Abstract

We present a symbol-by-symbol coherent optical receiver, which employs a novel, complex-weighted, decision-aided, maximum-likelihood (CW-DA-ML) carrier phase and frequency offset estimator. The CW-DA-ML carrier estimator uses a CW transversal filter to generate a carrier reference phasor, and the filter weights are automatically adapted on-line by linear regression on the observed signals. A complete modulo-R reduced frequency offset estimation (FOE) range of ±R/2 is achieved, independent of modulation format, where R is the symbol rate. Carrier phase and frequency tracking is achieved rapidly. The acquisition speed of frequency offset in quaternary phase-shift keying (4-PSK) signals is more than 5 times faster than that of differential FOE. A constant penalty of approximately 1 dB at bit-error rate of 10−4 is demonstrated for all frequency offsets in 4-PSK signals with laser-linewidth-symbol-duration product of 8×10−5.

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References

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  1. F. Derr, “Coherent optical QPSK intradyne system: concept and digital receiver realization,” J. Lightwave Technol.10(9), 1290–1296 (1992).
    [CrossRef]
  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(1), 12–21 (2006).
    [CrossRef]
  3. P. Y. Kam, “Maximum likelihood carrier phase recovery for linear suppressed-carrier digital data modulations,” IEEE Trans. Commun.34(6), 522–527 (1986).
    [CrossRef]
  4. S. Zhang, P. Y. Kam, J. Chen, and C. Yu, “Decision-aided maximum likelihood detection in coherent optical phase-shift-keying system,” Opt. Express17(2), 703–715 (2009).
    [CrossRef] [PubMed]
  5. “Integrable Tunable Laser Assembly Multi Source Agreement,” OIF-ITLA-MSA-01.1 (Optical Internetworking Forum, Los Angeles, 2005).
  6. A. Meiyappan, P. Y. Kam, and H. Kim, “Performance of decision-aided maximum-likelihood carrier phase estimation with frequency offset,” in Proc. OFC/NFOEC, Los Angeles, CA, 2012, paper OTu2G.6.
  7. A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett.19(6), 366–368 (2007).
    [CrossRef]
  8. W. J. Weber, “Differential encoding for multiple amplitude and phase shift keying systems,” IEEE Trans. Commun.26(3), 385–391 (1978).
    [CrossRef]
  9. K.-P. Ho, Phase-modulated Optical Communication (Springer, 2005).
  10. P. Y. Kam, S. S. Ng, and T. S. Ng, “Optimum symbol-by-symbol detection of uncoded digital data over the Gaussian channel with unknown carrier phase,” IEEE Trans. Commun.42(8), 2543–2552 (1994).
    [CrossRef]
  11. P. Y. Kam, K. H. Chua, and X. Yu, “Adaptive symbol-by-symbol reception of MPSK on the Gaussian channel with unknown carrier phase characteristics,” IEEE Trans. Commun.46(10), 1275–1279 (1998).
    [CrossRef]
  12. J. G. Proakis, Digital Communications (McGraw-Hill, 2008).
  13. U. Mengali and A. N. D' Andrea, Synchronization Techniques for Digital Receivers (Plenum Press, 1997).
  14. H. Meyr, M. Moeneclaey, and S. Fechtel, Digital Communication Receivers (John Wiley, 1997).
  15. T. Pfau, S. Hoffmann, and R. Noe, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightwave Technol.27(8), 989–999 (2009).
    [CrossRef]

2009

2007

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett.19(6), 366–368 (2007).
[CrossRef]

2006

1998

P. Y. Kam, K. H. Chua, and X. Yu, “Adaptive symbol-by-symbol reception of MPSK on the Gaussian channel with unknown carrier phase characteristics,” IEEE Trans. Commun.46(10), 1275–1279 (1998).
[CrossRef]

1994

P. Y. Kam, S. S. Ng, and T. S. Ng, “Optimum symbol-by-symbol detection of uncoded digital data over the Gaussian channel with unknown carrier phase,” IEEE Trans. Commun.42(8), 2543–2552 (1994).
[CrossRef]

1992

F. Derr, “Coherent optical QPSK intradyne system: concept and digital receiver realization,” J. Lightwave Technol.10(9), 1290–1296 (1992).
[CrossRef]

1986

P. Y. Kam, “Maximum likelihood carrier phase recovery for linear suppressed-carrier digital data modulations,” IEEE Trans. Commun.34(6), 522–527 (1986).
[CrossRef]

1978

W. J. Weber, “Differential encoding for multiple amplitude and phase shift keying systems,” IEEE Trans. Commun.26(3), 385–391 (1978).
[CrossRef]

Chen, J.

