- Email: [email protected]
Joint monitoring of chromatic dispersion, OSNR and inter-channel nonlinearity by LFM pilot
Optics and Laser Technology 111 (2019) 447–451
Contents lists available at ScienceDirect
Optics and Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Full length article
Joint monitoring of chromatic dispersion, OSNR and inter-channel nonlinearity by LFM pilot ⁎
T
⁎
Aiying Yanga, , Peng Guoa, , Wanli Wangb, Yueming Luc, Yaojun Qiaob a
School of Optoelectronics, Beijing Institute of Technology, Beijing 100081, China Beijing Key Laboratory of Space-ground Interconnection and Convergence, Beijing University of Posts and Telecommunications, Beijing 100876, China c Key Laboratory of Trustworthy Distributed Computing and Service, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China b
H I GH L IG H T S
CD, OSNR and inter-channel NL are monitored simultaneously by our method. • The CD estimation precision is improved by zero padding at the receiver. • The OSNR monitoring is insensitive to fiber NL. • The • Accurate inter-channel NL monitoring is achieved.
A R T I C LE I N FO
A B S T R A C T
Keywords: Metrology Fiber non-linear optics Fiber optics systems
A novel joint monitoring method is proposed for dynamic and reconfigurable optical transmission systems to estimate chromatic dispersion (CD), optical signal-to-noise ratio (OSNR) and inter-channel nonlinearity (NL) simultaneously. This method utilizes two linear-frequency modulation (LFM) pilots with different center frequencies at two polarizations. The CD is estimated by the peak position difference of two pilots in fractional domain. Compare to previous work of CD estimation, the monitoring precision of CD is improved by zero padding at the receiver. The OSNR and the inter-channel NL are obtained in frequency and fractional domain. By verification of 9-channel 28 GBaud wavelength division multiplexing QPSK and 16QAM systems after 1000 km transmission, it proves that this method achieves stable CD (<200 ps/nm error), nonlinearity tolerant OSNR and accurate inter-channel NL (<1 dB error) monitoring.
1. Introduction Chromatic dispersion (CD), optical signal-to-noise ratio (OSNR) and inter-channel nonlinearity (NL) are three of the most important parameters in optical long haul transmission system. Each of these three parameters judges the quality of the received signal and the performance of optical transmission system. The CD monitoring error may lead to clock recovery and carrier synchronization failure in optical transmission [1]. There are mainly two ways to estimate CD. The first approach is by statistical quantities of received signal. The statistical quantities include Peak to Average Power Ratio (PAPR) [2], fractional Fourier transformation (FrFT) of received signals [3] and so on. The second approach is by inserting special pilot such as sinusoidal signals [4], phase modulated tones [5] and amplitude modulated tones [6]. The OSNR is also important for system optimization [7] and the noise in OSNR refers to the amplified spontaneous emission (ASE) noise
⁎
specifically. Therefore the monitoring of OSNR is affected by optical fiber NL. To overcome the interference by fiber NL, both statistical approaches [8,9] and special plot approaches are proposed [10–12] to monitor OSNR. The fiber NL can degrade the system performance and the intra-channel NL can be efficiently compensated by digital backward propagation or perturbation method [13,14]. Therefore interchannel NL becomes the key interference for optical transmission. To monitor the power of inter-channel NL, Zhao et al. first proposed the method by angular squeezing of differential pilot (DP) [15]. However, the method in [15] underestimates the power of inter-channel NL and the reason is that carrier phase recovery which is conducted before angular squeezing of DP can remove part of the phase change induced by XPM effect. Then we proposed 2 inter-channel NL estimation methods. The inter-channel NL is monitored by FrFT of linear-frequency modulation (LFM) in [12] and by frequency domain extraction of DP in [16]. Compared to the method in [15], the power of inter-
Corresponding authors. E-mail addresses: [email protected] (A. Yang), [email protected] (P. Guo), [email protected] (Y. Qiao).
https://doi.org/10.1016/j.optlastec.2018.10.021 Received 22 June 2018; Received in revised form 3 October 2018; Accepted 12 October 2018 0030-3992/ © 2018 Elsevier Ltd. All rights reserved.
Optics and Laser Technology 111 (2019) 447–451
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zero padding) and sampling frequency fs , the optimum order is
channel NL is not underestimated anymore and the computational complexity is reduced in [12,16]. For dynamic and reconfigurable wavelength division multiplexing (WDM) systems, each channel may have different paths. Therefore the accumulated CD, OSNR and NL of each channel are different at the receiver. Inserting a pilot in the channel under test is a promising way for parameter monitoring in dynamic and reconfigurable WDM networks. In [17], the CD is monitored by FrFT of LFM signal. The CD monitoring method in [17] has quite good robustness against ASE and NL noise. The monitoring precision of CD can be improved by utilizing larger frequency offset between 2 LFM signals. If 2 LFM signals are located at the same channel, the monitoring precision is limited because the bandwidth of 1 channel is restricted. The method in [12] cannot monitor the CD because there is no center frequency difference between LFM pilots. In this paper, we propose a new structure of time domain LFM pilot, which enables joint monitoring of CD, OSNR and inter-channel NL. To the best of our knowledge, it is the first time that CD, OSNR and interchannel NL are monitored simultaneously. By using LFM pilot with different center frequencies at 2 polarizations, the CD is monitored by FrFT after zero padding at the receiver, which improves the monitoring precision of CD compared to previous work. The power of ASE noise is measured in frequency domain to monitor OSNR and the OSNR monitoring is insensitive to nonlinear noise. At last the power of interchannel NL is calculated by the NL distribution difference between frequency domain and fractional domain. At last, the proposed multiparameter monitor is verified in 9-channel QPSK/16QAM systems with symbol rate 28 GBaud per channel.
