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• Abstract

SECTION I

## INTRODUCTION

Distributing local oscillator (LO) signals to remote antennas with highly stabilized and coherent phases is desired in many applications, especially in multi-antenna array systems, such as phased-array radar and connected-element interferometry [1]. In order to achieve unprecedented sensitivity and angular resolution, stable LO signals need to be delivered to different antennas ranging from hundred meters to tens of kilometers to coherently down-convert the received radio frequency (RF) signals [2]. Benefiting from its low loss and immunity to electromagnetic interference characteristics, optical fiber has usually been used to transfer the LO signals [3], [4]. However, the fiber link will suffer from the environment perturbations such as physical vibration and temperature fluctuations, which will degrade the phase stability of the LO signals [5]– [6][7].

Over the past few years, a lot of schemes have been proposed and demonstrated to actively compensate the phase variation induced by the fluctuations of the optical fiber [3] [4] [5]– [6][7] [8] [9] [10] [11] [12] [13]– [14][15]. A widely used way to achieve long distant and stable delivery is to tune the phase of the LO signal at the central station, by means of either in electronic devices like a voltage-controlled oscillator (VCO) [11] or in optics such as a cavity-length-changeable passively mode-locked laser [12], so that the phase at the remote end will be stable. High performance at short averaging times and large compensable range has been achieved. However, the electronic or optical VCOs have usually band limited frequency range, which makes the system only suitable for single LO signal delivery. Note that to remove residual spurious components so as to prevent reception interference at the remote antenna, multiple conversion is generally used to down-convert the RF signal [19], [20], which requires multiple LO signals at the same antenna. Traditional way is to transfer a reference signal to antenna to synchronize multiple LO signal sources or to generate multiple LO signals by frequency multipliers. In both ways, varying phase perturbations in associated electronics must be accounted for. An attractive way is to generate multiple LO signals in the central station and deliver them to different antennas with coherent phases. All antennas in array could share the same LO generating device in central station and meanwhile reduce the complexity and part count at remote ends. Since the schemes based on tuning the phase of the LO signals are band limited, many schemes based on adjusting the group delay of the link are designed [13]– [14][15], which have the potential of delivering multiple LO signals. In-loop tunable delay lines, such as piezoelectric fiber stretcher or motor-driven tunable optical delay line are widely used [14], [15], benefiting from their ultra-large RF bandwidth and short response time. However, due to the large temperature-dependent delay variation of standard fiber (35 $\hbox{ps/km/}^{\circ}\hbox{C}$) [13], LO signals delivery over tens of kilometers requires a significant tunable range. Piezoelectric fiber stretchers usually have very limited tunable range, up to several picoseconds [14]. Motor-driven optical delay lines can have a tunable range as large as 1 ns, but is still insufficient when the delivery distant comes to tens of kilometers. Thermally controlled fiber spool can be employed, but it may contribute little to the short-term phase stabilization [13].

In our previous work, we have demonstrated a long-distance LO signal delivery scheme, transferring a stable 2.42-GHz microwave signal over 54 km of spooled fiber in the laboratory [21]. A tunable laser is used to adjust the wavelength of the optical carrier. Since optical carriers with different wavelengths propagate at different velocities in fiber, a tunable delay line based on group dispersion can be realized to stabilize the link delay. The tunable delay capacity is automatically extended under longer fiber though the delay variation caused by environmental change will increase too, which means a very long delivery distance can be expected [21]. The experiment described in this paper, for the first time, show that multiple LO signals can be transferred to a remote end with active phase error compensation via a single optical carrier. One of the LO signals, acting as a reference single, is round-trip transferred between the central station and remote end, carrying the phase variation arises from the fiber link. The wavelength of optical carrier is adjusted according to the phase variation of the reference LO, to stabilize the delay of the fiber link. Once the delay of the link is stabilized, the phases of other LO signals that transferred through the fiber link will all be stabilized. A proof of concept experimental is carried out, LOs at frequencies of 2.46 GHz and 8 GHz are transferred through a 30-km fiber link, and significant phase drift compression is observed at both frequencies. The effect of higher order dispersion on the stability of different LO signals is discussed, and our theory shows that the fourth-order dispersion dominates the proposed combined stability.

