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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References

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    [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]
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    [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.
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  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).
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  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).
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2008 (3)

2007 (2)

2006 (2)

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]

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]

2005 (2)

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

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

Agrawal, G. P.

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

Chen, J.

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]

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.

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

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).

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]

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.

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.

Nóe, R.

R. Nóe, “PLL-free synchronous QPSK polarization multiplex/diversity receiver concept with digital I&Q baseband processing,” IEEE Photon. Technol. Lett. 17, 887–889 (2005).
[CrossRef]

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]

Yu, C.

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]

Zhang, S.

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]

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.

IEEE Photon. Technol. Lett. (3)

R. Nóe, “PLL-free synchronous QPSK polarization multiplex/diversity receiver concept with digital I&Q baseband processing,” IEEE Photon. Technol. Lett. 17, 887–889 (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]

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)

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]

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

Opt. Express (1)

Opt. Lett. (2)

Other (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).

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.

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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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