Abstract

We numerically investigate our proposed carrier phase and amplitude noise estimation (CPANE) algorithm using extend Kalman filter (EKF) for joint mitigation of linear and non-linear phase noise as well as amplitude noise on 4, 16 and 64 polarization multiplexed (PM) quadrature amplitude modulation (QAM) 224 Gb/s systems. The results are compared to decision directed (DD) carrier phase estimation (CPE), DD phase locked loop (PLL) and universal CPE (U-CPE) algorithms. Besides eliminating the necessity of phase unwrapping function, EKF-CPANE shows improved performance for both back-to-back (BTB) and transmission scenarios compared to the aforementioned algorithms. We further propose a weighted innovation approach (WIA) of the EKF-CPANE which gives an improvement of 0.3 dB in the Q-factor, compared to the original algorithm.

© 2016 Optical Society of America

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References

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2015 (3)

2014 (4)

L. Pakala and B. Schmauss., “Performance evaluation of modulation format independent carrier phase estimation and decision directed carrier phase estimation for fiber non-linearity mitigation,” Proc. SPIE 9288, 928808 (2014).
[Crossref]

L. Pakala and B. Schmauss, “Nonlinearity and phase noise mitigation using feed-forward carrier phase estimation and digital backward propagation in coherent QAM transmission,” Physics Procedia 56, 1353–1357 (2014).
[Crossref]

X. Liu, S. Chandrasekhar, P. J. Winzer, R. W. Tkach, and A. R. Chraplyvy, “Fiber nonlinearity tolerant super-channel transmission via nonlinear noise squeezing and generalized phase conjugated twin waves,” J. Lightwave Technol. 32(4), 766–775 (2014).
[Crossref]

T. Inoue and S. Namiki, “Carrier recovery for M-QAM signals based on a block estimation process with Kalman filter,” Opt. Express 22(13), 15376–15387 (2014).
[Crossref] [PubMed]

2013 (2)

Y. Gao, A. P. T. Lau, and C. Lu, “Modulation-format-independent carrier phase estimation for square M-QAM systems,” IEEE Photonics Technol. Lett. 25, 1073–1076 (2013).
[Crossref]

B. Szafraniec, T. S. Marshall, and B. Nebendahl, “Performance monitoring and measurement techniques for coherent optical systems,” J. Lightwave Technol. 31(4), 648–663 (2013).
[Crossref]

2012 (1)

C. Y. Lin, M. Holtmannspoetter, R. Asif, and B. Schmauss, “Nonlinear mitigation using carrier phase estimation and digital backward propagation in coherent QAM transmission,” Opt. Express 20, 405–412 (2012).
[Crossref]

2011 (1)

2010 (2)

2009 (3)

2008 (3)

2007 (3)

1997 (1)

D. D. Marcenac, D. Nesset, A. E. Kelly, M. Brierley, A. D. Ellis, D. G. Moodie, and C. W. Ford, “40 Gbit/s transmission over 406 km of NDSF using mid-span spectral inversion by four-wave-mixing in a 2 mm long semiconductor optical amplifier,” Electron. Lett. 33, 879–880 (1997).
[Crossref]

Asif, R.

C. Y. Lin, M. Holtmannspoetter, R. Asif, and B. Schmauss, “Nonlinear mitigation using carrier phase estimation and digital backward propagation in coherent QAM transmission,” Opt. Express 20, 405–412 (2012).
[Crossref]

Barletta, L.

T. Fehenberger, M. P. Yankov, L. Barletta, and N. Hanik, “Compensation of XPM interference by blind tracking of the nonlinear phase in WDM systems with QAM input,” in Proceedings of European Conference on Optical Communications (ECOC) (IEEE, 2015), pp. 1–3.

Barros, D. J. F.

Bayvel, P.

Bertolini, M.

Bisplinghoff, A.