SECTION II

## PRINCIPLE

The proposed multiple LO signals delivery scheme is illustrated in Fig. 1. In order to deliver multiple LO signals to remote location with stabilized phases, the delay variation of the fiber link, caused by environment perturbation, rather than the phase fluctuations of each LO signal, should be compensated. To achieve that, one of the LO signals, ${\rm RF}_{\rm ref}$, is used as a reference to obtain and compensate the delay variation of the fiber link. In the central station, the other LO signals to be delivered, $\hbox{LO}_{\rm i}$, ${\rm i} = 1, 2, \ldots, {\rm n}$, are combined together with ${\rm RF}_{\rm ref}$. The scheme uses a wavelength tunable laser (WTL) to provide CW optical carrier. Following the WTL, an electro-optic modulator (EOM) is used to encode the combined electric signal onto the optical carrier. After the modulation, the optical signal is fed through an optical circulator (CIR) to a fiber spool. At the remote end, part of the optical signal is reflected by a Faraday rotation mirror (FRM) and returned to the central station via the same fiber. The backward traveling light is then separated by the CIR and opto-electronically converted by a fast photo detector (PD). After that, the reference frequency is filtered out by a band pass filter (BPF) and phase compared with the original ${\rm RF}_{\rm ref}$, through a phase discriminator, generating an error signal which is applied to the WTL to alter the wavelength of the light and compensate the delay fluctuation. The forward and backward traveling lights have the same wavelength to ensure the signals experience the same delay. Rayleigh noise will arise to degrade the signal-to-noise ratio (SNR) at both ends of the link, but the influence could be reduced by deliberately allocating the optical power.

Fig. 1. Block diagram of the proposed phase-stabilized delivery for multiple LO signals. WTL, wavelength tunable laser; EOM, electro-optic modulator; CIR, circulator; FRM, Faraday rotation mirror; PD, photodiode; BPF, band pass filter.

### 2.1. Phase Stabilization of the Reference Signal

To understand the phase stabilization principle of multiple LO tones, we first consider the case of transferring ${\rm RF}_{\rm ref}$ alone without any other LO signals. After having been amplitude modulated at a quadrature-biased push–pull Mach–Zehnder modulator (MZM), the electrical field of the optical signal, with angular frequency $\omega_{\rm op}$, is given byTeX Source$$E_{I} \propto e^{- i \omega_{op}t}\left(1 + {m \over 2}\cos \omega_{rf}t\right)\eqno{\hbox{(1)}}$$ with the modulation frequency $\omega_{\rm rf}$ and the modulation depth ${\rm m} = {\rm V}_{\rm rf}/{\rm V}_{\pi}$. Since the phase of ${\rm RF}_{\rm ref}$ is the major concern, we have neglected the amplitude factors.

Suppose that the phase shift experienced by the optical field during its propagation in optical fiber is $\chi(\omega) = \beta(\omega){\rm z}$, where $\beta$ is the mode-propagation constant, and z is the length of the fiber link. After transmitted to the remote end and experienced a delay variation of $\Delta\tau_{\rm link}$, which is caused by environment perturbations along the fiber link, the optical field is given byTeX Source$$E_{O} \propto \exp \left\{- i\omega_{op}(t + \Delta \tau_{link}) + i\chi (\omega_{op})\right\} + {m \over 4}\exp \left\{- i(\omega_{op} \pm \omega_{rf})(t + \Delta \tau_{link}) + i\chi (\omega_{op} \pm \omega_{rf})\right\}. \eqno{\hbox{(2)}}$$ From Eq. (2), we can obtain the forward transmitted ${\rm RF}_{\rm ref}$ field at fundamental frequency TeX Source$$E_{fw} \propto mA\cos \left[\omega_{rf}t + \omega_{rf}\Delta \tau_{link} - {\chi (\omega_{op} + \omega_{rf}) - \chi (\omega_{op} - \omega_{rf}) \over 2}\right]\eqno{\hbox{(3)}}$$ whereTeX Source$$A = \cos \left[\left(2\chi (\omega_{op}) - \chi (\omega_{op} - \omega_{rf}) - \chi (\omega_{op} + \omega_{rf})\right)/2\right]\eqno{\hbox{(4)}}$$ is related to dispersion induced power fading, which has no effect on the phase of ${\rm RF}_{\rm ref}$ and is accordingly ignored in the following analysis.

