Cascaded Microwave Frequency Transfer Over 300-Km Fiber Link with Instability at the 10−18 Level

remote sensing

Article Cascaded Microwave Frequency Transfer over 300-km Fiber Link with Instability at the 10−18 Level

Wenxiang Xue 1,2, Wenyu Zhao 1,2,*, Honglei Quan 1,2,3, Yan Xing 1,2 and Shougang Zhang 1,2

1 National Time Service Center, Chinese Academy of Sciences, Xi’an 710600, China; xuewenxiang@ntsc.ac.cn (W.X.); [email protected] (H.Q.); [email protected] (Y.X.); [email protected] (S.Z.) 2 Key Laboratory of Time and Frequency Primary Standards, Chinese Academy of Sciences, Xi’an 710600, China 3 School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China * Correspondence: [email protected]; Tel.: +86-029-838-905-64

Abstract: Comparing and synchronizing atomic clocks between distant laboratories with ultra- stable frequency transfer are essential procedures in many fields of fundamental and applied science. Existing conventional methods for frequency transfer based on satellite links, however, are insufficient for the requirements of many applications. In order to achieve high-precision microwave frequency transfer over a thousand kilometers of fiber and to construct a fiber-based microwave transfer network, we propose a cascaded system for microwave frequency transfer consisting of three 100-km single-span spooled fiber links using an improved electronic phase compensation scheme. The × −14 × −18 transfer instability measured for the microwave signal reaches 1.1 10 at 1 s and 6.8 10 at 105 s, which agrees with the root-sum-square of each span contribution. It is feasible to extend the length of the fiber-based microwave frequency transfer up to 1200 km using 4 stages of our cascaded Citation: Xue, W.; Zhao, W.; Quan, H.; Xing, Y.; Zhang, S. Cascaded system, which is still sufficient to transfer modern cold atom microwave frequency standards. −15 −18 5 Microwave Frequency Transfer over Moreover, the transfer instability of 9.0 × 10 at 1 s and 9.0 × 10 at 10 s for a 100-MHz signal 300-km Fiber Link with Instability at is achieved. The residual phase noise power spectral density of the 300-km cascaded link measured the 10−18 Level. Remote Sens. 2021, 13, at 100-MHz is also obtained. The rejection frequency bandwidth of the cascaded link is limited by 2182. https://doi.org/10.3390/ the propagation delay of one single-span link. rs13112182 Keywords: fiber link; frequency transfer; cascaded system; transfer instability Academic Editor: Hugo Carreno-Luengo

Received: 12 April 2021 1. Introduction Accepted: 25 May 2021 Published: 3 June 2021 Long-haul and high-precision frequency transfer between distant laboratories plays a crucial role in numerous ﬁelds of fundamental and applied science, such as time and

Publisher’s Note: MDPI stays neutral frequency metrology [1,2], fundamental physics [3,4], and geodesy [5]. The synchronization with regard to jurisdictional claims in of distributed systems (such as phased-array radio telescopes [6–8], very long baseline published maps and institutional affil- interferometry (VLBI) [9,10], and multistatic radar systems [11,12]) are also applications. iations. At present, remote frequency comparison and synchronization is usually performed based on satellite links, including two-way satellite time and frequency transfer (TWSTT) as well as global positioning system (GPS) carrier-phase observations. However, owing to the non-reciprocity of links, these methods are limited by an instability of 10−15 after one day and do not provide the short-term stability necessary for synchronization applications [13]. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. Consequently, frequency transfer over satellite links is insufficient for many application This article is an open access article requirements. Fortunately, taking advantage of the low loss, high reliability and active distributed under the terms and phase stabilization potential of optical fiber, high stability has been demonstrated for conditions of the Creative Commons direct optical frequency transfer [14–17] and radio-frequency (RF) transmission using the Attribution (CC BY) license (https:// intensity modulation of an optical carrier [18–25] over fiber links. The instability of fiber- −20 4 creativecommons.org/licenses/by/ based optical frequency transfer reached the 10 level at 10 s over an urban fiber of more 4.0/). than 100 km [16,17], while microwave frequency transfer has presented an instability of

Remote Sens. 2021, 13, 2182. https://doi.org/10.3390/rs13112182 https://www.mdpi.com/journal/remotesensing Remote Sens. 2021, 13, 2182 2 of 13

10−19 level at one day over an urban fiber of about 80 km [19,20]. In addition, simultaneous dissemination of time (1 PPS) and frequency (10/100 MHz) signals generated by atomic clocks over fiber have also demonstrated fairly low residual instability [26,27]. There are two main limitations to the achievable length of distance extension of fiber- based frequency transfer. In the first place, the bandwidth fc of the link noise compensation is limited by the propagation delay τ of the fiber [28,29], which is simplified as fc < 1/4τ. In the second place, frequency transfer instability is dominated by the signal-to-noise ratio (SNR) of the output-detected signal, which is limited by the attenuation of the fiber link. In particular, in the case of microwave frequency transmission using the intensity modulation of an optical carrier, the power of the microwave signal detected at the end of the fiber link is attenuated by twice of link attenuation (expressed in dB) [30], and the performance of link noise compensation is degraded by the chromatic dispersion and polarization mode dispersion (PMD) effect of fiber [19,31]. Therefore, compared with the single-span transfer, the cascaded transfer with independent link noise compensation for each short segment is more suitable for ultra-long-distance fiber-based microwave frequency transfer. The earliest reported study of cascaded microwave frequency transfer has demonstrated an instability of 6 × 10−14 at 1 s and 5 × 10−17 at one-half day over 204-km urban fiber link consisting of two single-span links [32]. In 2016, a 1-GHz signal was transferred through 430 km of urban fiber link with an instability of 1.94 × 10−13 at 1 s and 1.34 × 10−16 at 104 s using a cascaded system consisting of two single-span links, which is a record distance of fiber-based microwave frequency transfer [33]. The National Time Service Center (NTSC) of the Chinese Academy of Sciences (CAS) undertakes the task to generate, maintain, and transmit the national standard of time (Bei- jing Time), which has already demonstrated an ultra-stable microwave frequency transfer over a 112-km urban fiber link with an instability of 4.2 × 10−15 at 1 s and 1.6 × 10−18 at one day [25]. In this work, to achieve microwave frequency transfer with high precision over a thousand kilometers of fiber and construct fiber-based microwave transfer network, we first used fiber spools to perform a microwave frequency transfer experiment with a cascaded system. Subsequently, we investigated the ultra-stable microwave frequency transfer over a 300-km fiber link with the cascaded system, which is composed of three single-span links. The frequency transfer instability of each span, as well as of the cascaded link, is investigated. The 300-km cascaded link reached an instability of 1.1 × 10−14 at 1 s and 6.8 × 10−18 at 105 s. The residual phase noise of the entire link was also measured. The bandwidth of the link noise compensation was unaffected by the length of the entire link.

