Abstract

We present a digital signal processing (DSP) scheme that performs hyperparameter tuning (HT) via Bayesian optimization (BO) to autonomously optimize memory tap distribution of Volterra series and adapt parameters used in the synthetization of a digital pre-distortion (DPD) filter for optical transmitters. Besides providing a time-efficient technique, this work demonstrates that the self-adaptation of DPD hyperparameters to correct the component-induced nonlinear distortions as different driver amplifier (DA) gains, symbol rates and modulation formats are used, leads to an improvement in transmitter performance. The scheme has been validated in back-to-back (b2b) experiments using dual-polarization (DP) 64 and 256 quadrature amplitude modulation (QAM) formats, and symbol rates of 64 and 80 GBd. For DP-64QAM at 64 GBd, it is shown that the DPD scheme reduces the required optical signal-to-noise ratio (OSNR) at a bit error ratio of 10-2 by 0.9 dB and 0.6 dB with respect to linear DPD and a heuristic nonlinear DPD approach, respectively. Moreover, we show that the proposed approach also reduces filter complexity by 75% in conjunction with the use of memory polynomials (MP), while achieving a similar performance to Volterra pre-distortion filters.

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2021 (1)

P. J. Freire, “Complex-valued neural network design for mitigation of signal distortions in optical links,” IEEE/OSA J. Lightw. Technol., vol. 39, no. 6, pp. 1696–1705, 2021.

2020 (4)

W. S. Saif, M. A. Esmail, A. M. Ragheb, T. A. Alshawi, and S. A. Alshebeili, “Machine learning techniques for optical performance monitoring and modulation format identification: A survey,” IEEE Commun. Surv. Tut., vol. 22, no. 4, pp. 2839–2882, 2020.

Y. Zhang, J. Xin, X. Li, and S. Huang, “Overview on routing and resource allocation based machine learning in optical networks,” Elsevier Opt. Fiber Technol., vol. 60, 2020, Art. no. .

G. Paryanti, H. Faig, L. Rokach, and D. Sadot, “A direct learning approach for neural network based pre-distortion for coherent nonlinear optical transmitter,” IEEE/OSA J. Lightw. Technol., vol. 38, no. 15, pp. 3883–3896, 2020.

T. Sasai, “Wiener-Hammerstein model and its learning for nonlinear digital pre-distortion of optical transmitters,” OSA Opt. Exp., vol. 28, no. 21, pp. 30952–30963, 2020.

2019 (2)

B. Spinnler, “Autonomous intelligent transponder enabling adaptive network optimization in a live network field trial,” IEEE/OSA J. Opt. Commun. Netw., vol. 11, no. 9, pp. C1–C9, 2019.

X. Dai, X. Li, M. Luo, and S. Yu, “Numerical simulation and experimental demonstration of accurate machine learning aided IQ time-skew and power-imbalance identification for coherent transmitters,” OSA Opt. Exp., vol. 27, no. 26, pp. 38367–38381, 2019.

2018 (3)

F. Musumeci, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tut., vol. 21, no. 2, pp. 1383–1408, 2018.

J. Zhang, M. Gao, W. Chen, and G. Shen, “Non-data-aided k-nearest neighbors technique for optical fiber nonlinearity mitigation,” IEEE/OSA J. Lightw. Technol., vol. 36, no. 17, pp. 3564–3572, 2018.

P. Händel, “Understanding normalized mean squared error in power amplifier linearization,” IEEE Microw. Wireless Compon. Lett., vol. 28, no. 11, pp. 1047–1049, 2018.

2017 (2)

T. A. Eriksson, H. Bülow, and A. Leven, “Applying neural networks in optical communication systems: Possible pitfalls,” IEEE Photon. Technol. Lett., vol. 29, no. 23, pp. 2091–2094, 2017.

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,” IEEE/OSA J. Lightw. Technol., vol. 35, no. 4, pp. 868–875, 2017.

2016 (2)

G. Khanna, B. Spinnler, S. Calabrò, E. De Man, and N. Hanik, “A robust adaptive pre-distortion method for optical communication transmitters,” IEEE Photon. Technol. Lett., vol. 28, no. 7, pp. 752–755, 2016.

P. W. Berenguer, T. Rahman, A. Napoli, M. Nölle, C. Schubert, and J. K. Fischer, “Nonlinear digital pre-distortion of transmitter components,” IEEE/OSA J. Lightw. Technol., vol. 34, no. 8, pp. 1739–1745, 2016.

2015 (2)

A. Napoli, “Next generation elastic optical networks: The vision of the european research project IDEALIST,” IEEE Commun. Mag., vol. 53, no. 2, pp. 152–162, 2015.

E. Giacoumidis, “Fiber nonlinearity-induced penalty reduction in CO-OFDM by ANN-based nonlinear equalization,” OSA Opt. Lett., vol. 40, no. 21, pp. 5113–5116, 2015.

2013 (1)

I. Miguel, “Cognitive dynamic optical networks [Invited],” IEEE/OSA J. Opt. Commun. Netw., vol. 5, no. 10, pp. 107–118, 2013.

2010 (1)

B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in stokes space,” OSA Opt. Exp., vol. 18, no. 17, pp. 17928–17939, 2010.

2009 (1)

T. Pfau, S. Hoffmann, and R. Noe, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” IEEE/OSA J. Lightw. Technol., vol. 27, no. 8, pp. 989–999, 2009.

1998 (3)

L. Prechelt, “Automatic early stopping using cross validation: Quantifying the criteria,” Elsevier Neural Netw., vol. 11, no. 4, pp. 761–767, 1998.

R. D. Nowak, “Penalized least squares estimation of volterra filters and higher order statistics,” IEEE Trans. Signal Process., vol. 46, no. 2, pp. 419–428, 1998.

C. You and D. Hong, “Nonlinear blind equalization schemes using complex-valued multilayer feedforward neural networks,” IEEE Trans. Neural Netw., vol. 9, no. 6, pp. 1442–1455, 1998.

