Abstract

We present a generalized framework of data-aided multi-symbol phase estimation (MSPE) for improving the receiver sensitivity of direct-detection optical m-ary differential phase-shift keying (DPSK) through the extraction of a more accurate phase reference. Derivations of the data-aided MSPE algorithms for quaternary DPSK (DQPSK), 8-ary DPSK, m-ary DPSK, and DPSK/ASK are provided. Simulations show that receiver sensitivity improvements of over 2 dB can be obtained with the data-aided MSPE, enabling the performances of direct-detection m-ary DPSK signals to approach those of coherent homodyne-detection without resorting to an optical local oscillator. Performance improvements in nonlinear transmission are briefly discussed, and an electronic nonlinear phase shift compensation scheme is introduced for DPSK/ASK. Also presented is a simple yet universal receiver platform for m-ary DPSK consisting of just one pair of optical I/Q demodulators and a digital signal processing unit.

© 2007 Optical Society of America

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  20. T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, "Forward error correction based on block turbo code with 3-bit soft decision for 10-Gb/s optical communication systems," IEEE J. Sel. Top. Quantum Electron. 10, 376-386 (2004).
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    [CrossRef]
  23. S. Savory and A. Hadjifotiou, "Laser linewidth requirements for optical DQPSK systems," IEEE Photon. Technol. Lett. 16, 930-932 (2004).
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  24. J. M. Kahn, "Modulation and diction techniques for optical communication systems," in Proceedings of OSA Topic Meeting on Coherent Optical Technologies and Applications (COTA)2006, paper CThC1.
  25. X. Liu, X. Wei, R. E. Slusher, C. J. and McKinstrie, "Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation," Opt. Lett. 27, 1616-1618 (2002).
    [CrossRef]
  26. G. Charlet, N. Maaref, J. Renaudier, H. Mardoyan, P. Tran, and S. Bigo, "Transmission of 40Gb/s QPSK with coherent detection over ultra long haul distance improved by nonlinearity mitigation," in Proceedings of European Conference on Optical Communications2006, post-deadline paper Th4.3.4.

2005 (3)

Y. Yadin, A. Bilenca, and M. Nazarathy, "Soft detection of multichip DPSK over the nonlinear fiber-optic channel," IEEE Photon. Technol. Lett. 17, 2001-2003 (2005).
[CrossRef]

M. Nazarathy and E. Simony, "Multichip differential phase encoded optical transmission," IEEE Photon. Technol. Lett. 17, 1133-1135 (2005).
[CrossRef]

A. H. Gnauck and P. J. Winzer, "Optical phase-shift-keyed transmission," J. Lightwave Technol. 23, 115-130 (2005).
[CrossRef]

2004 (6)

C. Kim and G. Li, "Direct-detection optical differential 8-level phase-shift keying (OD8PSK) for spectrally efficient transmission," Opt. Express 12, 3415-3421 (2004).
[CrossRef] [PubMed]

J. Lee, P. Roux, U.-V. Koc, T. Link, Y. Baeyens, and Y.-K. Chen, "A 5-b 10-GSample/s A/D converter for 10-Gb/s optical receivers," IEEE J. Solid-State Circuits 39, 1671 - 1679 (2004).
[CrossRef]

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, "Forward error correction based on block turbo code with 3-bit soft decision for 10-Gb/s optical communication systems," IEEE J. Sel. Top. Quantum Electron. 10, 376-386 (2004).
[CrossRef]

C. Xu, X. Liu, and X. Wei, "Differential phase-shift keying for high spectral efficiency optical transmissions," IEEE J. Sel. Top. Quantum Electron. 10, 281 - 293 (2004).
[CrossRef]

Y. Han, C. Kim, and G. Li, "Simplified receiver implementation for optical differential 8-level phase-shift keying," Electron. Lett. 40, 1372-1373 (2004).
[CrossRef]

S. Savory and A. Hadjifotiou, "Laser linewidth requirements for optical DQPSK systems," IEEE Photon. Technol. Lett. 16, 930-932 (2004).
[CrossRef]

2003 (1)

P. S. Cho, V. S. Grigoryan, Y. A. Godin, A. Salamon, and Y. Achiam, "Transmission of 25-Gb/s RZ-DQPSK signals with 25-GHz channel spacing over 1000 km of SMF-28 fiber," IEEE Photon. Technol. Lett. 15, 473-475 (2003).
[CrossRef]

2002 (1)

1995 (1)

H. Leib, "Data-aided noncoherent demodulation of DPSK," IEEE Trans. Commun. 43, 722-725 (1995).
[CrossRef]

1990 (2)

D. Divsalar and M. K. Simon, "Multiple-symbol differential detection of MPSK," IEEE Trans. Commun. 38, 300-308 (1990).
[CrossRef]

J. P. Gordon and L. F. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett. 15, 1351-1353 (1990).
[CrossRef] [PubMed]

Achiam, Y.

