Abstract

Spectrally-efficient optical communications systems employ polarization division multiplexing (PDM) as a practical solution, in order to double the capacity of a fiber link. Polarization demultiplexing can be performed electronically, using polarization-diversity coherent optical receivers. The primary goal of this paper is the optimal design, using the maximum-likelihood criterion, of polarization-diversity coherent optical receivers for polarization-multiplexed optical signals, in the absence of polarization mode dispersion (PMD). It is shown that simultaneous joint estimation of the symbols, over the two received states of polarization, yields optimal performance, in the absence of phase noise and intermediate frequency offset. In contrast, the commonly used zero-forcing polarization demultiplexer, followed by individual demodulation of the polarization-multiplexed tributaries, exhibits inferior performance, and becomes optimal only if the channel transfer matrix is unitary, e.g., in the absence of polarization dependent loss (PDL), and if the noise components at the polarization diversity branches have equal variances. In this special case, the zero-forcing polarization demultiplexer can be implemented by a 2$\,\times\,$2 lattice adaptive filter, which is controlled by only two independent real parameters. These parameters can be computed recursively using the constant modulus algorithm (CMA). We evaluate, by simulation, the performance of the aforementioned zero-forcing polarization demultiplexer in coherent optical communication systems using PDM quadrature phase shift keying (QPSK) signals. We show that it is, by far, superior, in terms of convergence accuracy and speed, compared to conventional CMA-based polarization demultiplexers. Finally, we experimentally test the robustness of the proposed constrained CMA polarization demultiplexer to realistic imperfections of polarization-diversity coherent optical receivers. The PMD and PDL tolerance of the proposed demultiplexer can be used as a benchmark in order to compare the performance of more sophisticated adaptive electronic PMD/PDL equalizers.

© 2010 IEEE

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  38. E. Karami, "Tracking performance of least squares MIMO channel estimation algorithm," IEEE Trans. Commun. 55, 2201-2209 (2007).
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  42. M. Valkama, M. Renfors, V. Koivunen, "Advanced methods for I/Q imbalance compensation in communication receivers," IEEE Trans. Signal Proc. 49, 2335-2344 (1998).
  43. D. Hoffmann, H. Heidrich, G. Wenke, R. Langenhorst, N. K. Cheung, "Integrated opticseight-port 90$^{\circ}$ hybrid on LiNbO$_{3}$," J. Lightw. Technol. 7, 794-798 (1989).
  44. N. Gisin, "Statistics of polarization dependent losses," Opt. Commun. 114, 399-405 (1995).
  45. I. Roudas, N. Antoniades, "Performance outages in CWDM optical networks due to the polarization-dependent gain of semiconductor optical amplifiers," IEEE Photon. Technol. Lett. 18, 48-50 (2007).

2009 (1)

X. Zhou, J. Yu, D. Qian, T. Wang, G. Zhang, P. D. Magill, "High-spectral-efficiency 114-Gb/s transmission using PolMux-RZ-8PSK modulation format and single-ended digital coherent detection technique," J. Lightw. Technol. 27, 146-152 (2009).

2008 (7)

H. Sun, K.-T. Wu, K. Roberts, "Real-time measurements of a 40 Gb/s coherent system," Opt. Exp. 16, 873-879 (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).

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

C. Laperle, B. Villeneuve, Z. Zhan, D. McGhan, H. Sun, M. O'Sullivan, "WDM performance and PMD tolerance of a coherent 40 Gbit/s dual-polarization QPSK transceiver," J. Lightw. Technol. 26, 168-175 (2008).

C. R. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E. D. Schmidt, T. Wuth, J. Geyer, E. De Man, G. D. Khoe, H. de Waardt, "Coherent equalization and POLMUX-RZ-DQPSK for robust 100-GE transmission," J. Lightw. Technol. 26, 64-72 (2008).

J. Renaudier, G. Charlet, M. Salsi, O. B. Pardo, H. Mardoyan, P. Tran, S. Bigo, "Linear fiber impairments mitigation of 40-Gbit/s polarization-multiplexed QPSK by digital processing in a coherent receiver," J. Lightw. Technol. 26, 36-42 (2008).

