Abstract

We experimentally demonstrate a transfer learning (TL) simplified multi-task deep neural network (MT-DNN) for joint optical signal-to-noise ratio (OSNR) monitoring and modulation format identification (MFI) from directly detected PDM-64QAM signals. First, we investigate the quality of amplitude histogram (AH) generation on the performance of OSNR monitoring and experimentally clarify the importance of higher electronic sampling rate in order to realize precise OSNR monitoring for high-order QAM format. Next, by implementing TL from simulation to experiment, when both 10Gbaud PDM-16QAM and PDM-64QAM signals are considered, the accuracy of MFI reaches 100% and the root-mean-square error (RMSE) of OSNR monitoring is 1.09dB over a range of 14-24dB and 23-34dB for PDM-16QAM and PDM-64QAM, respectively. Meanwhile, the used training samples and epochs can be substantially reduced by 24.5% and 44.4%, respectively. Since single photodetector (PD) and one TL simplified MT-DNN are used, the proposed optical performance monitoring (OPM) scheme with high cost performance can be applied for advanced modulation formats.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Since optical network becomes more dynamic, complex and transparent, optical performance monitoring (OPM) is indispensable to ensure high quality-of-service and reliable optical networking [1]. Optical signal-to-noise ratio (OSNR) is primarily desired for the OPM implementation for its immediate relationship with the bit error ratio (BER) of fiber optical transmission [2]. Moreover, as for the rapid development of elastic optical network, the digital signal processing (DSP) at the receiver side is sensitive to the used modulation format for various transmission scenarios. Therefore, modulation format identification (MFI) has become a critical task for the OPM implementation [3]. For many techniques realizing the OSNR monitoring and MFI [410], the choose of coherent detection with high sampling rate analog-to-digital converter (ADC) leads to a high cost OPM implementation, which is inconvenient for online real-time monitoring. Alternatively, relying on single one photodetector (PD) to realize the OSNR monitoring for advanced modulation formats is ideally desired. In particular, amplitude histogram (AH) is commonly used, because the AH generated by single PD can be used to statistically analyze the amplitude characteristics of received signal [11]. Recently, OSNR monitoring has been demonstrated by using the AH together with coherent detection for advanced modulation formats [6,7]. For those schemes, the modulation formats to be monitored can be up to polarization-division-multiplexed (PDM) 64-quadrature amplitude modulation (QAM) with the smallest mean-absolute error (MAE) of 1dB. However, as for the single PD direct detection, realizing precise OSNR monitoring by AH is only possible for PDM-16QAM signals with a root-mean-square error (RMSE) of 0.68dB [12]. Since PDM-64QAM will be deployed soon in next-generation long haul fiber optical transmission [13], low cost OSNR monitoring for high-order QAM formats is particularly important. Moreover, the quality of AH generation on the performance of OSNR monitoring has not been comprehensively investigated for high-order QAM formats.

Machine learning technique has been widely used in the OPM, due to its powerful autonomous learning capabilities [14,15]. However, as for the multi-task OPM, these methods have the disadvantage of requiring either multiple deep neural networks (DNNs) or other machine learning algorithms, in order to separately realize MFI and OSNR monitoring, leading to high calculation complexity and slow response [6,7,16]. Recently, we have demonstrated a multi-task DNN (MT-DNN) for joint OSNR monitoring and MFI from directly detected PDM-QAM signals [13]. However, MT-DNN needs to realize multiple tasks simultaneously, leading to a huge training cost. Moreover, as for all existing machine learning enabled OPM techniques [410], when the condition of transmission link varies, huge number of new training samples and epochs are compulsory to manage DNN correct operation, leading to heavy time consumption and less flexibility. Recently, transfer learning (TL) has been proposed for optical network [17,18]. By adjusting the weight of neurons based on the previous knowledge instead of random initialization, TL can greatly reduce the use of training samples to 35% for the DNN-based OSNR monitoring [17]. However, such method can only realize the OSNR monitoring by knowledge transfer between different experimental scenarios. Generally, in comparison with the experimental data, the simulation data have the advantages of easy generation and elastic acquisition. Therefore, it is possible to reduce the requested experimental samples and epochs for the MT-DNN enabled OPM, by the TL from simulation to experiment.

In current submission, the effect of AH generation on the performance of OSNR monitoring has been investigated, and we experimentally clarify the importance of higher electronic sampling rate to realize precise OSNR monitoring for high-order QAM format. Furthermore, based on single TL simplified MT-DNN, we can simultaneously realize both OSNR monitoring and MFI, with great reduction of MT-DNN complexity and training cost. Our experimental result shows that the MFI accuracy can reach 100% and the RMSE of OSNR monitoring is 1.09dB over a range from 14-24dB and 23-34dB for PDM-16QAM and PDM-64QAM, respectively. Meanwhile, the used samples and epochs can be reduced by 24.5% and 44.4%, respectively.

2. Operation principle

2.1 Amplitude histogram

As shown in Fig. 1, the AH reflects the statistical distribution of signal amplitudes. The number of bins of AH indicates the number of equally divided amplitudes, and the number of occurrences indicates the frequency of data occurred at each amplitude interval. As the OSNR of single modulation format is varied, the corresponding AH has tiny variation. In addition, the AH generated from various modulation formats has a greater difference. Subsequently, these features of AHs can be automatically extracted by DNN, for the implementation of OSNR monitoring and MFI. In this submission, since the fluctuation of AH under the condition of fixed OSNR will greatly affect the performance of OSNR monitoring, the relationship between the electronic sampling rate during the AH generation and precise OSNR monitoring of high-order QAM formats is explained in next section.

 figure: Fig. 1.

