Abstract

A novel decision-aided maximum likelihood (DA ML) technique is proposed to estimate the carrier phase in coherent optical phase-shift-keying system. The DA ML scheme is a totally linear computational algorithm which is feasible for on-line processing in the real systems. The simulation results show that the DA ML receiver can outperform the conventional Mth power scheme, especially when the nonlinear phase noise is dominant.

© 2009 Optical Society of America

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  1. A. H. Gnauck and P. J. Winzer, "Optical phase-shift-keyed transmission," J. Lightwave Technol. 23, 115-130 (2005).
    [CrossRef]
  2. E. Ip and J. M. Kahn, "Feedforward Carrier Recovery for Coherent Optical Communications," J. Lightwave Technol. 25, 2675-2692 (2007).
    [CrossRef]
  3. M. Nazarathy, X. Liu, L. Christen, Y. K. Lize, and A. Willner, "Self-coherent multisymbol detection of optical differential phase-shift-keying," J. Lightwave Technol. 26, 1921-1934 (2008).
    [CrossRef]
  4. R. No’e, "PLL-free synchronous QPSK polarization multiplex/diversity receiver concept with digital I&Q baseband processing," IEEE Photon. Technol. Lett. 17, 887-889 (2005).
    [CrossRef]
  5. L. G. Kazovsky, G. Kalogerakis, and W.-T. Shaw, "Homodyne phase-shift-keying systems: past challenges and future opportunities," J. Lightwave. Technol. 24, 4876-4884 (2006).
    [CrossRef]
  6. D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, "Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation," J. Lightwave Technol. 24, 12-21 (2006).
    [CrossRef]
  7. J. P. Gordon and L. F. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett. 15, 1351-1353 (1990).
    [CrossRef] [PubMed]
  8. H. Kim and A. H. Gnauck, "Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise," IEEE Photon. Technol. Lett. 15, 320-322 (2003).
    [CrossRef]
  9. S. Zhang, P. Y. Kam, J. Chen, and C. Yu, "Receiver sensitivity improvement using decision-aided maximum likelihood phase estimation in coherent optical DQPSK system," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2008), paper CThJJ2.
    [PubMed]
  10. G. P. Agrawal, Fiber-Optic Communication Systems (Wiley-Interscience, New York, 2002).
    [CrossRef]
  11. K. Kikuchi and S. Tsukamoto, "Evaluation of sensitivity of the digital coherent receiver," J. Lightwave Technol. 26, 1817-1822 (2008).
    [CrossRef]
  12. K.-P. Ho, Phase-Modulated Optical Communication Systems (Springer, New York, 2005).
  13. P. Y. Kam, "Maximum-likelihood carrier phase recovery for linear suppressed-carrier digital data modulations," IEEE Trans. Commun. COM-34, 522-527 (1986).
  14. S. Zhang, P. Y. Kam, J. Chen, and C. Yu, "Adaptive decision-aided maximum likelihood phase estimation in coherent optical DQPSK system," in Proceedings of Opto-Electronics and Communications Conference (2008), paper TuA-4.
  15. X. Wei, X. Liu, and C. Xu, "Numerical simulation of the SPM penalty in a 10-Gb/s RZ-DPSK system," IEEE Photon. Technol. Lett. 15, 1636-1638 (2003).
    [CrossRef]
  16. K.-P. Ho and J. M. Kahn, "Electronic compensation technique to mitigate nonlinear phase noise," J. Lightwave. Technol. 22, 779-783 (2004).
    [CrossRef]
  17. E. Ip and J. M. Kahn, "Digital equalization of chromatic dispersion and polarization mode dispersion," J. Lightwave Technol. 25, 2033-2043 (2007).
    [CrossRef]
  18. X. Liu, X. Wei, R. E. Slusher, and C. J. McKinstrie, "Improving transmission performance in differential phase shift-keyed systems by use of lumped nonlinear phase-shift compensation," Opt. Lett. 27, 1351-1353 (2002).
    [CrossRef]
  19. K. Kikuchi, "Electronic post-compensation for nonlinear phase fluctuations in a 1000-km 20-Gbit/s optical quadrature phase-shift keying transmission system using the digital coherent receiver," Opt. Express  16, 889-896 (2008).
    [CrossRef] [PubMed]

2008 (3)

2007 (2)

2006 (2)

D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, "Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation," J. Lightwave Technol. 24, 12-21 (2006).
[CrossRef]

L. G. Kazovsky, G. Kalogerakis, and W.-T. Shaw, "Homodyne phase-shift-keying systems: past challenges and future opportunities," J. Lightwave. Technol. 24, 4876-4884 (2006).
[CrossRef]

2005 (2)

