Abstract

We propose a novel frequency-domain adaptive equalizer in digital coherent optical receivers, which can reduce computational complexity of the conventional time-domain adaptive equalizer based on finite-impulse-response (FIR) filters. The proposed equalizer can operate on the input sequence sampled by free-running analog-to-digital converters (ADCs) at the rate of two samples per symbol; therefore, the arbitrary initial sampling phase of ADCs can be adjusted so that the best symbol-spaced sequence is produced. The equalizer can also be configured in the butterfly structure, which enables demultiplexing of polarization tributaries apart from equalization of linear transmission impairments. The performance of the proposed equalization scheme is verified by 40-Gbits/s dual-polarization quadrature phase-shift keying (QPSK) transmission experiments.

© 2011 OSA

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  1. K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation,” IEEE J. Sel. Top. Quantum Electron. 12(4), 563–570 (2006).
    [CrossRef]
  2. K. Kikuchi, “Coherent optical communications: historical perspectives and future directions,” in High Spectral Density Optical Communication Technology, M. Nakazawa, K. Kikuchi, and T. Miyazaki, eds (Springer, 2010), Chap. 2.
  3. C. R. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E.-D. Schmidt, T. Wuth, J. Geyer, E. De Man, Khoe Giok-Djan, and H. de Waardt, “Coherent equalization and POLMUX-RZ-DQPSK for robust 100-GE transmission,” J. Lightwave Technol. 26(1), 64–72 (2008).
    [CrossRef]
  4. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008).
    [CrossRef] [PubMed]
  5. K. Kikuchi, “Clock recovering characteristics of adaptive finite-impulse-response filters in digital coherent optical receivers,” Opt. Express 19(6), 5611–5619 (2011).
    [CrossRef] [PubMed]
  6. K. Roberts, M. O’Sullivan, Kuang-Tsan Wu, A. Han Sun, D. J. Awadalla, Krause, and C. Laperle, “Performance of dual-polarization QPSK for optical transport system,” J. Lightwave Technol. 27(16), 3546–3559 (2009).
    [CrossRef]
  7. B. Spinnler, “Equalizer design and complexity for digital coherent receivers,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1180–1192 (2010).
    [CrossRef]
  8. J. Leibrich and W. Rosenkranz, “Frequency domain equalization with minimum complexity in coherent optical transmission systems,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2010), paper OWV1.
  9. M. Selmi, P. Ciblat, Y. Jaouen, and C. Gosset, “Block versus adaptive MIMO equalization for coherent PolMux QAM transmission system,” in Proceedings of European Conference on Optical Communication (2010), paper Th.9.A.5.
  10. J. C. Geyer, C. R. S. Fludger, T. Duthel, C. Schulien, and B. Schmauss, “Efficient frequency domain chromatic dispersion compensation in a coherent polmux QPSK-receiver,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2010), paper OWV5.
  11. R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightwave Technol. 27(16), 3721–3728 (2009).
    [CrossRef]
  12. M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, A. Napoli, and B. Lankl, “Adaptive chromatic dispersion equalization for non-dispersion managed coherent systems,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2009), paper OMT1.
  13. R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, E. Yamada, H. Masuda, and Y. Miyamoto, “PMD compensation in optical coherent single carrier transmission using frequency-domain equalization,” Electron. Lett. 45(2), 124–125 (2009).
    [CrossRef]
  14. K. Ishihara, T. Kobayashi, R. Kudo, Y. Takatori, A. Sano, and Y. Miyamoto, “Frequency-domain equalization for coherent optical single-carrier transmission systems,” IEICE Trans. Commun. E92-B(12), 3736–3743 (2009).
    [CrossRef]
  15. J. J. Shynk, “Frequency-domain and multirate adaptive filtering,” IEEE Signal Process. Mag. 9(1), 14–37 (1992).
    [CrossRef]
  16. S. Haykin, Adaptive Filter Theory, 3rd ed., (Prentice Hall, 2001).
  17. Md. S. Faruk, Y. Mori, C. Zhang, and K. Kikuchi, “Proper polarization demultiplexing in coherent optical receiver using constant modulus algorithm with training mode,” in Proceedings of Optoelectronics and Communication Conference (2010), paper 9B3–3.
  18. 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]

2011 (1)

2010 (1)

B. Spinnler, “Equalizer design and complexity for digital coherent receivers,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1180–1192 (2010).
[CrossRef]

2009 (4)

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightwave Technol. 27(16), 3721–3728 (2009).
[CrossRef]

