Abstract

We propose – as a modification of the optical (RF) pilot scheme - a balanced phase modulation between two polarizations of the optical signal in order to generate correlated equalization enhanced phase noise (EEPN) contributions in the two polarizations. The method is applicable for n-level PSK system. The EEPN can be compensated, the carrier phase extracted and the nPSK signal regenerated by complex conjugation and multiplication in the receiver. The method is tested by system simulations in a single channel QPSK system at 56 Gb/s system rate. It is found that the conjugation and multiplication scheme in the Rx can mitigate the EEPN to within ½ orders of magnitude. Results are compared to using the Viterbi-Viterbi algorithm to mitigate the EEPN. The latter method improves the sensitivity more than two orders of magnitude. Important novel insight into the statistical properties of EEPN is identified and discussed in the paper.

© 2013 OSA

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  25. www.vpiphotonics.com
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    [CrossRef]
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    [CrossRef] [PubMed]
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  29. Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Express17(3), 1435–1441 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
  31. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Comparison of carrier phase estimation methods in coherent optical transmission systems influenced by equalization enhanced phase noise,” Opt. Commun.293, 54–60 (2013).
    [CrossRef]
  32. A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory29(4), 543–551 (1983).
    [CrossRef]
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    [CrossRef]

2013 (1)

T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Comparison of carrier phase estimation methods in coherent optical transmission systems influenced by equalization enhanced phase noise,” Opt. Commun.293, 54–60 (2013).
[CrossRef]

2012 (2)

G. Jacobsen, M. S. Lidón, T. Xu, S. Popov, A. T. Friberg, and Y. Zhang, “Influence of pre- and post-compensation of CD on EEPN in coherent multilevel systems,” J. Opt. Commun.32, 257–261 (2012).

R. Farhoudi, A. Ghazisaeidi, and L. A. Rusch, “Performance of carrier phase recovery for electronically dispersion compensated coherent systems,” Opt. Express20(24), 26568–26582 (2012).
[CrossRef] [PubMed]

2011 (4)

2010 (4)

2009 (2)

2008 (3)

2007 (1)

2004 (1)

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett.16(2), 674–676 (2004).
[CrossRef]

1985 (1)

P. S. Henry, “Lightwave primer,” IEEE J. Quantum Electron.21(12), 1862–1879 (1985).
[CrossRef]

1983 (1)

A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory29(4), 543–551 (1983).
[CrossRef]

Bayvel, P.

Colavolpe, G.

Farhoudi, R.

Fatadin, I.

Foggi, T.

Forestieri, E.

Friberg, A. T.

Gavioli, G.

Ghazisaeidi, A.

Henry, P. S.

P. S. Henry, “Lightwave primer,” IEEE J. Quantum Electron.21(12), 1862–1879 (1985).
[CrossRef]

Ho, K. P.

Ho, K.-P.

Igarashi, K.

Jacobsen, G.

T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Comparison of carrier phase estimation methods in coherent optical transmission systems influenced by equalization enhanced phase noise,” Opt. Commun.293, 54–60 (2013).
[CrossRef]

G. Jacobsen, M. S. Lidón, T. Xu, S. Popov, A. T. Friberg, and Y. Zhang, “Influence of pre- and post-compensation of CD on EEPN in coherent multilevel systems,” J. Opt. Commun.32, 257–261 (2012).

T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization,” Opt. Express19(8), 7756–7768 (2011).
[CrossRef] [PubMed]

G. Jacobsen, T. Xu, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Receiver implemented RF pilot tone phase noise mitigation in coherent optical nPSK and nQAM systems,” Opt. Express19(15), 14487–14494 (2011).
[CrossRef] [PubMed]

T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express18(15), 16243–16257 (2010).
[CrossRef] [PubMed]

G. Jacobsen, “Laser phase noise induced error rate floors in differential n-level phase-shift-keying coherent receivers,” Electron. Lett.46(10), 698–700 (2010).
[CrossRef]

Kamio, Y.

