Abstract

We analyze the clock-recovery process based on adaptive finite-impulse-response (FIR) filtering in digital coherent optical receivers. When the clock frequency is synchronized between the transmitter and the receiver, only five taps in half-symbol-spaced FIR filters can adjust the sampling phase of analog-to-digital conversion optimally, enabling bit-error rate performance independent of the initial sampling phase. Even if the clock frequency is not synchronized between them, the clock-frequency misalignment can be adjusted within an appropriate block interval; thus, we can achieve an asynchronous clock mode of operation of digital coherent receivers with block processing of the symbol sequence.

© 2011 Optical Society of America

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References

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  1. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16, 804–817 (2008).
    [Crossref] [PubMed]
  2. K. Kikuchi, High Spectral Density Optical Communication Technologies, edited by M. Nakazawa, K. Kikuchi, and T. Miyazaki (Springer, 2010), Chap. 2.
  3. K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation of with digital carrier phase estimation,” IEEE J. Sel. Top. Quantum Electron. 12, 563–570 (2006).
    [Crossref]
  4. D. N. Godard, “Self-recovering equalization and carrier tracking in two-dimensional data communication systems,” IEEE Trans. Commun. 28, 1867–1875 (1980).
    [Crossref]
  5. S. U. H. Qureshi, “Adaptive equalization,” IEEE Proc.  73, 1349–1387 (1985).
    [Crossref]
  6. G. Ungerboeck, “Fractional tap-spacing equalizer and consequences for clock recovery in data modems,” IEEE Trans. Commun. 24, 856–864 (1976).
    [Crossref]
  7. C. W. Farrow, “A continuously variable digital delay element,” in IEEE International Symposium on Circuits and Systems, Espoo, Finland, 2641–2645 (1988).
  8. H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing, 2nd ed. (Wiley-Interscience, 1997).
  9. H. M. Nguyen, K. Igarashi, K. Katoh, and K. Kikuchi, “Continuously-tunable optical delay line using PLC-based optical FIR filter,” in Conference on Lasers and Electro-Optics (CLEO 2010), San Jose, CA, USA, CFE2 (2010).
  10. Md. S. Faruk, Y. Mori, C. Zhang, K. Igarashi, and K. Kikuchi, “Multi-impairment monitoring from adaptive finite-impulse-response filters in a digital coherent receiver,” Opt. Express 18, 26929–26936 (2010).
    [Crossref]
  11. K. Kikuchi, “Polarization-demultiplexing algorithm in the digital coherent receiver,” in IEEE LEOS Summer Topical Meeting, Acapulco, Mexico, MC2.2 (2008).
  12. G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett. 22, 1129–1131 (2010).
    [Crossref]
  13. ITU-T Recommendation G.8251, “The control of jitter and wander within the optical transport network (OTN).”

2010 (2)

Md. S. Faruk, Y. Mori, C. Zhang, K. Igarashi, and K. Kikuchi, “Multi-impairment monitoring from adaptive finite-impulse-response filters in a digital coherent receiver,” Opt. Express 18, 26929–26936 (2010).
[Crossref]

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett. 22, 1129–1131 (2010).
[Crossref]

2008 (1)

2006 (1)

K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation of with digital carrier phase estimation,” IEEE J. Sel. Top. Quantum Electron. 12, 563–570 (2006).
[Crossref]

1985 (1)

S. U. H. Qureshi, “Adaptive equalization,” IEEE Proc.  73, 1349–1387 (1985).
[Crossref]

1980 (1)

D. N. Godard, “Self-recovering equalization and carrier tracking in two-dimensional data communication systems,” IEEE Trans. Commun. 28, 1867–1875 (1980).
[Crossref]

1976 (1)

G. Ungerboeck, “Fractional tap-spacing equalizer and consequences for clock recovery in data modems,” IEEE Trans. Commun. 24, 856–864 (1976).
[Crossref]

Bosco, G.

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett. 22, 1129–1131 (2010).
[Crossref]

Carena, A.

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett. 22, 1129–1131 (2010).
[Crossref]

Curri, V.

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett. 22, 1129–1131 (2010).
[Crossref]

Farrow, C. W.

C. W. Farrow, “A continuously variable digital delay element,” in IEEE International Symposium on Circuits and Systems, Espoo, Finland, 2641–2645 (1988).

Faruk, Md. S.

Fechtel, S. A.

H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing, 2nd ed. (Wiley-Interscience, 1997).

Forghieri, F.