2. Materials and Methods 2.1. Principle of Frequency Transfer System In fiber-based microwave frequency transfer, two approaches of phase compensation exist: optical path compensation (OPC) and electronic phase compensation (EPC) [34]. Although the OPC approach can achieve better transfer instability, the compensation actuator, which consists of a piezo-electric fiber stretcher and thermally-controlled fiber spool [31,35], is complex and has small dynamic range, which is inconvenient for extensive applications. On the contrary, the EPC approach has strong adaptability and little PMD fluctuation effect due to the voltage-controlled oscillator (VCO) used as an actuator [25], except that the performance is slightly poorer than that of the OPC approach. Therefore, in order to broaden the application range of the fiber-based microwave frequency transfer system, we adopted the EPC scheme. For fiber-based frequency transfer, the phase noise induced by the fiber link was measured by comparing the round-trip signal with the reference signal and compensating it in real time. In a typical implementation of microwave transfer over fiber based on the EPC approach, the forward and backward signals have the same frequency, which leads to the transfer instability being limited by Brillouin backscattering and parasitic reflections along the link, especially for long-distance fiber with more connectors and splices. For this reason, to suppress the influence of the backscattering and parasitic reflections, an Remote Sens. 2021, 13, x 3 of 14

ing it in real time. In a typical implementation of microwave transfer over fiber based on Remote Sens. 2021, 13, 2182the EPC approach, the forward and backward signals have the same frequency, which 3 of 13 leads to the transfer instability being limited by Brillouin backscattering and parasitic reflections along the link, especially for long-distance fiber with more connectors and splices. For this reason, to suppress the influence of the backscattering and parasitic reflections, animproved improved frequency frequency transfer transfer system system based based on on the the EPC EPC approach approach was was designed de- with two signed with differenttwo different microwave microwave frequencies frequenc fories the for forward the forward and backward and backward signals. signals. The schematic of The schematicthe of ﬁber-based the fiber-based frequency frequency transfer transfer system system is shown is shown in Figure in Figure1. 1.

Figure 1. SchematicFigure diagram 1. Schematic of fiber-based diagram transferof fiber-based system transfer principle. system VCO: principle. voltage-controlled VCO: voltage-controlled oscillator; PD: photodiode. oscillator; PD: photodiode. As shown in Figure1, the reference signal Vr can be expressed as: As shown in Figure 1, the reference signal can be expressed as: Vr ∝ sin(ωrt + ϕr) (1) ∝sin(+) (1) where ωr and ϕr stand for the angular frequency and the initial phase of the reference signal, where and stand for the angular frequency and the initial phase of the reference respectively. The frequency signal V is generated by a VCO, which can be expressed as: signal, respectively. The frequency signal is0 generated by a VCO, which can be expressed as: V0 ∝ sin(ω0t + ϕ0) (2) ∝sin(+) (2) where ω0 and ϕ0 represent the angular frequency and the initial phase of V0, respectively. where andNote that represent Equations the (1) angular and (2) frequency are derived and without the initial considering phase theof random, respec- phase noise of tively. Note thethat frequency Equations signal. (1) and (2) are derived without considering the random phase noise of the frequency signal. V0 modulates the intensity of the laser carrier and transmits it along the fiber link to the modulatesreceiving the (RX) intensity end. Atof the the laser RX end, carrier the and one-way transmits trip signal it along detected the fiber by link a fast to photodiode the receiving(PD2) (RX) canend. be At expressed the RX end, as: the one-way trip signal detected by a fast photodiode (PD2) can be expressed as: h i V ∝ sin ω t − τ + ϕ (3) ∝sinRX − +0 f 0 (3) where representswhere τf represents the forward the forwardpropagation propagation delay delayof the of fiber. the fiber. V RXis is frequen- frequency-divided cy-divided byby 4 4 with a low-noiselow-noise frequencyfrequency divider divider to to modulate modulate the the intensity intensity of theof the second sec- laser carrier ond laser carrierthat isthat used is toused generate to generate the backward the backward signal. signal. At the transmittingAt the transmitting (TX) end, (TX) the backward end, the backwardsignal is signal detected is detected by the second by the photodiodesecond photodiode (PD1), which (PD1), can which be expressed can be ex- as: pressed as: h i Vback ∝ sin ω0 t − τf − τb /4 + ϕ0/4 , (4) ∝sin − −4⁄ +⁄4, (4)

where representswhere τb therepresents backward the propagation backward propagation delay of the delayfiber, ofand the fiber, carries and V theback carries the round-trip phaseround-trip fluctuations phase fluctuationsaccumulated accumulated along the fiber. along the fiber. In the phaseIn comparison the phase comparison system, the system, reference the reference signal signal is power-splitVr is power-split into two into two arms. arms. In the Infirst the arm, first arm, is mixedVr is mixedwith with by aV 0double-balancedby a double-balanced mixer (DBM) mixer (DBM)to gener- to generate a ate a frequencyfrequency difference difference between between andV 0and. TheVr latter. The lattersignal signal is frequency-divided is frequency-divided by 4 by 4 with a with a low-noiselow-noise frequency frequency divider divider to generate to generate a signal a signal that can that be can expressed be expressed as: as: ∝sin( − )⁄ 4 +( − )4⁄ . (5) V1 ∝ sin [(ω0 − ωr)t/4+ (ϕ0 − ϕr)/4]. (5)

In the second arm, is mixed with by a DBM to generate a frequency difference In the second arm, Vr is mixed with Vback by a DBM to generate a frequency difference between and , which can be expressed as: between Vr and Vback, which can be expressed as: h i V2 ∝ sin (4ωr − ω0)t/4 + 4ϕr − ϕ0 + ω0τf + ω0τb /4 . (6)

Remote Sens. 2021, 13, 2182 4 of 13

V1 is phase-compared with V2 using a saturated DBM to produce an error signal including the noise of link and VCO, which can be expressed as: h i Ve ∝ sin (2ω0 − 5ωr)t/4 + 2ϕ0 − 5ϕr − ω0τf − ω0τb /4 . (7)

The error signal is processed in a loop ﬁlter F(p) and used to feedback the VCO. Thus, it can be inferred that ( ω0 = 5ωr/2 . (8) ω0 τf + τb = 2ϕ0 − 5ϕr

As a result, the frequency signal VRX at the RX end becomes: τf − τb V ∝ sin 5ω t − /2 + 5ϕ /2 . (9) RX r 2 r

We assume that the ﬁber link is reciprocal, that is τf = τb = τ. Thus, Equation (9) is reformulated as: VRX ∝ sin(5ωrt/2 + 5ϕr/2), (10)

which becomes coherent with the reference signal Vr, and the phase ﬂuctuations due to the ﬁber link are canceled. According to Equations (2) and (8), and the reciprocity assumption of the link, the frequency signal V0 becomes:

V0 ∝ sin[5ωr(t + τ)/2 + 5ϕr/2]. (11)

By comparing the phase of VRX to Vr and VRX to V0 in closed loop, the frequency transfer performance of compensation link and free link can be measured. According to the above analysis, the link noise can be compensated with the scheme shown in Figure1, as long as the frequency of the transmitted signal V0 is roughly 2.5 times that of the reference signal Vr. In the practical implementation of cascade transfer system over urban ﬁber links, it is preferred to use different frequencies of the transmitted signal for adjacent single-span links to suppress the inﬂuence of microwave leakage. In view of this, we designed two kinds of frequency transfer systems in different frequencies, in which the frequencies of reference signal and transmission signal were 4 GHz and 10 GHz, respectively (we called it 10-GHz transfer system), and the other frequencies were 3.6 GHz and 9 GHz, respectively (we called it 9-GHz transfer system).