A. Bisplinghoff, C. Vogel, T. Kupfer, S. Langenbach, and B. Schmauss, “Slip-reduced carrier phase estimation for coherent transmission in the presence of non- linear phase noise,” in Optical Fiber Communication (OFC) Conference, OSA Technical Digest (online) (Optical Society of America, 2013), paper OTu3I.1.

Blow, H.

Brierley, M.

D. D. Marcenac, D. Nesset, A. E. Kelly, M. Brierley, A. D. Ellis, D. G. Moodie, and C. W. Ford, “40 Gbit/s transmission over 406 km of NDSF using mid-span spectral inversion by four-wave-mixing in a 2 mm long semiconductor optical amplifier,” Electron. Lett. 33, 879–880 (1997).
[Crossref]

Chandrasekhar, S.

Chraplyvy, A. R.

Darwazeh, I.

L. Pessoa, H. M. Salgado, and I. Darwazeh, “Performance evaluation of phase estimation algorithms in equalized coherent optical systems,” IEEE Photonics Technol. Lett. 21(17), 1181–1183 (2009).
[Crossref]

de Oliveira, J. C. R. F.

Diniz, J.

Doberstein, A.

Ellis, A. D.

D. D. Marcenac, D. Nesset, A. E. Kelly, M. Brierley, A. D. Ellis, D. G. Moodie, and C. W. Ford, “40 Gbit/s transmission over 406 km of NDSF using mid-span spectral inversion by four-wave-mixing in a 2 mm long semiconductor optical amplifier,” Electron. Lett. 33, 879–880 (1997).
[Crossref]

Essiambre, R. J.

Estaran, J.

Fehenberger, T.

T. Fehenberger, M. P. Yankov, L. Barletta, and N. Hanik, “Compensation of XPM interference by blind tracking of the nonlinear phase in WDM systems with QAM input,” in Proceedings of European Conference on Optical Communications (ECOC) (IEEE, 2015), pp. 1–3.

Fischer, J. K.

Ford, C. W.

D. D. Marcenac, D. Nesset, A. E. Kelly, M. Brierley, A. D. Ellis, D. G. Moodie, and C. W. Ford, “40 Gbit/s transmission over 406 km of NDSF using mid-span spectral inversion by four-wave-mixing in a 2 mm long semiconductor optical amplifier,” Electron. Lett. 33, 879–880 (1997).
[Crossref]

Foschini, G. J.

Franciscangelis, C.

Gao, Y.

Y. Gao, A. P. T. Lau, and C. Lu, “Modulation-format-independent carrier phase estimation for square M-QAM systems,” IEEE Photonics Technol. Lett. 25, 1073–1076 (2013).
[Crossref]

Gavioli, G.

Goebel, B.

Gonzalez, N. G.

Haisch, H.

Hanik, N.

T. Fehenberger, M. P. Yankov, L. Barletta, and N. Hanik, “Compensation of XPM interference by blind tracking of the nonlinear phase in WDM systems with QAM input,” in Proceedings of European Conference on Optical Communications (ECOC) (IEEE, 2015), pp. 1–3.

Hecker de Carvalho, L. H.

Hoffmann, S.

Holtmannspoetter, M.

C. Y. Lin, M. Holtmannspoetter, R. Asif, and B. Schmauss, “Nonlinear mitigation using carrier phase estimation and digital backward propagation in coherent QAM transmission,” Opt. Express 20, 405–412 (2012).
[Crossref]

Hoshida, T.

L. Li, Z. Tao, L. Liu, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “XPM tolerant adaptive carrier phase recovery for coherent receiver based on phase noise monitoring,” in Proceedings of European Conference on Optical Communications (ECOC) (IEEE, 2009), pp. 1–2.

Idler, W.

Inoue, T.

Ip, E.

Jazayerifar, M.

Kahn, J. M.

Kelly, A. E.

D. D. Marcenac, D. Nesset, A. E. Kelly, M. Brierley, A. D. Ellis, D. G. Moodie, and C. W. Ford, “40 Gbit/s transmission over 406 km of NDSF using mid-span spectral inversion by four-wave-mixing in a 2 mm long semiconductor optical amplifier,” Electron. Lett. 33, 879–880 (1997).
[Crossref]

Killey, R. I.