Chen, Y.-K.

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett.19(6), 366–368 (2007).
[CrossRef]

Chua, K. H.

P. Y. Kam, K. H. Chua, and X. Yu, “Adaptive symbol-by-symbol reception of MPSK on the Gaussian channel with unknown carrier phase characteristics,” IEEE Trans. Commun.46(10), 1275–1279 (1998).
[CrossRef]

Derr, F.

F. Derr, “Coherent optical QPSK intradyne system: concept and digital receiver realization,” J. Lightwave Technol.10(9), 1290–1296 (1992).
[CrossRef]

Hoffmann, S.

Kam, P. Y.

S. Zhang, P. Y. Kam, J. Chen, and C. Yu, “Decision-aided maximum likelihood detection in coherent optical phase-shift-keying system,” Opt. Express17(2), 703–715 (2009).
[CrossRef] [PubMed]

P. Y. Kam, K. H. Chua, and X. Yu, “Adaptive symbol-by-symbol reception of MPSK on the Gaussian channel with unknown carrier phase characteristics,” IEEE Trans. Commun.46(10), 1275–1279 (1998).
[CrossRef]

P. Y. Kam, S. S. Ng, and T. S. Ng, “Optimum symbol-by-symbol detection of uncoded digital data over the Gaussian channel with unknown carrier phase,” IEEE Trans. Commun.42(8), 2543–2552 (1994).
[CrossRef]

P. Y. Kam, “Maximum likelihood carrier phase recovery for linear suppressed-carrier digital data modulations,” IEEE Trans. Commun.34(6), 522–527 (1986).
[CrossRef]

Kaneda, N.

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett.19(6), 366–368 (2007).
[CrossRef]

Katoh, K.

Kikuchi, K.

Koc, U.-V.

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett.19(6), 366–368 (2007).
[CrossRef]

Leven, A.

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett.19(6), 366–368 (2007).
[CrossRef]

Ly-Gagnon, D. S.

Ng, S. S.

P. Y. Kam, S. S. Ng, and T. S. Ng, “Optimum symbol-by-symbol detection of uncoded digital data over the Gaussian channel with unknown carrier phase,” IEEE Trans. Commun.42(8), 2543–2552 (1994).
[CrossRef]

Ng, T. S.

P. Y. Kam, S. S. Ng, and T. S. Ng, “Optimum symbol-by-symbol detection of uncoded digital data over the Gaussian channel with unknown carrier phase,” IEEE Trans. Commun.42(8), 2543–2552 (1994).
[CrossRef]

Noe, R.

Pfau, T.

Tsukamoto, S.

Weber, W. J.

W. J. Weber, “Differential encoding for multiple amplitude and phase shift keying systems,” IEEE Trans. Commun.26(3), 385–391 (1978).
[CrossRef]

Yu, C.

Yu, X.

P. Y. Kam, K. H. Chua, and X. Yu, “Adaptive symbol-by-symbol reception of MPSK on the Gaussian channel with unknown carrier phase characteristics,” IEEE Trans. Commun.46(10), 1275–1279 (1998).
[CrossRef]

Zhang, S.

IEEE Photon. Technol. Lett.

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett.19(6), 366–368 (2007).
[CrossRef]

IEEE Trans. Commun.

