Abstract

An analytical approach taking into account carrier phase estimation (CPE) is presented to predict performance of quadrature phase shift-keying (QPSK) systems using coherent detection. Using this approach, system performance is found as a function of symbol rate, local oscillator (LO) linewidth, chromatic dispersion (CD) and signal-to-noise ratio (SNR). A new expression is derived for the covariance matrix of the conditional probability density function (pdf) of the decision statistic. This pdf is used to find bit error rate (BER) semi-analytically. Our analytical derivation assumes perfect removal of data modulation which corresponds to an ideal decision feedback (DF) carrier recovery. The validity of the analytical pdf for predicting BER is verified for a wide range of system parameters of interest in long haul systems. In addition, our semi-analytical BER provides a lower bound for the Viterbi-Viterbi (VV) BER, while showing the analytical BER previously proposed in the literature shows an overly pessimistic prediction of VV BER performance. We show that inaccuracy in previous analysis stems from overly simple model for the CPE when compensating large accumulated dispersion electronically. Finally, we study extension of our results to quadrature amplitude modulation (QAM). Preliminary simulation results are promising but the accuracy of our semi-analytical approach for predicting BER should be investigated further.

© 2012 OSA

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  1. E. Ip, A. Lau, D. Barros, and J. Kahn, “Coherent detection in optical fiber systems,” Opt. Express16, 753–791 (2008).
    [CrossRef] [PubMed]
  2. R. Saunders, M. Traverso, T. Schmidt, and C. Malouin, “Economics of 100 Gb/s transport,” in Proc. of OFC (2010), Paper. NMB.2.
  3. T. Hoshida, H. Nakashima, T. Tanimura, S. Oda, Z. Tao, L. Liu, W. Yan, L. Li, and J. Rasmussen, “Network innovations brought by digital coherent receivers,” in Proc. of OFC (2010), Paper. NMB.4.
  4. E. Ip and J. Kahn, “Digital equalization of chromatic dispersion and polarization mode dispersion,” J. Lightwave Technol.25, 2033–2043 (2007).
    [CrossRef]
  5. E. Ip and J. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave. Technol.26, 3416–3425 (2008).
    [CrossRef]
  6. V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett.20, 1473–1475 (2008).
    [CrossRef]
  7. X. Chen, C. Kim, G. Li, and B. Zhou, “Numerical study of lumped dispersion compensation for 40-Gb/s return-to-zero differential phase-shift keying transmission,” IEEE Photon. Technol. Lett.19, 568–570 (2007).
    [CrossRef]
  8. C. Xie, “WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation,” Opt. Express17, 4815–4823 (2009).
    [CrossRef] [PubMed]
  9. D. Crivelli, H. Carter, and M. Hueda, “Adaptive digital equalization in the presence of chromatic dispersion, PMD, and phase noise in coherent fiber optic systems,” in Proc. of Globecom (2004), pp. 2545–2551.
  10. C. Xie, “Local oscillator phase noise induced penalties in optical coherent detection systems using electronic chromatic dispersion compensation,” in Proc. of OFC (2009), Paper. OMT.4.
  11. W. Shieh and K. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express16, 15718–15727 (2008).
    [CrossRef] [PubMed]
  12. I. Fatadin and S. Savory, “Impact of phase to amplitude noise conversion in coherent optical systems with digital dispersion compensation,” Opt. Express18, 16273–16278 (2010).
    [CrossRef] [PubMed]
  13. A. Lau, T. Shen, W. Shieh, and K. Ho, “Equalization-enhanced phase noise for 100Gb/s transmission and beyond with coherent detection,” Opt. Express18, 17239–17251 (2010).
    [CrossRef] [PubMed]
  14. K. Ho, A. Pak, Tao Lau, and W. Shieh, “Equalization-enhanced phase noise induced timing jitter,” Optics Letters36, 585–587 (2011).
    [CrossRef] [PubMed]
  15. S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. Rasmussen, “Interplay between local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in Proc. of ECOC (2010), Paper. Mo.1.C.2.
  16. T. Xu, G. Jacobsen, S. Popov, J. Li, A. Friberg, and Y. Zhang, “Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization,” Opt. Express19, 7756–7768 (2011).
    [CrossRef] [PubMed]
  17. Q. Zhuge, C. Chen, and D. Plant, “Dispersion-enhanced phase noise effects on reduced-guard-interval CO-OFDM transmission,” Opt. Express19, 4472–4484 (2011).
    [CrossRef] [PubMed]
  18. G. Colavolpe, T. Foggi, E. Forestieri, and M. Secondini, “Impact of phase noise and compensation techniques in coherent optical systems,” J. Lightwave Technol.29, 2790–2800 (2011).
    [CrossRef]
  19. M. Secondini, G. Meloni, T. Foggi, G. Colavolpe, L. Poti, and E. Forestieri, “Phase noise cancellation in coherent optical receivers by digital coherence enhancement,” in Proc. of ECOC (2010), Paper. P4.17.
  20. G. Colavolpe, T. Foggi, E. Forestieri, and M. Secondini, “Phase noise sensitivity and compensation techniques in long-haul coherent optical links,” in Proc. of Globcom (2010), pp. 1–6.
  21. Q. Zhuge, X. Xu, Z. El-Sahn, M. Mousa-Pasandi, M. Morsy-Osman, M. Chagnon, M. Qiu, and D. Plant, “Experimental investigation of the equalization-enhanced phase noise in long haul 56 Gbaud DP-QPSK systems,” Opt. Express20, 13841–13846 (2012).
    [CrossRef] [PubMed]
  22. M. Magarini, A. Spalvieri, F. Vacondio, M. Bertolini, M. Pepe, and G. Gavioli, “Empirical modeling and simulation of phase noise in long-haul coherent optical transmission systems,” Opt. Express19, 22455–22461 (2011).
    [CrossRef] [PubMed]
  23. S. Savory, “Digital filters for coherent optical receivers,” Opt. Express16, 804–817 (2008).
    [CrossRef] [PubMed]
  24. E. Ip and J. Kahn, “Feedforward carrier recovery for coherent optical communications,” J. Lightwave Technol.25, 2675–2692 (2007).
    [CrossRef]
  25. M. Taylor, “Phase estimation methods for optical coherent detection using digital signal processing,” J. Lightwave Technol.27, 901–914 (2009).
    [CrossRef]
  26. D. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. Lightwave Technol.24, 12–21 (2006).
    [CrossRef]