Fig. 1. AHs with 50 bins by a sampling rate of 25GSa/s under conditions of various OSNR values, (a) PDM-64QAM and (b) PDM-16QAM.

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2.2 MT-DNN

With full connections among different activation functions, a single task deep neural network (ST-DNN) can only solve a either classification problem or regression problem. Therefore, different problems cannot be solved by the ST-DNN simultaneously. For the OSNR monitoring, the output is continuous and therefore it is a regression problem. As for MFI, it belongs to a classification problem with several discrete outputs. The last layer of DNN uses the Softmax function as the activation function so that the output can be switched between 0 and 1. Softmax function is expressed in Eq. (1), where m is the number of neurons at the output layer. Each output vector corresponds to a specific situation. For example, “01” stands for “PDM-16QAM” signal and “10” stands for “PDM-64QAM” signal. However, MT-DNN can complete multiple tasks simultaneously by connecting different activation functions to various neurons [19], as shown in Fig. 2. For different tasks, the hidden layers of MT-DNN share the same mapping, which is called as the shared layer. Since our OPM implementation includes both MFI and the OSNR monitoring, the loss function of MFI and OSNR monitoring can be expressed as Eqs. (2) and (3):

$$\textrm{Softmax} \;({{x_i}} )= \frac{{{e^{{x_i}}}}}{{\sum\limits_i^m {{e^{{x_i}}}} }}.$$
$${L_1} ={-} \frac{1}{m}\left[ {\sum\limits_{i = 1}^m {{y_\textrm{i}}\log } \mathop {{y_i}}\limits^ \wedge{+} (1 - {y_\textrm{i}})\log\left( {1 - \mathop {{y_i}}\limits^ \wedge } \right)} \right].$$
$${L_\textrm{2}} = \frac{1}{m}{\sum\limits_{i = 1}^m {({y_i} - \mathop {{y_i}}\limits^ \wedge )} ^2}.$$
where ${y_i}$ and $\mathop {{y_i}}\limits^ \wedge $ belong to the actual output and the estimated output of MT-DNN, respectively. m belongs to the number of samples. After integration, the loss function L of the MT-DNN is simplified to Eq. (4):
$$L = {\lambda _\textrm{1}}{L_1} + {\lambda _\textrm{2}}{L_2}.$$
where L1 is cross entropy loss function and L2 is mean-square error (MSE) function, respectively. λ1 and λ2 are expressed as the weights of L1 and L2, respectively. The values of λ1 and λ2 affect the monitoring results of the neural network. Although MT-DNN can realize multiple tasks at the same time, its training overhead must increase with respect to the number of tasks. Once the link conditions change, MT-DNN needs to be retrained, resulting in a high training cost.

 figure: Fig. 2.

Fig. 2. MT-DNN structure with AHs bins vector as input and identified OSNRs and modulation formats as output.

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2.3 Transfer learning simplified MT-DNN

As shown in Fig. 3(a), the source domain DS and the target domain DT corresponds to the different machine learning application scenarios, respectively. Meanwhile, the source task TS and the target task TT corresponds to different output. TL can improve the learning process of DT by using the knowledge from DS and TS, as DS and DT are partially related [20]. When taking both simulation and experimental domains into consideration, there are certain similarities between them, which is helpful to the introduction of TL. Figure 3(b) shows our scheme to use TL during the MT-DNN training. Compared with only using experimental data for traditional method, TL first apply simulation data to pre-train the MT-DNN, then only small amount of experimental data is enough for subsequently experimental training. As a result, the number of AHs for the purpose of experimentally training and epochs can be substantially decreased for well pre-trained MT-DNN.

 figure: Fig. 3.

Fig. 3. (a) Schematic of transfer learning between different tasks, and (b) training process of TL simplified MT-DNN from simulation to experiment.

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3. Simulation setup and results

3.1 Simulation setup

Firstly, based on VPItransmissionMaker, we numerically generate four widely-used optical signals (PDM-QPSK/8QAM/16QAM/64QAM) modulated by a pseudo-random binary sequence (PRBS) with a length of 216 at 10Gbaud, as shown in Fig. 4. In order to be consistent with the experimental condition, we set the baud rate at 10Gbaud. The amplified spontaneous emission (ASE) noise loading is emulated by an erbium-doped fiber amplifier (EDFA), and a variable optical attenuator (VOA) is used to vary OSNRs of PDM-QPSK/8QAM/16QAM/64QAM signals over a range of 10−22 dB, 14−24 dB, 15−25dB, and 23-33dB, respectively, with a step of 1dB. Then the signals are transmitted over a section of standard single-mode fiber (SSMF), leading to the introduction of chromatic dispersion (CD) effect. After electronic sampling at various rates, we collect 20 AHs of individual OSNR value with a fixed modulation format. The bin number of AH is 50, and the training and testing sets are randomly selected by 75% and 25% of all AHs. Under the condition of back-to-back (B2B) transmission, we investigate the effect of OSNR monitoring error with electronic sampling rate for four modulation formats. The ST-DNN used in the simulation has 4 layers and the number of neurons in shared layers are 30 and 10, respectively. Then, we realize the OSNR monitoring and MFI for PDM-16QAM and PDM-64QAM signals by a 5 layers MT-DNN. The number of neurons from input layer to output layer are 50, 100, 50, 30, 2/1, respectively. After parameter optimization, when the weight of corresponding modulation format identification (MFI) is 1 (λ1 = 0.2), the variation of OSNR monitoring results and MFI accuracy with respect to the weight of the OSNR monitoring task (λ2) is numerically optimized. As for both OSNR monitoring and MFI, there exists an optimal weight for λ2 (λ2 = 1) in order to simultaneously achieve small error of OSNR monitoring and high accuracy of MFI. For the first three layers, the activation function is ReLU function. Meanwhile, the output layer chooses the Linear and Softmax function for the OSNR monitoring and MFI, respectively. In current submission, we select the Keras library combined with Tensorflow backend as the DNN model [21].

 figure: Fig. 4.