R. No’e, "PLL-free synchronous QPSK polarization multiplex/diversity receiver concept with digital I&Q baseband processing," IEEE Photon. Technol. Lett. 17, 887-889 (2005).
[CrossRef]

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

2004 (1)

K.-P. Ho and J. M. Kahn, "Electronic compensation technique to mitigate nonlinear phase noise," J. Lightwave. Technol. 22, 779-783 (2004).
[CrossRef]

2003 (2)

H. Kim and A. H. Gnauck, "Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise," IEEE Photon. Technol. Lett. 15, 320-322 (2003).
[CrossRef]

X. Wei, X. Liu, and C. Xu, "Numerical simulation of the SPM penalty in a 10-Gb/s RZ-DPSK system," IEEE Photon. Technol. Lett. 15, 1636-1638 (2003).
[CrossRef]

2002 (1)

1990 (1)

1986 (1)

P. Y. Kam, "Maximum-likelihood carrier phase recovery for linear suppressed-carrier digital data modulations," IEEE Trans. Commun. COM-34, 522-527 (1986).

Christen, L.

Gnauck, A. H.

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

H. Kim and A. H. Gnauck, "Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise," IEEE Photon. Technol. Lett. 15, 320-322 (2003).
[CrossRef]

Gordon, J. P.

Ho, K.-P.

K.-P. Ho and J. M. Kahn, "Electronic compensation technique to mitigate nonlinear phase noise," J. Lightwave. Technol. 22, 779-783 (2004).
[CrossRef]

Ip, E.

Kahn, J. M.

Kalogerakis, G.

L. G. Kazovsky, G. Kalogerakis, and W.-T. Shaw, "Homodyne phase-shift-keying systems: past challenges and future opportunities," J. Lightwave. Technol. 24, 4876-4884 (2006).
[CrossRef]

Kam, P. Y.

P. Y. Kam, "Maximum-likelihood carrier phase recovery for linear suppressed-carrier digital data modulations," IEEE Trans. Commun. COM-34, 522-527 (1986).

Katoh, K.

Kazovsky, L. G.

L. G. Kazovsky, G. Kalogerakis, and W.-T. Shaw, "Homodyne phase-shift-keying systems: past challenges and future opportunities," J. Lightwave. Technol. 24, 4876-4884 (2006).
[CrossRef]

Kikuchi, K.

Kim, H.

H. Kim and A. H. Gnauck, "Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise," IEEE Photon. Technol. Lett. 15, 320-322 (2003).
[CrossRef]

Liu, X.

Lize, Y. K.

Ly-Gagnon, D.-S.

McKinstrie, C. J.

Mollenauer, L. F.

Nazarathy, M.

Shaw, W.-T.

L. G. Kazovsky, G. Kalogerakis, and W.-T. Shaw, "Homodyne phase-shift-keying systems: past challenges and future opportunities," J. Lightwave. Technol. 24, 4876-4884 (2006).
[CrossRef]

Slusher, R. E.

Tsukamoto, S.

Wei, X.

Willner, A.

Winzer, P. J.

Xu, C.

X. Wei, X. Liu, and C. Xu, "Numerical simulation of the SPM penalty in a 10-Gb/s RZ-DPSK system," IEEE Photon. Technol. Lett. 15, 1636-1638 (2003).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

H. Kim and A. H. Gnauck, "Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise," IEEE Photon. Technol. Lett. 15, 320-322 (2003).
[CrossRef]

R. No’e, "PLL-free synchronous QPSK polarization multiplex/diversity receiver concept with digital I&Q baseband processing," IEEE Photon. Technol. Lett. 17, 887-889 (2005).
[CrossRef]

X. Wei, X. Liu, and C. Xu, "Numerical simulation of the SPM penalty in a 10-Gb/s RZ-DPSK system," IEEE Photon. Technol. Lett. 15, 1636-1638 (2003).
[CrossRef]

IEEE Trans. Commun. (1)

P. Y. Kam, "Maximum-likelihood carrier phase recovery for linear suppressed-carrier digital data modulations," IEEE Trans. Commun. COM-34, 522-527 (1986).

J. Lightwave Technol. (6)

J. Lightwave. Technol. (2)

K.-P. Ho and J. M. Kahn, "Electronic compensation technique to mitigate nonlinear phase noise," J. Lightwave. Technol. 22, 779-783 (2004).
[CrossRef]

L. G. Kazovsky, G. Kalogerakis, and W.-T. Shaw, "Homodyne phase-shift-keying systems: past challenges and future opportunities," J. Lightwave. Technol. 24, 4876-4884 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Other (4)

S. Zhang, P. Y. Kam, J. Chen, and C. Yu, "Adaptive decision-aided maximum likelihood phase estimation in coherent optical DQPSK system," in Proceedings of Opto-Electronics and Communications Conference (2008), paper TuA-4.