I. Fatadin, S. Savory, D. Ives, "Compensation of quadrature imbalance in an optical QPSK coherent receiver," IEEE Photon. Technol. Lett. 20, 1733-1735 (2008).

2007 (3)

E. Ip, J. M. Kahn, "Digital equalization of chromatic dispersion and polarization mode dispersion," J. Lightw. Technol. 25, 2033-2043 (2007).

E. Karami, "Tracking performance of least squares MIMO channel estimation algorithm," IEEE Trans. Commun. 55, 2201-2209 (2007).

I. Roudas, N. Antoniades, "Performance outages in CWDM optical networks due to the polarization-dependent gain of semiconductor optical amplifiers," IEEE Photon. Technol. Lett. 18, 48-50 (2007).

2006 (1)

M. T. Core, "Cross polarization interference cancellation for fiber optic systems," J. Lightw. Technol. 24, 305-312 (2006).

2005 (3)

R. Noé, "Phase noise tolerant synchronous QPSK/BPSK baseband-type intradyne receiver concept with feedforward carrier recovery," J. Lightw. Technol. 23, 802-808 (2005).

R. Noé, "PLL-free synchronous QPSK polarization multiplex/diversity receiver concept with digital I & Q baseband processing," IEEE Photon. Technol. Lett. 17, 887-889 (2005).

Y. Han, G. Li, "Coherent optical communication using polarization multiple-input-multiple-output," Opt. Exp. 13, 7527-7534 (2005).

2000 (1)

J. P. Gordon, H. Kogelnik, "PMD fundamentals: Polarization mode dispersion in optical fibers," PNAS 97, 4541-4550 (2000).

1998 (3)

M. Valkama, M. Renfors, V. Koivunen, "Advanced methods for I/Q imbalance compensation in communication receivers," IEEE Trans. Signal Proc. 49, 2335-2344 (1998).

C. R. Johnson Jr., P. Schniter, T. J. Edres, J. D. Behm, D. R. Brown, R. A. Casas, "Blind equalization using the constant modulus criterion: A review," Proc. IEEE 86, 1927-1950 (1998).

M. Morelli, U. Mengali, "Feedforward frequency estimation for PSK: A tutorial review," Eur. Trans. Telecommun. 9, 103-116 (1998).

1995 (1)

N. Gisin, "Statistics of polarization dependent losses," Opt. Commun. 114, 399-405 (1995).

1989 (1)

D. Hoffmann, H. Heidrich, G. Wenke, R. Langenhorst, N. K. Cheung, "Integrated opticseight-port 90$^{\circ}$ hybrid on LiNbO$_{3}$," J. Lightw. Technol. 7, 794-798 (1989).

1987 (1)

1985 (1)

J. R. Treichler, M. G. Larimore, "New processing techniques based on the constant modulus adaptive algorithm," IEEE Trans. Acoust., Speech, Signal Process. ASSP-33, 420-431 (1985).

1983 (1)

A. Viterbi, A. Viterbi, "Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission," IEEE Trans. Inf. Theory IT-29, 543-551 (1983).

1980 (1)

D. Godard, "Self-recovering equalization and carrier tracking in two dimensional data communication systems," IEEE Trans. Comm. 28, 1867-1875 (1980).

Appl. Opt. (1)

Eur. Trans. Telecommun. (1)

M. Morelli, U. Mengali, "Feedforward frequency estimation for PSK: A tutorial review," Eur. Trans. Telecommun. 9, 103-116 (1998).

IEEE Photon. Technol. Lett. (3)

I. Fatadin, S. Savory, D. Ives, "Compensation of quadrature imbalance in an optical QPSK coherent receiver," IEEE Photon. Technol. Lett. 20, 1733-1735 (2008).

R. Noé, "PLL-free synchronous QPSK polarization multiplex/diversity receiver concept with digital I & Q baseband processing," IEEE Photon. Technol. Lett. 17, 887-889 (2005).