Kramer, G.

Kschischang, F. R.

Kupfer, T.

A. Bisplinghoff, C. Vogel, T. Kupfer, S. Langenbach, and B. Schmauss, “Slip-reduced carrier phase estimation for coherent transmission in the presence of non- linear phase noise,” in Optical Fiber Communication (OFC) Conference, OSA Technical Digest (online) (Optical Society of America, 2013), paper OTu3I.1.

Kuschnerov, M.

K. Piyawanno, M. Kuschnerov, B. Spinnler, and B. Lankl, “Nonlinearity mitigation with carrier phase estimation for coherent receivers with higher order modulation formats,” in Topic Meeting in Lasers and Electro- Optics Society (IEEE, 2009), pp. 426–427.

Langenbach, S.

A. Bisplinghoff, C. Vogel, T. Kupfer, S. Langenbach, and B. Schmauss, “Slip-reduced carrier phase estimation for coherent transmission in the presence of non- linear phase noise,” in Optical Fiber Communication (OFC) Conference, OSA Technical Digest (online) (Optical Society of America, 2013), paper OTu3I.1.

Lankl, B.

K. Piyawanno, M. Kuschnerov, B. Spinnler, and B. Lankl, “Nonlinearity mitigation with carrier phase estimation for coherent receivers with higher order modulation formats,” in Topic Meeting in Lasers and Electro- Optics Society (IEEE, 2009), pp. 426–427.

Lau, A. P. T.

Y. Gao, A. P. T. Lau, and C. Lu, “Modulation-format-independent carrier phase estimation for square M-QAM systems,” IEEE Photonics Technol. Lett. 25, 1073–1076 (2013).
[Crossref]

E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, ”Coherent detection in optical fiber systems,” Opt. Express 16, 753–791 (2008).
[Crossref] [PubMed]

Li, L.

L. Li, Z. Tao, L. Liu, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “XPM tolerant adaptive carrier phase recovery for coherent receiver based on phase noise monitoring,” in Proceedings of European Conference on Optical Communications (ECOC) (IEEE, 2009), pp. 1–2.

Lin, C. Y.

C. Y. Lin, M. Holtmannspoetter, R. Asif, and B. Schmauss, “Nonlinear mitigation using carrier phase estimation and digital backward propagation in coherent QAM transmission,” Opt. Express 20, 405–412 (2012).
[Crossref]

Liu, L.

L. Li, Z. Tao, L. Liu, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “XPM tolerant adaptive carrier phase recovery for coherent receiver based on phase noise monitoring,” in Proceedings of European Conference on Optical Communications (ECOC) (IEEE, 2009), pp. 1–2.

Liu, X.

Lu, C.

Y. Gao, A. P. T. Lau, and C. Lu, “Modulation-format-independent carrier phase estimation for square M-QAM systems,” IEEE Photonics Technol. Lett. 25, 1073–1076 (2013).
[Crossref]

Magarini, M.

Marcenac, D. D.

D. D. Marcenac, D. Nesset, A. E. Kelly, M. Brierley, A. D. Ellis, D. G. Moodie, and C. W. Ford, “40 Gbit/s transmission over 406 km of NDSF using mid-span spectral inversion by four-wave-mixing in a 2 mm long semiconductor optical amplifier,” Electron. Lett. 33, 879–880 (1997).
[Crossref]

Marshall, T. S.

Monroy, I. T.

Moodie, D. G.

D. D. Marcenac, D. Nesset, A. E. Kelly, M. Brierley, A. D. Ellis, D. G. Moodie, and C. W. Ford, “40 Gbit/s transmission over 406 km of NDSF using mid-span spectral inversion by four-wave-mixing in a 2 mm long semiconductor optical amplifier,” Electron. Lett. 33, 879–880 (1997).
[Crossref]

Namiki, S.