arctan ((Tfs − 1) k / f s2 )
1+ [17]. D=
and the accumulated CD D can be obtained by (2)
ΔPh−ΔPv (λh−λ v ) fs cos (π /2 + arctan ((Tfs−1) k / f s2 )))
(2)
where ΔPh and ΔPv are the peak position differences of LFM signals before and after transmission in fractional domain for h and v polarizations and the corresponding wavelengths of LFM signals are λh and λ v . The monitoring resolution Dunit is expressed by (3).
Dunit =
1 (λh−λ v ) fs cos (π /2 + arctan ((Tfs−1) k / f s2 )))
(3)
When 2 LFM signals are inserted in a signal channel like the scheme in Fig. 1 and there is no zero padding at the receiver, the equivalent time T equals to the time duration of LFM pilot TLFM and the resolution is too high for CD monitoring. We should reduce the value of Dunit to achieve better resolution of CD monitoring. Since the frequency offset and sampling rate is limited, we have to change the equivalent time T or chirp rate k. According to the monotonicity of (3), larger equivalent time T or larger chirp rate k will both make the monitoring resolution lower. If the allocated time for LFM pilot is fixed to ensure the spectrum efficiency and monitoring stability, the bandwidth of the LFM pilot should be increased to make the chirp rate k larger. However, the ASE measurement will be affected more by nonlinear noise if the bandwidth of the LFM signals becomes larger. Therefore it is better to keep the chirp rate k unchanged. The best way to improve the monitoring resolution is by zero padding at the receiver to make the equivalent time T larger. After zero padding at the receiver, the optimum order of FrFT is increased and it makes the measurable chromatic dispersion smaller. The amplitudes of LFM pilot with and without zero padding in fractional domain are shown in Fig. 2 and the amplitude of the signal with zero padding is normalized to make the power unchanged. As depicted in Fig. 2, the number of points within the peak for the system with zero padding is much more than the system without zero padding at the receiver. Therefore the measurement precision of CD is improved by zero padding compared to our previous work [17]. After CD monitoring by (2) and CD compensation, the OSNR is calculated by (4) in frequency domain.
2. Principle of monitoring The LFM pilot is located in front of the payload and each frame contains one period of LFM pilot. The period is denoted by TLFM and the LFM signal of one period is expressed in (1). The power spectrum of LFM signal in frequency domain and fractional domain are shown in Fig. 1.
x (t ) = exp [j (2πfh / v t + πkt 2)]
π/2
(1)
where fh / v is the carrier frequency for h or v polarization and k is the chirp rate. As depicted in Fig. 1(c) and (d), there exists a peak difference in fractional domain after optimum order of FrFT if CD is not zero. To increase the CD estimation precision, the sampled signal is zero padded before FrFT. For digitally sampled signal with equivalent time T (after
Fig. 1. Power distribution of LFM pilot. (a) Frequency domain after transmission, h polarization; (b) frequency domain after transmission, v polarization; (c) fractional domain before and after transmission, h polarization; (d) fractional domain before and after transmission, v polarization. 448
Optics and Laser Technology 111 (2019) 447–451
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Fig. 2. Amplitude of LFM pilot with and without zero padding in fractional domain.
Fig. 4. (a) CD monitoring performance for QPSK system with different amount of accumulated CD; (b) OSNR monitoring performance for QPSK and 16QAM systems after 5 and 10 spans with different OSNR.
ASE measurement zone shown in Fig. 1(a) and (b), BAM is the bandwidth of ASE measurement zone, BSample is the bandwidth of the sampled signal and BR is the standard OSNR measurement bandwidth (12.5 GHz). The OSNR monitoring by (4) is insensitive to NL, as the methods demonstrated in [10–12]. After OSNR monitoring and optimum order of FrFT, the power of the signal in fractional domain with peak excluded can be seen as the combination of ASE noise and interchannel NL [12]. Therefore the inter-channel NL can be estimated by (5) by subtracting the power of the peak and the ASE noise measured in frequency domain. Fig. 3. (a) The schematic diagram of system for verification; (b) the frame structure for channel under test and interference channels. Top: Time domain. Bottom: Frequency domain.