I. Roudas, N. Antoniades, "Performance outages in CWDM optical networks due to the polarization-dependent gain of semiconductor optical amplifiers," IEEE Photon. Technol. Lett. 18, 48-50 (2007).

IEEE Trans. Acoust., Speech, Signal Process. (1)

J. R. Treichler, M. G. Larimore, "New processing techniques based on the constant modulus adaptive algorithm," IEEE Trans. Acoust., Speech, Signal Process. ASSP-33, 420-431 (1985).

IEEE Trans. Comm. (1)

D. Godard, "Self-recovering equalization and carrier tracking in two dimensional data communication systems," IEEE Trans. Comm. 28, 1867-1875 (1980).

IEEE Trans. Commun. (1)

E. Karami, "Tracking performance of least squares MIMO channel estimation algorithm," IEEE Trans. Commun. 55, 2201-2209 (2007).

IEEE Trans. Inf. Theory (1)

A. Viterbi, A. Viterbi, "Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission," IEEE Trans. Inf. Theory IT-29, 543-551 (1983).

IEEE Trans. Signal Proc. (1)

M. Valkama, M. Renfors, V. Koivunen, "Advanced methods for I/Q imbalance compensation in communication receivers," IEEE Trans. Signal Proc. 49, 2335-2344 (1998).

J. Lightw. Technol. (8)

D. Hoffmann, H. Heidrich, G. Wenke, R. Langenhorst, N. K. Cheung, "Integrated opticseight-port 90$^{\circ}$ hybrid on LiNbO$_{3}$," J. Lightw. Technol. 7, 794-798 (1989).

X. Zhou, J. Yu, D. Qian, T. Wang, G. Zhang, P. D. Magill, "High-spectral-efficiency 114-Gb/s transmission using PolMux-RZ-8PSK modulation format and single-ended digital coherent detection technique," J. Lightw. Technol. 27, 146-152 (2009).

J. Renaudier, G. Charlet, M. Salsi, O. B. Pardo, H. Mardoyan, P. Tran, S. Bigo, "Linear fiber impairments mitigation of 40-Gbit/s polarization-multiplexed QPSK by digital processing in a coherent receiver," J. Lightw. Technol. 26, 36-42 (2008).

R. Noé, "Phase noise tolerant synchronous QPSK/BPSK baseband-type intradyne receiver concept with feedforward carrier recovery," J. Lightw. Technol. 23, 802-808 (2005).

C. Laperle, B. Villeneuve, Z. Zhan, D. McGhan, H. Sun, M. O'Sullivan, "WDM performance and PMD tolerance of a coherent 40 Gbit/s dual-polarization QPSK transceiver," J. Lightw. Technol. 26, 168-175 (2008).

C. R. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E. D. Schmidt, T. Wuth, J. Geyer, E. De Man, G. D. Khoe, H. de Waardt, "Coherent equalization and POLMUX-RZ-DQPSK for robust 100-GE transmission," J. Lightw. Technol. 26, 64-72 (2008).

E. Ip, J. M. Kahn, "Digital equalization of chromatic dispersion and polarization mode dispersion," J. Lightw. Technol. 25, 2033-2043 (2007).

M. T. Core, "Cross polarization interference cancellation for fiber optic systems," J. Lightw. Technol. 24, 305-312 (2006).

Opt. Commun. (1)

N. Gisin, "Statistics of polarization dependent losses," Opt. Commun. 114, 399-405 (1995).

Opt. Exp. (4)

H. Sun, K.-T. Wu, K. Roberts, "Real-time measurements of a 40 Gb/s coherent system," Opt. Exp. 16, 873-879 (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).

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

Y. Han, G. Li, "Coherent optical communication using polarization multiple-input-multiple-output," Opt. Exp. 13, 7527-7534 (2005).

PNAS (1)

J. P. Gordon, H. Kogelnik, "PMD fundamentals: Polarization mode dispersion in optical fibers," PNAS 97, 4541-4550 (2000).