W. J. Weber, “Differential encoding for multiple amplitude and phase shift keying systems,” IEEE Trans. Commun.26(3), 385–391 (1978).
[CrossRef]

P. Y. Kam, S. S. Ng, and T. S. Ng, “Optimum symbol-by-symbol detection of uncoded digital data over the Gaussian channel with unknown carrier phase,” IEEE Trans. Commun.42(8), 2543–2552 (1994).
[CrossRef]

P. Y. Kam, K. H. Chua, and X. Yu, “Adaptive symbol-by-symbol reception of MPSK on the Gaussian channel with unknown carrier phase characteristics,” IEEE Trans. Commun.46(10), 1275–1279 (1998).
[CrossRef]

P. Y. Kam, “Maximum likelihood carrier phase recovery for linear suppressed-carrier digital data modulations,” IEEE Trans. Commun.34(6), 522–527 (1986).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Other

J. G. Proakis, Digital Communications (McGraw-Hill, 2008).

U. Mengali and A. N. D' Andrea, Synchronization Techniques for Digital Receivers (Plenum Press, 1997).

H. Meyr, M. Moeneclaey, and S. Fechtel, Digital Communication Receivers (John Wiley, 1997).

K.-P. Ho, Phase-modulated Optical Communication (Springer, 2005).

“Integrable Tunable Laser Assembly Multi Source Agreement,” OIF-ITLA-MSA-01.1 (Optical Internetworking Forum, Los Angeles, 2005).

A. Meiyappan, P. Y. Kam, and H. Kim, “Performance of decision-aided maximum-likelihood carrier phase estimation with frequency offset,” in Proc. OFC/NFOEC, Los Angeles, CA, 2012, paper OTu2G.6.

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Figures (5)

Fig. 1
Fig. 1

Phase and polarization diversity intradyne coherent receiver. LO: local oscillator, PBS: polarization beam splitter

Fig. 2
Fig. 2

Adaptation of arg( w ^ l ( k ) ) from Eq. (6) in one sample simulation run.

Fig. 3
Fig. 3

Ensemble-average squared error curves with three different ∆f and SNR values.

Fig. 4
Fig. 4

BER curves of block Mth power, DA-ML, and CW-DA-ML CE with different frequency offsets for (a) 4-PSK, and (b) 8-PSK.

Fig. 5
Fig. 5

FOE range of block Mth power CE, DA-ML CE, differential FOE, and CW-DA-ML CE for (a) 4-PSK, and (b) 8-PSK. Insets show enlarged sections of the frequency offset axis.

Tables (1)

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Table 1 Symbol-by-symbol receiver employing CW-DA-ML CE

Equations (9)

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r( k )= i I ( k )+j i Q ( k ) =χ P r P LO e j( 2πΔfTk+ϕ( k )+θ( k ) ) +χ P LO n ( k ) e j( 2πΔfTk θ LO ( k ) ) + i sh
r( k )=m( k ) e j( 2πΔfTk+θ( k ) ) +n( k ),k=0,1,2,
V( k+1 )=C( k ) l=1 L r( kl+1 ) m ^ *( kl+1 )
V ( k+1 )=C( k ) l=1 L w l ( k )r( kl+1 ) m ^ *( kl+1 )
J( k )= l=1 k | e( l ) | 2 = l=1 k | r( l ) m ^ ( l ) C( l1 ) w T ( k )y( l1 ) | 2
w ^ ( k )= Φ 1 ( k )z( k ),k1
m ^ ( k )= argmin 0iM1 | r( k ) V *( k ) S i |.
m ^ ( k )= argmin 0iM1 ( | r( k ) V *( k ) | 2 + | S i | 2 Re[ 2r( k ) V *( k ) S i * ] ) = argmin 0iM1 ( | S i | 2 Re[ 2r( k ) V *( k ) S i * ] ) = argmax 0iM1 Re[ r( k ) V *( k ) S i * 1 2 | S i | 2 ].
J ( k )=Ε [ | n( k ) m( k ) | 2 + | e j( Δωk+θ( k ) ) V ( k ) | 2 +( e j( Δωk+θ( k ) ) V ( k ) ) ( n( k ) m( k ) ) * + ( e j( Δωk+θ( k ) ) V ( k ) ) * ( n( k ) m( k ) ) ].

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