Fig. 4. Simulation setup for joint MFI and OSNR monitoring with a TL simplified MT-DNN and directly detected PDM-QAM signals.

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3.2 Effect of electrical sampling rate on the precise OSNR monitoring

First, as for various modulation formats, we realize the OSNR monitoring under conditions of variable electronic sampling rates by the ST-DNN. Generally, both RMSE and MAE are, defined in Eqs. (5) and (6), respectively, where ${\textrm{y}_\textrm{i}}$ and $\mathop {{\textrm{y}_\textrm{I}}}\limits^ \wedge $ are the real value and the predicted value from DNN, respectively. In comparison with MAE, RMSE is more sensitive to large deviations.

$$RMSE = \sqrt {\frac{{\sum\limits_{i = 1}^n {{{({y_i} - \mathop {{y_i}}\limits^ \wedge )}^2}} }}{n}} .$$
$$MAE = \frac{{\sum\limits_{i = 1}^n {({y_i} - \mathop {{y_i}}\limits^ \wedge )} }}{n}.$$
As shown in Fig. 5, when the sampling rate increases from 2GSa/s to 80GSa/s, the RMSE of OSNR monitoring for PDM-64QAM is decreased from 3.1dB to 1.40dB. Meanwhile, as for PDM-16QAM, PDM-8QAM and PDM-QPSK, the RMSE are correspondingly reduced from 1.34dB to 0.71dB, 1.15dB to 0.54dB, and 0.99dB to 0.32dB, respectively. When the electronic sampling rate is twice higher than the baud rate, the RMSE does not decrease further. Therefore, we infer that, when the electronic sampling rate increases, the intrinsic fluctuation of AH is accordingly mitigated, leading to the reduction of OSNR monitoring error. In comparison with the other modulation formats, the AH of PDM-64QAM is more complicated, indicating of its sensitivity to the electronic sampling rate. However, when the AH is generated by high electronic sampling rate, it is beneficial for the MT-DNN to realize precise OSNR monitoring. When we increase the electronic sampling rate of 10Gbaud PDM-64QAM signal to 20GSa/s, we can achieve the RMSE and MAE of OSNR monitoring at 1.40dB and 1.06dB, respectively, enabled by the high-precision AH and ST-DNN.

 figure: Fig. 5.

Fig. 5. RMSE variation of OSNR monitoring with respect to the electronic sampling rate during the testing process for various modulation formats.

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3.3 Effect of chromatic dispersion on the OSNR monitoring

We further investigate the CD effect on the performance of proposed OPM scheme. Here, we vary the SSMF length to bring a variable CD. We use 40km SSMF to introduce the CD effect, and the attenuation of SSMF is 0.2dB/km. Since the AH diagram varies significantly with respect to CD, due to the CD induced pulse broadening [12], the use of AH for the OPM implementation has a disadvantage of CD sensitivity [22]. Here, we investigate the effect of CD on the OSNR monitoring of PDM-64QAM by the ST-DNN. For the training of ST-DNN with the introduction of CD, it is the same as the back-to-back transmission. we collect 20 AHs of individual OSNR value with a fixed modulation format and CD value. The bin number of AH is 50, and the training and testing sets are randomly selected by 75% and 25% from all AHs.

As shown in Fig. 6, with the growing CD from 0 to 640ps/nm, the RMSE of OSNR monitoring for PDM-64QAM is increased from 1.42dB to 2.02dB, and the MAE is raised from 1.09dB to 1.43dB. As for PDM-16QAM, the RMSE and MAE are increased from 0.76dB to 1.04dB, and 0.55dB to 0.72dB, respectively. In comparison with PDM-16QAM signal, since the AH diagram of PDM-64QAM signal is more susceptible to CD, leading to its sensitivity with respect to the OSNR variation. Although PDM-64QAM has a low tolerance of CD, its monitoring error can still be accepted under the back-to-back scenario with a sufficiently high sampling rate. In current submission, we intend to clarify the impact of electronic sampling rate on the precision of AH and the positive role of TL for the MT-DNN.

 figure: Fig. 6.

Fig. 6. Both RMSE and MAE variation of OSNR monitoring with respect to the CD during the testing process.

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3.4 Results of MT-DNN under the B2B transmission

Subsequently, we choose a 20GSa/s sampling rate to realize both OSNR monitoring and MFI for 16QAM and 64QAM signals simultaneously. We collect 440 AHs and the training and testing sets are randomly selected by 75% and 25% from all AHs. As for the OSNR monitoring, RMSE of 1.05dB is observed in Fig. 7(a) for all testing datasets, and the maximum error of OSNR monitoring is less than 3.5dB. Figure 7(b) shows the MFI from two modulation formats can reach 100%. Furthermore, the pre-trained MT-DNN in the simulation will be transferred to experimental scenarios for the purpose of comparing the results of MT-DNN without TL.

 figure: Fig. 7.

Fig. 7. (a) OSNR monitoring error for the mixed signals under the condition of back-to-back transmission, and (b) MFI accuracy versus for PDM-16QAM and PDM-64QAM.