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett. 22, 1129–1131 (2010).
[Crossref]

Godard, D. N.

D. N. Godard, “Self-recovering equalization and carrier tracking in two-dimensional data communication systems,” IEEE Trans. Commun. 28, 1867–1875 (1980).
[Crossref]

Igarashi, K.

Md. S. Faruk, Y. Mori, C. Zhang, K. Igarashi, and K. Kikuchi, “Multi-impairment monitoring from adaptive finite-impulse-response filters in a digital coherent receiver,” Opt. Express 18, 26929–26936 (2010).
[Crossref]

H. M. Nguyen, K. Igarashi, K. Katoh, and K. Kikuchi, “Continuously-tunable optical delay line using PLC-based optical FIR filter,” in Conference on Lasers and Electro-Optics (CLEO 2010), San Jose, CA, USA, CFE2 (2010).

Katoh, K.

H. M. Nguyen, K. Igarashi, K. Katoh, and K. Kikuchi, “Continuously-tunable optical delay line using PLC-based optical FIR filter,” in Conference on Lasers and Electro-Optics (CLEO 2010), San Jose, CA, USA, CFE2 (2010).

Kikuchi, K.

Md. S. Faruk, Y. Mori, C. Zhang, K. Igarashi, and K. Kikuchi, “Multi-impairment monitoring from adaptive finite-impulse-response filters in a digital coherent receiver,” Opt. Express 18, 26929–26936 (2010).
[Crossref]

K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation of with digital carrier phase estimation,” IEEE J. Sel. Top. Quantum Electron. 12, 563–570 (2006).
[Crossref]

K. Kikuchi, High Spectral Density Optical Communication Technologies, edited by M. Nakazawa, K. Kikuchi, and T. Miyazaki (Springer, 2010), Chap. 2.

H. M. Nguyen, K. Igarashi, K. Katoh, and K. Kikuchi, “Continuously-tunable optical delay line using PLC-based optical FIR filter,” in Conference on Lasers and Electro-Optics (CLEO 2010), San Jose, CA, USA, CFE2 (2010).

K. Kikuchi, “Polarization-demultiplexing algorithm in the digital coherent receiver,” in IEEE LEOS Summer Topical Meeting, Acapulco, Mexico, MC2.2 (2008).

Meyr, H.

H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing, 2nd ed. (Wiley-Interscience, 1997).

Moeneclaey, M.

H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing, 2nd ed. (Wiley-Interscience, 1997).

Mori, Y.

Nguyen, H. M.

H. M. Nguyen, K. Igarashi, K. Katoh, and K. Kikuchi, “Continuously-tunable optical delay line using PLC-based optical FIR filter,” in Conference on Lasers and Electro-Optics (CLEO 2010), San Jose, CA, USA, CFE2 (2010).

Poggiolini, P.

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett. 22, 1129–1131 (2010).
[Crossref]

Qureshi, S. U. H.

S. U. H. Qureshi, “Adaptive equalization,” IEEE Proc.  73, 1349–1387 (1985).
[Crossref]

Savory, S. J.

Ungerboeck, G.

G. Ungerboeck, “Fractional tap-spacing equalizer and consequences for clock recovery in data modems,” IEEE Trans. Commun. 24, 856–864 (1976).
[Crossref]

Zhang, C.

IEEE J. Sel. Top. Quantum Electron. (1)

K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation of with digital carrier phase estimation,” IEEE J. Sel. Top. Quantum Electron. 12, 563–570 (2006).
[Crossref]

IEEE Photon. Technol. Lett. (1)

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett. 22, 1129–1131 (2010).
[Crossref]

IEEE Proc (1)

S. U. H. Qureshi, “Adaptive equalization,” IEEE Proc.  73, 1349–1387 (1985).
[Crossref]

IEEE Trans. Commun. (2)

G. Ungerboeck, “Fractional tap-spacing equalizer and consequences for clock recovery in data modems,” IEEE Trans. Commun. 24, 856–864 (1976).
[Crossref]

D. N. Godard, “Self-recovering equalization and carrier tracking in two-dimensional data communication systems,” IEEE Trans. Commun. 28, 1867–1875 (1980).
[Crossref]

Opt. Express (2)

Other (6)

K. Kikuchi, High Spectral Density Optical Communication Technologies, edited by M. Nakazawa, K. Kikuchi, and T. Miyazaki (Springer, 2010), Chap. 2.

ITU-T Recommendation G.8251, “The control of jitter and wander within the optical transport network (OTN).”