1997 (2)

R. Parisi, E. D. Di Claudio, G. Orlandi, and B. D. Rao, “Fast adaptive digital equalization by recurrent neural networks,” IEEE Trans. Signal Process., vol. 45, no. 11, pp. 2731–2739, 1997.

C. Eun and E. J. Powers, “A new volterra predistorter based on the indirect learning architecture,” IEEE Trans. Signal Process., vol. 45, no. 1, pp. 223–227, 1997.

Alshawi, T. A.

W. S. Saif, M. A. Esmail, A. M. Ragheb, T. A. Alshawi, and S. A. Alshebeili, “Machine learning techniques for optical performance monitoring and modulation format identification: A survey,” IEEE Commun. Surv. Tut., vol. 22, no. 4, pp. 2839–2882, 2020.

Alshebeili, S. A.

W. S. Saif, M. A. Esmail, A. M. Ragheb, T. A. Alshawi, and S. A. Alshebeili, “Machine learning techniques for optical performance monitoring and modulation format identification: A survey,” IEEE Commun. Surv. Tut., vol. 22, no. 4, pp. 2839–2882, 2020.

André, N.

A. Richter, S. Dris, and N. André, “On the analysis and emulation of nonlinear component characteristics,” in Proc. Opt. Fiber Commun. Conf. Exhib., San Diego, CA, USA, 2019, Paper Th.1.D.1.

Aref, V.

V. Bajaj, F. Buchali, M. Chagnon, S. Wahls, and V. Aref, “Single-channel 1.61 Tb/s optical coherent transmission enabled by neural network-based digital pre-distortion,” in Proc. Eur. Conf. Exhib. Opt. Commun., Brussels, Belgium, 2020, Paper. Tu.1.D.5.

Bajaj, V.

V. Bajaj, F. Buchali, M. Chagnon, S. Wahls, and V. Aref, “Single-channel 1.61 Tb/s optical coherent transmission enabled by neural network-based digital pre-distortion,” in Proc. Eur. Conf. Exhib. Opt. Commun., Brussels, Belgium, 2020, Paper. Tu.1.D.5.

Berenguer, P. W.

P. W. Berenguer, T. Rahman, A. Napoli, M. Nölle, C. Schubert, and J. K. Fischer, “Nonlinear digital pre-distortion of transmitter components,” IEEE/OSA J. Lightw. Technol., vol. 34, no. 8, pp. 1739–1745, 2016.

P. W. Berenguer, T. Rahman, A. Napoli, M. Nölle, C. Schubert, and J. K. Fischer, “Nonlinear digital pre-distortion of transmitter components,” in Proc. Eur. Conf. Exhib. Opt. Commun., Valencia, Spain, 2015, Paper Th.2.6.3.

Bernardini, A.

A. Bernardini, M. Carrarini, and S. De Fina, “The use of a neural net for copeing with nonlinear distortions,” in Proc. 20th Eur. Microw. Conf., Budapest, Hungary, 1990, pp. 1718–1723.

Bluemm, C.

M. Schaedler, M. Kuschnerov, S. Calabro, F. Pittala, C. Bluemm, and S. Pachnicke, “AI-based digital predistortion for IQ Mach-Zehnder modulators,” in Proc. Asia Comm. Photon. Conf., Chengdu, China, 2019, Paper S3B.3.

Buchali, F.

V. Bajaj, F. Buchali, M. Chagnon, S. Wahls, and V. Aref, “Single-channel 1.61 Tb/s optical coherent transmission enabled by neural network-based digital pre-distortion,” in Proc. Eur. Conf. Exhib. Opt. Commun., Brussels, Belgium, 2020, Paper. Tu.1.D.5.

Bülow, H.

T. A. Eriksson, H. Bülow, and A. Leven, “Applying neural networks in optical communication systems: Possible pitfalls,” IEEE Photon. Technol. Lett., vol. 29, no. 23, pp. 2091–2094, 2017.

Calabro, S.

M. Schaedler, M. Kuschnerov, S. Calabro, F. Pittala, C. Bluemm, and S. Pachnicke, “AI-based digital predistortion for IQ Mach-Zehnder modulators,” in Proc. Asia Comm. Photon. Conf., Chengdu, China, 2019, Paper S3B.3.

Calabrò, S.

G. Khanna, B. Spinnler, S. Calabrò, E. De Man, and N. Hanik, “A robust adaptive pre-distortion method for optical communication transmitters,” IEEE Photon. Technol. Lett., vol. 28, no. 7, pp. 752–755, 2016.

Carrarini, M.

A. Bernardini, M. Carrarini, and S. De Fina, “The use of a neural net for copeing with nonlinear distortions,” in Proc. 20th Eur. Microw. Conf., Budapest, Hungary, 1990, pp. 1718–1723.

Chagnon, M.

V. Bajaj, F. Buchali, M. Chagnon, S. Wahls, and V. Aref, “Single-channel 1.61 Tb/s optical coherent transmission enabled by neural network-based digital pre-distortion,” in Proc. Eur. Conf. Exhib. Opt. Commun., Brussels, Belgium, 2020, Paper. Tu.1.D.5.

Chen, W.

J. Zhang, M. Gao, W. Chen, and G. Shen, “Non-data-aided k-nearest neighbors technique for optical fiber nonlinearity mitigation,” IEEE/OSA J. Lightw. Technol., vol. 36, no. 17, pp. 3564–3572, 2018.

Ciblat, P.

M. Selmi, Y. Jaouen, and P. Ciblat, “Accurate digital frequency offset estimator for coherent polmux QAM transmission systems,” in Proc. 35th Eur. Conf. Opt. Commun., Vienna, Austria, 2009, pp. 1–2.

Dai, X.