M. Nakamura, Y. Kamio, and T. Miyazaki, “Linewidth-tolerant 10-Gbit/s 16-QAM transmission using a pilot-carrier based phase-noise cancelling technique,” Opt. Express16(14), 10611–10616 (2008).
[CrossRef] [PubMed]

M. Nakamura, Y. Kamio, and T. Miyazaki, “Pilot-carrier based linewidth-tolerant 8PSK self-homodyne using only one modulator,” in Proceeding of IEEE European Conference on Optical Communication (Berlin, Germany, 2007), .
[CrossRef]

Katoh, K.

Kikuchi, K.

Killey, R. I.

Lau, A. P. T.

Li, J.

Lidón, M. S.

G. Jacobsen, M. S. Lidón, T. Xu, S. Popov, A. T. Friberg, and Y. Zhang, “Influence of pre- and post-compensation of CD on EEPN in coherent multilevel systems,” J. Opt. Commun.32, 257–261 (2012).

Miyazaki, T.

M. Nakamura, Y. Kamio, and T. Miyazaki, “Linewidth-tolerant 10-Gbit/s 16-QAM transmission using a pilot-carrier based phase-noise cancelling technique,” Opt. Express16(14), 10611–10616 (2008).
[CrossRef] [PubMed]

M. Nakamura, Y. Kamio, and T. Miyazaki, “Pilot-carrier based linewidth-tolerant 8PSK self-homodyne using only one modulator,” in Proceeding of IEEE European Conference on Optical Communication (Berlin, Germany, 2007), .
[CrossRef]

Mori, Y.

Nakamura, M.

M. Nakamura, Y. Kamio, and T. Miyazaki, “Linewidth-tolerant 10-Gbit/s 16-QAM transmission using a pilot-carrier based phase-noise cancelling technique,” Opt. Express16(14), 10611–10616 (2008).
[CrossRef] [PubMed]

M. Nakamura, Y. Kamio, and T. Miyazaki, “Pilot-carrier based linewidth-tolerant 8PSK self-homodyne using only one modulator,” in Proceeding of IEEE European Conference on Optical Communication (Berlin, Germany, 2007), .
[CrossRef]

Popov, S.

Rusch, L. A.

Savory, S. J.

Secondini, M.

Shen, T. S. R.

Shieh, W.

Taylor, M. G.

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett.16(2), 674–676 (2004).
[CrossRef]

Vanin, E.

Viterbi, A. J.

A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory29(4), 543–551 (1983).
[CrossRef]

Viterbi, A. M.

A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory29(4), 543–551 (1983).
[CrossRef]

Wang, K.

Xie, C.

Xu, T.

Zhang, C.

Zhang, Y.

Electron. Lett. (1)

G. Jacobsen, “Laser phase noise induced error rate floors in differential n-level phase-shift-keying coherent receivers,” Electron. Lett.46(10), 698–700 (2010).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. S. Henry, “Lightwave primer,” IEEE J. Quantum Electron.21(12), 1862–1879 (1985).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett.16(2), 674–676 (2004).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory29(4), 543–551 (1983).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Commun. (1)

G. Jacobsen, M. S. Lidón, T. Xu, S. Popov, A. T. Friberg, and Y. Zhang, “Influence of pre- and post-compensation of CD on EEPN in coherent multilevel systems,” J. Opt. Commun.32, 257–261 (2012).

Opt. Commun. (1)

T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Comparison of carrier phase estimation methods in coherent optical transmission systems influenced by equalization enhanced phase noise,” Opt. Commun.293, 54–60 (2013).
[CrossRef]

Opt. Express (12)

R. Farhoudi, A. Ghazisaeidi, and L. A. Rusch, “Performance of carrier phase recovery for electronically dispersion compensated coherent systems,” Opt. Express20(24), 26568–26582 (2012).
[CrossRef] [PubMed]

T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization,” Opt. Express19(8), 7756–7768 (2011).
[CrossRef] [PubMed]

G. Jacobsen, T. Xu, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Receiver implemented RF pilot tone phase noise mitigation in coherent optical nPSK and nQAM systems,” Opt. Express19(15), 14487–14494 (2011).
[CrossRef] [PubMed]

S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express15(5), 2120–2126 (2007).
[CrossRef] [PubMed]

S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express16(2), 804–817 (2008).
[CrossRef] [PubMed]

