Abstract

In coherent optical systems laser phase noise can interact with digital equalization to cause equalization-enhanced impairments, which are a major obstacle for applying higher order modulation formats in coherent optical systems with digital chromatic dispersion compensation. In this paper a code-aided expectation maximization method to track phase noise in such systems is presented. A common measure of laser phase noise is the linewidth. It is shown that with $\sim 11\%$ redundancy, the laser linewidth tolerance for 975 km transmission distance can be increased by $50\%$, or the system reach for a laser linewidth of 5 MHz can be doubled. A phase-noise-robust 16-point 4–4–4–4 ring constellation was found to have better performance compared to 16QAM and a 2–6–8 ring constellations. Performance can be further improved with a lower code rate and fewer pilot symbols. It is also shown that algorithmic complexity can be reduced without significant reduction in the performance by reducing iterations and using low complexity codes.

© 2013 IEEE

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  2. W. Shieh, X. Yi, Y. Ma, Q. Yang, "Coherent optical OFDM: has its time come? [invited]," J. Opt. Netw. 7, 234-255 (2008).
  3. S. J. Savory, G. Gavioli, R. I. Killey, P. Bayvel, "Electronic compensation of chromatic dispersion using a digital coherent receiver," Opt. Exp. 15, 2120-2126 (2007 ).
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  9. C. Xie, "WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation," Opt. Exp. 17, 4815-4823 (2009 ).
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  25. T. Moon, "The expectation-maximization algorithm," IEEE Signal Process. Mag. 13, 47 -60 (1996).
  26. O. V. Sinkin, R. Holzlöhner, J. Zweck, C. R. Menyuk, "Optimization of the split-step Fourier method in modeling optical-fiber communications systems," J. Lightw. Technol. 21, 61-68 (2003).
  27. L. Zhang, private communication, Oct. 2012..
  28. S. Fujisawa, D. Ogasahara, E. de Gabory, T. Ito, K. Fukuchi, "Mitigation of intra-channel nonlinear distortions based on PAPR reduction with CD pre-compensation in real-time 50 Gbps PM-QPSK transmission," Proc. Opto-Electron. Commun. Conf. (2012) pp. 439-440 .

2011 (2)

T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, Y. Zhang, "Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization," Opt. Exp. 19, 7756-7768 (2011).

K.-P. Ho, A. P. T. Lau, W. Shieh, "Equalization-enhanced phase noise induced timing jitter," Opt. Lett. 36, 585-587 (2011).

2010 (2)

E. Ip, J. Kahn, "Fiber impairment compensation using coherent detection and digital signal processing ," J. Lightw. Technol. 28, 502-519 (2010).

F. Chang, K. Onohara, T. Mizuochi, "Forward error correction for 100 G transport networks," IEEE Commun. Mag. 48, S48-S55 (2010).

2008 (3)

S. J. Savory, "Digital filters for coherent optical receivers ," Opt. Exp. 16, 804-817 (2008).

E. Ip, A. P. T. Lau, D. J. F. Barros, J. M. Kahn, "Coherent detection in optical fiber systems ," Opt. Exp. 16, 753-791 (2008).

W. Shieh, X. Yi, Y. Ma, Q. Yang, "Coherent optical OFDM: has its time come? [invited]," J. Opt. Netw. 7, 234-255 (2008).

2006 (1)

W. J. Higley, P. Roux, W. A. Kuperman, "Relationship between time reversal and linear equalization in digital communications," J. Acoust. Soc. Am. 120, 35-37 (2006).

2005 (1)

N. Noels, V. Lottici, A. Dejonghe, H. Steendam, M. Moeneclaey, M. Luise, L. Vandendorpe, "A theoretical framework for soft-information-based synchronization in iterative (Turbo) receivers," EURASIP J. Wireless Commun. Netw. 2005, 117-129 (2005).

2003 (1)

O. V. Sinkin, R. Holzlöhner, J. Zweck, C. R. Menyuk, "Optimization of the split-step Fourier method in modeling optical-fiber communications systems," J. Lightw. Technol. 21, 61-68 (2003).

2002 (1)

K. Azadet, E. Haratsch, H. Kim, F. Saibi, J. Saunders, M. Shaffer, L. Song, M.-L. Yu, "Equalization and FEC techniques for optical transceivers," IEEE J. Solid-State Circuits 37, 317-327 (2002).

1996 (1)

T. Moon, "The expectation-maximization algorithm," IEEE Signal Process. Mag. 13, 47 -60 (1996).

J. Opt. Netw. (1)

W. Shieh, X. Yi, Y. Ma, Q. Yang, "Coherent optical OFDM: has its time come? [invited]," J. Opt. Netw. 7, 234-255 (2008).

EURASIP J. Adv. Signal Process. (1)

H. Wymeersch, M. Moeneclaey, "Iterative code-aided ML phase estimation and phase ambiguity resolution ," EURASIP J. Adv. Signal Process. 2005, 981-988 (2005 ).