P. S. Cho, V. S. Grigoryan, Y. A. Godin, A. Salamon, and Y. Achiam, "Transmission of 25-Gb/s RZ-DQPSK signals with 25-GHz channel spacing over 1000 km of SMF-28 fiber," IEEE Photon. Technol. Lett. 15, 473-475 (2003).
[CrossRef]

Akita, M.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, "Forward error correction based on block turbo code with 3-bit soft decision for 10-Gb/s optical communication systems," IEEE J. Sel. Top. Quantum Electron. 10, 376-386 (2004).
[CrossRef]

Baeyens, Y.

J. Lee, P. Roux, U.-V. Koc, T. Link, Y. Baeyens, and Y.-K. Chen, "A 5-b 10-GSample/s A/D converter for 10-Gb/s optical receivers," IEEE J. Solid-State Circuits 39, 1671 - 1679 (2004).
[CrossRef]

Bilenca, A.

Y. Yadin, A. Bilenca, and M. Nazarathy, "Soft detection of multichip DPSK over the nonlinear fiber-optic channel," IEEE Photon. Technol. Lett. 17, 2001-2003 (2005).
[CrossRef]

Chen, Y.-K.

J. Lee, P. Roux, U.-V. Koc, T. Link, Y. Baeyens, and Y.-K. Chen, "A 5-b 10-GSample/s A/D converter for 10-Gb/s optical receivers," IEEE J. Solid-State Circuits 39, 1671 - 1679 (2004).
[CrossRef]

Cho, P. S.

P. S. Cho, V. S. Grigoryan, Y. A. Godin, A. Salamon, and Y. Achiam, "Transmission of 25-Gb/s RZ-DQPSK signals with 25-GHz channel spacing over 1000 km of SMF-28 fiber," IEEE Photon. Technol. Lett. 15, 473-475 (2003).
[CrossRef]

Divsalar, D.

D. Divsalar and M. K. Simon, "Multiple-symbol differential detection of MPSK," IEEE Trans. Commun. 38, 300-308 (1990).
[CrossRef]

Fujita, H.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, "Forward error correction based on block turbo code with 3-bit soft decision for 10-Gb/s optical communication systems," IEEE J. Sel. Top. Quantum Electron. 10, 376-386 (2004).
[CrossRef]

Gnauck, A. H.

Godin, Y. A.

P. S. Cho, V. S. Grigoryan, Y. A. Godin, A. Salamon, and Y. Achiam, "Transmission of 25-Gb/s RZ-DQPSK signals with 25-GHz channel spacing over 1000 km of SMF-28 fiber," IEEE Photon. Technol. Lett. 15, 473-475 (2003).
[CrossRef]

Gordon, J. P.

Grigoryan, V. S.

P. S. Cho, V. S. Grigoryan, Y. A. Godin, A. Salamon, and Y. Achiam, "Transmission of 25-Gb/s RZ-DQPSK signals with 25-GHz channel spacing over 1000 km of SMF-28 fiber," IEEE Photon. Technol. Lett. 15, 473-475 (2003).
[CrossRef]

Hadjifotiou, A.

S. Savory and A. Hadjifotiou, "Laser linewidth requirements for optical DQPSK systems," IEEE Photon. Technol. Lett. 16, 930-932 (2004).
[CrossRef]

Han, Y.

Y. Han, C. Kim, and G. Li, "Simplified receiver implementation for optical differential 8-level phase-shift keying," Electron. Lett. 40, 1372-1373 (2004).
[CrossRef]

Kim, C.