2012 (1)

2011 (5)

2010 (2)

2009 (2)

2008 (5)

E. Ip, A. Lau, D. Barros, and J. Kahn, “Coherent detection in optical fiber systems,” Opt. Express16, 753–791 (2008).
[CrossRef] [PubMed]

S. Savory, “Digital filters for coherent optical receivers,” Opt. Express16, 804–817 (2008).
[CrossRef] [PubMed]

W. Shieh and K. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express16, 15718–15727 (2008).
[CrossRef] [PubMed]

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

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett.20, 1473–1475 (2008).
[CrossRef]

2007 (3)

X. Chen, C. Kim, G. Li, and B. Zhou, “Numerical study of lumped dispersion compensation for 40-Gb/s return-to-zero differential phase-shift keying transmission,” IEEE Photon. Technol. Lett.19, 568–570 (2007).
[CrossRef]

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

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

2006 (1)

2004 (1)

D. Crivelli, H. Carter, and M. Hueda, “Adaptive digital equalization in the presence of chromatic dispersion, PMD, and phase noise in coherent fiber optic systems,” in Proc. of Globecom (2004), pp. 2545–2551.

Barros, D.

Bertolini, M.

Carena, A.

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett.20, 1473–1475 (2008).
[CrossRef]

Carter, H.

D. Crivelli, H. Carter, and M. Hueda, “Adaptive digital equalization in the presence of chromatic dispersion, PMD, and phase noise in coherent fiber optic systems,” in Proc. of Globecom (2004), pp. 2545–2551.

Chagnon, M.

Chen, C.

Chen, X.

X. Chen, C. Kim, G. Li, and B. Zhou, “Numerical study of lumped dispersion compensation for 40-Gb/s return-to-zero differential phase-shift keying transmission,” IEEE Photon. Technol. Lett.19, 568–570 (2007).
[CrossRef]

Colavolpe, G.