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4. Experimental setup and results

4.1 Experimental setup

As shown in Fig. 8, with the help of arbitrary waveform generator (AWG, Tektronix 7122C), we generate two widely-used optical signals (PDM-16/64QAM) for coherent fiber optical transmission system at 10GBaud. An Erbium-doped fiber amplifier (EDFA) and a variable optical attenuator (VOA) are used to vary the OSNR value. As a result, the OSNRs of received PDM-16QAM and PDM-64QAM signals are at the range of 14−24dB and 23−34dB, respectively, with a resolution of ∼1dB. At the receiver side, after being filtered by an optical band pass filter (OBPF) with 3dB bandwidth of 0.8nm, the optical signal is equally divided into two parts by a 50:50 optical coupler. By using an optical spectrum analyzer (OSA) with a resolution of 0.1nm, the OSNR of received signal can be characterized. Meanwhile, after the other part is directly detected by a PD with 3dB bandwidth of 10GHz, the electrical signals are sampled by a digital sampling oscilloscope (DSO, Tektronix DPO73304D). The AHs with 50 bins of both modulation formats and OSNR values are generated. In order to verify the results at different sampling rates, the ST-DNN and MT-DNN used in the experiment is the same as that in the simulation. Instead of training a MT-DNN with experimentally generated AHs, the TL simplified MT-DNN is pre-trained by 440 AHs generated by numerical simulation.

 figure: Fig. 8.

Fig. 8. Experimental setup of MFI and OSNR monitoring with a TL simplified MT-DNN and directly detected PDM-QAM signals.

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4.2 Experimental verification of electrical sampling rate effect

As shown in Fig. 9(a), when the sampling rate increases from 625MSa/s to 25GSa/s, the RMSE of OSNR monitoring for PDM-64QAM is decreased from 4.2dB to 1.45dB, and the MAE is decreased from 3.48dB to 1.17dB. As for PDM-16QAM, the RMSE and MAE are reduced from 1.78 dB to 0.83 dB, and 1.22 dB to 0.58dB, respectively. Therefore, we can infer that, when the sampling rate increases, the intrinsic fluctuation of AH is accordingly mitigated, leading to the error reduction of OSNR monitoring. In comparison with the PDM-16QAM signal, the AH of PDM-64QAM signal is more complicated, indicating of its sensitivity to the sampling rate. As shown in Fig. 9(b), “AH points” represents the number of points required for each AH, when the sampling rate of 10Gbaud PDM-16QAM signal is 625MSa/s and the number of points in the AH increases from 10000 to 50000, the RMSE and MAE can be significantly decreased. However, when the number of points in the PDM-16QAM AH continually increase from 50000 to 100000, there is almost no promotion of MAE and RMSE. Therefore, the precise AH is only determined by the sampling rate, when the AH points are sufficient. When we increase the sampling rate to 25GS/s, we can experimentally achieve the RMSE and MAE of OSNR monitoring at 1.45dB and 1.17dB, respectively, enabled by the high-precision AH and ST-DNN. We can conclude that the experimental results agree well with the numerical simulations.

 figure: Fig. 9.

Fig. 9. (a) Both RMSE and MAE variation of OSNR monitoring with respect to the sampling rate. (b) Both RMSE and MAE variation of OSNR monitoring with respect to the AH points for PDM-16QAM at 625MSa/s sampling rate.

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4.3 Results and discussions of TL simplified MT-DNN

Furthermore, we investigate the benefit of TL for our proposed approach. We optimize the used ratio of total AHs for the purpose of training from 20% to 80%, with the step of 10%. As shown in Fig. 10(a), by using TL, only 243 experimentally generated AHs are enough to ensure the RMSE below 1.1dB, while 322 experimentally generated AHs are indispensable to train a MT-DNN without the use of TL, indicating of 24.5% reduction of experimentally generated AHs. Meanwhile, for both cases, the RMSE of OSNR monitoring can be reduced to less than 1.1dB with adequately training AHs. For insufficient training AHs, the RMSE of TL simplified MT-DNN is much smaller than that of MT-DNN without the use of TL. Therefore, since the collection of plenty experimental data may be time-consumed for practical OPM application, TL is effective to reduce the number of required AHs for MT-DNN. Moreover, when it comes to the training time, TL can satisfy the time consumption of OSNR monitoring with fewer epochs, as shown in Fig. 10(b). Only 1000 epochs are enough to ensure both 100% MFI accuracy and RMSE of OSNR monitoring below 1.1dB. However, the MT-DNN without the use of TL needs 1800 epochs. As a result, the TL from simulation to experiment can successfully reduce the training data and time of MT-DNN by 24.5% and 44.4%, respectively. As shown in Fig. 11(a), the RMSE of OSNR monitoring is 1.09dB for PDM-16QAM and PDM-64QAM, respectively, and Fig. 11(b) shows the accuracy of MFI can reach 100%. Since our proposed scheme only require single one PD without coherent detection and one TL simplified MT-DNN for multi-parameters monitoring, instead of the use of multiple ST-DNNs, our proposed OPM scheme has the advantages of low training cost and low implementation complexity, which is ideally desired for future agile optical network.

 figure: Fig. 10.

Fig. 10. (a) RMSE of OSNR monitoring with respect to the number of training AHs, and (b) both MFI accuracy and RMSE of OSNR monitoring with respect to the training epochs.

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 figure: Fig. 11.

Fig. 11. (a) OSNR monitoring error for all signals with two modulation formats, and (b) MFI accuracy versus for PDM-16QAM and PDM-64QAM.

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5. Conclusion

We firstly investigate the fluctuation of AH generation on the performance of OSNR monitoring, and the significance of higher electronic sampling rate for precise OSNR monitoring of PDM-64QAM has been experimentally verified. Subsequently, for two commonly-used PDM-QAM signals, we have experimentally realized joint MFI and OSNR monitoring, based on the precise AH generated by higher sampling rate together with a TL simplified MT-DNN. For both 10Gbaud PDM-16QAM and PDM-64QAM signals, the accuracy of MFI can experimentally reach 100% and the RMSE of OSNR monitoring is 1.09dB over a range of 14-24dB and 23-34dB for PDM-16QAM and PDM-64QAM, respectively. Furthermore, by implementing TL from simulation to experiment, the requested training samples and epochs are reduced by 24.5% and 44.4%, respectively. Owing to its characteristic of low cost and simple implementation, the proposed OPM scheme has potentials for next generation coherent fiber optic transmission system.

