Open Access
Add to BibSonomy
Abstract
We propose and experimentally demonstrate modulation format-independent optical performance monitoring (OPM) based on a multi-task artificial neural network (MT-ANN). Optical power measurements at a series of center wavelengths adjusted using a widely tunable optical bandpass filter (OBPF) are used as the input features for a MT-ANN to simultaneously realize high-precision optical signal-to-noise ratio (OSNR) and launch power monitoring and baud rate identification (BRI). This technique is insensitive to chromatic dispersion (CD) and polarization mode dispersion (PMD). The experimental verification in a 9-channel WDM system shows that for 10 Gbaud QPSK and 32 Gbaud PDM-16QAM signals with OSNR in the range of 1–30 dB, the OSNR mean absolute error (MAE) and root mean square error (RMSE) are 0.28 dB and 0.48 dB, respectively. For launch power in the range of 0–8 dBm, the MAE and RMSE of the launch power monitoring are 0.034 dB and 0.066 dB, respectively, and the identification accuracy for both baud rates is 100%. Furthermore, this technique utilizes a single MT-ANN instead of three ANNs to realize the simultaneous monitoring of three OPM parameters, which greatly reduces the cost and complexity.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
With the continuous development of new techniques such as virtual reality (VR), fifth-generation mobile communications (5G), and the Internet of Things (IoT), the dramatic growth in global network traffic has resulted in an increase in optical network capacity. To meet the ever-increasing demand for bandwidth and improve the spectrum efficiency, the dense wavelength division multiplexing (DWDM) technique and an advanced optical signal modulation format have been widely adopted in optical networks [1]. In addition, elastic optical networks (EONs) enabled by deploying reconfigurable optical add-drop multiplexers (ROADMs) [2] and flexible transceivers have been proposed in recent years to fully utilize the resources at the physical layer. Under such conditions, optical performance monitoring (OPM) is important for reducing operating costs, optimizing resource utilization, and ensuring the operation, management, and maintenance of optical networks.
The optical signal-to-noise ratio (OSNR) [3] is one of the most critical OPM parameters because it is closely related to the signal bit error rate (BER) and can provide early warning of BER degradation. Researchers have proposed diverse novel in-band OSNR monitoring techniques for coherent optical fiber transmission systems in recent years. These schemes include but are not limited to methods based on statistical moments [4], error vector magnitude (EVM) [5], amplitude histograms (AHs) [6], the Stokes parameter [7], polarization nulling [8], and reference optical spectrum [9–11]. To cater for more flexible, dynamic, and transparent link conditions in future optical networks, the digital signal processing (DSP) algorithm of the digital coherent receiver at the receiving end needs to match the selected signal modulation format and baud rate [12]. Therefore, both modulation format identification (MFI) and baud rate identification (BRI) are key tasks in OPM implementations. These tasks may be accomplished using techniques based on AHs [13], asynchronous delay-tap sampling portraits (ADTPs) [14], the variational Bayesian expectation maximization algorithm [15], signal cumulants [16], and digital frequency-offset loading [17]. It should be noted that most of these techniques focus on MFI rather than BRI [13–17]. In addition to the amplified spontaneous emission (ASE) noise introduced by the optical amplifier [18], the nonlinearities caused by the Kerr effect in the fiber also limit the performance of the optical network. The quality of the signal (QoS) after transmission will be degraded by signal and signal-noise interactions. Therefore, it is necessary to monitor the nonlinear noise in an optical network. Owing to the relationship between the launch power and nonlinear noise, the launch power is selected as a proxy for nonlinear noise in this study [19].