G. Colavolpe, T. Foggi, E. Forestieri, and M. Secondini, “Impact of phase noise and compensation techniques in coherent optical systems,” J. Lightwave Technol.29, 2790–2800 (2011).
[CrossRef]

M. Secondini, G. Meloni, T. Foggi, G. Colavolpe, L. Poti, and E. Forestieri, “Phase noise cancellation in coherent optical receivers by digital coherence enhancement,” in Proc. of ECOC (2010), Paper. P4.17.

G. Colavolpe, T. Foggi, E. Forestieri, and M. Secondini, “Phase noise sensitivity and compensation techniques in long-haul coherent optical links,” in Proc. of Globcom (2010), pp. 1–6.

Crivelli, D.

D. Crivelli, H. Carter, and M. Hueda, “Adaptive digital equalization in the presence of chromatic dispersion, PMD, and phase noise in coherent fiber optic systems,” in Proc. of Globecom (2004), pp. 2545–2551.

Curri, V.

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett.20, 1473–1475 (2008).
[CrossRef]

El-Sahn, Z.

Fatadin, I.

Foggi, T.

G. Colavolpe, T. Foggi, E. Forestieri, and M. Secondini, “Impact of phase noise and compensation techniques in coherent optical systems,” J. Lightwave Technol.29, 2790–2800 (2011).
[CrossRef]

M. Secondini, G. Meloni, T. Foggi, G. Colavolpe, L. Poti, and E. Forestieri, “Phase noise cancellation in coherent optical receivers by digital coherence enhancement,” in Proc. of ECOC (2010), Paper. P4.17.

G. Colavolpe, T. Foggi, E. Forestieri, and M. Secondini, “Phase noise sensitivity and compensation techniques in long-haul coherent optical links,” in Proc. of Globcom (2010), pp. 1–6.

Forestieri, E.

G. Colavolpe, T. Foggi, E. Forestieri, and M. Secondini, “Impact of phase noise and compensation techniques in coherent optical systems,” J. Lightwave Technol.29, 2790–2800 (2011).
[CrossRef]

M. Secondini, G. Meloni, T. Foggi, G. Colavolpe, L. Poti, and E. Forestieri, “Phase noise cancellation in coherent optical receivers by digital coherence enhancement,” in Proc. of ECOC (2010), Paper. P4.17.

G. Colavolpe, T. Foggi, E. Forestieri, and M. Secondini, “Phase noise sensitivity and compensation techniques in long-haul coherent optical links,” in Proc. of Globcom (2010), pp. 1–6.

Forghieri, F.

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett.20, 1473–1475 (2008).
[CrossRef]

Friberg, A.

Gavioli, G.

Ho, K.

Hoshida, T.

S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. Rasmussen, “Interplay between local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in Proc. of ECOC (2010), Paper. Mo.1.C.2.

T. Hoshida, H. Nakashima, T. Tanimura, S. Oda, Z. Tao, L. Liu, W. Yan, L. Li, and J. Rasmussen, “Network innovations brought by digital coherent receivers,” in Proc. of OFC (2010), Paper. NMB.4.

Hueda, M.

D. Crivelli, H. Carter, and M. Hueda, “Adaptive digital equalization in the presence of chromatic dispersion, PMD, and phase noise in coherent fiber optic systems,” in Proc. of Globecom (2004), pp. 2545–2551.

Ip, E.

Jacobsen, G.

Kahn, J.

Katoh, K.

Kikuchi, K.

Kim, C.

X. Chen, C. Kim, G. Li, and B. Zhou, “Numerical study of lumped dispersion compensation for 40-Gb/s return-to-zero differential phase-shift keying transmission,” IEEE Photon. Technol. Lett.19, 568–570 (2007).
[CrossRef]

Koizumi, N.

S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. Rasmussen, “Interplay between local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in Proc. of ECOC (2010), Paper. Mo.1.C.2.

Lau, A.

Lau, Tao

K. Ho, A. Pak, Tao Lau, and W. Shieh, “Equalization-enhanced phase noise induced timing jitter,” Optics Letters36, 585–587 (2011).
[CrossRef] [PubMed]

Li, G.

X. Chen, C. Kim, G. Li, and B. Zhou, “Numerical study of lumped dispersion compensation for 40-Gb/s return-to-zero differential phase-shift keying transmission,” IEEE Photon. Technol. Lett.19, 568–570 (2007).
[CrossRef]

Li, J.

Li, L.