Under the assumption that the forward and backward propagations, through the same fiber link, experience the same time delay, the round-trip transferred ${\rm RF}_{\rm ref}$ could be expressed asTeX Source$$E_{rt} \propto \cos \left[\omega_{rf}t + 2 \omega_{rf}\Delta \tau_{link} - \left(\chi (\omega_{op} + \omega_{rf}) - \chi (\omega_{op} - \omega_{rf})\right) \right].\eqno{\hbox{(5)}}$$ By comparing the phase of round-trip transferred with original ${\rm RF}_{\rm ref}$, we can obtain a phase error signal TeX Source$$\Delta \varphi = 2\omega_{rf}\Delta \tau_{link} - \left(\chi (\omega_{op} + \omega_{rf}) - \chi (\omega_{op} - \omega_{rf})\right)\eqno{\hbox{(6)}}$$ which is a function of optical carrier frequency $\omega_{\rm op}$. The phase error is then digitalized and used to feedback control the frequency $\omega_{\rm op}$, as well as the wavelength $\lambda$, of the optical carrier. Once the carrier frequency changes, the phase error will vary accordingly. A classic proportional–integral–derivative (PID) algorithm is used during the above feedback control. As long as the PID phase tracking at the central station adjusts the wavelength of tunable laser so that the round-trip phase fluctuation $\Delta \varphi$ is stabilized at zero, the phase fluctuation in the remote end, which is actually half of $\Delta\varphi$, will also be stabilized.

### 2.2. Phase Stabilization of Other LO Signals

From Eq. (3), after one-way transmission, the phase shift of ${\rm RF}_{\rm ref}$ isTeX Source$$\theta (\omega_{rf}, \omega_{op}) = \omega_{rf}\Delta \tau_{link} - {\chi (\omega_{op} + \omega_{rf}) - \chi (\omega_{op} - \omega_{rf}) \over 2}.\eqno{\hbox{(7)}}$$ Accordingly, the propagation delay ${\rm RF}_{\rm ref}$ experienced is given by TeX Source$$\tau (\omega_{rf}, \omega_{op}) = {d\theta \over d\omega_{rf}} = \Delta \tau_{link} - {\chi^{\prime}(\omega_{op} + \omega_{rf}) + \chi^{\prime}(\omega_{op} - \omega_{rf}) \over 2}. \eqno{\hbox{(8)}}$$ Expanding $\chi(\omega)$ in a Taylor seriesTeX Source$$\chi (\omega) = \sum_{k = 0}^{\infty} {\chi^{(k)}(\omega_{op}) \over k!}(\omega - \omega_{op})^{k}\eqno{\hbox{(9)}}$$ and then combing Eq. (8) with Eq. (9), we obtain TeX Source$$\tau (\omega_{rf}, \omega_{op}) = \Delta \tau_{link} - \sum_{k = 0}^{\infty} {\chi^{(2k + 1)}(\omega_{op}) \over (2k)!}\, \omega_{rf}^{2k}.\eqno{\hbox{(10)}}$$

Consider the situation that an LO signal with angular frequency at $\omega_{\rm lo}$ is modulated on the same optical carrier and transferred with ${\rm RF}_{\rm ref}$. There will be a delay difference between the LO signal and ${\rm RF}_{\rm ref}$TeX Source$$\Delta_{rf}\tau (\omega_{op}) = \tau (\omega_{lo}, \omega_{op}) - \tau (\omega_{rf}, \omega_{op}) = \sum_{k = 1}^{\infty} {\chi^{(2k + 1)}(\omega_{op}) \over (2k)!}\left(\omega_{rf}^{2k} - \omega_{lo}^{2k}\right).\eqno{\hbox{(11)}}$$ Equation (11) indicates that while the phase of ${\rm RF}_{\rm ref}$ is stabilized, the delay $\omega_{\rm lo}$ experienced will be different from $\omega_{\rm rf}$, due to the frequency difference between $\omega_{\rm lo}$ and $\omega_{\rm rf}$. The delay difference will not be a problem as long as it stays constant. However, in our scheme the wavelength (frequency) of the optical carrier needs to be adjusted constantly to stabilize the phase of ${\rm RF}_{\rm ref}$. While the optical carrier frequency changes from $\omega_{{\rm op}1}$ to $\omega_{{\rm op}2}$, there will be a variation on the delay difference, which could be given byTeX Source$$\Delta_{op} \Delta_{rf}\tau = \Delta_{rf}\tau (\omega_{op2}) - \Delta_{rf}\tau (\omega_{op1}) = \sum_{k = 1}^{\infty} {\chi^{(2k + 1)}(\omega_{op2}) - \chi^{(2k + 1)}(\omega_{op1}) \over (2k)!}\left(\omega_{rf}^{2k} - \omega_{lo}^{2k}\right). \eqno{\hbox{(12)}}$$ The variation of the delay difference is related to both radio frequency and optical carrier frequency.