Nebendahl, B.

Nesset, D.

D. D. Marcenac, D. Nesset, A. E. Kelly, M. Brierley, A. D. Ellis, D. G. Moodie, and C. W. Ford, “40 Gbit/s transmission over 406 km of NDSF using mid-span spectral inversion by four-wave-mixing in a 2 mm long semiconductor optical amplifier,” Electron. Lett. 33, 879–880 (1997).
[Crossref]

Noe, R.

Oda, S.

L. Li, Z. Tao, L. Liu, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “XPM tolerant adaptive carrier phase recovery for coherent receiver based on phase noise monitoring,” in Proceedings of European Conference on Optical Communications (ECOC) (IEEE, 2009), pp. 1–2.

Pakala, L.

L. Pakala and B. Schmauss., “Performance evaluation of modulation format independent carrier phase estimation and decision directed carrier phase estimation for fiber non-linearity mitigation,” Proc. SPIE 9288, 928808 (2014).
[Crossref]

L. Pakala and B. Schmauss, “Nonlinearity and phase noise mitigation using feed-forward carrier phase estimation and digital backward propagation in coherent QAM transmission,” Physics Procedia 56, 1353–1357 (2014).
[Crossref]

L. Pakala and B. Schmauss, “Non-linear mitigation using carrier phase estimation and K-means clustering,” in Proceedings of Photonics Networks; 16. ITG Symposium (IEEE, 2015), pp. 1–5.

L. Pakala and B. Schmauss, “Extended Kalman filtering for simultaneous phase and amplitude noise mitigation in WDM systems,” in Proceedings of Transparent Optical Networks 17th International Conference (ICTON) (IEEE, 2015), pp. 1–4.
[Crossref]

L. Pakala and B. Schmauss, “Improved decision directed carrier phase estimation for nonlinearity mitigation in 16-QAM systems,” in 16th Int. Conf. Proc. Transparent Opt. Netw. (ICTON) (IEEE, 2014), pp. 1–4.

L. Pakala and B. Schmauss, “Joint compensation of phase and amplitude noise using extended Kalman filter in coherent QAM systems,” in Proceedings of European Conference on Optical Communications (ECOC) (IEEE, 2014), pp. 1–3.

Pan, C.

Pepe, M.

Pessoa, L.

L. Pessoa, H. M. Salgado, and I. Darwazeh, “Performance evaluation of phase estimation algorithms in equalized coherent optical systems,” IEEE Photonics Technol. Lett. 21(17), 1181–1183 (2009).
[Crossref]

Petermann, K.

Peucheret, C.

Pfau, T.

Piels, M.

Piyawanno, K.

K. Piyawanno, M. Kuschnerov, B. Spinnler, and B. Lankl, “Nonlinearity mitigation with carrier phase estimation for coherent receivers with higher order modulation formats,” in Topic Meeting in Lasers and Electro- Optics Society (IEEE, 2009), pp. 426–427.

Rasmussen, J. C.

L. Li, Z. Tao, L. Liu, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “XPM tolerant adaptive carrier phase recovery for coherent receiver based on phase noise monitoring,” in Proceedings of European Conference on Optical Communications (ECOC) (IEEE, 2009), pp. 1–2.

Richter, T.

Ros, F. D.

Sackey, I.

Salgado, H. M.

L. Pessoa, H. M. Salgado, and I. Darwazeh, “Performance evaluation of phase estimation algorithms in equalized coherent optical systems,” IEEE Photonics Technol. Lett. 21(17), 1181–1183 (2009).
[Crossref]

Savory, S. J.

Schmalen, L.

Schmauss, B.