In recent years, machine learning (ML) has attracted great interest in optical networks research, and many studies have proposed applying machine learning in OPM. These schemes include, but are not limited to, artificial neural networks (ANNs) [20], deep neural networks (DNNs) [6], convolutional neural networks (CNNs) [21], principal component analysis (PCA) [22], and Gaussian process regression (GPR) [23,24]. However, these schemes implement only single-task monitoring. When multiple OPM parameters need to be monitored simultaneously, multiple models must be used, which increases the complexity and wastes resources. To solve this problem, several OPM schemes based on multi-task artificial neural networks (MT-ANNs) and asynchronous amplitude histograms (AAHs) have been proposed [25,26]. Although all these schemes can realize the simultaneous monitoring of multiple OPM parameters and hence reduce computational complexity and improve resource utilization, they still have the following disadvantages: (1) The AAHs are sensitive to linear impairments such as dispersion. Excessive dispersion will cause their performance to deteriorate or even fail. (2) To make the AAHs insensitive to linear impairments, it is necessary to add a DSP compensation algorithm after sampling, which increases the complexity and cost of the scheme. (3) When advanced modulation formats are applied and OSNR degradation is severe, the performance of schemes using AAHs will be degraded.
To overcome the above shortcomings, we propose a novel cost-effective and distributed OPM scheme to realize simultaneous OSNR and launch power monitoring and BRI. In the scheme, the center wavelength of a widely tunable optical bandpass filter (OBPF) [27] is adjusted and the corresponding output optical power measured using a low-speed photodiode (PD) with a bandwidth of several GHz. The measurement results are then used as the input features of the MT-ANN. The experimental results show that the proposed scheme can realize BRI and high-precision OSNR and launch power monitoring simultaneously, and is modulation format-independent and insensitive to chromatic dispersion (CD) and polarization mode dispersion (PMD). Moreover, transmission information such as transmission distance is not required for our proposed OPM technique. This means that our proposed monitor can be deployed at the intermediate nodes for link monitoring without the knowledge of any transmission information.
2. Operation principle
2.1 Proposed OPM scheme
As shown in Fig. 1, the proposed OPM monitor comprises a commercial widely-tunable OBPF, a low-speed photodiode (PD), and a signal processor. It can be placed anywhere along the transmission link, including at the intermediate nodes. The workflow of the entire OPM monitor comprises the tapping of the optical signal by the optical coupler, followed by filtering by the OBPF, and finally measurement of the corresponding optical power. In practical scenarios, optical power measurements can be used as the input features of an integrated trained MT-ANN for OPM (called MT-ANN-OPM) in the signal processor. Specifically, as shown in Fig. 2, we use the wavelength resolution (${\lambda _r}$) as a fixed step to adjust the center wavelength of the tunable OBPF and traverse the entire C-band. The optical power measurements are recorded at all the filter positions. We found that when both the optical power measurements and OPM parameters correspond to the same monitored channel, the optical power measurements at different OSNRs, baud rates, and launch powers are distinctive.
Fig. 1. Schematic diagram of the proposed OPM, which can be placed after any intermediate node. OA: optical amplifier, OPM: optical performance monitoring, OBPF: tunable optical bandpass filter, PD: low-speed photodiode.
Fig. 2. Adjustment of the center wavelength of the tunable OBPF with wavelength resolution ${\lambda _r}$. The solid black lines represent the signal optical spectrum, and the dashed red lines represent the filter shape of the tunable OBPF.
In detail, we set the channel interval of the DWDM system as $\varDelta \lambda $ and the tuning step of the widely-tunable OBPF as the wavelength resolution ${\lambda _r}$. For each channel we want to monitor, there are a total of $\varDelta \lambda \textrm{ / }{\lambda _r}$ optical power measurements that can be collected. This is equivalent to using the widely-tunable OBPF to filter the monitoring channel $\varDelta \lambda \textrm{ / }{\lambda _r}$ times and measuring the corresponding optical power as the input features of the subsequent MT-ANN. In this study, the samples for both the training and testing phases consist of an input feature vector and an output label vector. The input feature vector contains $\varDelta \lambda \textrm{ / }{\lambda _r}$ optical power measurements, and the output label vector is composed of three OPM parameters, namely the OSNR, baud rate, and launch power.