Y. Han, C. Kim, and G. Li, "Simplified receiver implementation for optical differential 8-level phase-shift keying," Electron. Lett. 40, 1372-1373 (2004).
[CrossRef]

C. Kim and G. Li, "Direct-detection optical differential 8-level phase-shift keying (OD8PSK) for spectrally efficient transmission," Opt. Express 12, 3415-3421 (2004).
[CrossRef] [PubMed]

Kobayashi, T.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, "Forward error correction based on block turbo code with 3-bit soft decision for 10-Gb/s optical communication systems," IEEE J. Sel. Top. Quantum Electron. 10, 376-386 (2004).
[CrossRef]

Koc, U.-V.

J. Lee, P. Roux, U.-V. Koc, T. Link, Y. Baeyens, and Y.-K. Chen, "A 5-b 10-GSample/s A/D converter for 10-Gb/s optical receivers," IEEE J. Solid-State Circuits 39, 1671 - 1679 (2004).
[CrossRef]

Kubo, K.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, "Forward error correction based on block turbo code with 3-bit soft decision for 10-Gb/s optical communication systems," IEEE J. Sel. Top. Quantum Electron. 10, 376-386 (2004).
[CrossRef]

Kuno, K.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, "Forward error correction based on block turbo code with 3-bit soft decision for 10-Gb/s optical communication systems," IEEE J. Sel. Top. Quantum Electron. 10, 376-386 (2004).
[CrossRef]

Lee, J.

J. Lee, P. Roux, U.-V. Koc, T. Link, Y. Baeyens, and Y.-K. Chen, "A 5-b 10-GSample/s A/D converter for 10-Gb/s optical receivers," IEEE J. Solid-State Circuits 39, 1671 - 1679 (2004).
[CrossRef]

Leib, H.

H. Leib, "Data-aided noncoherent demodulation of DPSK," IEEE Trans. Commun. 43, 722-725 (1995).
[CrossRef]

Li, G.

C. Kim and G. Li, "Direct-detection optical differential 8-level phase-shift keying (OD8PSK) for spectrally efficient transmission," Opt. Express 12, 3415-3421 (2004).
[CrossRef] [PubMed]

Y. Han, C. Kim, and G. Li, "Simplified receiver implementation for optical differential 8-level phase-shift keying," Electron. Lett. 40, 1372-1373 (2004).
[CrossRef]

Link, T.

J. Lee, P. Roux, U.-V. Koc, T. Link, Y. Baeyens, and Y.-K. Chen, "A 5-b 10-GSample/s A/D converter for 10-Gb/s optical receivers," IEEE J. Solid-State Circuits 39, 1671 - 1679 (2004).
[CrossRef]

Liu, X.

C. Xu, X. Liu, and X. Wei, "Differential phase-shift keying for high spectral efficiency optical transmissions," IEEE J. Sel. Top. Quantum Electron. 10, 281 - 293 (2004).
[CrossRef]

X. Liu, X. Wei, R. E. Slusher, C. J. and McKinstrie, "Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation," Opt. Lett. 27, 1616-1618 (2002).
[CrossRef]

Miyata, Y.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, "Forward error correction based on block turbo code with 3-bit soft decision for 10-Gb/s optical communication systems," IEEE J. Sel. Top. Quantum Electron. 10, 376-386 (2004).
[CrossRef]

Mizuochi, T.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, "Forward error correction based on block turbo code with 3-bit soft decision for 10-Gb/s optical communication systems," IEEE J. Sel. Top. Quantum Electron. 10, 376-386 (2004).
[CrossRef]

Mollenauer, L. F.

Motoshima, K.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, "Forward error correction based on block turbo code with 3-bit soft decision for 10-Gb/s optical communication systems," IEEE J. Sel. Top. Quantum Electron. 10, 376-386 (2004).
[CrossRef]

Nazarathy, M.

Y. Yadin, A. Bilenca, and M. Nazarathy, "Soft detection of multichip DPSK over the nonlinear fiber-optic channel," IEEE Photon. Technol. Lett. 17, 2001-2003 (2005).
[CrossRef]

M. Nazarathy and E. Simony, "Multichip differential phase encoded optical transmission," IEEE Photon. Technol. Lett. 17, 1133-1135 (2005).
[CrossRef]

Ouchi, K.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, "Forward error correction based on block turbo code with 3-bit soft decision for 10-Gb/s optical communication systems," IEEE J. Sel. Top. Quantum Electron. 10, 376-386 (2004).
[CrossRef]

Roux, P.

