Open Access
Add to BibSonomy
Abstract
The Five-hundred-meter Aperture Spherical radio Telescope (FAST) located in Guizhou, China, is a very sensitive single dish telescope. Due to the large size of the telescope, optical fiber is used for the transmission of the 3-km astronomical signal from the telescope to the signal processing center. The optical fibers are suspended in the air above the telescope reflector, very easy to slide when the telescope feed cabin moves, resulting in phase drifts for the transmission signal. This phase drift has a negative impact on the observation mode of very long baseline interferometry, and can be compensated by the frequency transfer system in the FAST. In this manuscript, we propose a new phase drift compensation scheme, which is denoted as data-aided channel equalization scheme. The proposed scheme is based on a hypothesis of linear phase relationship between different wavelengths in the same optical fiber, and uses the channel response information of the data-aided channel to conduct signal recovery for the astronomical signal channel. Not only the phase drift, but also the frequency-dependent distortion of the broadband transmission link can be compensated. The proposed scheme has simple transmission structure, and the function part is well modularized, so that the Astronomer users can easily turn it on or off. In the proof-of-concept experiments, the estimation deviation can be significantly reduced by estimated channel responses averaging over training sequence repetitions, showing very high accuracy of the astronomical signal channel estimation.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The Five-hundred-meter Aperture Spherical radio Telescope (FAST) located in Guizhou, China, has a diameter of 500 m. FAST operates at frequencies ranging from 70 to 3000 MHz and is the most sensitive single dish telescope in this frequency range. Fig. 1 shows an aerial view of FAST. A feed cabin, which is driven by six cable robots, is hang 140 m above the reflector to receive the astronomical radio signal [1]. Fig. 2 shows the detailed structure of the cable robot. The steel cables bear the heavy of the feed cabin and the cable robot itself. The drawstring and optical fibers hung down over the steel cable. Due to the large receiver bandwidth and long observation time, the data quantity is too large to be saved locally in the size-limited feed cabin. The FAST uses optical fibers to transmit the received signal from feed cabin to the processing center 3 km away. When the FAST scans the sky, the steel cables pull the feed cabin and keep it on the so-called “focused surface” [1]. Even when observing a single target in tracking mode, it is necessary to move the feed cabin to compensate for the angular change caused by the earth rotation. During the movement of the feed cabin, the length of the steel cable between the feed cabin and the cable tower changes, resulting that the optical fiber hang below the movable clamps slides like a curtain. The fiber type is G.657, which is insensitive to fiber bending and guarantees low vibration of optical power when fiber slide happens. However, the optical fiber still has a phase drifting effect during fiber slide, which has a negative impact on the observation mode of very long baseline interferometry (VLBI) [2]. The phase drift can be detected and compensated in the round-trip transmission by the frequency transfer technology [3–6], and the phase correction system in FAST also uses this technology.
Since the transfer of the astronomical signal is actually an one-direction transmission from the feed cabin to the processing center, and the demand of phase compensation happens only at the processing center side, there are two types of signal recovery technique in the optical communication research field that can monitor the phase of the transmitted signal, which are the blind equalization and the data-aided equalization [7]. The blind equalization, such as CMA, MMA, and DD-LMS, uses characteristic of the constellation for signal recovery [8,9]. The astronomical signal is the radiation of the celestial body. The model of such signal is white noise, which can not be equalized by its constellation information. The data-aided equalization is transparent to the modulation format. The system channel response can be estimated by the inserted known data [7,10–12]. However, the signal information would be lost if we replace some part of the continued astronomical signal with assisting data. Furthermore, the data-aided equalization is hard to identify burst phase shift.
Currently, FAST has deployed 144 optical fibers to support the signal transmission for 25 receivers in the feed cabin. FAST uses “one channel per fiber” signal transmission method, that is, 25 received signals are transmitted through 25 different fibers. Therefore, the transmission system needs to monitor independent phase drifts of 25 signals.
In this paper, we propose a data-aided channel equalization scheme. The astronomical signal would not be transmitted through different fibers, but transmitted in one single fiber by wavelength-division-multiplexing (WDM) method. Two data-aided channels are also transmitted in the same fiber. A hypothesis is introduced that the channel responses of different wavelengths in the same fiber have linear relationship. Base on such hypothesis, the channel response, including not only the phase drift, but also the frequency-dependent power distortion of different astronomical signals, can be recovered in the processing center by using the estimated channel information of the two data-aided channels. Thanks to the WDM structure, the proposed scheme has a compact system structure. The rest of the paper is outlined as follows. In Section 2, we introduce the principle of the proposed scheme. In Section 3, we conduct proof-of-concept experiments to test the hypothesis and the proposed scheme. Finally, the conclusions are drawn in Section 4.