In the test phase, the test dataset is applied to the trained MT-ANN, and then the estimated OPM parameters can be obtained from the output label vector. After comparing it with the corresponding actual value, we obtain error indices such as the root mean square error (RMSE), mean absolute error (MAE), and classification accuracy to evaluate the performance of our proposed OPM scheme. The RMSE and MAE are defined in Eqs. (1) and (2), respectively, where $\textrm{y}$ is the actual value, $\hat{y}$ the estimated value, m the number of samples, and i denotes the $i$-th sample:
2.2 MT-ANN
A typical artificial neural network is usually composed of three parts: the input layer, the hidden layer, and the output layer. The Tanh and ReLu functions given in Eq. (3) and Eq. (4) respectively are commonly used as the neuron activation functions in the hidden layer. The activation function in the output layer differs depending on the output task (regression or classification). For a classification task, the activation function of the output layer should be the Softmax function given in Eq. (5). On the other hand, a regression task requires the linear function to be selected as the activation function of the output layer.
Different loss functions need to be defined according to the type of task at the output. For classification tasks, we usually select the categorical cross-entropy (CE) in Eq. (6) as the loss function. For regression tasks, we usually select the mean square error (MSE) in Eq. (7) as the loss function. It should be noted that $\textrm{y}$ is the actual value, $\hat{y}$ is the estimated value, m denotes the number of samples, i the $i$-th sample, b the $b$-th category, and C the number of categories to be classified.
The network structure of the MT-ANN used is schematically shown in Fig. 3. The input and hidden layer of the MT-ANN share the same structure as a typical single-task artificial neural network (ST-ANN). In the hidden layer, the Tanh function is used as the activation function. The MT-ANN requires multiple output layers for multiple tasks. Each output layer has a specific activation function and loss function. For the two regression tasks of OSNR and launch power monitoring, the linear function and MSE are selected as the activation function of the output layer and the loss function, respectively. For the classification task of BRI, we select the Softmax function and categorical cross-entropy as the activation function and loss function of the output layer, respectively. To calculate the total loss function $Los{s_{total}}$, the loss functions of these different tasks should be weighted and summed, as shown in Eq. (8), where $Los{s_1}$, $Los{s_2}$ and $Los{s_3}$ are the OSNR monitoring, BRI, and launch power monitoring loss functions, respectively, and $\alpha ,\; \beta $, and $\gamma $ are their respective corresponding weights.
The different tasks should be balanced to avoid any one of them dominating the training, which will result in obvious performance differences between the tasks. The weights are used to unify the scales of the loss functions. Therefore, optimizing the three weights plays an important role in improving the monitoring performance.
3. Experimental setup
Figure 4 shows the experimental setup to demonstrate our proposed OPM scheme. At the transmitter side, we set up 9 channels at 50 GHz (0.4 nm) intervals. The channel with the center wavelength of 1550.12 nm is the monitoring channel, and the remaining 8 channels are interference channels. The lights from the nine channels were combined by a multiplexer (MUX), and then modulated by an IQ modulator under the control of the electric drive signal from an arbitrary waveform generator (AWG) to generate the required signals. Specifically, we generated a 10 Gbaud NRZ-QPSK signal using an AWG (Tektronix: 7122B) and a single-polarization IQ modulator, and a 32 Gbaud PDM-16QAM signal using another AWG (Keysight: M9502A) and a polarization multiplexing IQ modulator. Next, the output optical signal was amplified by an erbium-doped fiber amplifier (EDFA), and then launched into the transmission fiber. The transmission link was composed of N spans of 80 km SSMF whose CD and PMD coefficients are typically around 17 ps/(nm·km) and 0.1ps/km1/2. At the end of each span, a backward Raman amplifier was used to fully compensate for the span losses. It should be noted that the launch power and transmission distance were changed to realize different conditions in our experiments. ASE noise generated by the ASE noise source (EXFO FLS-2300B) was introduced at the end of the link. Different ASE noise powers were obtained by adjusting a variable optical attenuator (VOA) to change the OSNR. The signal, together with different ASE noise powers, were then sent to the OPM monitor and the optical spectrum analyzer (OSA). The reference OSNR of the signal can be calculated using the On/Off method based on OSA. The commercial OBPF used in the experiment has a super-Gaussian shape with a 0.2 nm 3 dB bandwidth, and a wavelength resolution of 0.02 nm. The bandwidth of the low-speed PD is only a few gigahertz, so this scheme is cost-effective. For each specific system condition and signal format, we collected 5 samples consisting of an input feature vector and an output label vector for each individual OSNR. Finally, after generating the total sample dataset, we randomly divided the total sample dataset into the training sample dataset comprising 70% of the samples and the test sample dataset comprising the remaining 30% of the samples.