J. Lee, P. Roux, U.-V. Koc, T. Link, Y. Baeyens, and Y.-K. Chen, "A 5-b 10-GSample/s A/D converter for 10-Gb/s optical receivers," IEEE J. Solid-State Circuits 39, 1671 - 1679 (2004).
[CrossRef]

Salamon, A.

P. S. Cho, V. S. Grigoryan, Y. A. Godin, A. Salamon, and Y. Achiam, "Transmission of 25-Gb/s RZ-DQPSK signals with 25-GHz channel spacing over 1000 km of SMF-28 fiber," IEEE Photon. Technol. Lett. 15, 473-475 (2003).
[CrossRef]

Savory, S.

S. Savory and A. Hadjifotiou, "Laser linewidth requirements for optical DQPSK systems," IEEE Photon. Technol. Lett. 16, 930-932 (2004).
[CrossRef]

Shimizu, K.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, "Forward error correction based on block turbo code with 3-bit soft decision for 10-Gb/s optical communication systems," IEEE J. Sel. Top. Quantum Electron. 10, 376-386 (2004).
[CrossRef]

Simon, M. K.

D. Divsalar and M. K. Simon, "Multiple-symbol differential detection of MPSK," IEEE Trans. Commun. 38, 300-308 (1990).
[CrossRef]

Simony, E.

M. Nazarathy and E. Simony, "Multichip differential phase encoded optical transmission," IEEE Photon. Technol. Lett. 17, 1133-1135 (2005).
[CrossRef]

Slusher, R. E.

Tagami, H.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, "Forward error correction based on block turbo code with 3-bit soft decision for 10-Gb/s optical communication systems," IEEE J. Sel. Top. Quantum Electron. 10, 376-386 (2004).
[CrossRef]

Wei, X.

C. Xu, X. Liu, and X. Wei, "Differential phase-shift keying for high spectral efficiency optical transmissions," IEEE J. Sel. Top. Quantum Electron. 10, 281 - 293 (2004).
[CrossRef]

X. Liu, X. Wei, R. E. Slusher, C. J. and McKinstrie, "Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation," Opt. Lett. 27, 1616-1618 (2002).
[CrossRef]

Winzer, P. J.

Xu, C.

C. Xu, X. Liu, and X. Wei, "Differential phase-shift keying for high spectral efficiency optical transmissions," IEEE J. Sel. Top. Quantum Electron. 10, 281 - 293 (2004).
[CrossRef]

Yadin, Y.

Y. Yadin, A. Bilenca, and M. Nazarathy, "Soft detection of multichip DPSK over the nonlinear fiber-optic channel," IEEE Photon. Technol. Lett. 17, 2001-2003 (2005).
[CrossRef]

Yoshida, H.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, "Forward error correction based on block turbo code with 3-bit soft decision for 10-Gb/s optical communication systems," IEEE J. Sel. Top. Quantum Electron. 10, 376-386 (2004).
[CrossRef]

Electron. Lett. (1)

Y. Han, C. Kim, and G. Li, "Simplified receiver implementation for optical differential 8-level phase-shift keying," Electron. Lett. 40, 1372-1373 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, "Forward error correction based on block turbo code with 3-bit soft decision for 10-Gb/s optical communication systems," IEEE J. Sel. Top. Quantum Electron. 10, 376-386 (2004).
[CrossRef]

C. Xu, X. Liu, and X. Wei, "Differential phase-shift keying for high spectral efficiency optical transmissions," IEEE J. Sel. Top. Quantum Electron. 10, 281 - 293 (2004).
[CrossRef]

IEEE J. Solid-State Circuits (1)

J. Lee, P. Roux, U.-V. Koc, T. Link, Y. Baeyens, and Y.-K. Chen, "A 5-b 10-GSample/s A/D converter for 10-Gb/s optical receivers," IEEE J. Solid-State Circuits 39, 1671 - 1679 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

P. S. Cho, V. S. Grigoryan, Y. A. Godin, A. Salamon, and Y. Achiam, "Transmission of 25-Gb/s RZ-DQPSK signals with 25-GHz channel spacing over 1000 km of SMF-28 fiber," IEEE Photon. Technol. Lett. 15, 473-475 (2003).
[CrossRef]