X. Dai, X. Li, M. Luo, and S. Yu, “Numerical simulation and experimental demonstration of accurate machine learning aided IQ time-skew and power-imbalance identification for coherent transmitters,” OSA Opt. Exp., vol. 27, no. 26, pp. 38367–38381, 2019.

De Fina, S.

A. Bernardini, M. Carrarini, and S. De Fina, “The use of a neural net for copeing with nonlinear distortions,” in Proc. 20th Eur. Microw. Conf., Budapest, Hungary, 1990, pp. 1718–1723.

De Man, E.

G. Khanna, B. Spinnler, S. Calabrò, E. De Man, and N. Hanik, “A robust adaptive pre-distortion method for optical communication transmitters,” IEEE Photon. Technol. Lett., vol. 28, no. 7, pp. 752–755, 2016.

Di Claudio, E. D.

R. Parisi, E. D. Di Claudio, G. Orlandi, and B. D. Rao, “Fast adaptive digital equalization by recurrent neural networks,” IEEE Trans. Signal Process., vol. 45, no. 11, pp. 2731–2739, 1997.

Diniz, J. C. M.

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,” IEEE/OSA J. Lightw. Technol., vol. 35, no. 4, pp. 868–875, 2017.

Dris, S.

A. Richter, S. Dris, and N. André, “On the analysis and emulation of nonlinear component characteristics,” in Proc. Opt. Fiber Commun. Conf. Exhib., San Diego, CA, USA, 2019, Paper Th.1.D.1.

Elschner, R.

M. Nölle, M. S. Erkılınc, R. Emmerich, C. Schmidt-Langhorst, R. Elschner, and C. Schubert, “Characterization and linearization of high bandwidth integrated optical transmitter modules,” in Proc. Eur. Conf. Exhib. Opt. Commun., 2020, Paper Tu2D-4.

Emmerich, R.

M. Nölle, M. S. Erkılınc, R. Emmerich, C. Schmidt-Langhorst, R. Elschner, and C. Schubert, “Characterization and linearization of high bandwidth integrated optical transmitter modules,” in Proc. Eur. Conf. Exhib. Opt. Commun., 2020, Paper Tu2D-4.

Eriksson, T. A.

T. A. Eriksson, H. Bülow, and A. Leven, “Applying neural networks in optical communication systems: Possible pitfalls,” IEEE Photon. Technol. Lett., vol. 29, no. 23, pp. 2091–2094, 2017.

Erkilinc, M. S.

M. Nölle, M. S. Erkılınc, R. Emmerich, C. Schmidt-Langhorst, R. Elschner, and C. Schubert, “Characterization and linearization of high bandwidth integrated optical transmitter modules,” in Proc. Eur. Conf. Exhib. Opt. Commun., 2020, Paper Tu2D-4.

Esmail, M. A.

W. S. Saif, M. A. Esmail, A. M. Ragheb, T. A. Alshawi, and S. A. Alshebeili, “Machine learning techniques for optical performance monitoring and modulation format identification: A survey,” IEEE Commun. Surv. Tut., vol. 22, no. 4, pp. 2839–2882, 2020.

Eun, C.

C. Eun and E. J. Powers, “A new volterra predistorter based on the indirect learning architecture,” IEEE Trans. Signal Process., vol. 45, no. 1, pp. 223–227, 1997.

Faig, H.

G. Paryanti, H. Faig, L. Rokach, and D. Sadot, “A direct learning approach for neural network based pre-distortion for coherent nonlinear optical transmitter,” IEEE/OSA J. Lightw. Technol., vol. 38, no. 15, pp. 3883–3896, 2020.

Fischer, J. K.

P. W. Berenguer, T. Rahman, A. Napoli, M. Nölle, C. Schubert, and J. K. Fischer, “Nonlinear digital pre-distortion of transmitter components,” IEEE/OSA J. Lightw. Technol., vol. 34, no. 8, pp. 1739–1745, 2016.

P. W. Berenguer, T. Rahman, A. Napoli, M. Nölle, C. Schubert, and J. K. Fischer, “Nonlinear digital pre-distortion of transmitter components,” in Proc. Eur. Conf. Exhib. Opt. Commun., Valencia, Spain, 2015, Paper Th.2.6.3.

Fludger, C. R. S.

C. R. S. Fludger and T. Kupfer, “Transmitter impairment mitigation and monitoring for high baud-rate, high order modulation systems,” in Proc. Eur. Conf. Exhib. Opt. Commun., Dusseldorf, Germany, 2016, pp. 1–3.

Freire, P. J.

P. J. Freire, “Complex-valued neural network design for mitigation of signal distortions in optical links,” IEEE/OSA J. Lightw. Technol., vol. 39, no. 6, pp. 1696–1705, 2021.

Gao, M.

J. Zhang, M. Gao, W. Chen, and G. Shen, “Non-data-aided k-nearest neighbors technique for optical fiber nonlinearity mitigation,” IEEE/OSA J. Lightw. Technol., vol. 36, no. 17, pp. 3564–3572, 2018.

Giacoumidis, E.

E. Giacoumidis, “Fiber nonlinearity-induced penalty reduction in CO-OFDM by ANN-based nonlinear equalization,” OSA Opt. Lett., vol. 40, no. 21, pp. 5113–5116, 2015.

Gupta, S.

T. T. Joy, S. Rana, S. Gupta, and S. Venkatesh, “Hyperparameter tuning for big data using bayesian optimisation,” in Proc. Int. Conf. Pattern Recognit., Cancun, Mexico, 2016, pp. 2574–2579.

Häger, C.

C. Häger and H. D. Pfister, “Nonlinear interference mitigation via deep neural networks,” in Proc. Opt. Fiber Commun. Conf. Expo., San Diego, CA, USA, 2018, Paper W.3.A.4.

Händel, P.

P. Händel, “Understanding normalized mean squared error in power amplifier linearization,” IEEE Microw. Wireless Compon. Lett., vol. 28, no. 11, pp. 1047–1049, 2018.

Hanik, N.