Fig. 4. Experimental setup. Mux: multiplexer, AWG: arbitrary waveform generator, EDFA: erbium-doped fiber amplifier, VOA: variable optical attenuator, OSA: optical spectrum analyzer.
As the channel spacing in this experiment was 0.4 nm and the wavelength resolution was 0.02 nm, 20 optical power measurements were obtained to form the input feature vector of the monitoring channel. The recorded baud rate (“01” stands for 10 Gbaud and “10” stands for 32 Gbaud) and the launch power of the signal were combined with the reference OSNR to form the output label vector of the sample. The Keras library based on the TensorFlow backbone was used to implement the MT-ANN construction, training, and testing because of its extremely high operability and ease of implementation. Because the size of the sample dataset was not very large, we used a relatively small network with 2 hidden layers. Each layer had 64 neurons. Generally, if there is not much training data available, it is better to use a small network with fewer hidden layers (usually 1 or 2) to avoid overfitting. After the network structure of the MT-ANN was determined, the Adam algorithm was selected as the optimizer. We also used 4-fold cross-validation to reliably evaluate the model, optimize the MT-ANN hyperparameters, and preventing overfitting during the training phase.
4. Results analysis
According communication theory, the signal spectrum does no depend on the modulation format. It changes with baud rate and roll-off factor. In ideal case, the optical spectrum of QPSK, 16QAM, 64QAM are same. Through theoretical analysis, we found that the input feature vector used can be obtained by filtering the optical spectrum several times, and that the optical spectrum is independent of the modulation format. Our proposed scheme should hence be transparent to the modulation format. To further investigate the performance of the proposed OPM scheme and verify its insensitivity to CD and PMD and its transparency to the modulation format, we adjusted the OSNR of the link under different system conditions. The corresponding transmission distance and launch power for 10 Gbaud QPSK and 32 Gbaud PDM-16QAM are given in Table 1 and Table 2, respectively. Each column in Table 1 and Table 2 represents a specific system condition setting, under different experimental conditions, the accumulated CD is from 8160 ps/nm to 32640 ps/nm and the accumulated DGD is from 2.2 ps to 4.4 ps. 615 and 590 samples were generated under the system conditions listed in Table 1 and Table 2, respectively. We then mixed the 1205 samples to generate the final sample dataset. Thus, there were 845 samples in the training dataset and 360 samples in the test dataset. It should be noted that we standardized each input feature such that the average value of each input feature was 0 and the standard deviation of each input feature was 1.
Table 1. System conditions for 10 Gbaud QPSK signal
Table 2. System conditions for 32 Gbaud PDM-16QAM signal
As mentioned previously, the weight of the loss for each task has an impact on the OPM performance. A severely unbalanced loss contribution will result in optimization of almost only the task with the largest loss value. The loss scales of the different tasks are very different, so it is necessary to use weights to balance the loss contributions from different tasks. For convenience, we list the loss weight ratio pairs ($\alpha $ to $\beta $, $\gamma $ to $\beta $) in Table 3. In this experiment, we found that the cross-entropy loss of BRI was smaller than the MSE loss of OSNR and launch power monitoring, so we did not consider the cases where the loss weight ratios are greater than 1. The MAE of the OSNR and launch power as well as the accuracy of BRI versus the loss weight ratio pair are shown in Fig. 5.
Fig. 5. OSNR and launch power monitoring average MAE as well as BRI average accuracy versus the loss weight ratio pair during the testing phase.
Table 3. Loss weight ratio pair no.