OSNR = 10 × lg ( = 10 × lg (
Pinter − channelNL = PTotal−PPeak−PASE = PTotal−PPeak−BSample NAM / BAM
where PPeak is the power of the peak in fractional domain. To make the CD monitoring resolution smaller, we utilize the method of zero padding on the LFM signal, which increases the equivalent time T. After CD monitoring, CD needs to be compensated for the following OSNR and NL monitoring. To reduce the complexity of CD compensation, zero padding is removed from the signal. At last, OSNR and NL are monitored after CD compensation. According to our simulation, the
(PTotal − PASE ) BAM ) NAM BR (PTotal − BSample NAM / BAM ) BAM NAM BR
)
(5)
(4)
where PTotal is the total power of the received signal, PASE is the total power of ASE noise in the received signal, NAM is the power of noise in 449
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Fig. 5. (a) Inter-channel NL monitoring performance for QPSK and 16QAM systems after 5 and 10 spans with different OSNR; (b) inter-channel NL monitoring performance for QPSK and 16QAM systems after 5 and 10 spans with different launch power.
fiber loss 0.2 dB/km and CD coefficient 16 ps/nm/km. The nonlinear coefficient is set to 1.31 W−1 km−1. The linewidths of the lasers in transmitter and receiver are set to 100 kHz. After de-multiplexing of the channel under test, the signal is sampled with the sampling rate 56 GSa/s. The sampled pilot is zero padded before and after the sampled sequence with equivalent time 16 times the period of LFM pilot when measuring CD. The ASE measurement zone is located at 0 frequency and BAM is 3 GHz. To verify the inter-channel NL monitoring performance, the reference value of inter-channel NL is obtained by the same method in [12].
precision of OSNR and inter-channel NL monitoring is almost the same with or without zero padding. Above all, CD estimation needs zero padding for better monitoring resolution. The OSNR and inter-channel NL monitoring don’t need zero padding for lower complexity.
3. System setup The proposed monitoring method is verified by Virtual Photonics Inc. (VPI) Transmission Maker. The schematic diagram is depicted in Fig. 3(a) and the frame structure is shown in Fig. 3(b). Two polarizations are both utilized and the symbol rate is 28 GBaud for both QPSK and 16QAM systems. There are 9 channels with channel space 50 GHz and the center channel is under test with LFM pilot inserted as Fig. 3(b). Before multiplexing 9 channels, each channel is Gaussian filtered with bandwidth 40 GHz. The frame size of each channel is 16384 symbols and the LFM pilot occupies 2048 symbols. Each frame contains one period of LFM pilot and the bandwidth of LFM pilot is 7 GHz. The center frequencies for h and v polarizations are negative and positive 20 GHz respectively. The center frequency of the data is the same as the carrier. The link we use is Standard Single Mode Fiber with each span 100 km,
4. Results First we test the monitoring performance of CD and OSNR with different pre-set OSNR. The total launch power for 9 channels is fixed at 14 dBm. The CD and OSNR is monitored at the end of each span after activating the “Add ASE” module shown in Fig. 3(a). The ASE noise in the Erbium Doped Fiber Amplifier (EDFA) s is removed. As depicted in Fig. 4(a), the estimated CD is almost the same as the pre-set CD and the estimation error is lower than 200 ps/nm. For QPSK system with pre-set 450
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NL monitoring also has low estimation error (within 1 dB after 1000 km transmission).
OSNR value from 0 dB to 25 dB, the estimation performance of CD barely changes, which reveals that our CD estimation method has excellent robustness against noise. Then we test the OSNR monitoring performance in Fig. 4(b). The largest estimation error for OSNR monitoring is 2.74 dB, when the pre-set OSNR is 27 dB after 10 spans and the modulation format is QPSK. We find that there is more interchannel NL in the ASE measurement zone of QPSK system, which results in the OSNR estimation performance difference between QPSK and 16QAM system. We also find that the estimation error of OSNR becomes larger for larger number of spans. The reason is that the residual NL contained in the ASE measurement zone is larger for larger number of spans. The launch power per channel is 4.46 dBm (14 dBm for 9 channels) and the nonlinearity is extremely large after 10 spans transmission. For larger pre-set OSNR, the OSNR estimation error will be more obvious because the power of ASE noise becomes less compared to the power of nonlinear noise in the ASE measurement zone. Second we compare the monitored inter-channel NL with the reference value. To verify the inter-channel NL monitoring robustness against ASE noise, the launch power per channel is fixed to be 4.46 dBm (14 dBm for 9 channels). The ASE noise in the EDFAs is removed and the “Add ASE” module is activated. The inter-channel NL monitoring results with different OSNR are shown in Fig. 5(a). The estimation of inter-channel NL is precise and the estimation error of inter-channel NL is within 1 dB for both QPSK and 16QAM systems after 500 km and 1000 km transmission with pre-set OSNR value from 12 dB to 27 dB. Then we deactivate the “Add ASE” module and the noise figure of each EDFA is set to be 6 dB. We test the inter-channel NL performance with total launch power of 9 channels from 10 dBm to 16 dBm, which is depicted in Fig. 5(b). The monitoring error of inter-channel NL is within 1 dB except for the QPSK system after 500 km transmission. The estimation error becomes larger for QPSK system after 500 km transmission because the power of inter-channel NL is smaller and the estimation error becomes more obvious compared to the reference value.