Y. Yadin, A. Bilenca, and M. Nazarathy, "Soft detection of multichip DPSK over the nonlinear fiber-optic channel," IEEE Photon. Technol. Lett. 17, 2001-2003 (2005).
[CrossRef]

S. Savory and A. Hadjifotiou, "Laser linewidth requirements for optical DQPSK systems," IEEE Photon. Technol. Lett. 16, 930-932 (2004).
[CrossRef]

M. Nazarathy and E. Simony, "Multichip differential phase encoded optical transmission," IEEE Photon. Technol. Lett. 17, 1133-1135 (2005).
[CrossRef]

IEEE Trans. Commun. (2)

D. Divsalar and M. K. Simon, "Multiple-symbol differential detection of MPSK," IEEE Trans. Commun. 38, 300-308 (1990).
[CrossRef]

H. Leib, "Data-aided noncoherent demodulation of DPSK," IEEE Trans. Commun. 43, 722-725 (1995).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Express (1)

Opt. Lett. (2)

Other (12)

A. H. Gnauck, P. J. Winzer, S. Chandrasekhar, and C. Dorrer, "Spectrally efficient (0.8 b/s/Hz) 1-Tb/s (25 × 42.7 Gb/s) RZ-DQPSK transmission over 28 100-km SSMF spans with 7 optical add/drops," in Proceedings of European Conference on Optical Communications2004, post-deadline paper Th4.4.1.

J.-X. Cai, M. Nissov, C. R. Davidson, W. Anderson, Y. Cai, A. N. Pilipetskii, D. G. Foursa, W. W. Patterson, P. C. Corbett, A. J. Lucero, and NealS.  Bergano, "Improved margin in long-haul 40 Gb/s systems using bit-synchronously modulated RZ-DQPSK," in Proceedings of Optical Fiber Communications Conference2006, paper PDP33.

S. Hayase, N. Kikuchi, K. Sekine, and S. Sasaki, "Chromatic dispersion and SPM tolerance of 8-state/symbol (binary ASK and QPSK) modulated signal," in Proceedings of Optical Fiber Communications Conference2004, paper ThM3.

K.-P. Ho, Phase-modulated optical communication systems (Springer, New York, 2005).

D. van den Borne, S. Jansen, G. Khoe, H. de Wardt, S. Calabro, and E. Gottwald, "Differential quadrature phase shift keying with close to homodyne performance based on multi-symbol phase estimation," IEE Seminar on Optical Fiber Comm. and Electronic Signal. Processing, Ref. No. 2005-11310 (2005).

X. Liu, "Data-aided multi-symbol phase estimation for receiver sensitivity enhancement in optical DQPSK," in Proceedings of OSA Topic Meeting on Coherent Optical Technologies and Applications (COTA)2006, paper CThB4.

X. Liu, "Receiver sensitivity improvement in optical DQPSK and DQPSK/ASK through data-aided multi-symbol phase estimation," in Proceedings of European Conference on Optical Communications2006, paper We2.5.6.

X. Liu, S. Chandrasekhar, A. H. Gnauck, C. R. Doerr, I. Kang,D. Kilper, L. L. Buhl, and J. Centanni, "DSP-enabled compensation of demodulator phase error and sensitivity improvement in direct-detection 40-Gb/s DQPSK," in Proceedings of European Conference on Optical Communications2006, post-deadline paper Th4.4.5.

J. M. Kahn, "Modulation and diction techniques for optical communication systems," in Proceedings of OSA Topic Meeting on Coherent Optical Technologies and Applications (COTA)2006, paper CThC1.

G. Charlet, N. Maaref, J. Renaudier, H. Mardoyan, P. Tran, and S. Bigo, "Transmission of 40Gb/s QPSK with coherent detection over ultra long haul distance improved by nonlinearity mitigation," in Proceedings of European Conference on Optical Communications2006, post-deadline paper Th4.3.4.

X. Liu, "Digital implementation of soft detection for 3-chip-DBPSK with improved receiver sensitivity and dispersion tolerance," in Proceedings of Optical Fiber Communications Conference2006, paper OTuI2.

R. Griffin, R. Johnstone, R. Walker, S. Wadsworth, A. Carter, and M. Wale, "Integrated DQPSK transmitter for dispersion-tolerant and dispersion-managed DWDM transmission," in Proceedings of Optical Fiber Communications Conference2003, Paper FP6.