EURASIP J. Wireless Commun. Netw. (1)

N. Noels, V. Lottici, A. Dejonghe, H. Steendam, M. Moeneclaey, M. Luise, L. Vandendorpe, "A theoretical framework for soft-information-based synchronization in iterative (Turbo) receivers," EURASIP J. Wireless Commun. Netw. 2005, 117-129 (2005).

IEEE Commun. Mag. (1)

F. Chang, K. Onohara, T. Mizuochi, "Forward error correction for 100 G transport networks," IEEE Commun. Mag. 48, S48-S55 (2010).

IEEE J. Solid-State Circuits (1)

K. Azadet, E. Haratsch, H. Kim, F. Saibi, J. Saunders, M. Shaffer, L. Song, M.-L. Yu, "Equalization and FEC techniques for optical transceivers," IEEE J. Solid-State Circuits 37, 317-327 (2002).

IEEE Signal Process. Mag. (1)

T. Moon, "The expectation-maximization algorithm," IEEE Signal Process. Mag. 13, 47 -60 (1996).

J. Acoust. Soc. Am. (1)

W. J. Higley, P. Roux, W. A. Kuperman, "Relationship between time reversal and linear equalization in digital communications," J. Acoust. Soc. Am. 120, 35-37 (2006).

J. Lightw. Technol. (3)

E. Ip, J. Kahn, "Fiber impairment compensation using coherent detection and digital signal processing ," J. Lightw. Technol. 28, 502-519 (2010).

O. V. Sinkin, R. Holzlöhner, J. Zweck, C. R. Menyuk, "Optimization of the split-step Fourier method in modeling optical-fiber communications systems," J. Lightw. Technol. 21, 61-68 (2003).

S. Zhang, P.-Y. Kam, C. Yu, J. Chen, "Decision-aided carrier phase estimation for coherent optical communications," J. Lightw. Technol. 28, 1597-1607 (2010 ).

Opt. Exp. (1)

T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, Y. Zhang, "Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization," Opt. Exp. 19, 7756-7768 (2011).

Opt. Exp. (5)

C. Xie, "WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation," Opt. Exp. 17, 4815-4823 (2009 ).

S. J. Savory, "Digital filters for coherent optical receivers ," Opt. Exp. 16, 804-817 (2008).

S. J. Savory, G. Gavioli, R. I. Killey, P. Bayvel, "Electronic compensation of chromatic dispersion using a digital coherent receiver," Opt. Exp. 15, 2120-2126 (2007 ).

X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, G. Li, "Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing," Opt. Exp. 16, 880-888 (2008 ).

E. Ip, A. P. T. Lau, D. J. F. Barros, J. M. Kahn, "Coherent detection in optical fiber systems ," Opt. Exp. 16, 753-791 (2008).

Opt. Lett. (1)

Other (11)

C. M. Bishop, Pattern Recognition and Machine Learning (Information Science and Statistics).   Secaucus, NJ, USA: Springer-Verlag Inc., 2006, pp. 144–146..

W. Shieh and K.-P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Exp., vol. 16, no. 20, pp. 15 718–15 727, Sep. 2008..

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. Exp., vol. 18, no. 16, pp. 17 239–17 251, Aug. 2010. .

G. P. Agrawal, Fiber-Optic Communication Systems (Wiley , 2002) pp. 116-118.

I. Fatadin and S. J. Savory, “Impact of phase to amplitude noise conversion in coherent optical systems with digital dispersion compensation,” Opt. Exp., vol. 18, no. 15, pp. 16 273–16 278, Jul. 2010..

S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, J. Rasmussen, "Interplay between local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system," Proc. Eur. Conf. Opt. Commun. (2010) pp. 1-3.

N. Noels, C. Herzet, A. Dejonghe, V. Lottici, H. Steendam, M. Moeneclaey, M. Luise, L. Vandendorpe, "Turbo synchronization: an EM algorithm interpretation," Proc. IEEE Int. Conf. Commun. (2003) pp. 2933-2937.

D. J. MacKay and E. A. Ratzer. (2003, Jan.) “Gallager codes for high rate applications,” [Online]. Available: http://www.cs.toronto.edu/ mackay/highrate.pdf.

J. Dauwels, S. Korl, and H.-A. Loeliger, “Expectation maximization for joint decoding and phase estimation,” in Proc. 8th Int. Symp. Commun. Theory Appl., 2005, pp. 87–90..

L. Zhang, private communication, Oct. 2012..

S. Fujisawa, D. Ogasahara, E. de Gabory, T. Ito, K. Fukuchi, "Mitigation of intra-channel nonlinear distortions based on PAPR reduction with CD pre-compensation in real-time 50 Gbps PM-QPSK transmission," Proc. Opto-Electron. Commun. Conf. (2012) pp. 439-440 .

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