Acknowledgement This work is supported by National Natural Science Foundation of China (Grant No. 61427813) and National Key R&D Program (Grant No. 2016YFB0800302). References [1] F.N. Hauske, Z. Zhang, C. Li, C. Xie, Q. Xiong, Precise, robust and least complexity cd estimation, OFX/NFOEC, 2011, pp. 1–3. [2] C. Xie, Chromatic dispersion estimation for single-carrier coherent optical communications, IEEE Photonics Technol. Lett. 25 (10) (2013) 992–995. [3] A. Yang, X. Chen, Method for measuring chromatic dispersion of optical fiber link through fractional order fourier transformation, China Patent (201410752087.8). [4] Y. Lu, C. Baker, L. Chen, X. Bao, Chromatic-dispersion monitor based on a differential phase-shift method using a Kerr phase-interrogator, IEEE Photonics J. 7 (2) (2015) 1–6. [5] M.N. Petersen, Z. Pan, S. Lee, S.A. Havstad, A.E. Willner, Online chromatic dispersion monitoring and compensation using a single inband subcarrier tone, IEEE Photonics Technol. Lett. 14 (4) (2002) 570–572. [6] T.E. Dimmick, G. Rossi, D.J. Blumenthal, Optical dispersion monitoring technique using double sideband subcarriers, Photonics Technol. Lett. IEEE 12 (7) (2000) 900–902. [7] S.J. Savory, Congestion aware routing in nonlinear elastic optical networks, IEEE Photonics Technol. Lett. 26 (26) (2014) 1057–1060. [8] Z. Dong, A.P.T. Lau, C. Lu, OSNR monitoring for QPSK and 16-QAM systems in presence of fiber nonlinearities for digital coherent receivers, Opt. Express 20 (17) (2012) 19520–19534, https://doi.org/10.1364/OE.20.019520. [9] A. Kashi, Q. Zhuge, J. Cartledge, A. Borowiec, C. Douglas, C. Laperle, M. O’sullivan, Fiber nonlinear noise-to-signal ratio monitoring using artificial neural networks, European Conference on Optical Communication, 2017 p. M.2.F.. [10] L. Dou, Z. Tao, Y. Zhao, S. Oda, Y. Aoki, T. Hoshida, J.C. Rasmussen, Differential pilots aided in-band OSNR monitor with large nonlinear tolerance, Optical Fiber Communications Conference and Exhibition, 2015 p. W4D.3. [11] L. Dou, T. Yamauchi, X. Su, Z. Tao, S. Oda, Y. Aoki, T. Hoshida, J. Rasmussen, An accurate nonlinear noise insensitive OSNR monitor, Optical Fiber Communication Conference and Exposition, 2016 p. W3A.5. [12] W. Wang, A. Yang, P. Guo, Y. Lu, Y. Qiao, Joint OSNR and interchannel nonlinearity estimation method based on fractional fourier transform, J. Lightwave Technol. 35 (20) (2017) 4497–4506, https://doi.org/10.1109/JLT.2017.2744666. [13] Y. Gao, J.H. Ke, J.C. Cartledge, K.P. Zhong, Implication of parameter values on lowpass filter assisted digital back propagation for DP 16-QAM, Photonics Technol. Lett. IEEE 25 (10) (2013) 917–920. [14] L. Dou, Z. Tao, L. Li, W. Yan, A low complexity pre-distortion method for intrachannel nonlinearity, Optical Fiber Communication Conference and Exposition, 2011, pp. 1–3. [15] Y. Zhao, Z. Tao, S. Oda, Y. Aoki, T. Hoshida, Pilot based cross phase modulation power estimation, Optical Fiber Communications Conference and Exhibition, 2017 p. W1G.2. [16] W. Wang, A. Yang, P. Guo, Y. Lu, Y. Qiao, Monitoring inter-channel nonlinearity based on differential pilot, Opt. Commun. 417 (2018) 24–29. [17] W. Wang, Y. Qiao, A. Yang, P. Guo, A novel noise-insensitive chromatic dispersion estimation method based on fractional fourier transform of LFM signals, IEEE Photonics J. 9 (1) (2017) 1–12, https://doi.org/10.1109/JPHOT.2016.2647207.
