Abstract

A unified framework was recently developed for optimizing the bit error rate (BER) incurred in the simultaneous differential modulation of the optical resources of polarization, phase, and/or amplitude, extending the conventional Stokes' parameters of polarization optics to a set of D<sup>2</sup> generalized Stokes' parameters (GSPs). Novel optimal receiver structures were identified for multienergy polarization shift keying (POLSK), the optimality of differential phase amplitude shift keying (DPASK) and multichip differential phase shift keying (MC-DPSK) modulation formats was assessed, and optimal receivers for combinations of POLSK and DPSK were formulated. In this paper, the probability of error performance was evaluated for the newly introduced family of advanced modulation formats combining differential phase, polarization, and/or amplitude modulation, generically described as multichip differential state of POLSK. The symbol error rate and the BER for such systems are derived here in terms of the geometry of Stokes' signal space (the space of GSPs). The resulting formalism is applied to assess the performance of recently introduced MC-DPSK and MUB-coded systems (differential phase constellations based on maximally unbiased bases), as well as DPASK formats, establishing improved tradeoffs between sensitivity and spectral efficiency relative to conventional optical DPSK systems.

© 2007 IEEE

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  1. M. Nazarathy, E. Simony, "Stokes space optimal detection of differential phase and polarization shift keying modulation ," J. Lightw. Technol. 24, 1978-1988 (2006).
  2. S. Betti, F. Curti, G. De Marchis, E. Iannone, "Phase noise and polarization state insensitive optical coherent systems," J. Lightw. Technol 8, 756-767 (1990).
  3. S. Betti, F. Curti, G. De Marchis, E. Iannone, "A novel multilevel coherent optical system: 4-Quadrature signaling," J. Lightw. Technol. 9, 514-523 (1991).
  4. S. Betti, G. De Marchis, E. Iannone, "Polarization modulated direct detection optical transmission systems," J. Lightw. Technol. 10, 1985-1997 (1992).
  5. S. Benedetto, P. Poggiolini, "Theory of polarization shift keying modulation," IEEE Trans. Commun. 40, 708-720 (1992).
  6. S. Benedetto, P. T. Poggiolini, "Multilevel polarization shift keying: Optimum receiver structure and performance evaluation ," IEEE Trans. Commun. 42, 21174-1185 (1994).
  7. S. Betti, F. Curti, G. De Marchis, E. Iannone, "Multilevel coherent optical system based on Stokes' parameters modulation," J. Lightw. Technol. 8, 1127-1136 (1990).
  8. R. S. Vodhanel, "5 Gb/s direct optical DPSK modulation of a 1530-nm DFB laser," IEEE Photon. Technol. Lett. 13, 884-886 (2001).
  9. R. A. Griffin, R. Johnstone, R. Walker, J. Hall, S. Wadsworth, K. Berry, A. Carter, M. Wale, J. Hughes, P. Jerram, N. Parsons, "10 Gb/s optical differential quadrature phase shift key (DQSK) transmission using GaAs/AlGaAs integration," Optical Fiber Commun. (OFC) AnaheimCA (2002) Paper PD-F6.
  10. P. J. Winzer, S. Chandrasekhar, "Impact of filtering on RZ-DPSK reception," IEEE Photon. Technol. Lett. 15, 840-842 (2003).
  11. C. Wree, J. Leibrich, D. Mohr, J. Eick, W. Rosenkranz, "Experimental investigation of receiver sensitivity of RZ-DQPSK modulation format using balanced detection," Optical Fiber Commun. (OFC) AtlantaGA Paper ThE5.
  12. M. Ohm, J. Speidel, "Quaternary optical ASK-DPSK and receivers with direct detection," IEEE Photon. Technol. Lett. 15, 159-161 (2003).
  13. X. Liu, Y. Kao, J. Leuthold, C. R. Doerr, L. F. Mollenauer, "Quaternary differential-phase-amplitude-shift-keying for DWDM transmission," Eur. Conf. Optical Commun. (ECOC) RiminiItaly (2003) Paper Th2.6.5.
  14. S. Hayase, N. Kikuchi, K. Sekine, S. Sasaki, "Proposal of 8-state per symbol (binary ASK and QPSK) 30-Gb/s optical modulation demodulation scheme," Eur. Conf. Optical Commun. (ECOC) RiminiItaly (2003) Paper Th2.6.4.
  15. N. Chi, J. Zhang, P. V. Holm-Nielsen, P. Jeppesen, "Transmission and transparent wavelength conversion of an optically labeled signal using ASK/DPSK orthogonal modulation," IEEE Photon. Technol. Lett. 15, 760-762 (2003).
  16. J. Hansryd, J. van Howe, C. Xu, "Nonlinear crosstalk and compensation in QDPASK optical communication systems," IEEE Photon. Technol. Lett. 15, 1975-1977 (2004).
  17. M. Nazarathy, E. Simony, "Generalized stokes parameters shift keying: A new perspective on optimal detection over electrical and optical vector incoherent channels," IEEE Trans. Commun. 54, 499-509 (2006).
  18. M. Nazarathy, E. Simony, "Multi-chip differential phase encoded optical transmission," IEEE Photon. Technol. Lett. 17, 1133-1135 (2005).
  19. M. K. Simon, S. M. Hinedi, W. Lindsey, Digital Communication Techniques: Signal Design and Detection (Prentice-Hall, 1995).
  20. M. Nazarathy, E. Simony, "Performance limits of multilevel DPSK," IEEE Photon. Technol. Lett. 17, 2310-2312 (2005).
  21. M. Nazarathy, E. Simony, Y. Yadin, "Analytical evaluation of bit error rates for hard detection of optical differential-phase-amplitude shift keying (DPASK)," J. Lightw. Technol. 24, 2248-2260 (2006).
  22. Y. Yadin, A. Bilenca, M. Nazarathy, "Soft detection of multi-chip DPSK over the non-linear fiber optic channel," IEEE Photon. Technol. Lett. 16, 2001-2003 (2004).
  23. S. Stein, "Unified analysis of certain coherent and non-coherent binary communication systems," IEEE Trans. Inf. Theory IT-10, 43-51 (1964).