S. Zhang, P. Y. Kam, J. Chen, and C. Yu, "Receiver sensitivity improvement using decision-aided maximum likelihood phase estimation in coherent optical DQPSK system," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2008), paper CThJJ2.
[PubMed]

G. P. Agrawal, Fiber-Optic Communication Systems (Wiley-Interscience, New York, 2002).
[CrossRef]

K.-P. Ho, Phase-Modulated Optical Communication Systems (Springer, New York, 2005).

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Figures (7)

Fig.1.
Fig.1.

A typical long-haul transmission system with a coherent receiver. ADC: Analog-to Digital Converters

Fig.2.
Fig.2.

DA ML receiver structure.

Fig. 3
Fig. 3

The structure of real-time QPSK DA ML receiver (L =2): D: Time delay. The input complex signal is formed by its real and imaginary parts.

Fig. 4.
Fig. 4.

Simulated BER performances of 40-Gb/s QPSK in a linear optical phase noise channel with two different schemes: DA ML and Mth power (L= 5, 10, σ=0.02).

Fig. 5.
Fig. 5.

Simulated BER performances of 40-Gb/s QPSK in linear optical phase noise channel with two different schemes: DA ML and Mth power (L= 5, 10, σ=0.05).

Fig. 6.
Fig. 6.

Simulated nonlinear phase effect of QPSK signals in a 22-span nonlinear optical channel (NA =22 and L=5).

Fig. 7.
Fig. 7.

Performances at the optimum input power versus no. of spans (NA ) when L=5: (a) BER performance and optimum input power. (b) Q-factor improvement over Mth power.

Equations (36)

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Er(t)=[Prej(θs(t)+ϕs(t))+ñx(t)]ejωctx+ñy(t)ejωcty
SASE=NA nsp (G1) h v
ELO(t)=PLOej(ωLOt+ϕLO(t))x
S=12[11111j1j]
iI(t)=14REr(t)+ELO(t)214REr(t)ELO(t)2+ish1
=RRe{Er(t)·ELO*(t)}+ish1
=RPrPLO·cos(ωIFt+θs(t)+ϕs(t)ϕLO(t))
+RPLORe{ñx(t)ej(ωIFtϕLO(t))}+ish1
iQ(t)=14REr(t)+jELO(t)214REr(t)jELO(t)2+ish2
=RPrPLO·sin(ωIFt+θs(t)+ϕs(t)ϕLO(t))
+RPLORe{ñx(t)ej(ωIFtϕLO(t)π/2)}+ish2
Nsh=eRPLO
NLOASE=R2PLOSASE(f)
σ2=2πΔυT
r(t)=iI(t)+j·iQ(t)+ñ(t)
SNRsym=R2PrPLO2·R2PLOSASE(f)R2/2NsNAnsp
r(k)=Esm(k) ejθ(k) +n(k)̃
p(r(k)θ(k),m(k))=1πN0exp(r(k)m(k)ejθ(k)2N0).
L(θ,k)=l=kLk1In[i=1M/2exp(Si)coshqi(l,θ)]+c
cosθ̂(k)l=kLk1i=1M/2exp(Si)sinhqi(l,θ̂(k))Im[r(l)Ci*]i=1M/2exp(Si)coshqi(l,θ̂(k))
=sinθ̂(k)l=kLk1i=1M/2exp(Si)sinhqi(l,θ̂(k))Re[r(l)Ci*]i=1M/2exp(Si)coshqi(l,θ̂(k))
θ̂(k)=arctan[l=kLk1Im[r(l)m̂*(l)]l=kLk1Re[r(l)m̂*(l)]]
V(k)l=kLk1r(l)m̂*(l)
qi(k)=argmaxRe[r(k)V*(k)ejϕi(k)]
qi(k)=sgn(Re[r(k)V*(k)])
qi(k)argmaxRe [2ejπ/4r(k)V*(k)ejϕi(k)ejπ/4]
=argmaxRe[μ(k)m*(k)].
m̂(k)=sgn(Re[μ(k)]+jsgn(Im[μ(k)])2.
2m̂(k)=±1±j2ejπ/4{1,j,1,j}{00,01,11,01}
μ(k)=2ejπ/4r(k)·2V*(k)
(Re[2ejπ/4r(k)]+jIm[2ejπ/4r(k)])
· (Re[2V*(k)]+jIm[2V*(k)])
youtre(t)=(2b̅01)xinre(2b̅11)xinim,
youtim(t)=(2b̅11)xinre(2b̅01)xinim
2V*(k)=[l=kLk12r(l)m̂*(l)]*=l=kLk12r*(l)m̂(l)ejπ/4
=l=kLk1[r(k)]*m̂(l),

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