2.2. Experimental Setup 2.2.1. 10-GHz and 9-GHz Transfer Systems Figure2 shows the detailed scheme of the 10-GHz transfer system over a 100-km fiber spool. The 4-GHz reference signal Vr was generated by a phase-locked dielectric resonant oscillator (PDRO), which was phase-locked on the 100-MHz signal generated by a passive Hydrogen maser (PHM) (Vremya-Ch, Nizhny Novgorod, Russia, VCH-1008). The transmission signal at 10-GHz was provided by a different PDRO phase-locked to a low-noise 100-MHz oven-controlled crystal oscillator (OCXO), which was modulated to the laser intensity by a Mach–Zehnder modulator (MZM) and transmitted to the RX end over the fiber link. The 10-GHz PDRO and 100-MHz OCXO were contained in an OSC-10GHz module, which is equivalent to the VCO in Figure1. At the RX end, the incoming 10-GHz signal was detected by a fast photodiode PD2 amplified by a low-noise amplifier (LNA) (Analog Devices, Wilmington, USA, HMC903LP3E), and frequency-divided by 4 with a low-noise frequency divider (Analog Devices, Wilmington, USA, HMC365) to generate a 2.5-GHz signal. The 2.5-GHz signal modulated the intensity of the second laser by MZM to transmit a backward signal to the TX end through the same fiber. The backward signal was detected by another fast photodiode PD1. The output signal Vback of PD1 was amplified by LNA (Qorvo, Greensboro, USA, TQP3M9008) and sent to a phase comparison system. By comparing the phases of Vr, V0, and Vback (see Figure1), the phase comparison system Remote Sens. 2021, 13, x 5 of 14 Remote Sens. 2021, 13, 2182 5 of 13

sent to a phase comparison system. By comparing the phases of , , and (see Figuregenerated 1), anthe errorphase signal, comparison which was system fed togenerated an active an loop error ﬁlter signal, to provide which a was control fed signal. to an Theactive ﬁber loop link filter noise to willprovide be compensated a control signal. by adjusting The fiber the link frequency noise will of thebe compensated 100-MHz OCXO by adjustingin the OSC-10GHz the frequency module. of Thethe loop100-MHz bandwidth OCXO of in the the compensation OSC-10GHz system module. was The less thanloop bandwidth500 Hz. of the compensation system was less than 500 Hz.

Figure 2. Schematic of the 10-GHz transfer transfer system system ov overer a a 100-km 100-km fiber fiber spool. spool. PDRO: PDRO: phase-locked phase-locked dielectric resonant resonant oscillator; oscillator; MZM: MZM: Mach–Zehnd Mach–Zehnderer modulator; modulator; DCF: DCF: dispersion-compensating dispersion-compensating fiber; Bi-EDFA: bidirectional erbium-doped fiber amplifier; LNA: low noise amplifier; OSC-10GHz: fiber; Bi-EDFA: bidirectional erbium-doped fiber amplifier; LNA: low noise amplifier; OSC-10GHz: containing a 100-MHz OCXO and a 10-GHz PDRO; BPF: band pass filter. containing a 100-MHz OCXO and a 10-GHz PDRO; BPF: band pass filter.

The 9-GHz9-GHz distributiondistribution system system is highlyis highly similar similar to the to10-GHz the 10-GHz system, system, where where the 4-GHz the 4-GHzand 10-GHz and 10-GHz components components need to be need replaced to be byreplaced 3.6-GHz by and 3.6-GHz 9-GHz and components, 9-GHz components, respectively. respectively.In the transfer system, each laser was a continuous wave tunable digital supermode distributedIn the transfer Braggreflector system, each (DS-DBR) laser was laser a tocontinuous be used inwave the tunable C-band digital window supermode covering distributedthe 1528-nm Bragg to 1563-nm reflector range. (DS-DBR) The wavelength laser to be used can bein the controlled C-band bywindow a 50-GHz covering (0.4-nm) the 1528-nmInternational to 1563-nm Telecommunications range. The wavelength Union (ITU) can wavelength be controlled grid. by In a order 50-GHz to overcome (0.4-nm) theIn- ternationalinfluence of Telecommunications coherent Rayleigh backscatter Union (ITU) noise, wavelength 0.4-nm differencegrid. In order was to set overcome between thethe wavelengthinfluence of ofcoherent the laser Rayleigh at the TX backscatter end and the no laserise, 0.4-nm at the RXdifference end, which was were set between 1550.92 nmthe wavelengthand 1550.52 of nm, the respectively. laser at the TX In end addition, and the to laser reduce at the the RX effect end, caused which bywere the 1550.92 chromatic nm anddispersion 1550.52 (~17 nm, ps/nm/km) respectively. of In fiber addition, on the frequencyto reduce transfer,the effect a dispersion-compensatingcaused by the chromatic dispersionfiber (DCF) (~17 module ps/nm/km) with a of loss fiber of abouton the 10frequency dB was transfer, inserted a at dispersion-compensating the TX end. Behind the fiberDCF, (DCF) a bidirectional module erbium-dopedwith a loss of about fiber amplifier10 dB was (Bi-EDFA) inserted withat the a TX gain end. of about Behind 10 the dB wasDCF, used a bidirectional to compensate erbium-doped the optical fiber loss amplifier caused by (Bi-EDFA) the DCF and with to a improvegain of about the SNR 10 dB at wasdetection. used to As compensate demonstrated the previouslyoptical loss [ 25ca],used the PMDby the effect DCF hasand a to slight improve influence the SNR on the at detection.fiber-based As microwave demonstrated frequency previously transfer [25], using the PMD the EPC effect approach. has a slight Therefore, influence there on was the fiber-basedno use of polarization microwave scramblers frequency totransfer average using out thethe PMDEPC approach. effect. Therefore, there was no use of polarization scramblers to average out the PMD effect. 2.2.2. Cascaded Microwave Frequency Transfer 2.2.2.A Cascaded cascaded Microwave system of microwave Frequency transferTransfer was established by connecting three single- spanA systems cascaded with system two frequencyof microwave converters. transfer The was cascaded established link by was connecting composed three of three sin- 100-kmgle-span fibersystems spools. with The two whole frequency system converters. was placed The within cascaded the link same was laboratory. composed The of ◦ threelaboratory 100-km temperature fiber spools. was The about whole 25 system± 1 C was and placed the period within of temperaturethe same laboratory. fluctuations The laboratorycaused by air-conditioningtemperature was wasabout about 25 ±40 1 °C min. and The the first period single-span of temperature link was fluctuations a 10-GHz causedtransfer by system, air-conditioning and the second was about and third 40 mi single-spann. The first linkssingle-s werepan both link 9-GHzwas a transfer10-GHz transfersystems. system, In the second and the span, second the DCF and and third Bi-EDFA single-span were notlinks used. were The both schematic 9-GHz diagramtransfer systems.of the constructed In the second cascaded span, transfer the DCF system and Bi-EDFA is depicted were in Figurenot used.3. In The order schematic to output dia- a 100-MHzgram of the signal constructed at the end cascaded of the cascaded transfer system, system a low-noiseis depicted 100-MHz in Figure OCXO 3. In was order phase- to locked to the received 9-GHz signal at the RX end of the third span via a 9-GHz PDRO.

Remote Sens. 2021, 13, x 6 of 14

output a 100-MHz signal at the end of the cascaded system, a low-noise 100-MHz OCXO was phase-locked to the received 9-GHz signal at the RX end of the third span via a 9-GHz PDRO. In order to evaluate the frequency transfer performance of cascaded systems, the frequency instability of cascaded link was measured by directly comparing the 100-MHz output signal from the cascaded system to the 100-MHz signal from the PHM with a phase noise and Allan deviation test set (PN & ADEV TS, Symmetricom 5125A). In ad- Remote Sens. 2021, 13, 2182 dition, the phase difference between the 9-GHz output signal from the cascaded system6 of 13 and the 4-GHz reference signal was measured by a home-made phase difference measurement system.

FigureFigure 3.3.Schematic Schematic ofof thethe cascadedcascaded transfertransfer system.system. E/O:E/O: electricalelectrical to optical; O/E: optical optical to to electrical. electrical.