Because the performance of the MT-ANN is affected by the random initialization, we evaluated the performance by obtaining the average MAE and classification accuracy from 5 random initializations to more accurately quantify the impact of the loss weight ratio pair. As shown in Fig. 5, the average accuracy of BRI was maintained at 100%. The performance of the OSNR and launch power monitoring changed continuously as the loss weight pair changed. After a comprehensive analysis, we finally selected pair No. 10 as the loss weight ratio for subsequent evaluation. In other words, we chose the ratio of $\alpha $ to $\beta $ and $\gamma $ to $\beta $ as 0.01 and 0.1, respectively.
After optimizing the loss weight ratio pair, we then evaluated the proposed MT-ANN-based OPM scheme. Figure 6(a) shows the results of OSNR monitoring. For OSNR in the range of approximately 1–30 dB, the designed MT-ANN works well, and the MAE and RMSE are 0.28 dB and 0.48 dB, respectively. In Fig. 6(b), we further analyze the experimental results in Fig. 6(a). As can be seen in Fig. 6(b), 95% of the absolute values of the OSNR monitoring errors are less than 1 dB, and the maximum error is less than 3.1 dB. Considering that the system conditions in Table 1 and Table 2 comprise different transmission distances and 2 modulation formats, the results of the OSNR monitoring prove that our proposed OPM scheme can realize high-precision OSNR monitoring that is insensitive to CD and PMD and transparent to the modulation format. Because our input feature vector consisted of only 20 optical power measurements, the results also indicate that our proposed OPM scheme does not require transmission information such as the transmission distance for OSNR monitoring.
Fig. 6. (a) Estimated OSNRs versus reference OSNRs and (b) error histogram for OSNR estimation during the testing phase.
The BRI results are shown in Fig. 7. The BRI accuracies for 10 Gbaud and 32 Gbaud are both 100%. The results for launch power monitoring are shown in Fig. 8(a). For launch power in the range of 0–8 dBm, high-precision monitoring with an MAE of 0.034 dB and RMSE of 0.066 dB is realized. Figure 8(b) shows a further analysis of the launch power monitoring results. 94% of the absolute values of the launch power monitoring errors are less than 0.12 dB, and the absolute value of the maximum error is less than 0.51 dB. Similarly, because the system conditions included different transmission distances and two modulation formats, we can conclude that our proposed OPM scheme can achieve high-precision launch power monitoring and that the BRI is insensitive to CD and PMD and transparent to the modulation format. Moreover, transmission information such as transmission distance is not necessary for BRI and launch power monitoring.
Fig. 8. (a) Estimated launch power versus reference launch power and (b) error histogram for launch power estimation during the testing phase.
Based on the above experimental results for the three tasks and theoretical analysis, we proved that the proposed MT-ANN-based OPM scheme can simultaneously realize high-precision OSNR and launch power monitoring as well as BRI without knowledge of the transmission information, and is insensitive to CD and PMD and transparent to the modulation format. Our proposed scheme does not require expensive coherent detection equipment; it only requires a widely tunable OBPF, a low-speed PD, and a signal processor with a single integrated MT-ANN to simultaneously carry out multi-parameter monitoring without the use of multiple ANNs. It has the advantages of low cost and low complexity, and is an ideal scheme for future heterogeneous optical networks.
5. Conclusion
In this paper, a cost-effective distributed OPM scheme based on MT-ANN is proposed and experimentally demonstrated in a 9-channel WDM system with a 50 GHz grid. Using a widely tunable OBPF, a low-speed PD, and a signal processor integrated with a MT-ANN, the proposed OPM scheme can realize high-precision monitoring of OSNR and launch power, and BRI simultaneously. The experimental results for both the 32 Gbaud PDM-16QAM and the 10 Gbaud QPSK signals show that for OSNR in the range of 1–30 dB, the MAE and RMSE of the OSNR monitoring are 0.28 dB and 0.48 dB, respectively. For launch power in the range of 0–8 dBm, the MAE and RMSE of the launch power monitoring are 0.034 dB and 0.066 dB, respectively. The BRI accuracy for both the 10 Gbaud and 32 Gbaud signals reached 100%. The OPM scheme utilizes a multi-task learning technique and a single MT-ANN instead of three ANNs to simultaneously monitor three OPM parameters, greatly reducing the complexity and cost. In addition, we find that our proposed OPM scheme is transparent to the modulation format and insensitive to CD and PMD. Moreover, because the cost of our scheme is low and the input feature vector consists of only 20 optical power measurements, our proposed OPM scheme has the potential to be applied at the intermediate nodes of optical networks and can be used without any prior knowledge of the transmission information such as transmission distance.