2. Scheme principle
Figure 3 shows the proposed equalization scheme. In the feed cabin, there are two types of optical transmitter, which are the data-aided channel transmitter (DCT) and the astronomical signal over fiber transmitter (ASOFT). In the ASOFT, each astronomical radio signal is modulated independently on an optical carrier. The astronomical signal is fed to the 90°electrical hybrid, and then the hybrid output signals are respectively sent to the two arms of the dual-drive Mach-Zehnder modulator (DMZM), thus forming the single sideband (SSB) modulation. The advantage of SSB signal is that it can be directly detected by the photodetector (PD). The ASOFT output signal ${E_{AT}}$ can be expressed as:
${J_n}({\cdot} )$ is the nth-order Bessel function of the first kind.
In the DCT, two lasers with different wavelength are used as optical carriers of data-aided channel. The training signal module generates repeated known radio signals, covering the frequency range of the astronomical signal. The training signal is also modulated by SSB modulation on the DMZM with the help of an electrical 90°hybrid. The training signal has root-raised cosine (RRC) pulse shaping. The output signal of the feed cabin is a WDM signal, containing the astronomical signal bands in the middle of the optical spectrum and data-aided channel bands at the both sides. Considering the small signal modulation of the training signal, the output signal of the feed cabin can be expressed as:
The angular frequency of DCT optical carrier is denoted as ${\omega _{os,k}}$. For the training signal, ${\omega _s}$ is its center radio angular frequency, and $s(t )$ is its equivalent baseband signal waveform. $r \cdot s(t )\textrm{ = }{{{V_s} \cdot s(t )} / {{V_\pi }}}$ is the modulation index on the modulator, where ${V_s}$ is the output voltage of the training signal.
After the Erbium doped fiber amplifier (EDFA), the signal is sent to the hanging optical fiber cable. The theory transmission loss of the 3 km G.657 fiber is as low as about 0.6 dB. In the processing center, a WDM demultiplexer (DEMUX) is used to separate the optical signals. Each band of the signal ${E_{TD}}$ contains only one optical carrier and one signal sideband, which is then detected by an independent PD. Under the small signal modulation, ${J_1}({{m_i}{A_i}(t )} )\approx {J_1}({{m_i}} )\cdot {A_i}(t )$, and ${J_1}({r \cdot s(t )} )\approx {J_1}(r )\cdot s(t )$. The output photocurrent of the PD is given by
The transmission link can be modeled as a conventional Additive White Gaussian Noise (AWGN) channel, in which the noise is mainly the amplifier spontaneous emission (ASE) noise introduced by the EDFA. For AWGN channel, best estimation performance is achieved using noise-like sequences with good autocorrelation properties. Constant amplitude zero autocorrelation (CAZAC) sequence has flat Fourier transform and zero autocorrelation, and is one of the optimum sequences for maximum-likelihood channel estimation in the AWGN model [13,14]. The CAZAC sequence we used for training sequence is also referred to Zadoff-Chu sequence, which is defined as
In the processing center, the PD photocurrents $i(t )$ in Eq. (4) are digitized and jointly processed with all signal wavelength, so that all signals are processed under the same clock. Therefore, signals at different wavelength would not suffer from additional drifting phase shift in the processing center. We assume that the channel response of different wavelength in the same transmission fiber has linear relationship, which means that the channel responses of the astronomical signal bands can be interpolated from the estimated channel responses of the two data-aided channels. The proposed equalization scheme is based on the frequency domain equalization algorithm. In fact, time domain equalization algorithm can also calculate the equalization filter taps for signal recovery [8,9,15]. However, the time-domain equalization algorithm uses the transmitted symbols for equalization filter taps training. This convergence mechanism results in the estimated channel response not being the current instantaneous response, but the result of long-term convergence training. Therefore, once the phase drift occurs, it is difficult for the time-domain equalization algorithm to detect it immediately. As for the frequency domain equalization algorithm, it has low complexity, and use training sequence to directly estimate the instantaneous phase response [7,10–12,16], which is suitable for channel monitoring scenarios. Fig. 4 shows the detailed DSP procedure in the processing center. After signal acquisition, the data-aided channel signals are firstly down converted to the base band. Matched filtering provides the best detection concerning the signal to noise ratio (SNR). Frequency domain channel estimation is conducted on each training sequence [16]. The estimation results are the amplitude and phase responses versus frequency. The real time channel responses of astronomical signal channels are interpolated from the two estimated channel responses of data-aided channels. Then, the equalization filter taps are calculated based on the interpolated channel responses. During the time domain filtering, not only the phase drift, but also the real-time frequency-dependent system amplitude distortion can be compensated. It should be pointed out that the transmitter in the feed cabin does not need an external clock, because the processing center can recover the transmitter's clock from the signal. This kind of clock recovery can use the traditional digital clock recovery algorithm [17–19], or the frequency domain estimation algorithm proposed in this article, where the clock comes from the long-term phase response. Specifically, the clock frequency difference between the transmitter and the receiver is calculated from the slope of the receiver-end phase response on the time axis.
