Abstract

We present a comparative analysis of three popular digital filters for chromatic dispersion compensation: a time-domain least mean square adaptive filter, a time-domain fiber dispersion finite impulse response filter, and a frequency-domain blind look-up filter. The filters are applied to equalize the chromatic dispersion in a 112-Gbit/s non-return-to-zero polarization division multiplexed quadrature phase shift keying transmission system. The characteristics of these filters are compared by evaluating their applicability for different fiber lengths, their usability for dispersion perturbations, and their computational complexity. In addition, the phase noise tolerance of these filters is also analyzed.

© 2010 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
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  13. M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, M. S. Alfiad, A. Napoli, and B. Lankl, “DSP for coherent single-carrier receivers,” J. Lightwave Technol. 27(16), 3614–3622 (2009).
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    [CrossRef]
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  22. 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).
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  25. K. Kikuchi, and S. Y. Kim, “Investigation of nonlinear impairment effects on optical quadrature phase-shift keying signals transmitted through a long-haul system,” in Proceedings of IEEE Laser and Electro-Optics Society Summer Topical Meetings (Acapulco, Mexico, 2008), pp. 131–132.
  26. G. Goldfarb, M. G. Taylor, and G. Li, “Experimental demonstration of fiber impairment compensation using the split-step finite-impulse-response filtering method,” IEEE Photon. Technol. Lett. 20(22), 1887–1889 (2008).
    [CrossRef]
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    [CrossRef]
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2010

M. Khafaji, H. Gustat, F. Ellinger, and C. Scheytt, “General time-domain representation of chromatic dispersion in single-mode fibers,” IEEE Photon. Technol. Lett. 22, 314–316 (2010).
[CrossRef]

T. Xu, G. Jacobsen, S. Popov, J. Li, K. Wang, and A. T. Friberg, “Normalized LMS digital filter for chromatic dispersion equalization in 112-Gbit/s PDM-QPSK coherent optical transmission system,” Opt. Commun. 283(6), 963–967 (2010).
[CrossRef]

2009

2008

2007

E. Ip and J. M. Kahn, “Digital equalization of chromatic dispersion and polarization mode dispersion,” J. Lightwave Technol. 25(8), 2033–2043 (2007).
[CrossRef]

G. Goldfarb and G. Li, “Chromatic dispersion compensation using digital IIR filtering with coherent detection,” IEEE Photon. Technol. Lett. 19(13), 969–971 (2007).
[CrossRef]

2005

2004

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. 16(2), 674–676 (2004).
[CrossRef]

1985

P. S. Henry, “Lightwave primer,” IEEE J. Quantum Electron. 21(12), 1862–1879 (1985).
[CrossRef]

Alfiad, M. S.

Buchali, F.

Bulow, H.

De Man, E.

de Waardt, H.

Duthel, T.

Ellinger, F.

M. Khafaji, H. Gustat, F. Ellinger, and C. Scheytt, “General time-domain representation of chromatic dispersion in single-mode fibers,” IEEE Photon. Technol. Lett. 22, 314–316 (2010).
[CrossRef]

Fludger, C. R. S.

Friberg, A. T.

T. Xu, G. Jacobsen, S. Popov, J. Li, K. Wang, and A. T. Friberg, “Normalized LMS digital filter for chromatic dispersion equalization in 112-Gbit/s PDM-QPSK coherent optical transmission system,” Opt. Commun. 283(6), 963–967 (2010).
[CrossRef]

Geyer, J.

Goldfarb, G.

G. Goldfarb, M. G. Taylor, and G. Li, “Experimental demonstration of fiber impairment compensation using the split-step finite-impulse-response filtering method,” IEEE Photon. Technol. Lett. 20(22), 1887–1889 (2008).
[CrossRef]

G. Goldfarb and G. Li, “Chromatic dispersion compensation using digital IIR filtering with coherent detection,” IEEE Photon. Technol. Lett. 19(13), 969–971 (2007).
[CrossRef]

Gustat, H.

M. Khafaji, H. Gustat, F. Ellinger, and C. Scheytt, “General time-domain representation of chromatic dispersion in single-mode fibers,” IEEE Photon. Technol. Lett. 22, 314–316 (2010).
[CrossRef]

Han, Y.

Hauske, F. N.

Henry, P. S.

P. S. Henry, “Lightwave primer,” IEEE J. Quantum Electron. 21(12), 1862–1879 (1985).
[CrossRef]

Igarashi, K.

Ip, E.

Ishihara, K.