2006

M. Nazarathy, E. Simony, "Stokes space optimal detection of differential phase and polarization shift keying modulation ," J. Lightw. Technol. 24, 1978-1988 (2006).

M. Nazarathy, E. Simony, "Generalized stokes parameters shift keying: A new perspective on optimal detection over electrical and optical vector incoherent channels," IEEE Trans. Commun. 54, 499-509 (2006).

M. Nazarathy, E. Simony, Y. Yadin, "Analytical evaluation of bit error rates for hard detection of optical differential-phase-amplitude shift keying (DPASK)," J. Lightw. Technol. 24, 2248-2260 (2006).

2005

M. Nazarathy, E. Simony, "Multi-chip differential phase encoded optical transmission," IEEE Photon. Technol. Lett. 17, 1133-1135 (2005).

M. Nazarathy, E. Simony, "Performance limits of multilevel DPSK," IEEE Photon. Technol. Lett. 17, 2310-2312 (2005).

2004

Y. Yadin, A. Bilenca, M. Nazarathy, "Soft detection of multi-chip DPSK over the non-linear fiber optic channel," IEEE Photon. Technol. Lett. 16, 2001-2003 (2004).

J. Hansryd, J. van Howe, C. Xu, "Nonlinear crosstalk and compensation in QDPASK optical communication systems," IEEE Photon. Technol. Lett. 15, 1975-1977 (2004).

2003

P. J. Winzer, S. Chandrasekhar, "Impact of filtering on RZ-DPSK reception," IEEE Photon. Technol. Lett. 15, 840-842 (2003).

M. Ohm, J. Speidel, "Quaternary optical ASK-DPSK and receivers with direct detection," IEEE Photon. Technol. Lett. 15, 159-161 (2003).

N. Chi, J. Zhang, P. V. Holm-Nielsen, P. Jeppesen, "Transmission and transparent wavelength conversion of an optically labeled signal using ASK/DPSK orthogonal modulation," IEEE Photon. Technol. Lett. 15, 760-762 (2003).

2001

R. S. Vodhanel, "5 Gb/s direct optical DPSK modulation of a 1530-nm DFB laser," IEEE Photon. Technol. Lett. 13, 884-886 (2001).

1994

S. Benedetto, P. T. Poggiolini, "Multilevel polarization shift keying: Optimum receiver structure and performance evaluation ," IEEE Trans. Commun. 42, 21174-1185 (1994).

1992

S. Betti, G. De Marchis, E. Iannone, "Polarization modulated direct detection optical transmission systems," J. Lightw. Technol. 10, 1985-1997 (1992).

S. Benedetto, P. Poggiolini, "Theory of polarization shift keying modulation," IEEE Trans. Commun. 40, 708-720 (1992).

1991

S. Betti, F. Curti, G. De Marchis, E. Iannone, "A novel multilevel coherent optical system: 4-Quadrature signaling," J. Lightw. Technol. 9, 514-523 (1991).

1990

S. Betti, F. Curti, G. De Marchis, E. Iannone, "Multilevel coherent optical system based on Stokes' parameters modulation," J. Lightw. Technol. 8, 1127-1136 (1990).

S. Betti, F. Curti, G. De Marchis, E. Iannone, "Phase noise and polarization state insensitive optical coherent systems," J. Lightw. Technol 8, 756-767 (1990).

1964

S. Stein, "Unified analysis of certain coherent and non-coherent binary communication systems," IEEE Trans. Inf. Theory IT-10, 43-51 (1964).

IEEE Photon. Technol. Lett.