To see how much the variation of the delay difference could be, we ignore the high-order term of Eq. (12) and consider only the first non-zero term as follows: TeX Source$$\Delta_{op}\Delta_{rf}\tau \approx {\chi^{(3)}(\omega_{op2}) - \chi^{(3)}(\omega_{op1}) \over 2}\left(\omega_{rf}^{2} - \omega_{lo}^{2}\right).\eqno{\hbox{(13)}}$$ One can conclude that the residual unstabilized delay variation of other LO tones, when the ${\rm RF}_{\rm ref}$ is stabilized, is dominated by the fourth-order dispersion of the fiber link.

We have measured the $\chi^{(2)}$ of a 30-km optical fiber link (used in the following experiment) at discrete wavelengths and the results, as well as the fitted $\chi^{(2)}$, are plotted in Fig. 2(a). The frequency of ${\rm RF}_{\rm ref}$ is chosen to be 2.46 GHz, and we assume the initial wavelength of optical carrier is 1545 nm since it is in the middle of the adjusting range of our WTL. The variation of the delay difference, which is plotted in Fig. 2(b) with different $\omega_{\rm lo}$ $(\omega_{\rm lo} - \omega_{\rm rf})$ and $\omega_{{\rm op}2} \(\lambda_{2})$, is less than $2 \times 10^{-3} \\hbox{ps}$, which could be neglected in practice. The results indicate that high-order dispersion will hardly affect the stabilization of the LO signal. As long as the phase of ${\rm RF}_{\rm ref}$ is stabilized, the phase of the LO signal will also be stabilized.

Fig. 2. (a) Fitted (blue line) $\chi^{(2)}$ according to measurement (red points) at different wavelength of 30-km fiber link. (b) The variation of delay difference between ${\rm RF}_{\rm ref}$ and LO when the wavelength changes. The frequency of ${\rm RF}_{\rm ref}$ is 2.46 GHz, and the initial wavelength of optical carrier is assumed to be 1545 nm.
SECTION III

## EXPERIMENT AND RESULTS

A proof of concept experiment is carried out, and its setup is illustrated in Fig. 3, which follows the scheme of Fig. 1. Two reels of standard G.652 single-mode optical fiber, which have lengths of 10 km and 20 km, respectively, are located in the laboratory. A motorized variable optical delay line (MDL) is inserted into the fiber loop to simulate the rapid delay fluctuation of a real environment. The MDL is controlled by a computer and has delay variation speed of 1 ps/s and tunable range of 500 ps. Besides the MDL, the fast fluctuation of temperature also brings a great influence to the delay variation, since the fiber is located in an open environment instead of buried. According to the typical 7 $\hbox{ppm/}^{\circ}\hbox{C}$ thermal coefficient of delay for standard G.652 single-mode optical fiber, one degree variation of temperature would bring a delay change of 1.05 ns.

Fig. 3. Experiment setup of the proposed phase-stabilized delivery for multiple LO signals. MDL, motorized variable optical delay line; OSC, oscilloscope; SA, spectrum analyzer.

In the experiment, two LO signals, $\hbox{LO}_{0} = 2.46 \\hbox{GHz}$ and $\hbox{LO}_{1} = 8 \\hbox{GHz}$, are transferred to the remote end. The two LO signals are generated from two signal generators which are synchronized by the same 10 MHz reference to maintain a constant phase difference. The frequencies of the LO signals should be selected so that they would not be affected by any harmonics and intermodulations. The EOM, which is used to encode the LO signals on the optical carrier, is kept at quadrature point using a bias controller. An Erbium-doped fiber amplifier (EDFA) is located at port 3 of the CIR to increase the power of the round-trip transferred optical signal. Following the EDFA, a PD and a narrow BPF is used to recover and select the 2.46-GHz signal. The 2.46-GHz signal is also used as the reference signal. At the remote end, optical signal is launched into a 90:10 optical coupler. The high power output is reflected back to the same fiber link by a FRM while the low power output is boosted by another EDFA. After amplification, $\hbox{LO}_{0}$ and $\hbox{LO}_{1}$ are recovered from optical domain and filtered out. The WTL has linewidth up to several megahertz, which greatly reduced the coherence between the Rayleigh backscattered light and the signal light. No RF power fluctuation is observed at both PDs located in the central station and remote end.