M. Nakamura, Y. Kamio, and T. Miyazaki, “Linewidth-tolerant 10-Gbit/s 16-QAM transmission using a pilot-carrier based phase-noise cancelling technique,” Opt. Express16(14), 10611–10616 (2008).
[CrossRef] [PubMed]

W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express16(20), 15718–15727 (2008).
[CrossRef] [PubMed]

Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Express17(3), 1435–1441 (2009).
[CrossRef] [PubMed]

C. Xie, “WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation,” Opt. Express17(6), 4815–4823 (2009).
[CrossRef] [PubMed]

T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express18(15), 16243–16257 (2010).
[CrossRef] [PubMed]

I. Fatadin and S. J. Savory, “Impact of phase to amplitude noise conversion in coherent optical systems with digital dispersion compensation,” Opt. Express18(15), 16273–16278 (2010).
[CrossRef] [PubMed]

A. P. T. Lau, T. S. R. Shen, W. Shieh, and K.-P. Ho, “Equalization-enhanced phase noise for 100 Gb/s transmission and beyond with coherent detection,” Opt. Express18(16), 17239–17251 (2010).
[CrossRef] [PubMed]

Opt. Lett. (1)

Other (13)

S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka, “20-Gb/s OFDM transmission over 4,160-km SSFM enabled by RF-pilot tone for phase noise compensation”, in Proceeding of Conference on Optical Fiber Communications, (Anaheim, California, 2007), paper PDP 15.

www.vpiphotonics.com

M. Nakamura, Y. Kamio, and T. Miyazaki, “Pilot-carrier based linewidth-tolerant 8PSK self-homodyne using only one modulator,” in Proceeding of IEEE European Conference on Optical Communication (Berlin, Germany, 2007), .
[CrossRef]

G. P. Agrawal, Fiber-optic communication systems 3rd Edition (John Wiley & Sons, Inc., 2002), Chap. 2.

J. G. Proakis, Digital Communications 5th Edition (McGraw-Hill Companies, Inc., 2008), Chap. 10.

A. Färbert, S. Langenbach, N. Stojanovic, C. Dorschky, T. Kupfer, C. Schulien, J. P. Elbers, H. Wernz, H. Griesser, and C. Glingener, “Performance of a 10.7 Gb/s Receiver with digital equaliser using maximum likelihood sequence estimation,” in Proceeding of IEEE European Conference on Optical Communication (Stockholm, Sweden, 2004), paper Th4.1.5.

S. J. Savory, “Compensation of fibre impairments in digital coherent systems,” in Proceeding of IEEE European Conference on Optical Communication (Brussels, Belgium, 2008), paper Mo.3.D.1.

K. Ishihara, T. Kobayashi, R. Kudo, Y. Takatori, A. Sano, E. Yamada, H. Masuda, and Y. Miyamoto, “Coherent optical transmission with frequency-domain equalization,” in Proceeding of IEEE European Conference on Optical Communication (Brussels, Belgium, 2008), paper We.2.E.3.

M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, A. Napoli, and B. Lankl, “Adaptive chromatic dispersion equalization for non-dispersion managed coherent systems,” in Proceeding of IEEE Conference on Optical Fiber Communication (San Diego, California, 2009), paper OMT1.
[CrossRef]

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, E. Yamada, H. Masuda, Y. Miyamoto, and M. Mizoguchi, “Two-stage overlap frequency domain equalization for long-haul optical systems,” in Proceeding of IEEE Conference on Optical Fiber Communication (San Diego, California, 2009), paper OMT3.
[CrossRef]

A. P. T. Lau, W. Shieh, and K. P. Ho, “Equalization-enhanced phase noise for 100Gb/s transmission with coherent detection,” in Proceedings of OptoElectronics and Communications Conference (Hong Kong, 2009), paper FQ3.