3. Experimental results
Proof-of-concept experiments are carried out according to Fig. 3. To study the relation of channel response at different wavelength, the astronomical signals are replaced by two other training sequence channels. Therefore, there are altogether four data-aided channels transmitted through the optical fiber at four evenly distributed wavelengths. Fig. 5 shows the cable robot we use in the experiment. The cable robot is designed and manufactured according to FAST’s design. The optical fiber cable we use in the experiment is the same batch of the fiber cables as FAST. The steel cable is connected to a weight, which is driven by an electric motor. In the experiment, the optical signal goes through about 60 m G.657 fiber. In Fig. 1 and 2, the cable length between the feed cabin and cable tower is about 300 m. The fiber slide happens only under the part of movable clamp, which have less than 200 m optical fiber. Therefore, the transmission length in the experiment is comparable to FAST. The linewidth of laser diodes in the feed cabin end is about 100 kHz. The 2.4 Gbaud training sequences with the center frequency at 2 GHz are generated by an arbitrary waveform generator (AWG). The frequency resolution is linearly correlated to the pattern length of the training sequence. The roll-off factor of RRC pulse is 0.1. A waveshaper (Finisar-4000s) is used as the WDM DEMUX.
Figure 6 shows the measured signal optical spectra before and after the transmission link with a resolution of 0.02nm. The black curve shows the signal spectra before the EDFA. The blue, green, orange, and red curves stand for the signals spectra of 4 separate branches after WDM DEMUX, respectively. The transmitted signal goes from the spectrum in black to spectrum of other colors through the EDFA, the optical fiber and the WDM DEMUX. The EDFA provides a signal power gain of 13 dB, amplifying the signal from 2 dBm to 15 dBm. The transmission fiber and the WDM DEMUX result in a total power loss of 12 dB, including the theoretical attenuation of 6 dB due to signal division from 1 to 4 fibers.
Figure 7 shows the channel estimation result on one CAZAC sequence, which reflects the static channel response of the transmission system. The frequency resolution is linearly correlated to the pattern length of the training sequence, which is $N = 128$ in the experiment. Therefore, the channel estimation results are distributed evenly at 128 frequency points from 0.8 GHz to 3.2 GHz. Due to the roll-off factor of 0.1, 115 (calculated from $128 \times ({1 - 0.1} )$) results from 0.92 GHz to 3.08 GHz are shown in Fig. 7. Figure 7(a) shows the amplitude response, while Fig. 7(b) shows the phase response. The distortions, especially in Fig. 7(a), are the frequency-dependent loss of the system, which mainly comes from the bandwidth-limit effect of the AWG, modulators, PDs and the processer. It must be emphasized that the bandwidth-limit effect of the AWG only happens in the data-aided channel. In the practical scenario, the AWG needs to pre-compensate its amplitude response.
Fig. 7. Channel estimation result by one CAZAC sequence. (a) Amplitude response, (b) phase response.
Figure 8(a) shows the estimated amplitude response of channel 1 along with training sequence repeating of 50 times. One training sequence takes 53.3 ns. The estimated amplitude response fluctuates due to the system ASE noise. Figure 8(b) is the superposition of all points of Fig. 8 (a) in time domain. Since each channel estimation is based on the training sequence at different time, the noises that interfere to different channel estimations are irrelevant. Therefore, by averaging the estimation results, the influence of noise on the estimation can be effectively reduced. Theoretically, under static channel condition, the estimation accuracy is positively correlated with the averaging number. Figure 8(c) is the estimated amplitude response averaged with nearby 4 results. Figure 8(c) shows that, by averaging estimation results over training sequence repetitions, the channel estimation deviation due to the ASE noise is reduced.