R. S. Vodhanel, "5 Gb/s direct optical DPSK modulation of a 1530-nm DFB laser," IEEE Photon. Technol. Lett. 13, 884-886 (2001).

P. J. Winzer, S. Chandrasekhar, "Impact of filtering on RZ-DPSK reception," IEEE Photon. Technol. Lett. 15, 840-842 (2003).

M. Ohm, J. Speidel, "Quaternary optical ASK-DPSK and receivers with direct detection," IEEE Photon. Technol. Lett. 15, 159-161 (2003).

N. Chi, J. Zhang, P. V. Holm-Nielsen, P. Jeppesen, "Transmission and transparent wavelength conversion of an optically labeled signal using ASK/DPSK orthogonal modulation," IEEE Photon. Technol. Lett. 15, 760-762 (2003).

J. Hansryd, J. van Howe, C. Xu, "Nonlinear crosstalk and compensation in QDPASK optical communication systems," IEEE Photon. Technol. Lett. 15, 1975-1977 (2004).

M. Nazarathy, E. Simony, "Multi-chip differential phase encoded optical transmission," IEEE Photon. Technol. Lett. 17, 1133-1135 (2005).

M. Nazarathy, E. Simony, "Performance limits of multilevel DPSK," IEEE Photon. Technol. Lett. 17, 2310-2312 (2005).

Y. Yadin, A. Bilenca, M. Nazarathy, "Soft detection of multi-chip DPSK over the non-linear fiber optic channel," IEEE Photon. Technol. Lett. 16, 2001-2003 (2004).

IEEE Trans. Commun.

M. Nazarathy, E. Simony, "Generalized stokes parameters shift keying: A new perspective on optimal detection over electrical and optical vector incoherent channels," IEEE Trans. Commun. 54, 499-509 (2006).

S. Benedetto, P. Poggiolini, "Theory of polarization shift keying modulation," IEEE Trans. Commun. 40, 708-720 (1992).

S. Benedetto, P. T. Poggiolini, "Multilevel polarization shift keying: Optimum receiver structure and performance evaluation ," IEEE Trans. Commun. 42, 21174-1185 (1994).

IEEE Trans. Inf. Theory

S. Stein, "Unified analysis of certain coherent and non-coherent binary communication systems," IEEE Trans. Inf. Theory IT-10, 43-51 (1964).

J. Lightw. Technol

S. Betti, F. Curti, G. De Marchis, E. Iannone, "Phase noise and polarization state insensitive optical coherent systems," J. Lightw. Technol 8, 756-767 (1990).

J. Lightw. Technol.

S. Betti, F. Curti, G. De Marchis, E. Iannone, "A novel multilevel coherent optical system: 4-Quadrature signaling," J. Lightw. Technol. 9, 514-523 (1991).

S. Betti, G. De Marchis, E. Iannone, "Polarization modulated direct detection optical transmission systems," J. Lightw. Technol. 10, 1985-1997 (1992).

S. Betti, F. Curti, G. De Marchis, E. Iannone, "Multilevel coherent optical system based on Stokes' parameters modulation," J. Lightw. Technol. 8, 1127-1136 (1990).

M. Nazarathy, E. Simony, Y. Yadin, "Analytical evaluation of bit error rates for hard detection of optical differential-phase-amplitude shift keying (DPASK)," J. Lightw. Technol. 24, 2248-2260 (2006).

M. Nazarathy, E. Simony, "Stokes space optimal detection of differential phase and polarization shift keying modulation ," J. Lightw. Technol. 24, 1978-1988 (2006).

Other

M. K. Simon, S. M. Hinedi, W. Lindsey, Digital Communication Techniques: Signal Design and Detection (Prentice-Hall, 1995).

X. Liu, Y. Kao, J. Leuthold, C. R. Doerr, L. F. Mollenauer, "Quaternary differential-phase-amplitude-shift-keying for DWDM transmission," Eur. Conf. Optical Commun. (ECOC) RiminiItaly (2003) Paper Th2.6.5.

S. Hayase, N. Kikuchi, K. Sekine, S. Sasaki, "Proposal of 8-state per symbol (binary ASK and QPSK) 30-Gb/s optical modulation demodulation scheme," Eur. Conf. Optical Commun. (ECOC) RiminiItaly (2003) Paper Th2.6.4.

C. Wree, J. Leibrich, D. Mohr, J. Eick, W. Rosenkranz, "Experimental investigation of receiver sensitivity of RZ-DQPSK modulation format using balanced detection," Optical Fiber Commun. (OFC) AtlantaGA Paper ThE5.

R. A. Griffin, R. Johnstone, R. Walker, J. Hall, S. Wadsworth, K. Berry, A. Carter, M. Wale, J. Hughes, P. Jerram, N. Parsons, "10 Gb/s optical differential quadrature phase shift key (DQSK) transmission using GaAs/AlGaAs integration," Optical Fiber Commun. (OFC) AnaheimCA (2002) Paper PD-F6.

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