2.2.3.In Frequency order to Conversion evaluate the for frequency the Cascaded transfer System performance of cascaded systems, the frequency instability of cascaded link was measured by directly comparing the 100-MHz The frequency of output signal in the first span was 10 GHz, while the frequency of output signal from the cascaded system to the 100-MHz signal from the PHM with a phase reference signal in the second span was 3.6 GHz. Therefore, we needed to use a frequency noise and Allan deviation test set (PN & ADEV TS, Symmetricom 5125A). In addition, the conversion module (FC1) to convert the 10-GHz signal to a 3.6-GHz one. Similarly, be- phase difference between the 9-GHz output signal from the cascaded system and the 4-GHz tween the second span and the third span, a frequency conversion module (FC2) was also reference signal was measured by a home-made phase difference measurement system. needed to convert the 9-GHz signal to a 3.6-GHz one. Figure 4 shows the simplified schematic2.2.3. Frequency of the frequency Conversion conversion. for the Cascaded The frequency System conversion design was inspired by the harmonic of low-noise frequency divider. The schematic diagram of FC1 is shown in The frequency of output signal in the first span was 10 GHz, while the frequency of Figure 4a. The input 10-GHz signal was frequency-divided by 10 with a low noise fre- reference signal in the second span was 3.6 GHz. Therefore, we needed to use a frequency quency divider (Analog Devices, Wilmington, USA, HMC361 & HMC438) while the 4th conversion module (FC1) to convert the 10-GHz signal to a 3.6-GHz one. Similarly, between (4 GHz) and 2nd (2 GHz) harmonics were extracted from the divided signal, respectively. the second span and the third span, a frequency conversion module (FC2) was also needed Theto convert 2-GHz the signal 9-GHz was signal frequency-divided to a 3.6-GHz one. to 400 Figure MHz4 showswith a thefrequency simplified divider schematic (Analog of Devices,the frequency Wilmington, conversion. USA, The HMC438) frequency and conversion sent into designthe intermediate was inspired frequency by the harmonic (IF) port of low-noisethe microwave frequency DBM divider. to be mixed The schematic with the diagram 4-GHz ofsignal FC1 isand shown to generate in Figure the4a. final The 3.6-GHzinput 10-GHz signal. signal Figure was 4b frequency-dividedshows the schematic by diagram 10 with aof lowthe noiseFC2 which frequency was used divider to convert(Analog the Devices, 9-GHz Wilmington, signal to a USA,3.6-GHz HMC361 one. The & HMC438) 9-GHz frequency while the 4thsignal (4 GHz)was frequen- and 2nd cy-divided(2 GHz) harmonics by 10 (Analog were extracted Devices, from Wilmington, the divided USA, signal, HMC361 respectively. & HMC438) The 2-GHz and the signal 4th washarmonic frequency-divided (3.6 GHz) was to selected, 400 MHz and with amplified a frequency to output divider a (Analogpower of Devices, about 7 Wilmington, dBm. USA,The HMC438) additional and sentnoise into of thethe intermediatefrequency conversion frequency (IF)module, port ofwhich the microwave is expressed DBM in termsto be mixedof overlapping with the 4-GHzAllan deviation, signal and was to generate measured the by final heterodyne 3.6-GHz signal.frequency Figure meas-4b urementshows the with schematic two identical diagram frequency of the FC2 conversion which was modules. used to convert It should the be 9-GHz noted signal that two to a identical3.6-GHz one.modules The 9-GHzwere used, frequency with signaleach connected was frequency-divided to a common by power 10 (Analog supply Devices, and a Remote Sens. 2021, 13, x 7 of 14 Wilmington,common input USA, signal. HMC361 & HMC438) and the 4th harmonic (3.6 GHz) was selected, and amplified to output a power of about 7 dBm.

(a) (b)

FigureFigure 4. 4. SimplifiedSimpliﬁed schematic schematic of of the the frequency frequency conversion conversion module. module. (a ()a )Schematic Schematic of of FC1; FC1; (b (b) )Schematic Schematic of of FC2. FC2.

2.3. PhaseThe Difference additional Measurement noise of the frequencySystem conversion module, which is expressed in terms of overlappingThe performance Allan deviation,of frequency was transfer measured is bynormally heterodyne evaluated frequency by the measurement comparison with of the phase of the reference signal and the received signal in the compensated link. In the fiber-based microwave transfer, it is impossible to directly measure the phase difference between microwave signals using commercial devices. Therefore, we designed a heterodyne system to measure the frequency transfer instability. Figure 5 presents the schematic diagram of the heterodyne phase measurement system. The received 10-GHz or 9-GHz signal was frequency-divided by 10 or 9, bandpass-filtered at 4 GHz to select a 4 GHz signal, and amplified with LNA. The output signal of LNA was mixed with the 4-GHz reference signal delivered via the 4-GHz PDRO in a DBM to produce a direct current (DC) voltage (). It should be noted that the DBM operated in a saturated mode, and thus the () became nearly independent of input signal level variations and was only proportional to the phase difference between two input signals. In addition, the input signals of DBM were in quadrature using a phase shifter (not shown in Figure 5), so that () was the most sensitive to the phase difference between two inputs of DBM and was approximately equal to 0. We measured () using a multimeter (Keysight, Santa Rosa, USA 3458A) with an effective measurement bandwidth of about 3 Hz. The relative normalized phase fluctuations (), also known as propagation delay fluctuations in the fiber link, is given by

() ≈1⁄ ⋅()⁄⁄2 ,() ≈0, (12)

where represents the peak-to-peak voltage of the () when the phase of the 4-GHz reference signal changes for 2. The time domain instability of the frequency transfer, expressed in terms of overlapping Allan deviation, is concerned with characterizing the ().

Figure 5. Schematic of heterodyne phase measurement system.

3. Results 3.1. The Single-Span Link The performance of each single-span link was evaluated by a home-made measurement system prior to the cascaded frequency transfer. The transfer instability of each compensated single-span link in terms of overlapping Allan deviation was calculated from the propagation delay fluctuations of fiber, as shown in Figure 6a. These results are compared with previous results over a 112-km urban fiber with a controlled temperature of electronics package (violet trace) [25]. Figure 6a also shows the instability of the 100-km free-running spooled fiber link (black trace) to highlight the effect of the com-

Remote Sens. 2021, 13, x 7 of 14

(a) (b) Figure 4. Simplified schematic of the frequency conversion module. (a) Schematic of FC1; (b) Schematic of FC2.

2.3. Phase Difference Measurement System The performance of frequency transfer is normally evaluated by the comparison of the phase of the reference signal and the received signal in the compensated link. In the fiber-based microwave transfer, it is impossible to directly measure the phase difference between microwave signals using commercial devices. Therefore, we designed a heterodyne system to measure the frequency transfer instability. Figure 5 presents the schematic diagram of the heterodyne phase measurement system. The received 10-GHz or 9-GHz signal was frequency-divided by 10 or 9, bandpass-filtered at 4 GHz to select a 4 GHz signal, and amplified with LNA. The output signal of LNA was mixed with the Remote Sens. 2021, 13, 2182 7 of 13 4-GHz reference signal delivered via the 4-GHz PDRO in a DBM to produce a direct current (DC) voltage (). It should be noted that the DBM operated in a saturated two identical frequency conversion modules. It should be noted that two identical modules weremode, used, with and each thus connected the to a common() power became supply and nearly a common independent input signal. of input signal level variations and 2.3.was Phase only Difference proportional Measurement System to the phase difference between two input signals. In addition, the The performance of frequency transfer is normally evaluated by the comparison of the phaseinput of the signals reference signal of and DBM the received were signal in in quadrature the compensated link. using In the fiber- a phase shifter (not shown in Figure 5), so based microwave() transfer, it is impossible to directly measure the phase difference between microwavethat signals using was commercial the most devices. sensitive Therefore, we designed to the a heterodyne phase system difference between two inputs of DBM and towas measure approximately the frequency transfer instability. equal Figure to5 presents0. We the measured schematic diagram () of using a multimeter (Keysight, Santa the heterodyne phase measurement system. The received 10-GHz or 9-GHz signal was frequency-dividedRosa, USA by 3458A) 10 or 9, bandpass-filtered with an ateffective 4 GHz to select measurem a 4 GHz signal, andent bandwidth of about 3 Hz. The relative amplified with LNA. The output signal of LNA was mixed with the 4-GHz reference signalnormalized delivered via the phase 4-GHz PDRO fluctuations in a DBM to produce () a direct, also current known (DC) voltage as propagation delay fluctuations in the V(t). It should be noted that the DBM operated in a saturated mode, and thus the V(t) becamefiber nearly link, independent is given of input by signal level variations and was only proportional to the phase difference between two input signals. In addition, the input signals of DBM were in quadrature using a phase shifter (not shown in Figure5), so that V(t) was the most sensitive to the phase difference between two inputs() of≈1 DBM⁄ and was ⋅ approximately()⁄⁄2 ,() ≈0, (12) equal to 0. We measured V(t) using a multimeter (Keysight, Santa Rosa, USA 3458A) withwhere an effective measurement represents bandwidth the of about peak-to-peak 3 Hz. The relative normalized voltage phase of the () when the phase of the 4-GHz fluctuations x(t), also known as propagation delay fluctuations in the fiber link, is given by reference signal changes for 2. The time domain instability of the frequency transfer, x(t) ≈ 1/ωr · V(t)/ Vpp/2 , V(t) ≈ 0, (12) expressed in terms of overlapping Allan deviation, is concerned with characterizing the where Vpp represents the peak-to-peak voltage of the V(t) when the phase of the 4-GHz reference(). signal changes for 2π. The time domain instability of the frequency transfer, expressed in terms of overlapping Allan deviation, is concerned with characterizing the x(t).