Funding
National Key Research and Development Program of China (2018YFB2200900).
Acknowledgments
The authors wish to thank Dr. Shaohua Yu and Zhixue He from the Wuhan Research Institute of Posts and Telecommunications for their help.
Disclosures
The authors declare no conflicts of interest.
References
1. Z. Dong, F. N. Khan, Q. Sui, K. Zhong, C. Lu, and A. P. T. Lau, “Optical performance monitoring: A review of current and future technologies,” J. Lightwave Technol. 34(2), 525–543 (2016). [CrossRef]
2. J. C. Cartledge, “Performance of coherent optical fiber transmission systems,” Front. Optoelectron. 11(2), 128–133 (2018). [CrossRef]
3. A. D. Shiner, M. E Mousa-Pasandi, M. Qiu, M. A. Reimer, E. Y. Park, M. Hubbard, Q. Zhuge, F. J. V. Caballero, and M. O’Sullivan, “Neural network training for OSNR estimation from prototype to product,” in Proc. Optical Fiber Communication Conference (OSA, 2020), paper M4E.2.
4. C. Zhu, A. V. Tran, S. Chen, L. B. Du, C. C. Do, T. Anderson, A. J. Lowery, and E. Skafidas, “Statistical moments-based OSNR monitoring for coherent optical systems,” Opt. Express 20(16), 17711–17721 (2012). [CrossRef]
5. R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012). [CrossRef]
6. F. N. Khan, K. Zhong, X. Zhou, W. H. Al-Arashi, C. Yu, C. Lu, and A. P. T. Lau, “Joint OSNR monitoring and modulation format identification in digital coherent receivers using deep neural networks,” Opt. Express 25(15), 17767–17776 (2017). [CrossRef]
7. L. Lundberg, H. Sunnerud, and P. Johannisson, “In-band OSNR monitoring of PM-QPSK using the Stokes parameters,” in Proc. Optical Fiber Communication Conference (OFC, 2015), paper W4D. 5.
8. J. H. Lee, H. Y. Choi, S. K. Shin, and Y. C. Chung, “A review of the polarization-nulling technique for monitoring optical-signal-to-noise ratio in dynamic WDM networks,” J. Lightwave Technol. 24(11), 4162–4171 (2006). [CrossRef]
9. Z. Dong, K. Zhong, X. Zhou, C. Lu, A. P. T. Lau, Y. Lu, and L. Li, “Modulation-format-independent OSNR monitoring insensitive to cascaded filtering effects by low-cost coherent receptions and RF power measurements,” Opt. Express 23(12), 15971–15982 (2015). [CrossRef]
10. G. Yin, S. Cui, C. Ke, and D. Liu, “Reference optical spectrum based in-band OSNR monitoring method for EDFA amplified multispan optical fiber transmission system with cascaded filtering effect,” IEEE Photonics J. 10(3), 1–10 (2018). [CrossRef]
11. F. Locatelli, K. Christodoulopoulos, M. S. Moreolo, J. M. Fàbrega, and S. Spadaro, “Machine learning-based in-band OSNR estimation from optical spectra,” IEEE Photonics Technol. Lett. 31(24), 1929–1932 (2019). [CrossRef]
12. Y. Li, Q. Zheng, J. Han, and W. Li, “Low complexity carrier phase estimation for m-QAM optical communication systems,” Photonics Netw. Commun. 38(1), 121–128 (2019). [CrossRef]
13. F. N. Khan, Y. Zhou, A. P. T. Lau, and C. Lu, “Modulation format identification in heterogeneous fiber-optic networks using artificial neural networks,” Opt. Express 20(11), 12422–12431 (2012). [CrossRef]
14. F. N. Khan, Y. Yu, M. C. Tan, W. H. Al-Arashi, C. Yu, A. P. T. Lau, and C. Lu, “Experimental demonstration of joint OSNR monitoring and modulation format identification using asynchronous single channel sampling,” Opt. Express 23(23), 30337–30346 (2015). [CrossRef]