5. Conclusion A novel multi-parameter monitor for dynamic and reconfigurable WDM networks is proposed by utilizing a new structure of LFM pilot. It is the first time that CD, OSNR and inter-channel NL are monitored by the same plot. This method enables the function to monitor CD compared to previous proposed joint OSNR and inter-channel NL estimation method. The CD monitoring precision is also improved by zero-padding at the receiver compared to previous LFM pilot method of CD estimation. The estimation is verified with 9-channel 28 GBaud QPSK/16QAM after 1000 km transmission. The CD monitor has high precision (within 200 ps/nm) and the CD estimation results reveals excellent robustness against noise with pre-set OSNR as low as 0 dB. The OSNR estimation is also insensitive to NL for low pre-set OSNR values. The inter-channel
451
Contents lists available at ScienceDirect
Optics and Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Full length article
Joint monitoring of chromatic dispersion, OSNR and inter-channel nonlinearity by LFM pilot ⁎
T
⁎
Aiying Yanga, , Peng Guoa, , Wanli Wangb, Yueming Luc, Yaojun Qiaob a
School of Optoelectronics, Beijing Institute of Technology, Beijing 100081, China Beijing Key Laboratory of Space-ground Interconnection and Convergence, Beijing University of Posts and Telecommunications, Beijing 100876, China c Key Laboratory of Trustworthy Distributed Computing and Service, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China b
H I GH L IG H T S
CD, OSNR and inter-channel NL are monitored simultaneously by our method. • The CD estimation precision is improved by zero padding at the receiver. • The OSNR monitoring is insensitive to fiber NL. • The • Accurate inter-channel NL monitoring is achieved.
A R T I C LE I N FO
A B S T R A C T
Keywords: Metrology Fiber non-linear optics Fiber optics systems
A novel joint monitoring method is proposed for dynamic and reconfigurable optical transmission systems to estimate chromatic dispersion (CD), optical signal-to-noise ratio (OSNR) and inter-channel nonlinearity (NL) simultaneously. This method utilizes two linear-frequency modulation (LFM) pilots with different center frequencies at two polarizations. The CD is estimated by the peak position difference of two pilots in fractional domain. Compare to previous work of CD estimation, the monitoring precision of CD is improved by zero padding at the receiver. The OSNR and the inter-channel NL are obtained in frequency and fractional domain. By verification of 9-channel 28 GBaud wavelength division multiplexing QPSK and 16QAM systems after 1000 km transmission, it proves that this method achieves stable CD (<200 ps/nm error), nonlinearity tolerant OSNR and accurate inter-channel NL (<1 dB error) monitoring.
1. Introduction Chromatic dispersion (CD), optical signal-to-noise ratio (OSNR) and inter-channel nonlinearity (NL) are three of the most important parameters in optical long haul transmission system. Each of these three parameters judges the quality of the received signal and the performance of optical transmission system. The CD monitoring error may lead to clock recovery and carrier synchronization failure in optical transmission [1]. There are mainly two ways to estimate CD. The first approach is by statistical quantities of received signal. The statistical quantities include Peak to Average Power Ratio (PAPR) [2], fractional Fourier transformation (FrFT) of received signals [3] and so on. The second approach is by inserting special pilot such as sinusoidal signals [4], phase modulated tones [5] and amplitude modulated tones [6]. The OSNR is also important for system optimization [7] and the noise in OSNR refers to the amplified spontaneous emission (ASE) noise
⁎
specifically. Therefore the monitoring of OSNR is affected by optical fiber NL. To overcome the interference by fiber NL, both statistical approaches [8,9] and special plot approaches are proposed [10–12] to monitor OSNR. The fiber NL can degrade the system performance and the intra-channel NL can be efficiently compensated by digital backward propagation or perturbation method [13,14]. Therefore interchannel NL becomes the key interference for optical transmission. To monitor the power of inter-channel NL, Zhao et al. first proposed the method by angular squeezing of differential pilot (DP) [15]. However, the method in [15] underestimates the power of inter-channel NL and the reason is that carrier phase recovery which is conducted before angular squeezing of DP can remove part of the phase change induced by XPM effect. Then we proposed 2 inter-channel NL estimation methods. The inter-channel NL is monitored by FrFT of linear-frequency modulation (LFM) in [12] and by frequency domain extraction of DP in [16]. Compared to the method in [15], the power of inter-
Corresponding authors. E-mail addresses: [email protected] (A. Yang), [email protected] (P. Guo), [email protected] (Y. Qiao).
https://doi.org/10.1016/j.optlastec.2018.10.021 Received 22 June 2018; Received in revised form 3 October 2018; Accepted 12 October 2018 0030-3992/ © 2018 Elsevier Ltd. All rights reserved.
Optics and Laser Technology 111 (2019) 447–451
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zero padding) and sampling frequency fs , the optimum order is
channel NL is not underestimated anymore and the computational complexity is reduced in [12,16]. For dynamic and reconfigurable wavelength division multiplexing (WDM) systems, each channel may have different paths. Therefore the accumulated CD, OSNR and NL of each channel are different at the receiver. Inserting a pilot in the channel under test is a promising way for parameter monitoring in dynamic and reconfigurable WDM networks. In [17], the CD is monitored by FrFT of LFM signal. The CD monitoring method in [17] has quite good robustness against ASE and NL noise. The monitoring precision of CD can be improved by utilizing larger frequency offset between 2 LFM signals. If 2 LFM signals are located at the same channel, the monitoring precision is limited because the bandwidth of 1 channel is restricted. The method in [12] cannot monitor the CD because there is no center frequency difference between LFM pilots. In this paper, we propose a new structure of time domain LFM pilot, which enables joint monitoring of CD, OSNR and inter-channel NL. To the best of our knowledge, it is the first time that CD, OSNR and interchannel NL are monitored simultaneously. By using LFM pilot with different center frequencies at 2 polarizations, the CD is monitored by FrFT after zero padding at the receiver, which improves the monitoring precision of CD compared to previous work. The power of ASE noise is measured in frequency domain to monitor OSNR and the OSNR monitoring is insensitive to nonlinear noise. At last the power of interchannel NL is calculated by the NL distribution difference between frequency domain and fractional domain. At last, the proposed multiparameter monitor is verified in 9-channel QPSK/16QAM systems with symbol rate 28 GBaud per channel.