FigureFigure 5. Schematic 5. Schematic of heterodyne phase of measurementheterodyne system. phase measurement system. 3. Results 3.1. The Single-Span Link 3. TheResults performance of each single-span link was evaluated by a home-made measurement system prior to the cascaded frequency transfer. The transfer instability of each compensated single-span link in terms of overlapping Allan deviation was calculated from3.1. the The propagation Single-Span delay fluctuations Link of fiber, as shown in Figure6a. These results are compared with previous results over a 112-km urban fiber with a controlled temperature of electronicsThe performance package (violet trace) [25of]. Figure each6a also single-span shows the instability li ofnk the was evaluated by a home-made meas- 100-km free-running spooled fiber link (black trace) to highlight the effect of the compensation,urement which was system measured by prior comparing to the the 100-MHz cascaded OCXO for noise frequenc compensationy transfer. The transfer instability of each at the TX end with the 100-MHz OCXO at the RX end of third span in closed loop using 5125A.compensatedFigure6b shows thesingle-span instability of the frequency link conversionin terms module of FC1 overlapping (wine Allan deviation was calculated trace)from and FC2the (orange propagation trace). The bump delay around 2000 fluctuations s is due to a periodic of fluctuation fiber, as shown in Figure 6a. These results are compared with previous results over a 112-km urban fiber with a controlled temperature of electronics package (violet trace) [25]. Figure 6a also shows the instability of the 100-km free-running spooled fiber link (black trace) to highlight the effect of the com-

Remote Sens. 2021, 13, x 8 of 14

Remote Sens. 2021, 13, 2182 pensation, which was measured by comparing the 100-MHz OCXO for noise compensa-8 of 13 tion at the TX end with the 100-MHz OCXO at the RX end of third span in closed loop using 5125A. Figure 6b shows the instability of the frequency conversion module FC1 (winein the trace) laboratory and FC2 temperature (orange trace). while The the slopebump change around around 2000 s is 1000 due s to is duea periodic to laboratory fluctu- ationtemperature in the laboratory drift. temperature while the slope change around 1000 s is due to laboratory temperature drift.

(a) (b)

Figure 6. TransferTransfer instability instability of of 100-km 100-km single-span single-span link link and and frequency frequency conversion conversion module. module. (a) Instability (a) Instability of 100-km of 100-km sin- single-spangle-span link; link; (b) (Instabilityb) Instability of frequency of frequency conversion conversion module. module.

While the fiber fiber link noise was compensated, the transfer instability of the firstfirst span (blue trace)trace) andand thethe thirdthird span span (red (red trace) trace) was was 3 ×3 ×10 10−15−15 atat 11 ssand and better better than than 2 2× ×10 10−−1717 at 104 s.s. It It was was observed that the second span exhibited an instability (magenta trace) that was lessless thanthan thethe performance performance of of the the other other two two spans, spans, which which is mainly is mainly due due to the to absencethe ab- senceof DCF. of InDCF. addition, In addition, the ratio the of ratio the transferof the transfer instability instability between between each span each was span irregular. was irregular.The main The reason main is reason that the is first that and the the first second and the spans second were spans more sensitivewere more to temperaturesensitive to temperaturedue to the direct due frequencyto the direct division frequency scheme division in the scheme absence in of the phase absence lock of loop phase (PLL) lock at looptheir (PLL) RX end at as their well RX as theend absence as well ofas DCFthe absence in the second of DCF span. in the The second additional span. noise The ofaddi- the tionalfrequency noise conversion of the frequency module, conversion especially formodu FC1,le, wasespecially equivalent for FC1, to that was of equivalent the first span, to thatand of is thereforethe first span, not negligible and is therefore for the not cascaded negligible link. for the cascaded link.

3.2. The The Cascaded Cascaded Link Figure 77 presents presents the the frequency frequency transfer transfer instability instability of theof the 200-km 200-km cascaded cascaded compen- com- sated link composed of a ﬁrst span and a third span. An instability of 6.8 × 10−15 at 1 s pensated link composed of a first span and a third span. An instability of 6.8 × 10−15 at 1 s and 5.1 × 10−18 at 105 s (black trace) was obtained by measuring the phase difference and 5.1 × 10−18 at 105 s (black trace) was obtained by measuring the phase difference be- between the 4-GHz reference signal and the 9-GHz output signal with the home-made tween the 4-GHz reference signal and the 9-GHz output signal with the home-made system. The transfer instability of the 100-MHz signal measured directly by 5125A with a system. The transfer instability of the 100-MHz signal measured directly by 5125A with a 0.5 Hz noise equivalent bandwidth (blue trace) was roughly consistent with the instability 0.5 Hz noise equivalent bandwidth (blue trace) was roughly consistent with the instabil- of microwave signal as measured by the home-made system. The difference between the ity of microwave signal as measured by the home-made system. The difference between transfer instability of the 100-MHz signal and that of the microwave signal was mainly the transfer instability of the 100-MHz signal and that of the microwave signal was caused by temperature-dependent contributions of PDRO which generate 4 GHz reference mainly caused by temperature-dependent contributions of PDRO which generate 4 GHz signal, PDRO at the end of the cascaded system, and the home-made system. The combina- reference signal, PDRO at the end of the cascaded system, and the home-made system. tion of the ﬁrst span, the second span, and FC1 contributions in a root-sum-square process The(red trace)combination is basically of inthe agreement first span, with the the second experimental span, result.and FC1 contributions in a root-sum-squareFigure8 shows process the frequency (red trace) transfer is basica instabilitylly in agreement of the 300-km with cascaded the experimental compensated result.link. We could obtain a frequency instability of 1.1 × 10−14 at 1 s and 6.8 × 10−18 at 105 s (blackFigure trace) 8 as shows measured the frequency by the home-made transfer instability system. The of transferthe 300-km instability cascaded of 100-MHzcompen- −14 −18 5 satedsignal link. measured We could directly obtain by a 5125Afrequency was instability 9.0 × 10− 15of at1.1 1 × s 10 and at 9.0 1× s and10− 186.8at × 10105 s at (blue 10 strace). (black The trace) frequency as measured transfer instabilityby the home of the-made 300-km system. cascaded The link tran alsosfer basically instability agreed of with the root-sum-square of each span and frequency conversion contributions (red trace). A summary of the relevant references and the present work is outlined in Table1. Our