Fig. 8. (a) The estimated amplitude response along with training sequence repetition of 50 times. (b) Superposition of estimated results in time domain, and then (c) averaging with 4 nearby results.
Figure 9(a) shows the estimated phase response of the channel 1 along with training sequence repeating of 50 times. The estimated phase response also fluctuates due to system ASE noise. Figure 9(b) is the superposition of all points of Fig. 9 (a) in the time domain. Figure 9(c) is the estimated phase response averaged with nearby 4 results. Figure 9(c) shows that, the estimated phase response deviation can also be mitigated by averaging over training sequence repetitions. For the moving cable in the practical system, the signal’s phase will drift. The averaging number of results cannot be too large, because it will lead to high computational complexity, and furthermore take up a long period of training sequences, hereby weakening the ability to track sudden phase changes. In extreme cases, if the phase shift changes quickly, the long-term averaging will erase the phase change information during the averaging time length, resulting in the estimation result not accurately reflecting the real instantaneous phase response. In practical applications, the averaging length should be optimized according to the system requirements.
Fig. 9. (a) The estimated phase response along with training sequence repetition of 50 times. (b) Superposition of estimated results in time domain, and then (c) averaging with 4 nearby results.
By turning on the driving motor, the weight in the Fig. 5 goes up and down, drawing the steel cable moving back and forward. The hanged optical cables slide unregularly due to the slide of the movable clamp. The actual motion of FAST is that the feed cabin is pulled by multiple steel cables. Obviously, for each steel cable in the FAST system, the sliding mode of the optical fiber hanging below it is consistent with the sliding that occurred in the experiment. Figure 10(a) shows the phase drifting results within relatively long observation time. There are eight estimated phase response results presented within the time duration of 90 s. Each phase response curve is the average value of estimated results from 50 training sequences. Figure 10(b) is the superposition of all curves of Fig. 10(a) in time domain, noting that the overall phase offset between results from different observation time is removed. Figure 10(b) shows that, after removing the overall phase offset, the estimated phase responses almost overlap. The detailed phase responses of each channel are shown in the insets of Fig. 10(b). The estimation deviation is very low because each curve is the average value of 50 estimation results. Fig. 10 shows that, despite the detected phase shifting unregularly, the phase relation between different channels keeps the same. Therefore, the linear relationship of phase response is thus validated in our experiment, meaning that we can restore the phase response of astronomical signal channel with data-aided channels.
Fig. 10. (a) Estimated phase responses at different observation time, and (b) superposition of estimated results in time domain.
4. Conclusion
We propose a data-aided channel equalization scheme as a new technology to solve the phase drift problem in the signal transmission system of the FAST. The hypothesis of linear phase relationship between different wavelengths in the same optical fiber is verified in the proof-of-concept experiment. Base on this hypothesis, the processing center can use the estimated channel information of the two data-aided channels to recover the broadband channel response of different astronomical signals, including phase and amplitude response. Since all of the received signals in the feed cabin are transmitted in the same fiber by the WDM method, the signal recovery of the all astronomical signal channels only needs two data-aided channels, which makes the system structure very simple. In the experiment, the fluctuation of estimation results can be significantly reduced by conducting value averaging over training sequence repetitions. The proposed scheme features the advantage of simple structure, large bandwidth monitoring, high estimation accuracy and good modularity, providing a promising new solution for radio telescopes VLBI observation.