arctan ((Tfs − 1) k / f s2 )
1+ [17]. D=
and the accumulated CD D can be obtained by (2)
ΔPh−ΔPv (λh−λ v ) fs cos (π /2 + arctan ((Tfs−1) k / f s2 )))
(2)
where ΔPh and ΔPv are the peak position differences of LFM signals before and after transmission in fractional domain for h and v polarizations and the corresponding wavelengths of LFM signals are λh and λ v . The monitoring resolution Dunit is expressed by (3).
Dunit =
1 (λh−λ v ) fs cos (π /2 + arctan ((Tfs−1) k / f s2 )))
(3)
When 2 LFM signals are inserted in a signal channel like the scheme in Fig. 1 and there is no zero padding at the receiver, the equivalent time T equals to the time duration of LFM pilot TLFM and the resolution is too high for CD monitoring. We should reduce the value of Dunit to achieve better resolution of CD monitoring. Since the frequency offset and sampling rate is limited, we have to change the equivalent time T or chirp rate k. According to the monotonicity of (3), larger equivalent time T or larger chirp rate k will both make the monitoring resolution lower. If the allocated time for LFM pilot is fixed to ensure the spectrum efficiency and monitoring stability, the bandwidth of the LFM pilot should be increased to make the chirp rate k larger. However, the ASE measurement will be affected more by nonlinear noise if the bandwidth of the LFM signals becomes larger. Therefore it is better to keep the chirp rate k unchanged. The best way to improve the monitoring resolution is by zero padding at the receiver to make the equivalent time T larger. After zero padding at the receiver, the optimum order of FrFT is increased and it makes the measurable chromatic dispersion smaller. The amplitudes of LFM pilot with and without zero padding in fractional domain are shown in Fig. 2 and the amplitude of the signal with zero padding is normalized to make the power unchanged. As depicted in Fig. 2, the number of points within the peak for the system with zero padding is much more than the system without zero padding at the receiver. Therefore the measurement precision of CD is improved by zero padding compared to our previous work [17]. After CD monitoring by (2) and CD compensation, the OSNR is calculated by (4) in frequency domain.
2. Principle of monitoring The LFM pilot is located in front of the payload and each frame contains one period of LFM pilot. The period is denoted by TLFM and the LFM signal of one period is expressed in (1). The power spectrum of LFM signal in frequency domain and fractional domain are shown in Fig. 1.
x (t ) = exp [j (2πfh / v t + πkt 2)]
π/2
(1)
where fh / v is the carrier frequency for h or v polarization and k is the chirp rate. As depicted in Fig. 1(c) and (d), there exists a peak difference in fractional domain after optimum order of FrFT if CD is not zero. To increase the CD estimation precision, the sampled signal is zero padded before FrFT. For digitally sampled signal with equivalent time T (after
Fig. 1. Power distribution of LFM pilot. (a) Frequency domain after transmission, h polarization; (b) frequency domain after transmission, v polarization; (c) fractional domain before and after transmission, h polarization; (d) fractional domain before and after transmission, v polarization. 448
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Fig. 2. Amplitude of LFM pilot with and without zero padding in fractional domain.
Fig. 4. (a) CD monitoring performance for QPSK system with different amount of accumulated CD; (b) OSNR monitoring performance for QPSK and 16QAM systems after 5 and 10 spans with different OSNR.
ASE measurement zone shown in Fig. 1(a) and (b), BAM is the bandwidth of ASE measurement zone, BSample is the bandwidth of the sampled signal and BR is the standard OSNR measurement bandwidth (12.5 GHz). The OSNR monitoring by (4) is insensitive to NL, as the methods demonstrated in [10–12]. After OSNR monitoring and optimum order of FrFT, the power of the signal in fractional domain with peak excluded can be seen as the combination of ASE noise and interchannel NL [12]. Therefore the inter-channel NL can be estimated by (5) by subtracting the power of the peak and the ASE noise measured in frequency domain. Fig. 3. (a) The schematic diagram of system for verification; (b) the frame structure for channel under test and interference channels. Top: Time domain. Bottom: Frequency domain.