Remote Sens. 2021, 13, x 9 of 14

100-MHz signal measured directly by 5125A was 9.0 × 10−15 at 1 s and 9.0 × 10−18 at 105 s Remote Sens. 2021, 13, 2182 9 of 13 100-MHz(blue trace). signal The measured frequency directly transfer by instabilit 5125A ywas of the9.0 300-km× 10−15 at cascaded 1 s and 9.0link × also 10−18 basically at 105 s (blueagreed trace). with The the frequencyroot-sum-square transfer of instabilit each spany of and the 300-kmfrequency cascaded conversion link alsocontributions basically agreed(red trace). with Athe summary root-sum-square of the relevant of each references span and andfrequency the present conversion work contributionsis outlined in (redresultsTable trace). 1. clearly Our A results summary demonstrate clearly of thedemonstrate either relevant better references eith performanceer better and performance orthe feature present longer or work feature distance is outlined longer at dis- the in Tablecomparabletance 1.at Ourthe performance.comparableresults clearly performance. In demonstrate addition, In it eith isaddition, reasonableer better it isperformance toreasonable expect that toor theexpectfeature performance that longer the dis-per- of tancetheformance 300-km at the of cascadedcomparable the 300-km compensated performance.cascaded compensated link In couldaddition, be link improved it couldis reasonable be by improved using to expect DCF by in usingthat the the secondDCF per- in formancespanthe second link. of span the 300-km link. cascaded compensated link could be improved by using DCF in the second span link.

FigureFigure 7.7. TransferTransfer instabilityinstability ofof 200-km200-km cascadedcascaded compensatedcompensated link composed of a first ﬁrst span and a Figurethirdthird span.span. 7. Transfer instability of 200-km cascaded compensated link composed of a first span and a third span.

Figure 8. Transfer instability of 300-km cascaded compensated link. Figure 8. TransferTransfer instability of 300-km cascaded compensated link.

RemoteRemote Sens.Sens.2021 2021,,13 13,, 2182x 1010 of 1314

TableTable 1.1. CharacteristicsCharacteristics of of cascaded cascaded fiber-based ﬁber-based mi microwavecrowave frequency frequency transfer transfer compared compared with with previousprevious studies. L: length of fiber ﬁber link; N:: numbers numbers of of single-span; single-span; σσyy(1(1 s): s): fractional fractional instability instability at at 1 s; σy(104 s):4 fractional instability at 10,000 s; MF: measurement frequency. 1 s; σy(10 s): fractional instability at 10,000 s; MF: measurement frequency.

Works L (km) N σy (1 s) σy (104 s)4 MF (GHz) Works L (km) N σy (1 s) σy (10 s) MF (GHz) Ref. [33] 430 2 19 × 10−14 13 × 10−17 1 Ref. [33] 430 2 19 × 10−14 13 × 10−17 1 −14 −17 Ref. [[32]32] 204 204 2 2 6 × 106 × 10−14 ~20~20 ×× 1010− 17 1 Ref. [[36]36] 145145 1 3 3 1.3 ×1.3 10×−1410 −14 4.14.1 ×× 1010−17− 17 0.1 −14 −17 1.1 × 10 −14 5.3 × 10 − 17 9 This work 300 1 3 1.1 × 10 5.3 × 10 9 This work 1 3 −15 −17 300 9.0 ×9.0 10× 10 −15 3.83.8 ×× 1010− 17 0.1 1 1 spooledspooled ﬁber. fiber.

The residualresidual phasephase noisenoise powerpower spectralspectral densitydensity (PSD)(PSD) ofof thethe 300-km300-km cascadedcascaded linklink (blue(blue trace)trace) andand thethe 200-km200-km cascadedcascaded linklink (red(red trace)trace) measuredmeasured atat 100100 MHzMHz areare bothboth shownshown inin FigureFigure9 ,9, which which were were obtained obtained simultaneously simultaneously with with the transferthe transfer instability instability of the of 100-MHzthe 100-MHzsignal. signal. These These results results were compared were co withmpared the noisewith ofthe the noise 100-km of free-runningthe 100-km spooledfree-running fiber spooled link (black fiber trace) link (black together trace) with to thegether residual with the phase residu noiseal phase of the noise third of span the (magentathird span trace). (magenta The trace). rejection The frequency rejection frequency bandwidth bandwidth of the cascaded of the linkcascaded was less link than was 500less Hzthan, which 500 Hz, is inwhich agreement is in agreement with the with limit the due limit to the due propagation to the propagation delay of delay the single- of the spansingle-span link. It link. is possible It is possible to conclude to conclude this on thethis basis on the of thebasis noise of the of the noise 300-km of the cascaded 300-km link,cascaded the 200-km link, the cascaded 200-km cascaded link (composed link (compo of thesed first of spanthe first and span the thirdand the span), third and span), the thirdand the span third link. span The link. first The peak first of peak the 300-kmof the 300-km cascaded cascaded link noise link atnoise about at about 337 Hz 337 was Hz causedwas caused by the by feedback the feedback loop ofloop the of first the span. first Meanwhile,span. Meanwhile, the second the second peak at peak about at 384 about Hz and384 Hz the and third the peak third at aboutpeak at 454 about Hz were 454 Hz caused were by caused the feedback by the feedback loop of the loop third of spanthe third and thespan second and the span, second respectively. span, respectively.

Figure 9.9. Residual phase noise spectral densitydensity ofof thethe ﬁberfiber linklink measuredmeasured atat 100100 MHz.MHz.

4. Discussion The wholewhole systemsystem waswas located located in in the the same same laboratory laboratory so so that that the the transfer transfer instability instability of theof the signal signal could could be be conveniently conveniently measured. measured. However, However, due due to microwaveto microwave leakage, leakage, part part of theof the transmitted transmitted signal signal at the at TXthe end TX willend be will directly be directly coupled coupled to the RXto endthe RX without end without passing throughpassing through the optical the ﬁber, optical which fiber, will which result will in parasiticresult in parasitic phase shifts phase and shifts the performance and the per- degradationformance degradation of the frequency of the transfer.frequency For transfer. the system For deployedthe system with deployed urban ﬁberwith links,urban the fi-

Remote Sens. 2021, 13, 2182 11 of 13

coupling between the TX end and the RX end is impossible due to the two ends located in distant laboratories. In addition, in our system, to suppress the influence of coherent Rayleigh scattering, the wavelength of the forward laser is different from that of the backward laser by 0.4 nm. Consequently, the stability of frequency transfer can be reduced due to nonreciprocal noise caused by the chromatic dispersion in the optical fiber. Especially for urban fiber links with larger temperature fluctuation, the degradation of frequency transfer stability is more obvious. The propagation delay difference ∆τ between forward and backward signals caused by wavelength detuning ∆λ, combined with chromatic dispersion, can be expressed as: ∆τ = ∆λ · (D · L + DDCF · l), (13)

where D and DDCF represent the chromatic dispersion coefficients (expressed in ps/nm/km) of fiber link and DCF, respectively, and L and l denote the length (expressed in km) of fiber link and DCF, respectively. For urban fiber link, the wavelength detuning and DCF are independent of the link temperature. The sensitivity coefficient of ∆τ with respect to link temperature T is calculated by the partial derivation of Equation (13):