T. Hoshida, H. Nakashima, T. Tanimura, S. Oda, Z. Tao, L. Liu, W. Yan, L. Li, and J. Rasmussen, “Network innovations brought by digital coherent receivers,” in Proc. of OFC (2010), Paper. NMB.4.

Liu, L.

T. Hoshida, H. Nakashima, T. Tanimura, S. Oda, Z. Tao, L. Liu, W. Yan, L. Li, and J. Rasmussen, “Network innovations brought by digital coherent receivers,” in Proc. of OFC (2010), Paper. NMB.4.

Ly-Gagnon, D.

Magarini, M.

Malouin, C.

R. Saunders, M. Traverso, T. Schmidt, and C. Malouin, “Economics of 100 Gb/s transport,” in Proc. of OFC (2010), Paper. NMB.2.

Meloni, G.

M. Secondini, G. Meloni, T. Foggi, G. Colavolpe, L. Poti, and E. Forestieri, “Phase noise cancellation in coherent optical receivers by digital coherence enhancement,” in Proc. of ECOC (2010), Paper. P4.17.

Morsy-Osman, M.

Mousa-Pasandi, M.

Nakashima, H.

S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. Rasmussen, “Interplay between local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in Proc. of ECOC (2010), Paper. Mo.1.C.2.

T. Hoshida, H. Nakashima, T. Tanimura, S. Oda, Z. Tao, L. Liu, W. Yan, L. Li, and J. Rasmussen, “Network innovations brought by digital coherent receivers,” in Proc. of OFC (2010), Paper. NMB.4.

Oda, S.

T. Hoshida, H. Nakashima, T. Tanimura, S. Oda, Z. Tao, L. Liu, W. Yan, L. Li, and J. Rasmussen, “Network innovations brought by digital coherent receivers,” in Proc. of OFC (2010), Paper. NMB.4.

S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. Rasmussen, “Interplay between local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in Proc. of ECOC (2010), Paper. Mo.1.C.2.

Ohshima, C.

S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. Rasmussen, “Interplay between local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in Proc. of ECOC (2010), Paper. Mo.1.C.2.

Pak, A.

K. Ho, A. Pak, Tao Lau, and W. Shieh, “Equalization-enhanced phase noise induced timing jitter,” Optics Letters36, 585–587 (2011).
[CrossRef] [PubMed]

Pepe, M.

Plant, D.

Poggiolini, P.

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett.20, 1473–1475 (2008).
[CrossRef]

Popov, S.

Poti, L.

M. Secondini, G. Meloni, T. Foggi, G. Colavolpe, L. Poti, and E. Forestieri, “Phase noise cancellation in coherent optical receivers by digital coherence enhancement,” in Proc. of ECOC (2010), Paper. P4.17.

Qiu, M.

Rasmussen, J.

S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. Rasmussen, “Interplay between local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in Proc. of ECOC (2010), Paper. Mo.1.C.2.

T. Hoshida, H. Nakashima, T. Tanimura, S. Oda, Z. Tao, L. Liu, W. Yan, L. Li, and J. Rasmussen, “Network innovations brought by digital coherent receivers,” in Proc. of OFC (2010), Paper. NMB.4.

Saunders, R.

R. Saunders, M. Traverso, T. Schmidt, and C. Malouin, “Economics of 100 Gb/s transport,” in Proc. of OFC (2010), Paper. NMB.2.

Savory, S.

Schmidt, T.

R. Saunders, M. Traverso, T. Schmidt, and C. Malouin, “Economics of 100 Gb/s transport,” in Proc. of OFC (2010), Paper. NMB.2.

Secondini, M.

G. Colavolpe, T. Foggi, E. Forestieri, and M. Secondini, “Impact of phase noise and compensation techniques in coherent optical systems,” J. Lightwave Technol.29, 2790–2800 (2011).
[CrossRef]

M. Secondini, G. Meloni, T. Foggi, G. Colavolpe, L. Poti, and E. Forestieri, “Phase noise cancellation in coherent optical receivers by digital coherence enhancement,” in Proc. of ECOC (2010), Paper. P4.17.

G. Colavolpe, T. Foggi, E. Forestieri, and M. Secondini, “Phase noise sensitivity and compensation techniques in long-haul coherent optical links,” in Proc. of Globcom (2010), pp. 1–6.

Shen, T.

