopted in our system, thus reducing power consumption. In this regard, the system is simplified compared to those using several mixers. What's more, the PM modulator often generates multiple sidebands, which would introduce some intensity noises during the detection process and affect the SNR of the target RF signal. It would further deteriorate the frequency transfer stability. As the SNR of the phase modulated signal is comparable with the intensity modulated signal in our previous work [37], this impact becomes tolerable. More in-depth study about this issue will be carried out, such as analyzing the influence of multiple sidebands by using optical spectrum analyzer.

V. CONCLUSION
In this paper, more detailed experimental results and analysis are provided compared to our previous work [38]. In a word, we experimentally demonstrate stable 2.4 GHz signal transmission via a 125 km fiber optic link. The phase changes due to the fiber optic link could be effectively reduced using the passive phase noise compensation method. For the first time, we implement phase modulation instead of intensity modulation. When the frequency of the RF signal and the transmission distance are proper to obtain enough signal power for next device, our stable RF transfer system could work well. Under this circumstance, the advantage of the proposed scheme is robustness, because there is no active feedback device in our system. As the bias control technique is mature in intensity modulation system, the phase modulation would probably become less competitive than the intensity modulation method when the experimental parameters doesn't suitable. The measured frequency stability of the compensation system is 3.66 × 10 −13 at 1 s and 2.26 × 10 −16 at 10000 s. In practical applications of the RF transfer system, the issue of complexity and robustness should also be taken into account. The experimental solution in this paper can be applied to the synchronization of reference signals in the metropolitan fiber optic networks and it could provide stable signals for the end users in noisy optical networks.