G. Khanna, B. Spinnler, S. Calabrò, E. De Man, and N. Hanik, “A robust adaptive pre-distortion method for optical communication transmitters,” IEEE Photon. Technol. Lett., vol. 28, no. 7, pp. 752–755, 2016.

Hayes, M.

M. Hayes, Statistical Digital Signal Processing and Modeling. New York, NY, USA: John Wiley Sons, 1996.

Hoffmann, S.

T. Pfau, S. Hoffmann, and R. Noe, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” IEEE/OSA J. Lightw. Technol., vol. 27, no. 8, pp. 989–999, 2009.

Hong, D.

C. You and D. Hong, “Nonlinear blind equalization schemes using complex-valued multilayer feedforward neural networks,” IEEE Trans. Neural Netw., vol. 9, no. 6, pp. 1442–1455, 1998.

Huang, S.

Y. Zhang, J. Xin, X. Li, and S. Huang, “Overview on routing and resource allocation based machine learning in optical networks,” Elsevier Opt. Fiber Technol., vol. 60, 2020, Art. no. .

Jaouen, Y.

M. Selmi, Y. Jaouen, and P. Ciblat, “Accurate digital frequency offset estimator for coherent polmux QAM transmission systems,” in Proc. 35th Eur. Conf. Opt. Commun., Vienna, Austria, 2009, pp. 1–2.

Jones, R.

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,” IEEE/OSA J. Lightw. Technol., vol. 35, no. 4, pp. 868–875, 2017.

Joy, T. T.

T. T. Joy, S. Rana, S. Gupta, and S. Venkatesh, “Hyperparameter tuning for big data using bayesian optimisation,” in Proc. Int. Conf. Pattern Recognit., Cancun, Mexico, 2016, pp. 2574–2579.

Khanna, G.

G. Khanna, B. Spinnler, S. Calabrò, E. De Man, and N. Hanik, “A robust adaptive pre-distortion method for optical communication transmitters,” IEEE Photon. Technol. Lett., vol. 28, no. 7, pp. 752–755, 2016.

G. Khanna, “A memory polynomial based digital pre-distorter for high power transmitter components,” in Proc. Opt. Fiber Commun. Conf. Expo., Los Angeles, CA, USA, 2017, Paper M.2.C.4.

Kupfer, T.

C. R. S. Fludger and T. Kupfer, “Transmitter impairment mitigation and monitoring for high baud-rate, high order modulation systems,” in Proc. Eur. Conf. Exhib. Opt. Commun., Dusseldorf, Germany, 2016, pp. 1–3.

Kuschnerov, M.

M. Schaedler, M. Kuschnerov, S. Calabro, F. Pittala, C. Bluemm, and S. Pachnicke, “AI-based digital predistortion for IQ Mach-Zehnder modulators,” in Proc. Asia Comm. Photon. Conf., Chengdu, China, 2019, Paper S3B.3.

Leven, A.

T. A. Eriksson, H. Bülow, and A. Leven, “Applying neural networks in optical communication systems: Possible pitfalls,” IEEE Photon. Technol. Lett., vol. 29, no. 23, pp. 2091–2094, 2017.

Li, X.

Y. Zhang, J. Xin, X. Li, and S. Huang, “Overview on routing and resource allocation based machine learning in optical networks,” Elsevier Opt. Fiber Technol., vol. 60, 2020, Art. no. .

X. Dai, X. Li, M. Luo, and S. Yu, “Numerical simulation and experimental demonstration of accurate machine learning aided IQ time-skew and power-imbalance identification for coherent transmitters,” OSA Opt. Exp., vol. 27, no. 26, pp. 38367–38381, 2019.

Lin, Y.-Y.

Y.-Y. Lin, “Reduction in complexity of volterra filter by employing ℓ0-Regularization in 112-Gbps PAM-4 VCSEL optical interconnect,” in Proc. Opt. Fiber Commun. Conf. Expo., San Diego, CA, USA, 2020, Paper Th2A.51.

Luo, M.

X. Dai, X. Li, M. Luo, and S. Yu, “Numerical simulation and experimental demonstration of accurate machine learning aided IQ time-skew and power-imbalance identification for coherent transmitters,” OSA Opt. Exp., vol. 27, no. 26, pp. 38367–38381, 2019.

Marshall, T.

B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in stokes space,” OSA Opt. Exp., vol. 18, no. 17, pp. 17928–17939, 2010.

Mathews, V. J.

V. J. Mathews and G. L. Sicuranza, Polynomial Signal Process.New York, NY, USA: John Wiley Sons, 2000.

Miguel, I.

I. Miguel, “Cognitive dynamic optical networks [Invited],” IEEE/OSA J. Opt. Commun. Netw., vol. 5, no. 10, pp. 107–118, 2013.

Mockus, J.

J. Mockus, V. Tiesis, and A. Zilinskas, The Application of Bayesian Methods For Seeking the Extremum. New York, NY, USA: North Holland, 1978.

Musumeci, F.

F. Musumeci, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tut., vol. 21, no. 2, pp. 1383–1408, 2018.

Napoli, A.

P. W. Berenguer, T. Rahman, A. Napoli, M. Nölle, C. Schubert, and J. K. Fischer, “Nonlinear digital pre-distortion of transmitter components,” IEEE/OSA J. Lightw. Technol., vol. 34, no. 8, pp. 1739–1745, 2016.

A. Napoli, “Next generation elastic optical networks: The vision of the european research project IDEALIST,” IEEE Commun. Mag., vol. 53, no. 2, pp. 152–162, 2015.

P. W. Berenguer, T. Rahman, A. Napoli, M. Nölle, C. Schubert, and J. K. Fischer, “Nonlinear digital pre-distortion of transmitter components,” in Proc. Eur. Conf. Exhib. Opt. Commun., Valencia, Spain, 2015, Paper Th.2.6.3.

Neary, P.