Shieh, W.

Spalvieri, A.

Tanaka, T.

S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. Rasmussen, “Interplay between local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in Proc. of ECOC (2010), Paper. Mo.1.C.2.

Tanimura, T.

S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. Rasmussen, “Interplay between local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in Proc. of ECOC (2010), Paper. Mo.1.C.2.

T. Hoshida, H. Nakashima, T. Tanimura, S. Oda, Z. Tao, L. Liu, W. Yan, L. Li, and J. Rasmussen, “Network innovations brought by digital coherent receivers,” in Proc. of OFC (2010), Paper. NMB.4.

Tao, Z.

T. Hoshida, H. Nakashima, T. Tanimura, S. Oda, Z. Tao, L. Liu, W. Yan, L. Li, and J. Rasmussen, “Network innovations brought by digital coherent receivers,” in Proc. of OFC (2010), Paper. NMB.4.

S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. Rasmussen, “Interplay between local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in Proc. of ECOC (2010), Paper. Mo.1.C.2.

Taylor, M.

Traverso, M.

R. Saunders, M. Traverso, T. Schmidt, and C. Malouin, “Economics of 100 Gb/s transport,” in Proc. of OFC (2010), Paper. NMB.2.

Tsukamoto, S.

Vacondio, F.

Xie, C.

C. Xie, “WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation,” Opt. Express17, 4815–4823 (2009).
[CrossRef] [PubMed]

C. Xie, “Local oscillator phase noise induced penalties in optical coherent detection systems using electronic chromatic dispersion compensation,” in Proc. of OFC (2009), Paper. OMT.4.

Xu, T.

Xu, X.

Yan, W.

T. Hoshida, H. Nakashima, T. Tanimura, S. Oda, Z. Tao, L. Liu, W. Yan, L. Li, and J. Rasmussen, “Network innovations brought by digital coherent receivers,” in Proc. of OFC (2010), Paper. NMB.4.

Zhang, H.

S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. Rasmussen, “Interplay between local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in Proc. of ECOC (2010), Paper. Mo.1.C.2.

Zhang, Y.

Zhou, B.

X. Chen, C. Kim, G. Li, and B. Zhou, “Numerical study of lumped dispersion compensation for 40-Gb/s return-to-zero differential phase-shift keying transmission,” IEEE Photon. Technol. Lett.19, 568–570 (2007).
[CrossRef]

Zhuge, Q.

IEEE Photon. Technol. Lett. (2)

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett.20, 1473–1475 (2008).
[CrossRef]

X. Chen, C. Kim, G. Li, and B. Zhou, “Numerical study of lumped dispersion compensation for 40-Gb/s return-to-zero differential phase-shift keying transmission,” IEEE Photon. Technol. Lett.19, 568–570 (2007).
[CrossRef]

J. Lightwave Technol. (5)

J. Lightwave. Technol. (1)

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

Opt. Express (10)

Q. Zhuge, X. Xu, Z. El-Sahn, M. Mousa-Pasandi, M. Morsy-Osman, M. Chagnon, M. Qiu, and D. Plant, “Experimental investigation of the equalization-enhanced phase noise in long haul 56 Gbaud DP-QPSK systems,” Opt. Express20, 13841–13846 (2012).
[CrossRef] [PubMed]

I. Fatadin and S. Savory, “Impact of phase to amplitude noise conversion in coherent optical systems with digital dispersion compensation,” Opt. Express18, 16273–16278 (2010).
[CrossRef] [PubMed]

A. Lau, T. Shen, W. Shieh, and K. Ho, “Equalization-enhanced phase noise for 100Gb/s transmission and beyond with coherent detection,” Opt. Express18, 17239–17251 (2010).
[CrossRef] [PubMed]

Q. Zhuge, C. Chen, and D. Plant, “Dispersion-enhanced phase noise effects on reduced-guard-interval CO-OFDM transmission,” Opt. Express19, 4472–4484 (2011).
[CrossRef] [PubMed]

T. Xu, G. Jacobsen, S. Popov, J. Li, A. Friberg, and Y. Zhang, “Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization,” Opt. Express19, 7756–7768 (2011).
[CrossRef] [PubMed]