L. Pakala and B. Schmauss, “Nonlinearity and phase noise mitigation using feed-forward carrier phase estimation and digital backward propagation in coherent QAM transmission,” Physics Procedia 56, 1353–1357 (2014).
[Crossref]

C. Y. Lin, M. Holtmannspoetter, R. Asif, and B. Schmauss, “Nonlinear mitigation using carrier phase estimation and digital backward propagation in coherent QAM transmission,” Opt. Express 20, 405–412 (2012).
[Crossref]

L. Pakala and B. Schmauss, “Non-linear mitigation using carrier phase estimation and K-means clustering,” in Proceedings of Photonics Networks; 16. ITG Symposium (IEEE, 2015), pp. 1–5.

L. Pakala and B. Schmauss, “Extended Kalman filtering for simultaneous phase and amplitude noise mitigation in WDM systems,” in Proceedings of Transparent Optical Networks 17th International Conference (ICTON) (IEEE, 2015), pp. 1–4.
[Crossref]

A. Bisplinghoff, C. Vogel, T. Kupfer, S. Langenbach, and B. Schmauss, “Slip-reduced carrier phase estimation for coherent transmission in the presence of non- linear phase noise,” in Optical Fiber Communication (OFC) Conference, OSA Technical Digest (online) (Optical Society of America, 2013), paper OTu3I.1.

L. Pakala and B. Schmauss, “Joint compensation of phase and amplitude noise using extended Kalman filter in coherent QAM systems,” in Proceedings of European Conference on Optical Communications (ECOC) (IEEE, 2014), pp. 1–3.

L. Pakala and B. Schmauss, “Improved decision directed carrier phase estimation for nonlinearity mitigation in 16-QAM systems,” in 16th Int. Conf. Proc. Transparent Opt. Netw. (ICTON) (IEEE, 2014), pp. 1–4.

Schmauss., B.

L. Pakala and B. Schmauss., “Performance evaluation of modulation format independent carrier phase estimation and decision directed carrier phase estimation for fiber non-linearity mitigation,” Proc. SPIE 9288, 928808 (2014).
[Crossref]

Schubert, C.

Spalvieri, A.

Spinnler, B.

K. Piyawanno, M. Kuschnerov, B. Spinnler, and B. Lankl, “Nonlinearity mitigation with carrier phase estimation for coherent receivers with higher order modulation formats,” in Topic Meeting in Lasers and Electro- Optics Society (IEEE, 2009), pp. 426–427.

Szafraniec, B.

Tao, Z.

L. Li, Z. Tao, L. Liu, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “XPM tolerant adaptive carrier phase recovery for coherent receiver based on phase noise monitoring,” in Proceedings of European Conference on Optical Communications (ECOC) (IEEE, 2009), pp. 1–2.

Taylor, M. G.

Tkach, R. W.

Vacondio, F.

Vogel, C.

A. Bisplinghoff, C. Vogel, T. Kupfer, S. Langenbach, and B. Schmauss, “Slip-reduced carrier phase estimation for coherent transmission in the presence of non- linear phase noise,” in Optical Fiber Communication (OFC) Conference, OSA Technical Digest (online) (Optical Society of America, 2013), paper OTu3I.1.

Winzer, P. J.

Yan, W.

L. Li, Z. Tao, L. Liu, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “XPM tolerant adaptive carrier phase recovery for coherent receiver based on phase noise monitoring,” in Proceedings of European Conference on Optical Communications (ECOC) (IEEE, 2009), pp. 1–2.

Yankov, M. P.

T. Fehenberger, M. P. Yankov, L. Barletta, and N. Hanik, “Compensation of XPM interference by blind tracking of the nonlinear phase in WDM systems with QAM input,” in Proceedings of European Conference on Optical Communications (ECOC) (IEEE, 2015), pp. 1–3.

Zibar, D.