Funding

National Key Research and Development Program of China (2018YFB1801301); National Natural Science Foundation of China (61875061); Key project of R&D Program of Hubei Province (2018AAA041).

Acknowledgments

The authors would like to thank people who are fighting on the frontlines during the epidemic, especially in Wuhan. Without their bravery contribution, the revision is impossible.

Disclosures

The authors declare no conflicts of interest.

References

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2. 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]  

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14. F. N. Khan, C. Lu, and A. P. T. Lau, “Optical performance monitoring in fiber-optic networks enabled by machine learning techniques,” in Proc. Conf. Opt. Fiber Commun., (2018). M2F.3.

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References

  • View by:

  1. F. N. Khan, Z. Dong, C. Lu, A. P. T. Lau, X. Zhou, and C. Xie, Optical performance monitoring for fiber-optic communication networks (Wiley, 2016).
  2. 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]
  3. O. Gerstel, M. Jinno, A. Lord, and S. B. Yoo, “Elastic optical networking: A new dawn for the optical layer?” IEEE Commun. Mag. 50(2), s12–s20 (2012).
    [Crossref]
  4. 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]
  5. 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]
  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. Guesmi, A. M. Ragheb, H. Fathallah, and M. Menif, “Experimental Demonstration of Simultaneous Modulation Format/Symbol Rate Identification and Optical Performance Monitoring for Coherent Optical Systems,” J. Lightwave Technol. 36(11), 2230–2239 (2018).
    [Crossref]
  8. Z. Wang, A. Yang, P. Guo, and P. He, “OSNR and nonlinear noise power estimation for optical fiber communication systems using LSTM based deep learning technique,” Opt. Express 26(16), 21346–21357 (2018).
    [Crossref]
  9. 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]
  10. C. Wang, S. Fu, H. Wu, M. Luo, X. Li, M. Tang, and D. Liu, “Joint OSNR and CD monitoring in digital coherent receiver using long short-term memory neural network,” Opt. Express 27(5), 6936–6945 (2019).
    [Crossref]
  11. N. Hanik, A. Gladisch, C. Caspar, and B. Strebel, “Application of amplitude histograms to monitor performance of optical channels,” Electron. Lett. 35(5), 403–404 (1999).
    [Crossref]
  12. 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]
  13. M. Xu, J. Zhang, H. Zhang, Z. Jia, J. Wang, L. Cheng, L. A. Campos, and C. Knittle, “Multi-stage machine learning enhanced DSP for DP-64QAM coherent optical transmission systems,” in Proc. Conf. Opt. Fiber Commun., (2019). M2H.1.
  14. F. N. Khan, C. Lu, and A. P. T. Lau, “Optical performance monitoring in fiber-optic networks enabled by machine learning techniques,” in Proc. Conf. Opt. Fiber Commun., (2018). M2F.3.
  15. F. Musumeci, C. Rottondi, A. Nag, I. Macaluso, D. Zibar, M. Ruffini, and M. Tornatore, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tutorials 21(2), 1383–1408 (2019).
    [Crossref]
  16. J. Thrane, J. Wass, M. Piels, J. C. 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]
  17. L. Xia, J. Zhang, S. Hu, M. Zhu, Y. Song, and K. Qiu, “Transfer learning assisted deep neural network for OSNR estimation,” Opt. Express 27(14), 19398–19406 (2019).
    [Crossref]
  18. J. Zhang, L. Xia, M. Zhu, S. Hu, B. Xu, and K. Qiu, “Fast remodeling for nonlinear distortion mitigation based on transfer learning,” Opt. Lett. 44(17), 4243–4246 (2019).
    [Crossref]
  19. S. Ruder, “An overview of multi-task learning in deep neural networks,” arXiv preprint arXiv:1706.05098 (2017).
  20. S. J. Pan and Q. Yang, “A survey on transfer learning,” IEEE Trans. Knowl. Data Eng. 22(10), 1345–1359 (2010).
    [Crossref]
  21. M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, and M. Isard, “Tensorflow: A system for large-scale machine learning,” in 12th {USENIX} Symposium on Operating Systems Design and Implementation ({OSDI} 16), pp. 265–283 (2016).
  22. D. Wang, M. Wang, M. Zhang, Z. Zhang, H. Yang, J. Li, J. Li, and X. Chen, “Cost-effective and data size–adaptive OPM at intermediated node using convolutional neural network-based image processor,” Opt. Express 27(7), 9403–9419 (2019).
    [Crossref]

2019 (7)

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]

C. Wang, S. Fu, H. Wu, M. Luo, X. Li, M. Tang, and D. Liu, “Joint OSNR and CD monitoring in digital coherent receiver using long short-term memory neural network,” Opt. Express 27(5), 6936–6945 (2019).
[Crossref]

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]

F. Musumeci, C. Rottondi, A. Nag, I. Macaluso, D. Zibar, M. Ruffini, and M. Tornatore, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tutorials 21(2), 1383–1408 (2019).
[Crossref]

L. Xia, J. Zhang, S. Hu, M. Zhu, Y. Song, and K. Qiu, “Transfer learning assisted deep neural network for OSNR estimation,” Opt. Express 27(14), 19398–19406 (2019).
[Crossref]