C. Xie, “Local oscillator phase noise induced penalties in optical coherent detection systems using electronic chromatic dispersion compensation,” in Proceeding of IEEE Conference on Optical Fiber Communication (San Diego, California, 2009), paper OMT4.
[CrossRef]

S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. C. Rasmussen, “Interplay between Local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in Proceeding of IEEE European Conference on Optical Communication (Torino, Italy, 2010), paper Mo.1.C.2.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Block diagram for single channel nPSK system. Figure insert a) is the transmitter Tx) unit for the dual polarization distributed nPSK modulation case. Figure insert b) is for nPSK modulation in one polarization and using the orthogonal polarization signal for an optical (RF) pilot tone. In both cases carrier phase estimation is done in the conjugate multiplication in the Rx. The Viterbi-Viterbi algorithm may be used to filter the phase noise. N(t) shows the added optical noise which is used to measure the Bit-Error-Rate (BER) as a function of optical signal-to-noise ratio (OSNR). Figure abbreviations: Tx – transmitter; PBS – polarizing beam splitter; PBC – polarizing beam combiner; PRBS – pseudo random bit sequence ; LO – local oscillator; ADC – analogue to digital conversion; CD – chromatic dispersion.

Fig. 2
Fig. 2

BER for single channel QPSK coherent system of Fig. 1 for transmitter and Local Oscillator linewidths equal to 5 MHz. Results are for transmission distance of 2000 km. Three curves with markers are simulation results for different phase modulation balance as indicated by the α-value. The PRBS length is 216-1. Analytically specified BER-floors (Eq. (7)) are shown by dashed lines with specified ρ-values. Figure abbreviations: OSNR - optical signal-to-noise ratio.

Fig. 3
Fig. 3

Constellation diagrams for single channel QPSK coherent system of Fig. 1 for transmitter and Local Oscillator linewidths equal to 5 MHz. Results are for transmission distance of 2000 km and OSNR of 35 dB. Subfigures (a) and (d) are for α = 1 (classical QPSK system) with optical (RF) pilot tone carrier phase extraction (CPE) (a) and in addition using the Viterbi-Viterbi algorithm (d). Subfigures (b) and (e) are for distributed modulation QPSK (α = 0.5) with optical (RF) pilot tone CPE (b) and using in addition the Viterbi-Viterbi algorithm (e). Subfigures (c) and (f) are for classical QPSK with no optical (RF) pilot tone (using NLMS CPE) with Wiener phase noise and back-to-back transmission (Tx and LO linwidths of 103 MHz) (c) and using in addition the Viterbi-Viterbi algorithm (f).

Fig. 4
Fig. 4

BER for single channel QPSK coherent systems of Fig. 1. Curves are referred to the figure insert. Curves with α = 0.5 are for the distributed PSK modulation in two polarizations. Curves with α = 1 are for the full PSK modulation in one polarization and including an optical (RF) pilot tone in the orthogonal polarization state. Transmission distances are either back-to-back or 2000 km as indicated. Tx and LO laser have equal linwidths as specified in figure inserts. In the reference case with linewidths of 103 MHz and back-to-back transmission no optical (RF) pilot tone is included in the system and the carrier phase estimation is performed using a single tap NLMS filter (also indicated in the insert). Systems are compared using the Viterbi-Viterbi (VV) algorithm or not using it as indicated. The PRBS length for all cases is 216-1. Figure abbreviations: OSNR - optical signal-to-noise ratio; VV – Viterbi-Viterbi; PN – phase noise; NLMS – normalized least mean square.

Tables (1)

Tables Icon

Table 1 Complexity of carrier phase estimation (CPE) methods

Equations (7)

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

E s (t)=Aexp( j( φ s + φ Tx (t)+ φ LO (t)+ φ EEPN (t)+m(t) ) )
E RF (t)=Bexp( ( j( φ RF + φ Tx (t)+ φ LO (t)) ) )
E s (t) E RF * ( t )=BAexp(j( φ S φ RF + φ EEPN (t)+m(t)) )
E 1 (t) E 2 * ( t )=BAexp(j( φ 1 φ 2 +( 1ρ ) φ EEPN (t)+m(t)) )
σ EEPN 2 = π λ 2 2c DLΔ f LO T S 2πΔ f EE T s
Δ f Eff σ Tx 2 + σ LO 2 + σ EEPN 2 2π T S σ Eff 2 2π T s =Δ f Tx +Δ f LO +Δ f EE
BE R floor NLMS 1 log 2 n erfc( π n 2 σ Eff )

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