∂∆τ ∂D ∂L = ∆λ · · L + · D = ∆λ · L · (κ + D · α), (14) ∂T ∂T ∂T

where α = (∂L/∂T)/L represents the fiber thermal expansion coefficient, and κ = ∂D/∂T is the thermal coefficient of chromatic dispersion. For commercial SMF-28 fiber conform- ing to the ITU-T G.652 standard, α = 5.6 × 10−7/K [37], D = 17 ps/(nm · km), and κ = −1.45 × 10−3 ps/(nm·km·K) [38] at 1550 nm. Assuming a temperature fluctuation of 20 K in a day, the propagation delay difference of round-trip signal will fluctuate by 1.2 ps in one day over a 100-km fiber link. According to Equation (9), the received signal contains half of the link nonreciprocal noise in closed loop. Thus, there is 0.6 ps of residual delay fluctuation after link noise compensation, which will degrade the long-term instability of the frequency transfer. In order to reduce the impact caused by wavelength detuning, one effective approach is to use tunable lasers to tune the wavelength difference of less than 20 pm between forward and backward lasers by temperature tuning. The fluctuation in laser wavelength will lead to the change of ∆λ in Equation (13), and will also reduce the stability of frequency transfer. This problem can be overcome by better control of laser diode temperature and injection current. In addition, the DCF inserted in the fiber link can make D · L + DDCF · l ≈ 0, which can also significantly suppress the influence of laser wavelength fluctuation. Similarly to the nonreciprocal noise caused by the chromatic dispersion in the optical fiber, the noise induced by MZM cannot be compensated by our scheme either. Further improvement in frequency transfer instability can be obtained by improving the scheme to convert the additional noise of MZM into compensable noise.

5. Conclusions We have demonstrated a 300-km cascaded link consisting of three single-span links for microwave frequency transfer using electronic phase compensation. In this system, a frequency transfer instability of 1.1 × 10−14 at 1 s and 6.8 × 10−18 at 105 s was achieved. Using the PLL method, a 100-MHz signal delivered by PMH was transferred indirectly with an instability of 9.0 × 10−15 at 1 s and 9.0 × 10−18 at 105 s. The rejection frequency bandwidth of the cascaded link was limited by the propagation delay of the single-span link. Therefore, the cascade transfer scheme had better noise rejection than the single- span transfer over the same length ﬁber link. The transfer instability of the cascaded link agrees with the root-sum-square of each span and frequency conversion contributions. It is considered feasible to extend the ﬁber-based microwave frequency transfer length up to 1200 km with instability values better than 5 × 10−14 at 1 s and 5 × 10−17 at one day Remote Sens. 2021, 13, 2182 12 of 13

using 4 stages of our 300-km transfer system, which is still sufficient to transfer modern cold atom microwave frequency standards. As demonstrated previously [25], our scheme (see Figure1) also works for a single- span urban fiber link that is longer than 100 km, and the long-term transfer instability will be even better than that of the spooled fiber link (see Figure6a) due to the temperature controlled of the electronics package. Hence, for cascaded frequency transfer over an urban fiber link, the active temperature stabilization of each electronics package is needed to achieve better long-term instability. In the future, we aim to focus on microwave frequency transfer over a 1000-km urban fiber link with a cascaded system and the construction a fiber-based microwave transfer network.

Author Contributions: Data curation, W.X. and H.Q.; Methodology, W.X. and W.Z.; Project admin- istration, Y.X.; Software, W.X.; Validation, W.X. and H.Q.; Writing—original draft, W.X.; Writing— review & editing, W.Z. and S.Z. All authors have read and agreed to the published version of the manuscript. Funding: This research was supported by the National Natural Science Foundation of China (Grant Nos. 61825505 and 91536217), the West Light Foundation of the Chinese Academy of Sciences (Grant No. 29202082), and the Nature Science Foundation of Shaanxi (Grant No. S2019-JC-WT-0002). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Restrictions apply to the availability of these data. The ownership of data belongs to the National Time Service Center (NTSC). These data can be available from the corresponding author with the permission of NTSC. Acknowledgments: The authors would like to thank Tao Liu, Haifeng Jiang, and Wenge Guo for their constructive suggestions on this paper. Conﬂicts of Interest: The authors declare no conﬂict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

References 1. Hachisu, H.; Fujieda, M.; Nagano, S.; Gotoh, T.; Nogami, A.; Ido, T.; Falke, S.; Huntemann, N.; Grebing, C.; Lipphardt, B.; et al. Direct comparison of optical lattice clocks with an intercontinental baseline of 9000 km. Opt. Lett. 2014, 39, 4072–4075. [CrossRef] [PubMed] 2. Riehle, F. Optical clock networks. Nat. Photonics 2017, 11, 25–31. [CrossRef] 3. Shelkovnikov, A.; Butcher, R.J.; Chardonnet, C.; Amy-Klein, A. Stability of the proton-to-electron mass ratio. Phys. Rev. Lett. 2008, 100, 150801. [CrossRef] 4. Matveev, A.; Parthey, C.G.; Predehl, K.; Alnis, J.; Beyer, A.; Holzwarth, R.; Udem, T.; Wilken, T.; Kolachevsky, N.; Abgrall, M.; et al. Precision measurement of the hydrogen 1S-2S frequency via a 920-km fiber link. Phys. Rev. Lett. 2013, 110, 230801. [CrossRef] 5. Mehlstaubler, T.E.; Grosche, G.; Lisdat, C.; Schmidt, P.O.; Denker, H. Atomic clocks for geodesy. Rep. Prog. Phys. 2018, 81, 064401. [CrossRef] 6. Cliche, J.F.; Shillue, B. Precision timing control for radioastronomy—Maintaining femtosecond synchronization in the atacama large millimeter array. IEEE Control Syst. Mag. 2006, 26, 19–26. [CrossRef] 7. Schediwy, S.W.; Gozzard, D.R.; Gravestock, C.; Stobie, S.; Whitaker, R.; Malan, J.A.; Boven, P.; Grainge, K. The mid-frequency Square Kilometre Array phase synchronisation system. Publ. Astron. Soc. Aust. 2019, 36.[CrossRef] 8. Gozzard, D.R.; Schediwy, S.W.; Dodson, R.; Rioja, M.J.; Hill, M.; Lennon, B.; McFee, J.; Mirtschin, P.; Stevens, J.; Grainge, K. Astronomical verification of a stabilized frequency reference transfer system for the Square Kilometer Array. Astron. J. 2017, 154. [CrossRef] 9. Krehlik, P.; Buczek, Ł.; Kołodziej, J.; Lipiński,M.; Sliwczyński,Ł.;´ Nawrocki, J.; Noga´s,P.; Marecki, A.; Pazderski, E.; Ablewski, P.; et al. Fibre-optic delivery of time and frequency to VLBI station. Astron. Astrophys. 2017, 603, A48. [CrossRef] 10. Clivati, C.; Aiello, R.; Bianco, G.; Bortolotti, C.; De Natale, P.; Di Sarno, V.; Maddaloni, P.; Maccaferri, G.; Mura, A.; Negusini, M.; et al. Common-clock very long baseline interferometry using a coherent optical fiber link. Optica 2020, 7, 1031–1037. [CrossRef] 11. Lau, K.Y.; Lutes, G.F.; Tjoelker, R.L. Ultra-stable RF-over-fiber transport in NASA antennas, phased arrays and radars. J. Lightwave Technol. 2014, 32, 3440–3451. [CrossRef] 12. Johnsen, T. Time and frequency synchronization in multistatic radar. Consequences to usage of GPS disciplined references with and without GPS signals. In Proceedings of the 2002 IEEE Radar Conference, Long Beach, CA, USA, 25 April 2002; pp. 141–147. Remote Sens. 2021, 13, 2182 13 of 13