Funding
National Natural Science Foundation of China (61690195, 61801038, 61821001, U1831110); Fundamental Research Funds for the Central Universities (2019XD-A15-2).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. P. Jiang, Y. Yue, H. Gan, R. Yao, H. Li, G. Pan, J. Sun, D. Yu, H. Liu, N. Tang, L. Qian, J. Lu, J. Yan, B. Peng, S. Zhang, Q. Wang, Q. Li, and D. Li, “Commissioning progress of the FAST,” Sci. China: Phys., Mech. Astron. 62(5), 959502 (2019). [CrossRef]
2. D. Li and R. Duan, “FAST A+: A Cost-Effective Plan for Expanding FAST,” IEEE international conference on microwaves, antennas, communications and electronic systems, (2019). [CrossRef]
3. S. Foreman, K. Holman, D. Hudson, D. Jones, and J. Ye, “Remote transfer of ultrastable frequency references via fiber networks,” Rev. Sci. Instrum. 78(2), 021101 (2007). [CrossRef]
4. X. Chen, J. Zhang, J. Lu, X. Lu, X. Tian, B. Liu, H. Wu, T. Tang, K. Shi, and Z. Zhang, “Feed-forward digital phase compensation for long-distance precise frequency dissemination via fiber network,” Opt. Lett. 40(3), 371–374 (2015). [CrossRef]
5. C. Liu, T. Jiang, M. Chen, S. Yu, R. Wu, J. Shang, J. Duan, and W. Gu, “GVD-insensitive stable radio frequency phase dissemination for arbitrary-access loop link,” Opt. Express 24(20), 23376 (2016). [CrossRef]
6. J. Lin, Z. Wang, Z. Lei, J. Dong, Y. Wang, J. Shang, T. Jiang, B. Luo, and S. Yu, “Michelson interferometer based phase demodulation for stable time transfer over 1556 km fiber links,” Opt. Express 29(10), 14505–14512 (2021). [CrossRef]
7. M. Kuschnerov, M. Chouayakh, K. Plyawanno, B. Spinnler, E. de Man, P. Kainzmaier, M. Alfiad, A. Napoli, and B. Lankl, “Data-Aided Versus Blind Single-Carrier Coherent Receivers,” IEEE Photonics J. 2(3), 387–403 (2010). [CrossRef]
8. X. Zhou, “Digital signal processing for coherent multi-level modulation formats,” Chin. Opt. Lett. 8(9), 090401 (2010). [CrossRef]
9. X. Zhou, L. Nelson, P. Magill, R. Issac, B. Zhu, D. Peckham, P. Borel, and K. Carlson, “PDM-Nyquist-32QAM for 450-Gb/s Per-Channel WDM Transmission on the 50 GHz ITU-T Grid,” J. Lightwave Technol. 30(4), 553–559 (2012). [CrossRef]
10. Z. Zheng, R. Ding, F. Zhang, and Z. Chen, “1.76Tb/s Nyquist PDM 16QAM signal transmission over 714 km SSMF with the modified SCFDE technique,” Opt. Express 21(15), 17505–17511 (2013). [CrossRef]
11. C. Zhu, A. Tran, C. Do, S. Chen, T. Anderson, and E. Skafidas, “Digital Signal Processing for Training-Aided Coherent Optical Single-carrier Frequency-Domain Equalization Systems,” J. Lightwave Technol. 32(24), 4712–4722 (2014). [CrossRef]
12. R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent Optical Single Carrier Transmission Using Overlap Frequency Domain Equalization for Long-Haul Optical Systems,” J. Lightwave Technol. 27(16), 3721–3728 (2009). [CrossRef]
13. F. Pittala, F. N. Hauske, and Y. Ye, “Fast and robust CD and DGD estimation based on data-aided channel estimation,” in 13th Internat. Conf. on Transparent Opt. Netw. (ICTON), p. We.D1.5, (2011). [CrossRef]
14. U. Rohrs and L. Linde, “Some unique properties and applications of perfect squares minimum phase CAZAC sequences,” in Proc. South African Symp. Comm. Signal Process. (COMSIG), 155–160 (1992). [CrossRef]
15. F. Zhang, D. Wang, R. Ding, and Z. Chen, “Terabit Nyquist PDM-32QAM signal transmission with training sequence based time domain channel estimation,” Opt. Express 22(19), 23415–23426 (2014). [CrossRef]
16. Z. Zheng, F. Frey, P. Wilke Berenguer, and J. Fischer, “Low-complexity equalization scheme for multicarrier offset-QAM systems,” IEEE Photon. Tech. Lett. 29(23), 2075–2078 (2017). [CrossRef]
17. X. Zhou, “Efficient Clock and Carrier Recovery Algorithms for Single-Carrier Coherent Optical Systems,” IEEE Signal Process. Mag. 31(2), 35–45 (2014). [CrossRef]
18. X. Zhou and X. Chen, “Parallel implementation of all-digital timing recovery for high-speed and real-time optical coherent receivers,” Opt. Express 19(10), 9282 (2011). [CrossRef]
19. M. Kuschnerov, F. Hauske, K. Piyawanno, B. Spinnler, M. Alfiad, A. Napoli, and B. Lankl, “DSP for Coherent Single-Carrier Receivers,” J. Lightwave Technol. 27(16), 3614–3622 (2009). [CrossRef]