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of a data-aided MSPE receiver for optical DQPSK. BD: balanced detector. DFF: decision flip-flop. LOU: logic operation unit.

Fig. 2.
Fig. 2.

Schematic of a digital implementation of the data-aided MSPE for optical m-ary DPSK. AGC: automatic gain controller.

Fig. 3.
Fig. 3.

Simulated Q-factor (derived directly from BER) performance of the data-aided MSPE DQPSK receiver as compared to the conventional DQPSK receiver. The bit rate is 20 Gb/s and w=0.8.

Fig. 4.
Fig. 4.

Improvement in the Q-factor (derived directly from BER) by the data-aided MSPE for a DQPSK signal as a function of the number of past decisions used. OSNR= 10 dB and w=1.

Fig. 5.
Fig. 5.

Simulated BER performances of a 30-Gb/s 8-ary DPSK signal received with the data-aided MSPE receiver (N=8 and w=1) as compared to those with the conventional receiver.

Fig. 6.
Fig. 6.

Schematic of a data-aided MSPE receiver for optical DQPSK/ASK. TIA: transimpedance amplifier.

Fig. 7.
Fig. 7.

Simulated BER performance of the data-aided MSPE DQPSK/ASK receivers as compared to the conventional receiver. The bit rate is 30 Gb/s.

Tables (2)

Tables Icon

Table 1. Relation between the differential phase and the recovered data in optical DQPSK.

Tables Icon

Table 2. Relation between the differential phase and the recovered data in optical 8-ary DPSK.

Equations (45)