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, E. Yamada, H. Masuda, and Y. Miyamoto, “PMD compensation in optical coherent single carrier transmission using frequency-domain equalization,” Electron. Lett. 45(2), 124–125 (2009).
[CrossRef]

K. Ishihara, T. Kobayashi, R. Kudo, Y. Takatori, A. Sano, and Y. Miyamoto, “Frequency-domain equalization for coherent optical single-carrier transmission systems,” IEICE Trans. Commun. E92-B(12), 3736–3743 (2009).
[CrossRef]

K. Roberts, M. O’Sullivan, Kuang-Tsan Wu, A. Han Sun, D. J. Awadalla, Krause, and C. Laperle, “Performance of dual-polarization QPSK for optical transport system,” J. Lightwave Technol. 27(16), 3546–3559 (2009).
[CrossRef]

2008 (2)

2006 (2)

K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation,” IEEE J. Sel. Top. Quantum Electron. 12(4), 563–570 (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(1), 12–21 (2006).
[CrossRef]

1992 (1)

J. J. Shynk, “Frequency-domain and multirate adaptive filtering,” IEEE Signal Process. Mag. 9(1), 14–37 (1992).
[CrossRef]

Awadalla, D. J.

De Man, E.

de Waardt, H.

Duthel, T.

Fludger, C. R. S.

Geyer, J.

Han Sun, A.

Ishihara, K.

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightwave Technol. 27(16), 3721–3728 (2009).
[CrossRef]

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, E. Yamada, H. Masuda, and Y. Miyamoto, “PMD compensation in optical coherent single carrier transmission using frequency-domain equalization,” Electron. Lett. 45(2), 124–125 (2009).
[CrossRef]

K. Ishihara, T. Kobayashi, R. Kudo, Y. Takatori, A. Sano, and Y. Miyamoto, “Frequency-domain equalization for coherent optical single-carrier transmission systems,” IEICE Trans. Commun. E92-B(12), 3736–3743 (2009).
[CrossRef]

Katoh, K.

Khoe Giok-Djan,

Kikuchi, K.

Kobayashi, T.

K. Ishihara, T. Kobayashi, R. Kudo, Y. Takatori, A. Sano, and Y. Miyamoto, “Frequency-domain equalization for coherent optical single-carrier transmission systems,” IEICE Trans. Commun. E92-B(12), 3736–3743 (2009).
[CrossRef]

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, E. Yamada, H. Masuda, and Y. Miyamoto, “PMD compensation in optical coherent single carrier transmission using frequency-domain equalization,” Electron. Lett. 45(2), 124–125 (2009).
[CrossRef]

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightwave Technol. 27(16), 3721–3728 (2009).
[CrossRef]

Krause,

Kuang-Tsan Wu,

Kudo, R.

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightwave Technol. 27(16), 3721–3728 (2009).
[CrossRef]

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, E. Yamada, H. Masuda, and Y. Miyamoto, “PMD compensation in optical coherent single carrier transmission using frequency-domain equalization,” Electron. Lett. 45(2), 124–125 (2009).
[CrossRef]

K. Ishihara, T. Kobayashi, R. Kudo, Y. Takatori, A. Sano, and Y. Miyamoto, “Frequency-domain equalization for coherent optical single-carrier transmission systems,” IEICE Trans. Commun. E92-B(12), 3736–3743 (2009).
[CrossRef]

Laperle, C.

Ly-Gagnon, D.-S.

Masuda, H.

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, E. Yamada, H. Masuda, and Y. Miyamoto, “PMD compensation in optical coherent single carrier transmission using frequency-domain equalization,” Electron. Lett. 45(2), 124–125 (2009).
[CrossRef]

Miyamoto, Y.

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, E. Yamada, H. Masuda, and Y. Miyamoto, “PMD compensation in optical coherent single carrier transmission using frequency-domain equalization,” Electron. Lett. 45(2), 124–125 (2009).
[CrossRef]

K. Ishihara, T. Kobayashi, R. Kudo, Y. Takatori, A. Sano, and Y. Miyamoto, “Frequency-domain equalization for coherent optical single-carrier transmission systems,” IEICE Trans. Commun. E92-B(12), 3736–3743 (2009).
[CrossRef]

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightwave Technol. 27(16), 3721–3728 (2009).
[CrossRef]

O’Sullivan, M.

Roberts, K.

Sano, A.