Jacobsen, G.

T. Xu, G. Jacobsen, S. Popov, J. Li, K. Wang, and A. T. Friberg, “Normalized LMS digital filter for chromatic dispersion equalization in 112-Gbit/s PDM-QPSK coherent optical transmission system,” Opt. Commun. 283(6), 963–967 (2010).
[CrossRef]

Kahn, J. M.

Katoh, K.

Khafaji, M.

M. Khafaji, H. Gustat, F. Ellinger, and C. Scheytt, “General time-domain representation of chromatic dispersion in single-mode fibers,” IEEE Photon. Technol. Lett. 22, 314–316 (2010).
[CrossRef]

Khoe, G. D.

Kikuchi, K.

Klekamp, A.

Kobayashi, T.

Kudo, R.

Kuschnerov, M.

Lankl, B.

Li, G.

F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation,” IEEE Photonics J. 1(2), 144–152 (2009).
[CrossRef]

G. Goldfarb, M. G. Taylor, and G. Li, “Experimental demonstration of fiber impairment compensation using the split-step finite-impulse-response filtering method,” IEEE Photon. Technol. Lett. 20(22), 1887–1889 (2008).
[CrossRef]

G. Goldfarb and G. Li, “Chromatic dispersion compensation using digital IIR filtering with coherent detection,” IEEE Photon. Technol. Lett. 19(13), 969–971 (2007).
[CrossRef]

Y. Han and G. Li, “Coherent optical communication using polarization multiple-input-multiple-output,” Opt. Express 13(19), 7527–7534 (2005).
[CrossRef] [PubMed]

Li, J.

T. Xu, G. Jacobsen, S. Popov, J. Li, K. Wang, and A. T. Friberg, “Normalized LMS digital filter for chromatic dispersion equalization in 112-Gbit/s PDM-QPSK coherent optical transmission system,” Opt. Commun. 283(6), 963–967 (2010).
[CrossRef]

Miyamoto, Y.

Mori, Y.

Napoli, A.

Piyawanno, K.

Popov, S.

T. Xu, G. Jacobsen, S. Popov, J. Li, K. Wang, and A. T. Friberg, “Normalized LMS digital filter for chromatic dispersion equalization in 112-Gbit/s PDM-QPSK coherent optical transmission system,” Opt. Commun. 283(6), 963–967 (2010).
[CrossRef]

Sano, A.

Savory, S. J.

Scheytt, C.

M. Khafaji, H. Gustat, F. Ellinger, and C. Scheytt, “General time-domain representation of chromatic dispersion in single-mode fibers,” IEEE Photon. Technol. Lett. 22, 314–316 (2010).
[CrossRef]

Schmidt, E. D.

Schulien, C.

Spinnler, B.

Takatori, Y.

Taylor, M. G.

G. Goldfarb, M. G. Taylor, and G. Li, “Experimental demonstration of fiber impairment compensation using the split-step finite-impulse-response filtering method,” IEEE Photon. Technol. Lett. 20(22), 1887–1889 (2008).
[CrossRef]

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. 16(2), 674–676 (2004).
[CrossRef]

van den Borne, D.

Wang, K.

T. Xu, G. Jacobsen, S. Popov, J. Li, K. Wang, and A. T. Friberg, “Normalized LMS digital filter for chromatic dispersion equalization in 112-Gbit/s PDM-QPSK coherent optical transmission system,” Opt. Commun. 283(6), 963–967 (2010).
[CrossRef]

Wuth, T.

Xu, T.

T. Xu, G. Jacobsen, S. Popov, J. Li, K. Wang, and A. T. Friberg, “Normalized LMS digital filter for chromatic dispersion equalization in 112-Gbit/s PDM-QPSK coherent optical transmission system,” Opt. Commun. 283(6), 963–967 (2010).
[CrossRef]

Yaman, F.

F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation,” IEEE Photonics J. 1(2), 144–152 (2009).
[CrossRef]

Zhang, C.

IEEE J. Quantum Electron.

P. S. Henry, “Lightwave primer,” IEEE J. Quantum Electron. 21(12), 1862–1879 (1985).
[CrossRef]

IEEE Photon. Technol. Lett.