13. Bauch, A.; Achkar, J.; Bize, S.; Calonico, D.; Dach, R.; Hlavać,R.; Lorini, L.; Parker, T.; Petit, G.; Piester, D.; et al. Comparison between frequency standards in Europe and the USA at the 10−15 uncertainty level. Metrologia 2006, 43, 109–120. [CrossRef] 14. Jiang, H.; Kéfélian, F.; Crane, S.; Lopez, O.; Lours, M.; Millo, J.; Holleville, D.; Lemonde, P.; Chardonnet, C.; Amy-Klein, A.; et al. Long-distance frequency transfer over an urban fiber link using optical phase stabilization. J. Opt. Soc. Am. B 2008, 25, 2029–2035. [CrossRef] 15. Bercy, A.; Stefani, F.; Lopez, O.; Chardonnet, C.; Pottie, P.-E.; Amy-Klein, A. Two-way optical frequency comparisons at 5×10−21 relative stability over 100-km telecommunication network fibers. Phys. Rev. A 2014, 90, 061802. [CrossRef] 16. Deng, X.; Liu, J.; Jiao, D.D.; Gao, J.; Zang, Q.; Xu, G.J.; Dong, R.F.; Liu, T.; Zhang, S.G. Coherent transfer of optical frequency over 112 km with instability at the 10−20 level. Chin. Phys. Lett. 2016, 33, 114202. [CrossRef] 17. Guillou-Camargo, F.; Menoret, V.; Cantin, E.; Lopez, O.; Quintin, N.; Camisard, E.; Salmon, V.; Le Merdy, J.M.; Santarelli, G.; Amy-Klein, A.; et al. First industrial-grade coherent fiber link for optical frequency standard dissemination. Appl. Opt. 2018, 57, 7203–7210. [CrossRef] 18. Daussy, C.; Lopez, O.; Amy-Klein, A.; Goncharov, A.; Guinet, M.; Chardonnet, C.; Narbonneau, F.; Lours, M.; Chambon, D.; Bize, S.; et al. Long-distance frequency dissemination with a resolution of 10−17. Phys. Rev. Lett. 2005, 94, 203904. [CrossRef] 19. Lopez, O.; Amy-Klein, A.; Lours, M.; Chardonnet, C.; Santarelli, G. High-resolution microwave frequency dissemination on an 86-km urban optical link. Appl. Phys. B 2009, 98, 723–727. [CrossRef] 20. Wang, B.; Gao, C.; Chen, W.L.; Miao, J.; Zhu, X.; Bai, Y.; Zhang, J.W.; Feng, Y.Y.; Li, T.C.; Wang, L.J. Precise and continuous time and frequency synchronisation at the 5 × 10−19 accuracy level. Sci. Rep. 2012, 2, 556. [CrossRef][PubMed] 21. Sliwczynski, L.; Krehlik, P.; Buczek, L.; Lipinski, M. Frequency transfer in electronically stabilized fiber optic link exploiting bidirectional optical amplifiers. IEEE Trans. Instrum. Meas. 2012, 61, 2573–2580. [CrossRef] 22. Wang, S.; Sun, D.; Dong, Y.; Xie, W.; Shi, H.; Yi, L.; Hu, W. Distribution of high-stability 10 GHz local oscillator over 100 km optical fiber with accurate phase-correction system. Opt. Lett. 2014, 39, 888–891. [CrossRef][PubMed] 23. Huang, R.; Wu, G.; Li, H.; Chen, J. Fiber-optic radio frequency transfer based on passive phase noise compensation with frequency dividing and filtering. Opt. Lett. 2016, 41, 626–629. [CrossRef] 24. Schediwy, S.W.; Gozzard, D.R.; Stobie, S.; Malan, J.A.; Grainge, K. Stabilized microwave-frequency transfer using optical phase sensing and actuation. Opt. Lett. 2017, 42, 1648–1651. [CrossRef] 25. Xue, W.X.; Zhao, W.Y.; Quan, H.L.; Zhao, C.C.; Xing, Y.; Jiang, H.F.; Zhang, S.G. Microwave frequency transfer over a 112-km urban fiber link based on electronic phase compensation. Chin. Phys. B 2020, 29, 064209. [CrossRef] 26. Krehlik, P.; Sliwczynski, L.; Buczek, L.; Lipinski, M. Fiber-optic joint time and frequency transfer with active stabilization of the propagation delay. IEEE Trans. Instrum. Meas. 2012, 61, 2844–2851. [CrossRef] 27. Sliwczynski, L.; Krehlik, P.; Czubla, A.; Buczek, L.; Lipinski, M. Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km. Metrologia 2013, 50, 133–145. [CrossRef] 28. Newbury, N.R.; Williams, P.A.; Swann, W.C. Coherent transfer of an optical carrier over 251 km. Opt. Lett. 2007, 32, 3056–3058. [CrossRef] 29. Williams, P.A.; Swann, W.C.; Newbury, N.R. High-stability transfer of an optical frequency over long fiber-optic links. J. Opt. Soc. Am. B 2008, 25, 1284–1293. [CrossRef] 30. Urick, V.J.; Bucholtz, F.; Devgan, P.S.; McKinney, J.D.; Williams, K.J. Phase modulation with interferometric detection as an alternative to intensity modulation with direct detection for analog-photonic links. IEEE Trans. Microw. Theory Tech. 2007, 55, 1978–1985. [CrossRef] 31. Lopez, O.; Amy-Klein, A.; Daussy, C.; Chardonnet, C.; Narbonneau, F.; Lours, M.; Santarelli, G. 86-km optical link with a resolution of 2×10−18 for RF frequency transfer. Eur. Phys. J. D 2008, 48, 35–41. [CrossRef] 32. Fujieda, M.; Kumagai, M.; Nagano, S. Coherent microwave transfer over a 204-km telecom fiber link by a cascaded system. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 2010, 57, 168–174. [CrossRef] 33. Liu, Q.; Han, S.L.; Wang, J.L.; Feng, Z.T.; Chen, W.; Cheng, N.; Gui, Y.Z.; Cai, H.W.; Han, S.S. Simultaneous frequency transfer and time synchronization over a 430 km fiber backbone network using a cascaded system. Chin. Opt. Lett. 2016, 14, 5. [CrossRef] 34. Narbonneau, F.; Lours, M.; Bize, S.; Clairon, A.; Santarelli, G.; Lopez, O.; Daussy, C.; Amy-Klein, A.; Chardonnet, C. High resolution frequency standard dissemination via optical fiber metropolitan network. Rev. Sci. Instrum. 2006, 77, 064701. [CrossRef] 35. Zhao, C.C.; Zhao, W.Y.; Xue, W.X.; Quan, H.L.; Yan, L.L.; Guo, W.G.; Jiang, H.F.; Zhang, S.G. Microwave frequency dissemination via 50 km optical Fiber based on optical delay compensation. Acta Photonica Sin. 2020, 49, 806002. [CrossRef] 36. Gao, C.; Wang, B.; Zhu, X.; Yuan, Y.B.; Wang, L.J. Dissemination stability and phase noise characteristics in a cascaded, fiber-based long-haul radio frequency dissemination network. Rev. Sci. Instrum. 2015, 86, 093111. [CrossRef] 37. Bousonville, M.; Rausch, J. Velocity of signal delay changes in fibre optic cables. In Proceedings of the 9th European Workshop on Beam Diagnostics and Instrumentation for Particle Accelerators, DIPAC 2009, Basel, Switzerland, 25–27 May 2009; pp. 248–250. 38. Zhang, X.; Zhong, K.; Ming, H.; Jia, N.; Li, T.; Wang, A.X.; Wang, M.; Chi, J.; Sun, J. Experimental study on temperature dependence of dispersion of G.652 fiber and its effect on high speed optical communication system and compensation. In Proceedings of the Optoelectronic Devices and Integration III, Beijing, China, 22 November 2010.