J. Zhang, L. Xia, M. Zhu, S. Hu, B. Xu, and K. Qiu, “Fast remodeling for nonlinear distortion mitigation based on transfer learning,” Opt. Lett. 44(17), 4243–4246 (2019).
[Crossref]

D. Wang, M. Wang, M. Zhang, Z. Zhang, H. Yang, J. Li, J. Li, and X. Chen, “Cost-effective and data size–adaptive OPM at intermediated node using convolutional neural network-based image processor,” Opt. Express 27(7), 9403–9419 (2019).
[Crossref]

2018 (2)

2017 (2)

2016 (1)

2013 (1)

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]

2012 (2)

O. Gerstel, M. Jinno, A. Lord, and S. B. Yoo, “Elastic optical networking: A new dawn for the optical layer?” IEEE Commun. Mag. 50(2), s12–s20 (2012).
[Crossref]

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]

2010 (1)

S. J. Pan and Q. Yang, “A survey on transfer learning,” IEEE Trans. Knowl. Data Eng. 22(10), 1345–1359 (2010).
[Crossref]

1999 (1)

N. Hanik, A. Gladisch, C. Caspar, and B. Strebel, “Application of amplitude histograms to monitor performance of optical channels,” Electron. Lett. 35(5), 403–404 (1999).
[Crossref]

Abadi, M.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, and M. Isard, “Tensorflow: A system for large-scale machine learning,” in 12th {USENIX} Symposium on Operating Systems Design and Implementation ({OSDI} 16), pp. 265–283 (2016).

Al-Arashi, W. H.

Arlunno, V.

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]

Barham, P.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, and M. Isard, “Tensorflow: A system for large-scale machine learning,” in 12th {USENIX} Symposium on Operating Systems Design and Implementation ({OSDI} 16), pp. 265–283 (2016).

Borkowski, R.

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]

Caballero, A.

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]

Campos, L. A.

M. Xu, J. Zhang, H. Zhang, Z. Jia, J. Wang, L. Cheng, L. A. Campos, and C. Knittle, “Multi-stage machine learning enhanced DSP for DP-64QAM coherent optical transmission systems,” in Proc. Conf. Opt. Fiber Commun., (2019). M2H.1.

Caspar, C.

N. Hanik, A. Gladisch, C. Caspar, and B. Strebel, “Application of amplitude histograms to monitor performance of optical channels,” Electron. Lett. 35(5), 403–404 (1999).
[Crossref]

Chen, J.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, and M. Isard, “Tensorflow: A system for large-scale machine learning,” in 12th {USENIX} Symposium on Operating Systems Design and Implementation ({OSDI} 16), pp. 265–283 (2016).

Chen, X.

Chen, Z.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, and M. Isard, “Tensorflow: A system for large-scale machine learning,” in 12th {USENIX} Symposium on Operating Systems Design and Implementation ({OSDI} 16), pp. 265–283 (2016).

Cheng, L.

M. Xu, J. Zhang, H. Zhang, Z. Jia, J. Wang, L. Cheng, L. A. Campos, and C. Knittle, “Multi-stage machine learning enhanced DSP for DP-64QAM coherent optical transmission systems,” in Proc. Conf. Opt. Fiber Commun., (2019). M2H.1.

Cheng, Y.

Davis, A.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, and M. Isard, “Tensorflow: A system for large-scale machine learning,” in 12th {USENIX} Symposium on Operating Systems Design and Implementation ({OSDI} 16), pp. 265–283 (2016).

Dean, J.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, and M. Isard, “Tensorflow: A system for large-scale machine learning,” in 12th {USENIX} Symposium on Operating Systems Design and Implementation ({OSDI} 16), pp. 265–283 (2016).

Devin, M.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, and M. Isard, “Tensorflow: A system for large-scale machine learning,” in 12th {USENIX} Symposium on Operating Systems Design and Implementation ({OSDI} 16), pp. 265–283 (2016).

Diniz, J. C.

Dong, Z.

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]

F. N. Khan, Z. Dong, C. Lu, A. P. T. Lau, X. Zhou, and C. Xie, Optical performance monitoring for fiber-optic communication networks (Wiley, 2016).

Fathallah, H.

Fu, S.

Gerstel, O.

O. Gerstel, M. Jinno, A. Lord, and S. B. Yoo, “Elastic optical networking: A new dawn for the optical layer?” IEEE Commun. Mag. 50(2), s12–s20 (2012).
[Crossref]

Ghemawat, S.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, and M. Isard, “Tensorflow: A system for large-scale machine learning,” in 12th {USENIX} Symposium on Operating Systems Design and Implementation ({OSDI} 16), pp. 265–283 (2016).

Gladisch, A.

N. Hanik, A. Gladisch, C. Caspar, and B. Strebel, “Application of amplitude histograms to monitor performance of optical channels,” Electron. Lett. 35(5), 403–404 (1999).
[Crossref]

Guesmi, L.

Guo, P.

Hanik, N.

N. Hanik, A. Gladisch, C. Caspar, and B. Strebel, “Application of amplitude histograms to monitor performance of optical channels,” Electron. Lett. 35(5), 403–404 (1999).
[Crossref]

He, P.

Hoshida, T.

Hu, S.

Irving, G.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, and M. Isard, “Tensorflow: A system for large-scale machine learning,” in 12th {USENIX} Symposium on Operating Systems Design and Implementation ({OSDI} 16), pp. 265–283 (2016).

Isard, M.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, and M. Isard, “Tensorflow: A system for large-scale machine learning,” in 12th {USENIX} Symposium on Operating Systems Design and Implementation ({OSDI} 16), pp. 265–283 (2016).

Jia, Z.