Proc. IEEE (1)

C. R. Johnson Jr., P. Schniter, T. J. Edres, J. D. Behm, D. R. Brown, R. A. Casas, "Blind equalization using the constant modulus criterion: A review," Proc. IEEE 86, 1927-1950 (1998).

Other (20)

S. Haykin, Adaptive Filter Theory (Prentice-Hall, 1996).

C. S. Petrou, A. Vgenis, A. Kiourti, I. Roudas, J. Hurley, M. Sauer, J. Downie, Y. Mauro, S. Raghavan, "Impact of transmitter and receiver imperfections on the performance of coherent optical QPSK communication systems," Proc. LEOS 2008 (2008).

H. Meyr, M. Moeneclaey, S. Fechtel, Digital Communication Receivers: Channel Estimation and Signal Processing (Wiley, 1998).

S. Huard, Polarization of Light (Wiley, 1997).

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice Hall, 1993).

X. Zhou, J. Yu, D. Qian, T. Wang, G. Zhang, P. Magill, "8$\,\times\,$114 Gb/s, 25-GHz-spaced, polmux-RZ-8PSK transmission over 640 km of SSMF employing digital coherent detection and EDFA-only amplification," Proc. OFC 2008 (2008).

P. J. Winzer, A. J. Gnauck, "112-Gb/s polarization-multiplexed 16-QAM on a 25-GHz WDM grid," Proc. 34th Eur. Conf. Optical Communication (ECOC) (2008).

J. Proakis, Digital Communications (McGraw-Hill, 2000) pp. 177-178.

J. R. Barry, E. A. Lee, D. G. Messerschmitt, Digital Communication (Kluwer, 2003).

D. Tse, P. Viswanath, Fundamentals of Wireless Communication (Cambridge Univ. Press, 2005).

H. Sun, K.-T. Wu, Method for Quadrature Phase Angle Correction in a Coherent Receiver of a Dual-Polarization Optical Transport System U.S. Patent 6 917 031 (2005).

I. Roudas, M. Sauer, J. Hurley, Y. Mauro, S. Raghavan, "Compensation of coherent DQPSK receiver imperfections," Proc. IEEE LEOS Summer Topicals (2007).

K. Kikuchi, Optical Fiber Telecommunications (Academic, 2008) pp. 95-129.

M. Tseytlin, O. Ritterbush, A. Salamon, "Digital, endless polarization control for polarization multiplexed fiber-optic communications," Proc. OFC 2003 (2003).

S. Calabro, T. Dullweber, E. Gottwald, N. Hecker-Denschlag, E. Mullner, B. Opitz, G. Sebald, E. Schmidt, B. Spinnler, C. Weiske, H. Zech, "An electrical polarization-state controller and demultiplexer for polarization multiplexed optical signals," Proc. 29th Eur. Conf. Optical Communication (ECOC) (2003) pp. 950-951.

A. Leven, N. Kaneda, Y.-K. Chen, "A real-time CMA-based 10 Gb/s polarization demultiplexing coherent receiver implemented in an FPGA," Proc. OFC/NFOEC 2008 (2008).

K. Kikuchi, "Polarization-demultiplexing algorithm in the digital coherent receiver," Proc. IEEE LEOS Summer Topicals (2008).

H. Zhang, Z. Tao, L. Liu, S. Oda, T. Hoshida, J. C. Rasmussen, "Polarization demultiplexing based on independent component analysis in optical coherent receivers," Proc. 34th Eur. Conf. Optical Communication (ECOC) (2008).

D. E. Crivelli, H. S. Carter, M. R. Hueda, "Adaptive digital equalization in the presence of chromatic dispersion, PMD, and phase noise in coherent fiber optic systems," Proc. IEEE Global Telecommun. Conf. (GLOBECOM) (2004) pp. 2545-2551.

R. A. Horn, C. R. Johnson, Topics in Matrix Analysis (Cambridge Univ. Press, 1991).

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