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightwave Technol. 27(16), 3721–3728 (2009).
[CrossRef]

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, E. Yamada, H. Masuda, and Y. Miyamoto, “PMD compensation in optical coherent single carrier transmission using frequency-domain equalization,” Electron. Lett. 45(2), 124–125 (2009).
[CrossRef]

K. Ishihara, T. Kobayashi, R. Kudo, Y. Takatori, A. Sano, and Y. Miyamoto, “Frequency-domain equalization for coherent optical single-carrier transmission systems,” IEICE Trans. Commun. E92-B(12), 3736–3743 (2009).
[CrossRef]

Savory, S. J.

Schmidt, E.-D.

Schulien, C.

Shynk, J. J.

J. J. Shynk, “Frequency-domain and multirate adaptive filtering,” IEEE Signal Process. Mag. 9(1), 14–37 (1992).
[CrossRef]

Spinnler, B.

B. Spinnler, “Equalizer design and complexity for digital coherent receivers,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1180–1192 (2010).
[CrossRef]

Takatori, Y.

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightwave Technol. 27(16), 3721–3728 (2009).
[CrossRef]

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, E. Yamada, H. Masuda, and Y. Miyamoto, “PMD compensation in optical coherent single carrier transmission using frequency-domain equalization,” Electron. Lett. 45(2), 124–125 (2009).
[CrossRef]

K. Ishihara, T. Kobayashi, R. Kudo, Y. Takatori, A. Sano, and Y. Miyamoto, “Frequency-domain equalization for coherent optical single-carrier transmission systems,” IEICE Trans. Commun. E92-B(12), 3736–3743 (2009).
[CrossRef]

Tsukamoto, S.

van den Borne, D.

Wuth, T.

Yamada, E.

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, E. Yamada, H. Masuda, and Y. Miyamoto, “PMD compensation in optical coherent single carrier transmission using frequency-domain equalization,” Electron. Lett. 45(2), 124–125 (2009).
[CrossRef]

Electron. Lett. (1)

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, E. Yamada, H. Masuda, and Y. Miyamoto, “PMD compensation in optical coherent single carrier transmission using frequency-domain equalization,” Electron. Lett. 45(2), 124–125 (2009).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation,” IEEE J. Sel. Top. Quantum Electron. 12(4), 563–570 (2006).
[CrossRef]

B. Spinnler, “Equalizer design and complexity for digital coherent receivers,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1180–1192 (2010).
[CrossRef]

IEEE Signal Process. Mag. (1)

J. J. Shynk, “Frequency-domain and multirate adaptive filtering,” IEEE Signal Process. Mag. 9(1), 14–37 (1992).
[CrossRef]

IEICE Trans. Commun. (1)

K. Ishihara, T. Kobayashi, R. Kudo, Y. Takatori, A. Sano, and Y. Miyamoto, “Frequency-domain equalization for coherent optical single-carrier transmission systems,” IEICE Trans. Commun. E92-B(12), 3736–3743 (2009).
[CrossRef]

J. Lightwave Technol. (4)

Opt. Express (2)

Other (7)

K. Kikuchi, “Coherent optical communications: historical perspectives and future directions,” in High Spectral Density Optical Communication Technology, M. Nakazawa, K. Kikuchi, and T. Miyazaki, eds (Springer, 2010), Chap. 2.

J. Leibrich and W. Rosenkranz, “Frequency domain equalization with minimum complexity in coherent optical transmission systems,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2010), paper OWV1.

M. Selmi, P. Ciblat, Y. Jaouen, and C. Gosset, “Block versus adaptive MIMO equalization for coherent PolMux QAM transmission system,” in Proceedings of European Conference on Optical Communication (2010), paper Th.9.A.5.

J. C. Geyer, C. R. S. Fludger, T. Duthel, C. Schulien, and B. Schmauss, “Efficient frequency domain chromatic dispersion compensation in a coherent polmux QPSK-receiver,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2010), paper OWV5.

S. Haykin, Adaptive Filter Theory, 3rd ed., (Prentice Hall, 2001).

Md. S. Faruk, Y. Mori, C. Zhang, and K. Kikuchi, “Proper polarization demultiplexing in coherent optical receiver using constant modulus algorithm with training mode,” in Proceedings of Optoelectronics and Communication Conference (2010), paper 9B3–3.

M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, A. Napoli, and B. Lankl, “Adaptive chromatic dispersion equalization for non-dispersion managed coherent systems,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2009), paper OMT1.

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Figures (4)

Fig. 1
Fig. 1

Schematic of the proposed adaptive FDE. S/P denotes a serial-to-parallel converter and P/S a parallel-to-serial converter.

Fig. 2
Fig. 2

Schematics of the 40-Gbit/s QPSK transmission system for verifications of the proposed adaptive FDE.