M. Xu, J. Zhang, H. Zhang, Z. Jia, J. Wang, L. Cheng, L. A. Campos, and C. Knittle, “Multi-stage machine learning enhanced DSP for DP-64QAM coherent optical transmission systems,” in Proc. Conf. Opt. Fiber Commun., (2019). M2H.1.

Jinno, M.

O. Gerstel, M. Jinno, A. Lord, and S. B. Yoo, “Elastic optical networking: A new dawn for the optical layer?” IEEE Commun. Mag. 50(2), s12–s20 (2012).
[Crossref]

Jones, R.

Kato, T.

Khan, F. N.

Knittle, C.

M. Xu, J. Zhang, H. Zhang, Z. Jia, J. Wang, L. Cheng, L. A. Campos, and C. Knittle, “Multi-stage machine learning enhanced DSP for DP-64QAM coherent optical transmission systems,” in Proc. Conf. Opt. Fiber Commun., (2019). M2H.1.

Lau, A. P. T.

Li, J.

Li, X.

Liu, D.

Lord, A.

O. Gerstel, M. Jinno, A. Lord, and S. B. Yoo, “Elastic optical networking: A new dawn for the optical layer?” IEEE Commun. Mag. 50(2), s12–s20 (2012).
[Crossref]

Lu, C.

Luo, M.

Macaluso, I.

F. Musumeci, C. Rottondi, A. Nag, I. Macaluso, D. Zibar, M. Ruffini, and M. Tornatore, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tutorials 21(2), 1383–1408 (2019).
[Crossref]

Menif, M.

Monroy, I. T.

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]

Morikawa, H.

Musumeci, F.

F. Musumeci, C. Rottondi, A. Nag, I. Macaluso, D. Zibar, M. Ruffini, and M. Tornatore, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tutorials 21(2), 1383–1408 (2019).
[Crossref]

Nag, A.

F. Musumeci, C. Rottondi, A. Nag, I. Macaluso, D. Zibar, M. Ruffini, and M. Tornatore, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tutorials 21(2), 1383–1408 (2019).
[Crossref]

Pan, S. J.

S. J. Pan and Q. Yang, “A survey on transfer learning,” IEEE Trans. Knowl. Data Eng. 22(10), 1345–1359 (2010).
[Crossref]

Piels, M.

Qiu, K.

Ragheb, A. M.

Rottondi, C.

F. Musumeci, C. Rottondi, A. Nag, I. Macaluso, D. Zibar, M. Ruffini, and M. Tornatore, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tutorials 21(2), 1383–1408 (2019).
[Crossref]

Ruder, S.

S. Ruder, “An overview of multi-task learning in deep neural networks,” arXiv preprint arXiv:1706.05098 (2017).

Ruffini, M.

F. Musumeci, C. Rottondi, A. Nag, I. Macaluso, D. Zibar, M. Ruffini, and M. Tornatore, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tutorials 21(2), 1383–1408 (2019).
[Crossref]

Song, Y.

Strebel, B.

N. Hanik, A. Gladisch, C. Caspar, and B. Strebel, “Application of amplitude histograms to monitor performance of optical channels,” Electron. Lett. 35(5), 403–404 (1999).
[Crossref]

Sui, Q.

Tang, M.

Tanimura, T.

Thrane, J.

Tornatore, M.

F. Musumeci, C. Rottondi, A. Nag, I. Macaluso, D. Zibar, M. Ruffini, and M. Tornatore, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tutorials 21(2), 1383–1408 (2019).
[Crossref]

Wang, C.

Wang, D.

Wang, J.

M. Xu, J. Zhang, H. Zhang, Z. Jia, J. Wang, L. Cheng, L. A. Campos, and C. Knittle, “Multi-stage machine learning enhanced DSP for DP-64QAM coherent optical transmission systems,” in Proc. Conf. Opt. Fiber Commun., (2019). M2H.1.

Wang, M.

Wang, Z.

Wass, J.

Watanabe, S.

Wu, H.

Xia, L.

Xie, C.

F. N. Khan, Z. Dong, C. Lu, A. P. T. Lau, X. Zhou, and C. Xie, Optical performance monitoring for fiber-optic communication networks (Wiley, 2016).

Xu, B.

Xu, M.

M. Xu, J. Zhang, H. Zhang, Z. Jia, J. Wang, L. Cheng, L. A. Campos, and C. Knittle, “Multi-stage machine learning enhanced DSP for DP-64QAM coherent optical transmission systems,” in Proc. Conf. Opt. Fiber Commun., (2019). M2H.1.

Yang, A.

Yang, H.

Yang, Q.

S. J. Pan and Q. Yang, “A survey on transfer learning,” IEEE Trans. Knowl. Data Eng. 22(10), 1345–1359 (2010).
[Crossref]

Yoo, S. B.

O. Gerstel, M. Jinno, A. Lord, and S. B. Yoo, “Elastic optical networking: A new dawn for the optical layer?” IEEE Commun. Mag. 50(2), s12–s20 (2012).
[Crossref]

Yu, C.

Zhang, H.

M. Xu, J. Zhang, H. Zhang, Z. Jia, J. Wang, L. Cheng, L. A. Campos, and C. Knittle, “Multi-stage machine learning enhanced DSP for DP-64QAM coherent optical transmission systems,” in Proc. Conf. Opt. Fiber Commun., (2019). M2H.1.

Zhang, J.

Zhang, M.

Zhang, Z.

Zhong, K.

Zhou, X.

Zhou, Y.

Zhu, M.

Zibar, D.