Electron. Lett. (1)

D. D. Marcenac, D. Nesset, A. E. Kelly, M. Brierley, A. D. Ellis, D. G. Moodie, and C. W. Ford, “40 Gbit/s transmission over 406 km of NDSF using mid-span spectral inversion by four-wave-mixing in a 2 mm long semiconductor optical amplifier,” Electron. Lett. 33, 879–880 (1997).
[Crossref]

IEEE Photonics Technol. Lett. (2)

L. Pessoa, H. M. Salgado, and I. Darwazeh, “Performance evaluation of phase estimation algorithms in equalized coherent optical systems,” IEEE Photonics Technol. Lett. 21(17), 1181–1183 (2009).
[Crossref]

Y. Gao, A. P. T. Lau, and C. Lu, “Modulation-format-independent carrier phase estimation for square M-QAM systems,” IEEE Photonics Technol. Lett. 25, 1073–1076 (2013).
[Crossref]

J. Lightwave Technol. (12)

E. Ip and J. M. Kahn, “Digital equalization of chromatic dispersion and polarization mode dispersion,” J. Lightwave Technol. 25(8), 2033–2043 (2007).
[Crossref]

E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” J. Lightwave Technol. 25(9), 2675–2692 (2007).
[Crossref]

E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008).
[Crossref]

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Proc. SPIE (1)

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L. Pakala and B. Schmauss, “Improved decision directed carrier phase estimation for nonlinearity mitigation in 16-QAM systems,” in 16th Int. Conf. Proc. Transparent Opt. Netw. (ICTON) (IEEE, 2014), pp. 1–4.

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Figures (6)

Fig. 1
Fig. 1

Illustration of signal models to CPE and CPANE. (a) Input signal model to CPE. (b) Illustrates symbol recovery by CPE. (c) Illustrates recovered symbols from CPE and CPANE.

Fig. 2
Fig. 2

Block diagram of the proposed EKF-CPANE algorithm.

Fig. 3
Fig. 3

BER vs. OSNR curves for BTB performance using the considered CPE and CPANE algorithms. (a) 4-PM-QAM with laser linewidth of 1 MHz. (b) 16-PM-QAM with laser linewidth of 500 kHz. (c) 64-PM-QAM with laser linewidth of 330 kHz.

Fig. 4
Fig. 4

Simulation model of PM-m-QAM coherent transmission with DSP module.

Fig. 5
Fig. 5

Q-factor vs. launch power curves for the considered CPE and CPANE algorithms. (a) 4-PM-QAM over 1920 km of SSMF transmission. (b) 16-PM-QAM over 960 km of SSMF transmission. (c) 64-PM-QAM over 480 km of SSMF transmission.

Fig. 6
Fig. 6

Weighted innovation approach for EKF-CPANE. (a) The first quadrant of a 16-QAM constellation with the high decision error probability region marked in red. (b) Q-factor vs. launch power curves for 16-PM-QAM over 960 km of SSMF transmission for the EKF, WIA-EKF and IEKF CPANE algorithms.

Equations (22)

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

r k = a k e j θ k + n k
θ k = θ k 1 + w k
ϕ k = θ k + n k
a ^ k = r k e j θ ^ k with θ ^ k = 1 N N ϕ k
a ^ k 1 = r k e j ϕ k with θ ^ k = ϕ k
a ^ k 2 = r k e j θ k with θ ^ k = θ k
r k = a k e j ψ k
real ( ψ k ) = arg ( r k ) arg ( a k ) = θ k + n k
imag ( ψ k ) = log ( | r k | | a k | ) = n ˜ k
ψ k = ψ k 1 + w k
r k = a k e j ψ k + m k
ψ ^ k | k 1 = ψ ^ k 1 | k 1
P k | k 1 = P k 1 | k 1 + Q k
d k = decision ( t k ) where t k = r k e j ( 1 N N ψ ^ k N )
K k = P k | k 1 H k * ( H k P k | k 1 H k * + R k ) 1
H k = j d k e j ψ ^ k | k 1
v k = r k d k e j ψ ^ k | k 1 = r k r ^ k | k 1
ψ ^ k | k = ψ ^ k | k 1 + K k v k
P k | k = ( 1 K k H k ) P k | k 1
a ^ k = r k e j ψ ^ k
v k = r k d ˜ k e j ψ ^ k | k 1
d ˜ k = w 1 * d ^ k 1 + w 2 * d ^ k 2

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