P. Neary, “Automatic hyperparameter tuning in deep convolutional neural networks using asynchronous reinforcement learning,” in Proc. Int. Conf. Cogn. Comput., San Francisco, CA, USA, 2018, pp. 73–77.

Nebendahl, B.

B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in stokes space,” OSA Opt. Exp., vol. 18, no. 17, pp. 17928–17939, 2010.

Noe, R.

T. Pfau, S. Hoffmann, and R. Noe, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” IEEE/OSA J. Lightw. Technol., vol. 27, no. 8, pp. 989–999, 2009.

Nölle, M.

P. W. Berenguer, T. Rahman, A. Napoli, M. Nölle, C. Schubert, and J. K. Fischer, “Nonlinear digital pre-distortion of transmitter components,” IEEE/OSA J. Lightw. Technol., vol. 34, no. 8, pp. 1739–1745, 2016.

P. W. Berenguer, T. Rahman, A. Napoli, M. Nölle, C. Schubert, and J. K. Fischer, “Nonlinear digital pre-distortion of transmitter components,” in Proc. Eur. Conf. Exhib. Opt. Commun., Valencia, Spain, 2015, Paper Th.2.6.3.

M. Nölle, M. S. Erkılınc, R. Emmerich, C. Schmidt-Langhorst, R. Elschner, and C. Schubert, “Characterization and linearization of high bandwidth integrated optical transmitter modules,” in Proc. Eur. Conf. Exhib. Opt. Commun., 2020, Paper Tu2D-4.

North, R.

B. E. Watkins and R. North, “Predistortion of nonlinear amplifiers using neural networks,” in Proc. Mil. Commun. Conf., McLean, VA, USA, 1996, pp. 316–320.

Nowak, R. D.

R. D. Nowak, “Penalized least squares estimation of volterra filters and higher order statistics,” IEEE Trans. Signal Process., vol. 46, no. 2, pp. 419–428, 1998.

Orlandi, G.

R. Parisi, E. D. Di Claudio, G. Orlandi, and B. D. Rao, “Fast adaptive digital equalization by recurrent neural networks,” IEEE Trans. Signal Process., vol. 45, no. 11, pp. 2731–2739, 1997.

Pachnicke, S.

M. Schaedler, M. Kuschnerov, S. Calabro, F. Pittala, C. Bluemm, and S. Pachnicke, “AI-based digital predistortion for IQ Mach-Zehnder modulators,” in Proc. Asia Comm. Photon. Conf., Chengdu, China, 2019, Paper S3B.3.

Parisi, R.

R. Parisi, E. D. Di Claudio, G. Orlandi, and B. D. Rao, “Fast adaptive digital equalization by recurrent neural networks,” IEEE Trans. Signal Process., vol. 45, no. 11, pp. 2731–2739, 1997.

Paryanti, G.

G. Paryanti, H. Faig, L. Rokach, and D. Sadot, “A direct learning approach for neural network based pre-distortion for coherent nonlinear optical transmitter,” IEEE/OSA J. Lightw. Technol., vol. 38, no. 15, pp. 3883–3896, 2020.

M. Tzur, G. Paryanti, and D. Sadot, “Optimization of recurrent neural network-based pre-distorter for coherent optical transmitter via stochastic orthogonal decomposition,” in Proc. OSA Adv. Photon. Congr., 2020, Paper SpTh2I.5.

Pfau, T.

T. Pfau, S. Hoffmann, and R. Noe, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” IEEE/OSA J. Lightw. Technol., vol. 27, no. 8, pp. 989–999, 2009.

Pfister, H. D.

C. Häger and H. D. Pfister, “Nonlinear interference mitigation via deep neural networks,” in Proc. Opt. Fiber Commun. Conf. Expo., San Diego, CA, USA, 2018, Paper W.3.A.4.

Piels, M.

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,” IEEE/OSA J. Lightw. Technol., vol. 35, no. 4, pp. 868–875, 2017.

Pittala, F.

M. Schaedler, M. Kuschnerov, S. Calabro, F. Pittala, C. Bluemm, and S. Pachnicke, “AI-based digital predistortion for IQ Mach-Zehnder modulators,” in Proc. Asia Comm. Photon. Conf., Chengdu, China, 2019, Paper S3B.3.

Powers, E. J.

C. Eun and E. J. Powers, “A new volterra predistorter based on the indirect learning architecture,” IEEE Trans. Signal Process., vol. 45, no. 1, pp. 223–227, 1997.

Prechelt, L.

L. Prechelt, “Automatic early stopping using cross validation: Quantifying the criteria,” Elsevier Neural Netw., vol. 11, no. 4, pp. 761–767, 1998.

Ragheb, A. M.

W. S. Saif, M. A. Esmail, A. M. Ragheb, T. A. Alshawi, and S. A. Alshebeili, “Machine learning techniques for optical performance monitoring and modulation format identification: A survey,” IEEE Commun. Surv. Tut., vol. 22, no. 4, pp. 2839–2882, 2020.

Rahman, T.

P. W. Berenguer, T. Rahman, A. Napoli, M. Nölle, C. Schubert, and J. K. Fischer, “Nonlinear digital pre-distortion of transmitter components,” IEEE/OSA J. Lightw. Technol., vol. 34, no. 8, pp. 1739–1745, 2016.

P. W. Berenguer, T. Rahman, A. Napoli, M. Nölle, C. Schubert, and J. K. Fischer, “Nonlinear digital pre-distortion of transmitter components,” in Proc. Eur. Conf. Exhib. Opt. Commun., Valencia, Spain, 2015, Paper Th.2.6.3.

Rana, S.

T. T. Joy, S. Rana, S. Gupta, and S. Venkatesh, “Hyperparameter tuning for big data using bayesian optimisation,” in Proc. Int. Conf. Pattern Recognit., Cancun, Mexico, 2016, pp. 2574–2579.

Rao, B. D.