OSNR = 10 × lg ( = 10 × lg (
Pinter − channelNL = PTotal−PPeak−PASE = PTotal−PPeak−BSample NAM / BAM
where PPeak is the power of the peak in fractional domain. To make the CD monitoring resolution smaller, we utilize the method of zero padding on the LFM signal, which increases the equivalent time T. After CD monitoring, CD needs to be compensated for the following OSNR and NL monitoring. To reduce the complexity of CD compensation, zero padding is removed from the signal. At last, OSNR and NL are monitored after CD compensation. According to our simulation, the
(PTotal − PASE ) BAM ) NAM BR (PTotal − BSample NAM / BAM ) BAM NAM BR
)
(5)
(4)
where PTotal is the total power of the received signal, PASE is the total power of ASE noise in the received signal, NAM is the power of noise in 449
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Fig. 5. (a) Inter-channel NL monitoring performance for QPSK and 16QAM systems after 5 and 10 spans with different OSNR; (b) inter-channel NL monitoring performance for QPSK and 16QAM systems after 5 and 10 spans with different launch power.
fiber loss 0.2 dB/km and CD coefficient 16 ps/nm/km. The nonlinear coefficient is set to 1.31 W−1 km−1. The linewidths of the lasers in transmitter and receiver are set to 100 kHz. After de-multiplexing of the channel under test, the signal is sampled with the sampling rate 56 GSa/s. The sampled pilot is zero padded before and after the sampled sequence with equivalent time 16 times the period of LFM pilot when measuring CD. The ASE measurement zone is located at 0 frequency and BAM is 3 GHz. To verify the inter-channel NL monitoring performance, the reference value of inter-channel NL is obtained by the same method in [12].
precision of OSNR and inter-channel NL monitoring is almost the same with or without zero padding. Above all, CD estimation needs zero padding for better monitoring resolution. The OSNR and inter-channel NL monitoring don’t need zero padding for lower complexity.
3. System setup The proposed monitoring method is verified by Virtual Photonics Inc. (VPI) Transmission Maker. The schematic diagram is depicted in Fig. 3(a) and the frame structure is shown in Fig. 3(b). Two polarizations are both utilized and the symbol rate is 28 GBaud for both QPSK and 16QAM systems. There are 9 channels with channel space 50 GHz and the center channel is under test with LFM pilot inserted as Fig. 3(b). Before multiplexing 9 channels, each channel is Gaussian filtered with bandwidth 40 GHz. The frame size of each channel is 16384 symbols and the LFM pilot occupies 2048 symbols. Each frame contains one period of LFM pilot and the bandwidth of LFM pilot is 7 GHz. The center frequencies for h and v polarizations are negative and positive 20 GHz respectively. The center frequency of the data is the same as the carrier. The link we use is Standard Single Mode Fiber with each span 100 km,
4. Results First we test the monitoring performance of CD and OSNR with different pre-set OSNR. The total launch power for 9 channels is fixed at 14 dBm. The CD and OSNR is monitored at the end of each span after activating the “Add ASE” module shown in Fig. 3(a). The ASE noise in the Erbium Doped Fiber Amplifier (EDFA) s is removed. As depicted in Fig. 4(a), the estimated CD is almost the same as the pre-set CD and the estimation error is lower than 200 ps/nm. For QPSK system with pre-set 450
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NL monitoring also has low estimation error (within 1 dB after 1000 km transmission).
OSNR value from 0 dB to 25 dB, the estimation performance of CD barely changes, which reveals that our CD estimation method has excellent robustness against noise. Then we test the OSNR monitoring performance in Fig. 4(b). The largest estimation error for OSNR monitoring is 2.74 dB, when the pre-set OSNR is 27 dB after 10 spans and the modulation format is QPSK. We find that there is more interchannel NL in the ASE measurement zone of QPSK system, which results in the OSNR estimation performance difference between QPSK and 16QAM system. We also find that the estimation error of OSNR becomes larger for larger number of spans. The reason is that the residual NL contained in the ASE measurement zone is larger for larger number of spans. The launch power per channel is 4.46 dBm (14 dBm for 9 channels) and the nonlinearity is extremely large after 10 spans transmission. For larger pre-set OSNR, the OSNR estimation error will be more obvious because the power of ASE noise becomes less compared to the power of nonlinear noise in the ASE measurement zone. Second we compare the monitored inter-channel NL with the reference value. To verify the inter-channel NL monitoring robustness against ASE noise, the launch power per channel is fixed to be 4.46 dBm (14 dBm for 9 channels). The ASE noise in the EDFAs is removed and the “Add ASE” module is activated. The inter-channel NL monitoring results with different OSNR are shown in Fig. 5(a). The estimation of inter-channel NL is precise and the estimation error of inter-channel NL is within 1 dB for both QPSK and 16QAM systems after 500 km and 1000 km transmission with pre-set OSNR value from 12 dB to 27 dB. Then we deactivate the “Add ASE” module and the noise figure of each EDFA is set to be 6 dB. We test the inter-channel NL performance with total launch power of 9 channels from 10 dBm to 16 dBm, which is depicted in Fig. 5(b). The monitoring error of inter-channel NL is within 1 dB except for the QPSK system after 500 km transmission. The estimation error becomes larger for QPSK system after 500 km transmission because the power of inter-channel NL is smaller and the estimation error becomes more obvious compared to the reference value.