F. Musumeci, C. Rottondi, A. Nag, I. Macaluso, D. Zibar, M. Ruffini, and M. Tornatore, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tutorials 21(2), 1383–1408 (2019).
[Crossref]

J. Thrane, J. Wass, M. Piels, J. C. 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]

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]

Electron. Lett. (1)

N. Hanik, A. Gladisch, C. Caspar, and B. Strebel, “Application of amplitude histograms to monitor performance of optical channels,” Electron. Lett. 35(5), 403–404 (1999).
[Crossref]

IEEE Commun. Mag. (1)

O. Gerstel, M. Jinno, A. Lord, and S. B. Yoo, “Elastic optical networking: A new dawn for the optical layer?” IEEE Commun. Mag. 50(2), s12–s20 (2012).
[Crossref]

IEEE Commun. Surv. Tutorials (1)

F. Musumeci, C. Rottondi, A. Nag, I. Macaluso, D. Zibar, M. Ruffini, and M. Tornatore, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tutorials 21(2), 1383–1408 (2019).
[Crossref]

IEEE Photonics Technol. Lett. (1)

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]

IEEE Trans. Knowl. Data Eng. (1)

S. J. Pan and Q. Yang, “A survey on transfer learning,” IEEE Trans. Knowl. Data Eng. 22(10), 1345–1359 (2010).
[Crossref]

J. Lightwave Technol. (3)

J. Opt. Commun. Netw. (1)

Opt. Express (7)

C. Wang, S. Fu, H. Wu, M. Luo, X. Li, M. Tang, and D. Liu, “Joint OSNR and CD monitoring in digital coherent receiver using long short-term memory neural network,” Opt. Express 27(5), 6936–6945 (2019).
[Crossref]

D. Wang, M. Wang, M. Zhang, Z. Zhang, H. Yang, J. Li, J. Li, and X. Chen, “Cost-effective and data size–adaptive OPM at intermediated node using convolutional neural network-based image processor,” Opt. Express 27(7), 9403–9419 (2019).
[Crossref]

L. Xia, J. Zhang, S. Hu, M. Zhu, Y. Song, and K. Qiu, “Transfer learning assisted deep neural network for OSNR estimation,” Opt. Express 27(14), 19398–19406 (2019).
[Crossref]

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]

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]

Z. Wang, A. Yang, P. Guo, and P. He, “OSNR and nonlinear noise power estimation for optical fiber communication systems using LSTM based deep learning technique,” Opt. Express 26(16), 21346–21357 (2018).
[Crossref]

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]

Opt. Lett. (1)

Other (5)

S. Ruder, “An overview of multi-task learning in deep neural networks,” arXiv preprint arXiv:1706.05098 (2017).

M. Xu, J. Zhang, H. Zhang, Z. Jia, J. Wang, L. Cheng, L. A. Campos, and C. Knittle, “Multi-stage machine learning enhanced DSP for DP-64QAM coherent optical transmission systems,” in Proc. Conf. Opt. Fiber Commun., (2019). M2H.1.

F. N. Khan, C. Lu, and A. P. T. Lau, “Optical performance monitoring in fiber-optic networks enabled by machine learning techniques,” in Proc. Conf. Opt. Fiber Commun., (2018). M2F.3.

F. N. Khan, Z. Dong, C. Lu, A. P. T. Lau, X. Zhou, and C. Xie, Optical performance monitoring for fiber-optic communication networks (Wiley, 2016).

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, and M. Isard, “Tensorflow: A system for large-scale machine learning,” in 12th {USENIX} Symposium on Operating Systems Design and Implementation ({OSDI} 16), pp. 265–283 (2016).

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Figures (11)

Fig. 1.
Fig. 1. AHs with 50 bins by a sampling rate of 25GSa/s under conditions of various OSNR values, (a) PDM-64QAM and (b) PDM-16QAM.
Fig. 2.
Fig. 2. MT-DNN structure with AHs bins vector as input and identified OSNRs and modulation formats as output.
Fig. 3.
Fig. 3. (a) Schematic of transfer learning between different tasks, and (b) training process of TL simplified MT-DNN from simulation to experiment.
Fig. 4.
Fig. 4. Simulation setup for joint MFI and OSNR monitoring with a TL simplified MT-DNN and directly detected PDM-QAM signals.
Fig. 5.
Fig. 5. RMSE variation of OSNR monitoring with respect to the electronic sampling rate during the testing process for various modulation formats.
Fig. 6.
Fig. 6. Both RMSE and MAE variation of OSNR monitoring with respect to the CD during the testing process.
Fig. 7.
Fig. 7. (a) OSNR monitoring error for the mixed signals under the condition of back-to-back transmission, and (b) MFI accuracy versus for PDM-16QAM and PDM-64QAM.
Fig. 8.
Fig. 8. Experimental setup of MFI and OSNR monitoring with a TL simplified MT-DNN and directly detected PDM-QAM signals.
Fig. 9.
Fig. 9. (a) Both RMSE and MAE variation of OSNR monitoring with respect to the sampling rate. (b) Both RMSE and MAE variation of OSNR monitoring with respect to the AH points for PDM-16QAM at 625MSa/s sampling rate.
Fig. 10.
Fig. 10. (a) RMSE of OSNR monitoring with respect to the number of training AHs, and (b) both MFI accuracy and RMSE of OSNR monitoring with respect to the training epochs.
Fig. 11.
Fig. 11. (a) OSNR monitoring error for all signals with two modulation formats, and (b) MFI accuracy versus for PDM-16QAM and PDM-64QAM.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

Softmax ( x i ) = e x i i m e x i .
L 1 = 1 m [ i = 1 m y i log y i + ( 1 y i ) log ( 1 y i ) ] .
L 2 = 1 m i = 1 m ( y i y i ) 2 .
L = λ 1 L 1 + λ 2 L 2 .
R M S E = i = 1 n ( y i y i ) 2 n .
M A E = i = 1 n ( y i y i ) n .

Metrics