R. Parisi, E. D. Di Claudio, G. Orlandi, and B. D. Rao, “Fast adaptive digital equalization by recurrent neural networks,” IEEE Trans. Signal Process., vol. 45, no. 11, pp. 2731–2739, 1997.

Rasmussen, C. E.

C. E. Rasmussen and C. K. Williams, Gaussian Processes for Machine Learning. Cambridge, MA, USA: MIT Press, 2006.

Richter, A.

A. Richter, S. Dris, and N. André, “On the analysis and emulation of nonlinear component characteristics,” in Proc. Opt. Fiber Commun. Conf. Exhib., San Diego, CA, USA, 2019, Paper Th.1.D.1.

Rokach, L.

G. Paryanti, H. Faig, L. Rokach, and D. Sadot, “A direct learning approach for neural network based pre-distortion for coherent nonlinear optical transmitter,” IEEE/OSA J. Lightw. Technol., vol. 38, no. 15, pp. 3883–3896, 2020.

Sadot, D.

G. Paryanti, H. Faig, L. Rokach, and D. Sadot, “A direct learning approach for neural network based pre-distortion for coherent nonlinear optical transmitter,” IEEE/OSA J. Lightw. Technol., vol. 38, no. 15, pp. 3883–3896, 2020.

M. Tzur, G. Paryanti, and D. Sadot, “Optimization of recurrent neural network-based pre-distorter for coherent optical transmitter via stochastic orthogonal decomposition,” in Proc. OSA Adv. Photon. Congr., 2020, Paper SpTh2I.5.

Saif, W. S.

W. S. Saif, M. A. Esmail, A. M. Ragheb, T. A. Alshawi, and S. A. Alshebeili, “Machine learning techniques for optical performance monitoring and modulation format identification: A survey,” IEEE Commun. Surv. Tut., vol. 22, no. 4, pp. 2839–2882, 2020.

Sasai, T.

T. Sasai, “Wiener-Hammerstein model and its learning for nonlinear digital pre-distortion of optical transmitters,” OSA Opt. Exp., vol. 28, no. 21, pp. 30952–30963, 2020.

Schaedler, M.

M. Schaedler, M. Kuschnerov, S. Calabro, F. Pittala, C. Bluemm, and S. Pachnicke, “AI-based digital predistortion for IQ Mach-Zehnder modulators,” in Proc. Asia Comm. Photon. Conf., Chengdu, China, 2019, Paper S3B.3.

Schetzen, M.

M. Schetzen, The Volterra and Wiener Theories of Nonlinear Systems. Malabar, FL, USA: John Wiley Sons, 1980.

Schmidt-Langhorst, C.

M. Nölle, M. S. Erkılınc, R. Emmerich, C. Schmidt-Langhorst, R. Elschner, and C. Schubert, “Characterization and linearization of high bandwidth integrated optical transmitter modules,” in Proc. Eur. Conf. Exhib. Opt. Commun., 2020, Paper Tu2D-4.

Schubert, C.

P. W. Berenguer, T. Rahman, A. Napoli, M. Nölle, C. Schubert, and J. K. Fischer, “Nonlinear digital pre-distortion of transmitter components,” IEEE/OSA J. Lightw. Technol., vol. 34, no. 8, pp. 1739–1745, 2016.

P. W. Berenguer, T. Rahman, A. Napoli, M. Nölle, C. Schubert, and J. K. Fischer, “Nonlinear digital pre-distortion of transmitter components,” in Proc. Eur. Conf. Exhib. Opt. Commun., Valencia, Spain, 2015, Paper Th.2.6.3.

M. Nölle, M. S. Erkılınc, R. Emmerich, C. Schmidt-Langhorst, R. Elschner, and C. Schubert, “Characterization and linearization of high bandwidth integrated optical transmitter modules,” in Proc. Eur. Conf. Exhib. Opt. Commun., 2020, Paper Tu2D-4.

Selmi, M.

M. Selmi, Y. Jaouen, and P. Ciblat, “Accurate digital frequency offset estimator for coherent polmux QAM transmission systems,” in Proc. 35th Eur. Conf. Opt. Commun., Vienna, Austria, 2009, pp. 1–2.

Sena, M.

M. Sena, “An autonomous identification and Pre-distortion scheme for cognitive transceivers using bayesian optimization,” in Proc. Eur. Conf. Exhib. Opt. Commun., Brussels, Belgium, 2020, Paper Tu.1.D.7.

Shen, G.

J. Zhang, M. Gao, W. Chen, and G. Shen, “Non-data-aided k-nearest neighbors technique for optical fiber nonlinearity mitigation,” IEEE/OSA J. Lightw. Technol., vol. 36, no. 17, pp. 3564–3572, 2018.

Sicuranza, G. L.

V. J. Mathews and G. L. Sicuranza, Polynomial Signal Process.New York, NY, USA: John Wiley Sons, 2000.

Spinnler, B.

B. Spinnler, “Autonomous intelligent transponder enabling adaptive network optimization in a live network field trial,” IEEE/OSA J. Opt. Commun. Netw., vol. 11, no. 9, pp. C1–C9, 2019.

G. Khanna, B. Spinnler, S. Calabrò, E. De Man, and N. Hanik, “A robust adaptive pre-distortion method for optical communication transmitters,” IEEE Photon. Technol. Lett., vol. 28, no. 7, pp. 752–755, 2016.

Szafraniec, B.

B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in stokes space,” OSA Opt. Exp., vol. 18, no. 17, pp. 17928–17939, 2010.

Thrane, J.

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,” IEEE/OSA J. Lightw. Technol., vol. 35, no. 4, pp. 868–875, 2017.

Tiesis, V.

J. Mockus, V. Tiesis, and A. Zilinskas, The Application of Bayesian Methods For Seeking the Extremum. New York, NY, USA: North Holland, 1978.

Tzur, M.