15. R. Borkowski, D. Zibar, A. Caballero, V. Arlunno, and I. T. Monroy, “Stokes space-based optical modulation format recognition for digital coherent receivers,” IEEE Photonics Technol. Lett. 25(21), 2129–2132 (2013). [CrossRef]
16. S. M. Bilal, G. Bosco, Z. Dong, A. P. T. Lau, and C. Lu, “Blind modulation format identification for digital coherent receivers,” Opt. Express 23(20), 26769–26778 (2015). [CrossRef]
17. S. Fu, Z. Xu, J. Lu, H. Jiang, Q. Wu, Z. Hu, M. Tang, D. Liu, and C. C.-K. Chan, “Modulation format identification enabled by the digital frequency-offset loading technique for hitless coherent transceiver,” Opt. Express 26(6), 7288–7296 (2018). [CrossRef]
18. Q. Feng, W. Li, and L. Huang, “Analysis of spontaneous Raman and Rayleigh scatterings in distributed fiber Raman amplification systems based on a random distributed model,” IEEE Photonics J. 9(6), 1–8 (2017). [CrossRef]
19. D. Lippiatt, S. Varughese, T. Richter, S. Tibuleac, and S. E. Ralph, “Joint linear and nonlinear noise estimation of optical links by exploiting carrier phase recovery,” in Proc. Optical Fiber Communication Conference (OFC, 2020), paper Th2A. 49.
20. J. Thrane, J. Wass, M. Piels, J. C. M. Diniz, R. Jones, and D. Zibar, “Machine learning techniques for optical performance monitoring from directly detected PDM-QAM signals,” J. Lightwave Technol. 35(4), 868–875 (2017). [CrossRef]
21. T. Tanimura, T. Hoshida, T. Kato, S. Watanabe, and H. Morikawa, “Convolutional neural network-based optical performance monitoring for optical transport networks,” J. Opt. Commun. Netw. 11(1), A52–A59 (2019). [CrossRef]
22. M. C. Tan, F. N. Khan, W. H. Al-Arashi, Y. Zhou, and A. P. T. Lau, “Simultaneous optical performance monitoring and modulation format/bit-rate identification using principal component analysis,” J. Opt. Commun. Netw. 6(5), 441–448 (2014). [CrossRef]
23. C. Hu, W. Li, H. Zheng, Q. Feng, Q. Zheng, and Y. Wang, “A novel cost-effective and distributed in-band OSNR monitoring method using Gaussian process regression,” IEEE Photonics J. 11(4), 1–12 (2019). [CrossRef]
24. C. Hu, H. Zheng, W. Li, Q. Feng, M. Mei, Y. Wang, and R. Yan, “Modulation-format-independent in-band OSNR monitoring technique using Gaussian process regression for a Raman amplified multi-span system with a cascaded filtering effect,” Opt. Express 28(7), 10134–10144 (2020). [CrossRef]
25. Y. Cheng, S. Fu, M. Tang, and D. Liu, “Multi-task deep neural network (MT-DNN) enabled optical performance monitoring from directly detected PDM-QAM signals,” Opt. Express 27(13), 19062–19074 (2019). [CrossRef]
26. Z. Wan, Z. Yu, L. Su, Y. Zhao, H. Zhang, and K. Xu, “Intelligent optical performance monitor using multi-task learning based artificial neural network,” Opt. Express 27(8), 11281–11291 (2019). [CrossRef]
27. S. Oda, Y. Aoki, M. Sekiya, Y. Akasaka, K. Sone, Jeng-Yuan Yang, and J. C. Rasmussen, “In-band OSNR monitor using an optical bandpass filter and optical power measurements for superchannel signals,” in Proc. European Conference and Exhibition on Optical Communication (ECOC, 2013), paper P.3.12.