Fig. 3
Fig. 3

BER characteristics of the proposed FDE and the conventional TDE adapted by CMA.

Fig. 4
Fig. 4

BER characteristics of the proposed FDE for 5 different sampling phases. These sampling phases are swept with an increment of 10% of the symbol interval.

Tables (1)

Tables Icon

Table 1 Computational Complexity of the Proposed FDE and the Conventional TDE Using FIR Filters Adapted by CMA When Use the Dual-Polarization QPSK Modulation Format

Equations (19)

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v x ( n ) = i = 0 N 1 h x x i ( n ) u x { ( n i ) T 2 } + i = 0 N 1 h x y i ( n ) u y { ( n i ) T 2 }  .
v x ( m ) = i = 0 N 1 h x x i ( m ) u x { ( 2 m + 1 i ) T 2 } + i = 0 N 1 h x y i ( m ) u y { ( 2 m + 1 i ) T 2 } = i = 0 N 1 h x x i ( m ) u x { ( m T i T 2 ) + T 2 } + i = 0 N 1 h x y i ( m ) u y { ( m T i T 2 ) + T 2 } = i = 0 N / 2 1 h x x 2 i ( m ) u x { ( m T 2 i T 2 ) + T 2 } + i = 0 N / 2 1 h x y 2 i ( m ) u y { ( m T 2 i T 2 ) + T 2 }         + i = 0 N / 2 1 h x x 2 i + 1 ( m ) u x { ( m T ( 2 i + 1 ) T 2 ) + T 2 } + i = 0 N / 2 1 h x y 2 i + 1 ( m ) u y { ( m T ( 2 i + 1 ) T 2 ) + T 2 } = i = 0 N / 2 1 h x x 2 i ( m ) u x { ( m i ) T + T 2 } + i = 0 N / 2 1 h x y 2 i ( m ) u y { ( m i ) T + T 2 }         + i = 0 N / 2 1 h x x 2 i + 1 ( m ) u x { ( m i ) T + T } + i = 0 N / 2 1 h x y 2 i + 1 ( m ) u y { ( m i ) T + T }  .
v x ( m ) = h x x e ( m ) * u x e ( m ) + h x y e ( m ) * u y e ( m ) + h x x o ( m ) * u x o ( m ) + h x y o ( m ) * u y o ( m )  ,
v y ( m ) = h y x e ( m ) u x e ( m ) + h y y e ( m ) u y e ( m ) + h y x o ( m ) u x o ( m ) + h y y o ( m ) u y o ( m )  ,
u x , y e ( m ) = [ u x , y ( 2 m ) , u x , y ( 2 m 2 ) , u x , y ( 2 m 4 ) , , u x , y ( 2 m 2 L ) ] T  ,
u x , y o ( m ) = [ u x , y ( 2 m + 1 ) , u x , y ( 2 m 1 ) , u x , y ( 2 m 3 ) , , u x , y ( 2 m 2 L + 1 ) ] T   .
h p q e ( m ) = [ h p q 0 ( m ) , h p q 2 ( m ) , h p q 2 L 2 ( m ) ] T ,
h p q o ( m ) = [ h p q 1 ( m ) , h p q 3 ( m ) , h p q 2 L 1 ( m ) ] T ,
V x ( k ) = H x x e ( k ) U x e ( k ) + H x x o ( k ) U x o ( k ) + H x y e ( k ) U y e ( k ) + H x y o ( k ) U y o ( k )  ,
V y ( k ) = H y x e ( k ) U x e ( k ) + H y x o ( k ) U x o ( k ) + H y y e ( k ) U y e ( k ) + H y y o ( k ) U y o ( k ) ,
U x , y e , o ( k ) = FFT [ u x , y e , o ( k L L ) , , u x , y e , o ( k L + L 1 ) ] T ,
H p q e , o ( k ) = FFT [ h p q e , o ( k ) ; O L ] T .
v x , y ( k ) = last  L  elements of IFFT{ V x , y ( k ) } ,
e x , y ( k ) = [ I L v x , y ( k ) conj { v x , y ( k ) } ] v x , y ( k ) ,
E x , y ( k ) = FFT [ O L ; e x , y ( k ) ] T   .
p q e , o ( k ) = first  L  terms of IFFT [ E p conj { U q e , o ( k ) } ] T   .
H p q e , o ( k + 1 ) = H p q e , o ( k ) + μ FFT [ p q e , o ( k ) ; O L ] T ,
C TDE = 6 N + 2 log 2 ( M ) ,
C FDE = 12 log 2 ( N ) + 10 log 2 ( M ) .

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