M. Tzur, G. Paryanti, and D. Sadot, “Optimization of recurrent neural network-based pre-distorter for coherent optical transmitter via stochastic orthogonal decomposition,” in Proc. OSA Adv. Photon. Congr., 2020, Paper SpTh2I.5.

Venkatesh, S.

T. T. Joy, S. Rana, S. Gupta, and S. Venkatesh, “Hyperparameter tuning for big data using bayesian optimisation,” in Proc. Int. Conf. Pattern Recognit., Cancun, Mexico, 2016, pp. 2574–2579.

Wahls, S.

V. Bajaj, F. Buchali, M. Chagnon, S. Wahls, and V. Aref, “Single-channel 1.61 Tb/s optical coherent transmission enabled by neural network-based digital pre-distortion,” in Proc. Eur. Conf. Exhib. Opt. Commun., Brussels, Belgium, 2020, Paper. Tu.1.D.5.

Wass, J.

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,” IEEE/OSA J. Lightw. Technol., vol. 35, no. 4, pp. 868–875, 2017.

Watkins, B. E.

B. E. Watkins and R. North, “Predistortion of nonlinear amplifiers using neural networks,” in Proc. Mil. Commun. Conf., McLean, VA, USA, 1996, pp. 316–320.

Williams, C. K.

C. E. Rasmussen and C. K. Williams, Gaussian Processes for Machine Learning. Cambridge, MA, USA: MIT Press, 2006.

Xin, J.

Y. Zhang, J. Xin, X. Li, and S. Huang, “Overview on routing and resource allocation based machine learning in optical networks,” Elsevier Opt. Fiber Technol., vol. 60, 2020, Art. no. .

You, C.

C. You and D. Hong, “Nonlinear blind equalization schemes using complex-valued multilayer feedforward neural networks,” IEEE Trans. Neural Netw., vol. 9, no. 6, pp. 1442–1455, 1998.

Yu, S.

X. Dai, X. Li, M. Luo, and S. Yu, “Numerical simulation and experimental demonstration of accurate machine learning aided IQ time-skew and power-imbalance identification for coherent transmitters,” OSA Opt. Exp., vol. 27, no. 26, pp. 38367–38381, 2019.

Zhang, J.

J. Zhang, M. Gao, W. Chen, and G. Shen, “Non-data-aided k-nearest neighbors technique for optical fiber nonlinearity mitigation,” IEEE/OSA J. Lightw. Technol., vol. 36, no. 17, pp. 3564–3572, 2018.

Zhang, Y.

Y. Zhang, J. Xin, X. Li, and S. Huang, “Overview on routing and resource allocation based machine learning in optical networks,” Elsevier Opt. Fiber Technol., vol. 60, 2020, Art. no. .

Zibar, D.

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,” IEEE/OSA J. Lightw. Technol., vol. 35, no. 4, pp. 868–875, 2017.

Zilinskas, A.

J. Mockus, V. Tiesis, and A. Zilinskas, The Application of Bayesian Methods For Seeking the Extremum. New York, NY, USA: North Holland, 1978.

Elsevier Neural Netw. (1)

L. Prechelt, “Automatic early stopping using cross validation: Quantifying the criteria,” Elsevier Neural Netw., vol. 11, no. 4, pp. 761–767, 1998.

Elsevier Opt. Fiber Technol. (1)

Y. Zhang, J. Xin, X. Li, and S. Huang, “Overview on routing and resource allocation based machine learning in optical networks,” Elsevier Opt. Fiber Technol., vol. 60, 2020, Art. no. .

IEEE Commun. Mag. (1)

A. Napoli, “Next generation elastic optical networks: The vision of the european research project IDEALIST,” IEEE Commun. Mag., vol. 53, no. 2, pp. 152–162, 2015.

IEEE Commun. Surv. Tut. (2)

F. Musumeci, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tut., vol. 21, no. 2, pp. 1383–1408, 2018.

W. S. Saif, M. A. Esmail, A. M. Ragheb, T. A. Alshawi, and S. A. Alshebeili, “Machine learning techniques for optical performance monitoring and modulation format identification: A survey,” IEEE Commun. Surv. Tut., vol. 22, no. 4, pp. 2839–2882, 2020.

IEEE Microw. Wireless Compon. Lett. (1)

P. Händel, “Understanding normalized mean squared error in power amplifier linearization,” IEEE Microw. Wireless Compon. Lett., vol. 28, no. 11, pp. 1047–1049, 2018.

IEEE Photon. Technol. Lett. (2)

T. A. Eriksson, H. Bülow, and A. Leven, “Applying neural networks in optical communication systems: Possible pitfalls,” IEEE Photon. Technol. Lett., vol. 29, no. 23, pp. 2091–2094, 2017.

G. Khanna, B. Spinnler, S. Calabrò, E. De Man, and N. Hanik, “A robust adaptive pre-distortion method for optical communication transmitters,” IEEE Photon. Technol. Lett., vol. 28, no. 7, pp. 752–755, 2016.

IEEE Trans. Neural Netw. (1)

C. You and D. Hong, “Nonlinear blind equalization schemes using complex-valued multilayer feedforward neural networks,” IEEE Trans. Neural Netw., vol. 9, no. 6, pp. 1442–1455, 1998.

IEEE Trans. Signal Process. (3)

R. Parisi, E. D. Di Claudio, G. Orlandi, and B. D. Rao, “Fast adaptive digital equalization by recurrent neural networks,” IEEE Trans. Signal Process., vol. 45, no. 11, pp. 2731–2739, 1997.

R. D. Nowak, “Penalized least squares estimation of volterra filters and higher order statistics,” IEEE Trans. Signal Process., vol. 46, no. 2, pp. 419–428, 1998.

C. Eun and E. J. Powers, “A new volterra predistorter based on the indirect learning architecture,” IEEE Trans. Signal Process., vol. 45, no. 1, pp. 223–227, 1997.