Acknowledgement This work is supported by National Natural Science Foundation of China (Grant No. 61427813) and National Key R&D Program (Grant No. 2016YFB0800302). References [1] F.N. Hauske, Z. Zhang, C. Li, C. Xie, Q. Xiong, Precise, robust and least complexity cd estimation, OFX/NFOEC, 2011, pp. 1–3. [2] C. Xie, Chromatic dispersion estimation for single-carrier coherent optical communications, IEEE Photonics Technol. Lett. 25 (10) (2013) 992–995. [3] A. Yang, X. Chen, Method for measuring chromatic dispersion of optical fiber link through fractional order fourier transformation, China Patent (201410752087.8). [4] Y. Lu, C. Baker, L. Chen, X. Bao, Chromatic-dispersion monitor based on a differential phase-shift method using a Kerr phase-interrogator, IEEE Photonics J. 7 (2) (2015) 1–6. [5] M.N. Petersen, Z. Pan, S. Lee, S.A. Havstad, A.E. Willner, Online chromatic dispersion monitoring and compensation using a single inband subcarrier tone, IEEE Photonics Technol. Lett. 14 (4) (2002) 570–572. [6] T.E. Dimmick, G. Rossi, D.J. Blumenthal, Optical dispersion monitoring technique using double sideband subcarriers, Photonics Technol. Lett. IEEE 12 (7) (2000) 900–902. [7] S.J. Savory, Congestion aware routing in nonlinear elastic optical networks, IEEE Photonics Technol. Lett. 26 (26) (2014) 1057–1060. [8] Z. Dong, A.P.T. Lau, C. Lu, OSNR monitoring for QPSK and 16-QAM systems in presence of fiber nonlinearities for digital coherent receivers, Opt. Express 20 (17) (2012) 19520–19534, https://doi.org/10.1364/OE.20.019520. [9] A. Kashi, Q. Zhuge, J. Cartledge, A. Borowiec, C. Douglas, C. Laperle, M. O’sullivan, Fiber nonlinear noise-to-signal ratio monitoring using artificial neural networks, European Conference on Optical Communication, 2017 p. M.2.F.. [10] L. Dou, Z. Tao, Y. Zhao, S. Oda, Y. Aoki, T. Hoshida, J.C. Rasmussen, Differential pilots aided in-band OSNR monitor with large nonlinear tolerance, Optical Fiber Communications Conference and Exhibition, 2015 p. W4D.3. [11] L. Dou, T. Yamauchi, X. Su, Z. Tao, S. Oda, Y. Aoki, T. Hoshida, J. Rasmussen, An accurate nonlinear noise insensitive OSNR monitor, Optical Fiber Communication Conference and Exposition, 2016 p. W3A.5. [12] W. Wang, A. Yang, P. Guo, Y. Lu, Y. Qiao, Joint OSNR and interchannel nonlinearity estimation method based on fractional fourier transform, J. Lightwave Technol. 35 (20) (2017) 4497–4506, https://doi.org/10.1109/JLT.2017.2744666. [13] Y. Gao, J.H. Ke, J.C. Cartledge, K.P. Zhong, Implication of parameter values on lowpass filter assisted digital back propagation for DP 16-QAM, Photonics Technol. Lett. IEEE 25 (10) (2013) 917–920. [14] L. Dou, Z. Tao, L. Li, W. Yan, A low complexity pre-distortion method for intrachannel nonlinearity, Optical Fiber Communication Conference and Exposition, 2011, pp. 1–3. [15] Y. Zhao, Z. Tao, S. Oda, Y. Aoki, T. Hoshida, Pilot based cross phase modulation power estimation, Optical Fiber Communications Conference and Exhibition, 2017 p. W1G.2. [16] W. Wang, A. Yang, P. Guo, Y. Lu, Y. Qiao, Monitoring inter-channel nonlinearity based on differential pilot, Opt. Commun. 417 (2018) 24–29. [17] W. Wang, Y. Qiao, A. Yang, P. Guo, A novel noise-insensitive chromatic dispersion estimation method based on fractional fourier transform of LFM signals, IEEE Photonics J. 9 (1) (2017) 1–12, https://doi.org/10.1109/JPHOT.2016.2647207.
5. Conclusion A novel multi-parameter monitor for dynamic and reconfigurable WDM networks is proposed by utilizing a new structure of LFM pilot. It is the first time that CD, OSNR and inter-channel NL are monitored by the same plot. This method enables the function to monitor CD compared to previous proposed joint OSNR and inter-channel NL estimation method. The CD monitoring precision is also improved by zero-padding at the receiver compared to previous LFM pilot method of CD estimation. The estimation is verified with 9-channel 28 GBaud QPSK/16QAM after 1000 km transmission. The CD monitor has high precision (within 200 ps/nm) and the CD estimation results reveals excellent robustness against noise with pre-set OSNR as low as 0 dB. The OSNR estimation is also insensitive to NL for low pre-set OSNR values. The inter-channel
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