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u I ( n ) = Re [ u ( n ) ] = Re [ e j π 4 y ( n ) ( n 1 ) * ] , u Q ( n ) = Im [ u ( n ) ] = Im [ e j π 4 y ( n ) ( n 1 ) * ] ,
z ( n 1 ) = y ( n 1 ) + w z ( n 2 ) exp [ j Δϕ ( n 1 ) ] ,
exp [ j . Δϕ ( n ) ] = c I ( n ) c Q ( n ) ¯ ( 1 ) c I ( n ) ¯ + j . c I ( n ) c Q ( n ) ( 1 ) c I ( n ) ¯ ,
x ( n ) = e j π 4 y ( n ) z ( n 1 ) * ,
x ( n ) = e j π 4 y ( n ) { y ( n 1 ) + w z ( n 2 ) exp [ j Δϕ ( n 1 ) ] } *
= u ( n ) + e j π 4 y ( n ) y ( n 1 ) * y ( n 1 ) * w z ( n 2 ) * exp [ j Δϕ ( n 1 ) ] .
= u ( n ) + w u ( n ) 1 y ( n 1 ) * z ( n 2 ) * exp [ j Δϕ ( n 1 ) ]
1 y ( n 1 ) * y ( n 1 ) .
x ( n ) u ( n ) + w u ( n ) y ( n 1 ) z ( n 2 ) * exp [ j Δϕ ( n 1 ) ]
= u ( n ) + w u ( n ) e j π 4 [ e j π 4 y ( n 1 ) z ( n 2 ) * ] exp [ j Δϕ ( n 1 ) ] .
= u ( n ) + w u ( n ) e j π 4 x ( n 1 ) exp [ j Δ ϕ ( n 1 ) ]
x I ( n ) = Re [ x ( n ) ] , x Q ( n ) = Im [ x ( n ) ] , and
x ( n ) u ( n ) + w u ( n ) x ( n 1 ) exp [ j Δϕ ( n 1 ) ] exp ( j π 4 ) .
z ( n 1 ) = y ( n 1 ) + p = 1 N { w p q = 1 p [ y ( n 1 q ) e j Δϕ ( n q ) ] } ,
x I ( n ) = Re [ x ( n ) ] , x Q ( n ) = Im [ x ( n ) ] , and
x ( n ) = u ( n ) + p = 1 N { w p e j p π 4 u ( n ) q = 1 p [ u ( n q ) e j Δϕ ( n q ) ] } .
BER = 1 2 erfc ( 1 2 10 Q ( d B ) 20 ) ,
u I ( n ) = Re [ u ( n ) ] = Re [ e j π 8 y ( n ) y ( n 1 ) * ] , u Q ( n ) = Im [ u ( n ) ] = Im [ e j π 8 y ( n ) y ( n 1 ) * ] .
x ( n ) u ( n ) + w u ( n ) x ( n 1 ) exp [ j Δϕ ( n 1 ) ] exp ( j π 8 ) .
c I ( n ) = [ x I ( n ) > 0 ] , c Q ( n ) = x Q ( n ) > 0 , and
c 3 ( n ) = [ x I ( n ) + x Q ( n ) > 0 ] [ x I ( n ) x Q ( n ) > 0 ] ,
exp ( j Δ ϕ ( n ) ) = A + jB , and
A = 1 2 c 1 ( n ) c 2 ( n ) c 3 ( n ) ¯ ( 1 ) c 1 ( n ) ¯ + { [ c 1 ( n ) c 2 ( n ) c 3 ( n ) ] × [ c 1 ( n ) c 2 ( n ) ¯ ] } ( 1 ) c 1 ( n ) ¯ ,
B = 1 2 c 1 ( n ) c 2 ( n ) c 3 ( n ) ¯ ( 1 ) c 2 ( n ) + { [ c 1 ( n ) c 2 ( n ) c 3 ( n ) ] × [ c 1 ( n ) c 2 ( n ) ] } ( 1 ) c 2 ( n ) ,
u I = Re e m y ( n ) y ( n 1 ) * , u Q = Im e m y ( n ) y ( n 1 ) * .
x ( n ) u ( n ) + w u ( n ) x ( n 1 ) exp [ j Δϕ ( n 1 ) ] exp ( j π m ) ,
x ( n ) = u ( n ) + p = 1 N { w p e j p π m u ( n ) q = 1 p [ u ( n q ) e j Δ ϕ ( n q ) ] } .
c 1 = c I = ( x I > 0 ) ,
c 2 = c Q = ( x Q > 0 ) ,
c 3 = [ ν ( π m + π 4 ) > 0 ] [ ν ( π m π 4 ) > 0 ] ,
c 4 = [ ν ( π m + π 8 ) > 0 ] [ ν ( π m 3 π 8 ) > 0 ] [ ν ( π m + 3 π 8 ) > 0 ] [ ν ( π m π 8 ) > 0 ] ,
c log 2 ( m ) = [ ν ( π m + 2 m π ) > 0 ] [ ν ( π m + 2 + 4 m π ) > 0 ] [ ν ( π m + m 2 2 m π ) > 0 ]
[ ν ( π m + 2 m π π 2 ) > 0 ] [ ν ( π m + 2 + 4 m π π 2 ) > 0 ] [ ν ( π m + m 2 2 m π π 2 ) > 0 ] ,
1 + 1 + n = 3 log 2 ( m ) 2 n 2 = 1 + 1 + i = 1 log 2 ( m ) 2 2 i = 1 + i = 0 log 2 ( m ) 2 2 i = 1 + 1 2 log 2 ( m ) 1 1 2 = 2 log 2 ( m ) 1 = m 2 .
( π m , π m π 2 ) , ( 3 π m , 3 π m π 2 ) , , ( ( m 2 1 ) π m , π m ) .
ν ( πp m ) = Re [ e jπp m y ( n ) y ( n 1 ) * ]
= Re [ e ( p 1 ) m e j π m y ( n ) y ( n 1 ) * ] = cos ( p 1 m π ) u I sin ( p 1 m π ) u Q .
ν ( πp m π 2 ) = Im [ e jπp m y ( n ) y ( n 1 ) * ]
= Im [ e ( p 1 ) m e j π m y ( n ) y ( n 1 ) * ] = sin ( p 1 m π ) u I + cos ( p 1 m π ) u Q .
y ( n ) = y ( n ) e ( n ) = P ( n ) e ( n ) ,
1 y ( n 1 ) * = 1 P ( n ) y ( n 1 ) .
x ( n ) = u ( n ) + w u ( n ) x ( n 1 ) P ( n 1 ) e j Δ ϕ ( n 1 ) e j π m .
x ( n ) = u ( n ) + p = 1 N { w p e j p π m u ( n ) q = 1 p [ u ( n q ) P ( n q ) e j Δ ϕ ( n q ) ] } .
ν ( n ) = u ( n ) exp { j c NL [ P ( n ) P ( n 1 ) ] } ,

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