C. W. Farrow, “A continuously variable digital delay element,” in IEEE International Symposium on Circuits and Systems, Espoo, Finland, 2641–2645 (1988).

H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing, 2nd ed. (Wiley-Interscience, 1997).

H. M. Nguyen, K. Igarashi, K. Katoh, and K. Kikuchi, “Continuously-tunable optical delay line using PLC-based optical FIR filter,” in Conference on Lasers and Electro-Optics (CLEO 2010), San Jose, CA, USA, CFE2 (2010).

K. Kikuchi, “Polarization-demultiplexing algorithm in the digital coherent receiver,” in IEEE LEOS Summer Topical Meeting, Acapulco, Mexico, MC2.2 (2008).

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Figures (5)

Fig. 1
Fig. 1 Bit-error rates calculated as a function of Eb/N0 for eight initial sampling phases when we apply Nyquist-rate sampling. Numbers of taps are 5 in (a), 17 in (b), and 65 in (c) and (d). In (a), (b), and (c), the roll-off parameter of the Nyquist filter α is 0, whereas in (d), α = 0.2. Red and black curves correspond to the x-polarization tributary and y-polarization tributary, respectively.

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Fig. 3
Fig. 3 Data structure in the asynchronous clock mode of operation. The symbol sequence consists of blocks containing training sequences at the head and null sequences at the tail.

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Fig. 2
Fig. 2 Bit-error rates calculated as a function of Eb/N0 for four initial sampling phases when we apply ×2 oversampling. Numbers of taps are 1 in (a), 3 in (b), and 5 in (c). In all cases, the roll-off parameter of the Nyquist filter α is 0.2. Red and black curves correspond to the x-polarization tributary and y-polarization tributary, respectively.

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Fig. 4
Fig. 4 Successful asynchronous clock mode of operation when the clock-frequency detuning is 2−12, the block length 213 symbols, and the tap length of FIR filters 9. (a): Bit-error rates as a function of Eb/N0. (b): The magnitude of error in the DD-LMS algorithm as a function of the symbol number. Red and black curves correspond to the x-polarization tributary and y-polarization tributary, respectively.

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Fig. 5
Fig. 5 Example of failed asynchronous clock mode of operation when the clock-frequency detuning is 2−12, the block length is increased to 214 symbols, and the tap length of FIR filters is kept at 9. (a): Bit-error rates as a function of Eb/N0. (b): The magnitude of error in the DD-LMS algorithm as a function of the symbol number. Red and black curves correspond to the x-polarization tributary and y-polarization tributary, respectively.

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Equations (14)

Equations on this page are rendered with MathJax. Learn more.

H ( ω ) = D ( ω ) U ( ω ) T K ,
H e q ( ω ) ≃ H ( ω ) − 1 = [ h x x ( ω ) h x y ( ω ) h y x ( ω ) h y y ( ω ) ] .
x → ( n ) = [ x ( n ) , x ( n − 1 ) , ⋯ , x ( n − k − 2 ) , x ( n − k − 1 ) ] T ,
y → ( n ) = [ x ( n ) , x ( n − 1 ) , ⋯ , x ( n − k − 2 ) , x ( n − k − 1 ) ] T .
h p → ( n ) = [ h p , 0 ( n ) , h p , 1 ( n ) , ⋯ , h p , ( k − 2 ) ( n ) , h p , ( k − 1 ) ( n ) ] T .
X ( n ) = h x x → ( n ) T x → ( n ) + h x y → ( n ) T y → ( n ) ,
Y ( n ) = h y x → ( n ) T x → ( n ) + h y y → ( n ) T y → ( n ) .
h x x → ( n + 1 ) = h x x → ( n ) + μ e X ( n ) x → ( n ) * ,
h x y → ( n + 1 ) = h x y → ( n ) + μ e X ( n ) y → ( n ) * ,
e X ( n ) = d X ( n ) − X ( n ) ,
h y x → ( n + 1 ) = h y x → ( n ) + μ e Y ( n ) x → ( n ) * ,
h y y → ( n + 1 ) = h y y → ( n ) + μ e Y ( n ) y → ( n ) * ,
e Y ( n ) = d Y ( n ) − Y ( n ) .
R ( ω ) = { 1 ⋯ 0 ≤ | ω T 2 π | < 1 − α 2 1 2 { 1 − sin [ π 2 α ( ω T π − 1 ) ] } ⋯ 1 − α 2 ≤ | ω T 2 π | < 1 + α 2 0 ⋯ 1 + α 2 ≤ | ω T 2 π | .

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