M. Magarini, A. Spalvieri, F. Vacondio, M. Bertolini, M. Pepe, and G. Gavioli, “Empirical modeling and simulation of phase noise in long-haul coherent optical transmission systems,” Opt. Express19, 22455–22461 (2011).
[CrossRef] [PubMed]

E. Ip, A. Lau, D. Barros, and J. Kahn, “Coherent detection in optical fiber systems,” Opt. Express16, 753–791 (2008).
[CrossRef] [PubMed]

S. Savory, “Digital filters for coherent optical receivers,” Opt. Express16, 804–817 (2008).
[CrossRef] [PubMed]

W. Shieh and K. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express16, 15718–15727 (2008).
[CrossRef] [PubMed]

C. Xie, “WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation,” Opt. Express17, 4815–4823 (2009).
[CrossRef] [PubMed]

Optics Letters (1)

K. Ho, A. Pak, Tao Lau, and W. Shieh, “Equalization-enhanced phase noise induced timing jitter,” Optics Letters36, 585–587 (2011).
[CrossRef] [PubMed]

Proc. of Globecom (1)

D. Crivelli, H. Carter, and M. Hueda, “Adaptive digital equalization in the presence of chromatic dispersion, PMD, and phase noise in coherent fiber optic systems,” in Proc. of Globecom (2004), pp. 2545–2551.

Other (6)

C. Xie, “Local oscillator phase noise induced penalties in optical coherent detection systems using electronic chromatic dispersion compensation,” in Proc. of OFC (2009), Paper. OMT.4.

R. Saunders, M. Traverso, T. Schmidt, and C. Malouin, “Economics of 100 Gb/s transport,” in Proc. of OFC (2010), Paper. NMB.2.

T. Hoshida, H. Nakashima, T. Tanimura, S. Oda, Z. Tao, L. Liu, W. Yan, L. Li, and J. Rasmussen, “Network innovations brought by digital coherent receivers,” in Proc. of OFC (2010), Paper. NMB.4.

S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. Rasmussen, “Interplay between local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in Proc. of ECOC (2010), Paper. Mo.1.C.2.

M. Secondini, G. Meloni, T. Foggi, G. Colavolpe, L. Poti, and E. Forestieri, “Phase noise cancellation in coherent optical receivers by digital coherence enhancement,” in Proc. of ECOC (2010), Paper. P4.17.

G. Colavolpe, T. Foggi, E. Forestieri, and M. Secondini, “Phase noise sensitivity and compensation techniques in long-haul coherent optical links,” in Proc. of Globcom (2010), pp. 1–6.

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Figures (5)

Fig. 1
Fig. 1

Block diagram of a coherent system.

Fig. 2
Fig. 2

(a) Cross section at Im{ŷk} = 0 of two-dimensional pdfs i) obtained by MC simulation (solid), ii) as developed in Eq. (11) (dashed) and iii) as reported in [13] (dot-dashed);L = 3000 km and Δν = 10 MHz, (b) error in pdf as a function of number of patterns for averaging in Eq. (11); pdf plotted in (a) uses 50 patterns.

Fig. 3
Fig. 3

BER versus (a) SNR (b) fiber length L (c) linewidth-symbol time product ΔνTs (d) SNR for different baud rates from MC simulation (markers) and semi-analytical pdfs (dashed). Baud rate in (a)–(c) is 28 Gbaud.

Fig. 4
Fig. 4

Penalty in dB at the BER of 3.8×10−3 from MC simulation (markers) and analytical pdf (dashed). DF is assumed for carrier recovery and baud rate is 28 Gbaud.

Fig. 5
Fig. 5

BER for 16QAM at 28 Gbaud for ideal DF and for our prediction of ideal DF performance from (10) and (11). BER versus (a) SNR (b) fiber length L (c) linewidth-symbol time product ΔνTs.