Experimentally, we compare the phase delivery stability without and with the proposed fluctuation compensation. The delay fluctuation of the 2.46-GHz signal is observed by a sampling oscilloscope (OSC), which is trigged by the same 2.46-GHz $\hbox{LO}_{0}$ at the central station. In the uncompensated delivery, the wavelength of the optical carrier is fixed at 1545 nm. Delay fluctuation of the waveform is measured and shown in Fig. 4(a) (blue line). Triangular wave with a peak-to-peak delay of 500 ps could clearly be observed since the MDL is continuously tuned back and forth. Meanwhile, environment perturbation, mostly the temperature fluctuation, has driven the delay fluctuation to around 650 ps. The temperature of the fiber has also been recorded and plotted in Fig. 4(a) (red line). One can notice a clear correlation between the temperature variation and delay fluctuation. The uncompensated total delay fluctuation is 1182.5 ps peak-to-peak. As a comparison, the stabilized 2.46-GHz signal is also measured, and the result is shown in Fig. 4(b). The delay fluctuation reflects the long-term stability of the compensation scheme [16]– [17][18]. The peak-to-peak delay fluctuation with active stabilization is 3.15 ps during $10^{4} \\hbox{s}$ recording time interval. The MDL works in the same way compared to the unstabilized condition, and the temperature change is shown in Fig. 4(b) (red line).

Fig. 4. Delay fluctuations (blue lines) of the 2.46-GHz LO signal and temperature (red lines) of the fiber spool (a) without stabilization and (b) with stabilization. An MDL is inserted into the fiber loop and tuned back and forth continuously to simulate the rapid delay fluctuation.

The delay fluctuation of the 8-GHz signal is also observed by the OSC, which is trigged by the same 8-GHz LO. Delay fluctuation of uncompensated delivery is 1034.6 ps peak-to-peak, as shown in Fig. 5(a) (blue line). While the active compensation is on, the delay fluctuation, shown in Fig. 5(b) (blue line), is suppressed to 2.08 ps peak-to-peak. The smaller delay fluctuation compared to 2.46-GHz LO is believed to be caused by the steeper waveform of 8-GHz signal, which leads to more accurate delay measurement at the OSC. The temperature variations are also recorded and shown in Fig. 5 (red lines).

Fig. 5. Delay fluctuations (blue lines) of the 8-GHz LO signal and temperature (red lines) of the fiber spool (a) without stabilization and (b) with stabilization. An MDL is inserted into the fiber loop and tuned back and forth continuously to simulate the rapid delay fluctuation.

The single sideband (SSB) phase noise between 3 Hz and $10^{6} \\hbox{Hz}$ has also been measured with a spectrum analyzer (SA), and the results are plotted in Fig. 6. The phase noise is degraded after 30-km delivery compared to the LO source. The noise of the stabilized and unstabilized situation, however, remains the same, which indicates that the compensation scheme has little effect on short-term stability.

Fig. 6. SSB phase noise of the (a) 2.46-GHz and (b) 8-GHz LO signals.
SECTION IV

## CONCLUSION

In summary, we proposed and demonstrated a multiple LO signal phase stabilization technique for long-distance fiber delivery. One of the LO signals, which acts as a reference single, is round-trip transferred between the central station and remote end, carrying the phase variation arises from the fiber link. The wavelength of optical carrier is adjusted according to the phase variation of the reference LO, to stabilize the delay of the fiber link. Once the delay of the link is stabilized, the phases of other LO signals that transferred through the fiber link will all be stabilized. The theoretical analysis shows that the fourth-order dispersion dominates the multiple phase stability of such combined delivery. Experimentally, LOs at frequencies of 2.46 GHz and 8 GHz have been transferred through a 30-km fiber link, significant phase drift compression is observed at both frequencies.

## Footnotes

This work was supported in part by the National 973 Program under Grant 2012CB315705; by the National Natural Science Foundation of China Program under Grants 61271042, 61302016, and 61335002; by the NCET-13-0682, and by the China Postdoctoral Science Foundation under Grant 2013M540891.

Corresponding author: A. Zhang (e-mail: zhanganxu@live.com).

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