IEEE/OSA J. Lightw. Technol. (6)

P. W. Berenguer, T. Rahman, A. Napoli, M. Nölle, C. Schubert, and J. K. Fischer, “Nonlinear digital pre-distortion of transmitter components,” IEEE/OSA J. Lightw. Technol., vol. 34, no. 8, pp. 1739–1745, 2016.

G. Paryanti, H. Faig, L. Rokach, and D. Sadot, “A direct learning approach for neural network based pre-distortion for coherent nonlinear optical transmitter,” IEEE/OSA J. Lightw. Technol., vol. 38, no. 15, pp. 3883–3896, 2020.

J. Zhang, M. Gao, W. Chen, and G. Shen, “Non-data-aided k-nearest neighbors technique for optical fiber nonlinearity mitigation,” IEEE/OSA J. Lightw. Technol., vol. 36, no. 17, pp. 3564–3572, 2018.

P. J. Freire, “Complex-valued neural network design for mitigation of signal distortions in optical links,” IEEE/OSA J. Lightw. Technol., vol. 39, no. 6, pp. 1696–1705, 2021.

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,” IEEE/OSA J. Lightw. Technol., vol. 35, no. 4, pp. 868–875, 2017.

T. Pfau, S. Hoffmann, and R. Noe, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” IEEE/OSA J. Lightw. Technol., vol. 27, no. 8, pp. 989–999, 2009.

IEEE/OSA J. Opt. Commun. Netw. (2)

I. Miguel, “Cognitive dynamic optical networks [Invited],” IEEE/OSA J. Opt. Commun. Netw., vol. 5, no. 10, pp. 107–118, 2013.

B. Spinnler, “Autonomous intelligent transponder enabling adaptive network optimization in a live network field trial,” IEEE/OSA J. Opt. Commun. Netw., vol. 11, no. 9, pp. C1–C9, 2019.

OSA Opt. Exp. (3)

X. Dai, X. Li, M. Luo, and S. Yu, “Numerical simulation and experimental demonstration of accurate machine learning aided IQ time-skew and power-imbalance identification for coherent transmitters,” OSA Opt. Exp., vol. 27, no. 26, pp. 38367–38381, 2019.

T. Sasai, “Wiener-Hammerstein model and its learning for nonlinear digital pre-distortion of optical transmitters,” OSA Opt. Exp., vol. 28, no. 21, pp. 30952–30963, 2020.

B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in stokes space,” OSA Opt. Exp., vol. 18, no. 17, pp. 17928–17939, 2010.

OSA Opt. Lett. (1)

E. Giacoumidis, “Fiber nonlinearity-induced penalty reduction in CO-OFDM by ANN-based nonlinear equalization,” OSA Opt. Lett., vol. 40, no. 21, pp. 5113–5116, 2015.

Other (21)

V. Bajaj, F. Buchali, M. Chagnon, S. Wahls, and V. Aref, “Single-channel 1.61 Tb/s optical coherent transmission enabled by neural network-based digital pre-distortion,” in Proc. Eur. Conf. Exhib. Opt. Commun., Brussels, Belgium, 2020, Paper. Tu.1.D.5.

M. Tzur, G. Paryanti, and D. Sadot, “Optimization of recurrent neural network-based pre-distorter for coherent optical transmitter via stochastic orthogonal decomposition,” in Proc. OSA Adv. Photon. Congr., 2020, Paper SpTh2I.5.

Y.-Y. Lin, “Reduction in complexity of volterra filter by employing ℓ0-Regularization in 112-Gbps PAM-4 VCSEL optical interconnect,” in Proc. Opt. Fiber Commun. Conf. Expo., San Diego, CA, USA, 2020, Paper Th2A.51.

P. Neary, “Automatic hyperparameter tuning in deep convolutional neural networks using asynchronous reinforcement learning,” in Proc. Int. Conf. Cogn. Comput., San Francisco, CA, USA, 2018, pp. 73–77.

M. Schaedler, M. Kuschnerov, S. Calabro, F. Pittala, C. Bluemm, and S. Pachnicke, “AI-based digital predistortion for IQ Mach-Zehnder modulators,” in Proc. Asia Comm. Photon. Conf., Chengdu, China, 2019, Paper S3B.3.

P. W. Berenguer, T. Rahman, A. Napoli, M. Nölle, C. Schubert, and J. K. Fischer, “Nonlinear digital pre-distortion of transmitter components,” in Proc. Eur. Conf. Exhib. Opt. Commun., Valencia, Spain, 2015, Paper Th.2.6.3.

M. Schetzen, The Volterra and Wiener Theories of Nonlinear Systems. Malabar, FL, USA: John Wiley Sons, 1980.

A. Richter, S. Dris, and N. André, “On the analysis and emulation of nonlinear component characteristics,” in Proc. Opt. Fiber Commun. Conf. Exhib., San Diego, CA, USA, 2019, Paper Th.1.D.1.

C. Häger and H. D. Pfister, “Nonlinear interference mitigation via deep neural networks,” in Proc. Opt. Fiber Commun. Conf. Expo., San Diego, CA, USA, 2018, Paper W.3.A.4.

T. T. Joy, S. Rana, S. Gupta, and S. Venkatesh, “Hyperparameter tuning for big data using bayesian optimisation,” in Proc. Int. Conf. Pattern Recognit., Cancun, Mexico, 2016, pp. 2574–2579.

J. Mockus, V. Tiesis, and A. Zilinskas, The Application of Bayesian Methods For Seeking the Extremum. New York, NY, USA: North Holland, 1978.

M. Sena, “An autonomous identification and Pre-distortion scheme for cognitive transceivers using bayesian optimization,” in Proc. Eur. Conf. Exhib. Opt. Commun., Brussels, Belgium, 2020, Paper Tu.1.D.7.

G. Khanna, “A memory polynomial based digital pre-distorter for high power transmitter components,” in Proc. Opt. Fiber Commun. Conf. Expo., Los Angeles, CA, USA, 2017, Paper M.2.C.4.

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