Equations (37)

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H C D ( j ω ) = exp ( j 1 2 β 2 L ω 2 )
w n = j T 2 2 π β 2 L exp ( j T 2 2 β 2 L n 2 )
N n N , N = π β 2 L T 2
ϕ ^ k = Arg { m = k N B k + N B r m x m * }
Δ n , k = ϕ R ( k T n T ) ϕ R ( k T )
ϕ ^ k ϕ R ( k T ) + ϕ T ( k T ) + n Re { w n p d ( n T ) } Δ n , k + n k + n k
y k x [ k ] + n = N N s n , k Δ n , k + n ˜ k
s n , k = j i x i w n p d [ ( k n ) T i T s ] j x [ k ] Re { w n p d ( n T ) }
s n , k = j i x i w n p d [ ( k n ) T i T s ]
y k = x [ k ] + n = N 1 [ ( Δ n , k Δ n + 1 , k ) m = N n s m , k ] + n = 1 N [ ( Δ n , k Δ n 1 , k ) m = n N s m , k ] + n k
f ( y k | x [ k ] ) = 1 | P | X P f ( y k | X )
ε = y k S | f M C ( y k ) f ( y k ) | d y k
BER = 2 Q ( 1 / σ n 2 + σ e e p n 2 )
r k = n = N N w n i = x i p d [ ( k n ) T i T s ] e j ϕ R [ ( k n ) T ] + n k
n = N N w n i = x i p d [ ( k n ) T i T s ] = x [ k ]
r k = x [ k ] ( 1 + q k ) e j ϕ R ( k T ) + n k
q k = n = N N w n ( e j Δ n , k 1 ) i = x i x [ k ] p d [ ( k n ) T i T s ]
Δ n , k = ϕ R ( k T n T ) ϕ R ( k T )
q k n = N N j Δ n , k w n i = x i x [ k ] p d [ ( k n ) T i T s ]
1 2 N B + 1 m = k N B k + N B r m x [ m ] * 1 2 N B + 1 e j ϕ R ( k T ) m q m + e j ϕ R ( k T ) + n ˜ k
m q m = j m n Δ n , k w n p d ( n T ) + m , n , x i x [ m ] x i x [ m ] j Δ n , k w n p d [ ( m n ) T i T s ]
m q m ( 2 N B + 1 ) n j Δ n , k w n p d ( n T )
e j ϕ R ( k T ) { 1 + 1 + n j Δ n , k w n p d ( n T ) } + n ˜ k + n ˜ k
ϕ ^ k ϕ R ( k T ) + Arg { 1 + n j Δ n , k w n p d ( n T ) } + n k + n k
ϕ ^ k ϕ R ( k T ) + n Δ n , k Re { w n p d ( n T ) } + n k + n k
θ k = m , n , i [ m ] Δ n , k Re x i x [ m ] w n p d [ ( m n ) T i T s ]
ϕ ^ k ϕ R ( k T ) + ϕ T ( k T ) + θ k + n Δ n , k Re { w n p d ( n T ) } + n k + n k
y k = n w n i x i p d [ ( k n ) T i T s ] e j ϕ R ( ( k n ) T ) e j ϕ ^ k + n k
y k = n w n i x i p d [ ( k n ) T i T s ] e j Δ n , k e j Re l w l p d ( l T ) Δ l , k + n ˜ k
e j Δ n , k l e j Δ l , k Re { w l p d ( l T ) } ( 1 + j Δ n , k ) l ( 1 j Δ l , k Re { w l p d ( l T ) } ) 1 + j Δ n , k l j Δ l , k Re { w l p d ( l T ) }
y k = ( 1 l j Δ l , k Re { w l p d ( l T ) } ) n w n i x i p d [ ( k n ) T i T s ] + n j Δ n , k w n i x i p d [ ( k n ) T i T s ] + n ˜ k x [ k ] x [ k ] l j Δ l , k Re { w l p d ( l T ) } + n j Δ n , k w n i x i p d [ ( k n ) T i T s ] + n ˜ k
s n , k = j i x i w n p d [ ( k n ) T i T s ] j x [ k ] Re { w n p d ( n T ) }
y k = x [ k ] + n Δ n , k s n , k + n ˜ k
C = σ 2 [ c 11 + σ ˜ 2 / σ 2 c 12 c 21 c 22 + σ ˜ 2 / σ 2 ]
c 11 = i = N 1 ( n = N i Re { s n , k } ) 2 + i = 1 N ( n = i N Re { s n , k } ) 2 ,
c 22 = i = N 1 ( n = N i Im { s n , k } ) 2 + i = 1 N ( n = i N Im { s n , k } ) 2 ,
c 12 = c 21 = i = N 1 ( n = N i Re { s n , k } n = N i Im { s n , k } ) + i = 1 N ( n = i N Re { s n , k } n = i N Im { s n , k } )

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