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. 16(2), 674–676 (2004).
[CrossRef]

G. Goldfarb and G. Li, “Chromatic dispersion compensation using digital IIR filtering with coherent detection,” IEEE Photon. Technol. Lett. 19(13), 969–971 (2007).
[CrossRef]

M. Khafaji, H. Gustat, F. Ellinger, and C. Scheytt, “General time-domain representation of chromatic dispersion in single-mode fibers,” IEEE Photon. Technol. Lett. 22, 314–316 (2010).
[CrossRef]

G. Goldfarb, M. G. Taylor, and G. Li, “Experimental demonstration of fiber impairment compensation using the split-step finite-impulse-response filtering method,” IEEE Photon. Technol. Lett. 20(22), 1887–1889 (2008).
[CrossRef]

IEEE Photonics J.

F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation,” IEEE Photonics J. 1(2), 144–152 (2009).
[CrossRef]

J. Lightwave Technol.

Opt. Commun.

T. Xu, G. Jacobsen, S. Popov, J. Li, K. Wang, and A. T. Friberg, “Normalized LMS digital filter for chromatic dispersion equalization in 112-Gbit/s PDM-QPSK coherent optical transmission system,” Opt. Commun. 283(6), 963–967 (2010).
[CrossRef]

Opt. Express

Other

G. P. Agrawal, Fiber-optic communication systems 3rd Edition (John Wiley & Sons, Inc., 2002), Chap. 2.

J. G. Proakis, Digital communications 5th Edition (McGraw-Hill Companies, Inc., 2008), Chap.10.

S. J. Savory, “Compensation of fibre impairments in digital coherent systems,” in Proceeding of IEEE European Conference on Optical Communication (Brussels, Belgium, 2008), paper Mo.3.D.1.

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 Proceeding of IEEE Conference on Optical Fiber Communication (San Diego, California, 2009), paper OMT1.

www.vpiphotonics.com

A. Färbert, S. Langenbach, N. Stojanovic, C. Dorschky, T. Kupfer, C. Schulien, J. P. Elbers, H. Wernz, H. Griesser, and C. Glingener, “Performance of a 10.7 Gb/s receiver with digital equaliser using maximum likelihood sequence estimation,” in Proceeding of IEEE European Conference on Optical Communication (Stockholm, Sweden, 2004), paper Th4.1.5.

A. V. Oppenheim, R. W. Schafer, and R. John, Buck, Discrete-time signal processing 2nd Edition (Prentice Hall, 1999).

J. G. Proakis, and D. G. Manolakis, Digital signal processing 4th Edition (Prentice Hall, 2006).

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, E. Yamada, H. Masuda, Y. Miyamoto, and M. Mizoguchi, “Two-stage overlap frequency domain equalization for long-haul optical systems,” in Proceeding of IEEE Conference on Optical Fiber Communication (San Diego, California, 2009), paper OMT3.

S. Haykin, Adaptive filter theory 4th Edition (Prentice Hall, 2001).

S. J. Savory, “Digital signal processing options in long haul transmission,” in Proceeding of IEEE Conference on Optical Fiber Communication (San Diego, California, 2008), paper OTuO3.

K. Kikuchi, and S. Y. Kim, “Investigation of nonlinear impairment effects on optical quadrature phase-shift keying signals transmitted through a long-haul system,” in Proceedings of IEEE Laser and Electro-Optics Society Summer Topical Meetings (Acapulco, Mexico, 2008), pp. 131–132.

B. Spinnler, F. N. Hauske, and M. Kuschnerov, “Adaptive equalizer complexity in coherent optical receivers,” in Proceeding of IEEE European Conference on Optical Communication (Brussels, Belgium, 2008), paper We.2.E.4.

B. Spinnler, “Complexity of algorithms for digital coherent receivers,” in Proceeding of IEEE European Conference on Optical Communication (Vienna, Austria, 2009), paper 7.3.6.

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Figures (12)

Fig. 1
Fig. 1

Schematic of DSP modules in coherent receiver. The adaptive equalization is validated, when fixed CD filters are employed.

Fig. 2
Fig. 2

Taps weights of LMS filter. (a) Tap weights magnitudes convergence. (b) Converged tap weights magnitudes distribution.

Fig. 3
Fig. 3

Tap weights of FD- FIR filter.

Fig. 4
Fig. 4

Schematic of blind look-up adaptive filter.

Fig. 5
Fig. 5

Schematic of 112-Gbit/s NRZ-PDM-QPSK coherent optical transmission system. PBS: polarization beam splitter, MZI: Mach-Zehnder interferometer, OBPF: optical band-pass filter, PIN: PiN diode, LPF: low-pass filter.

Fig. 6
Fig. 6

CD compensation using three digital filters neglecting fiber loss. (a) BER with OSNR. (b) BER with fiber length at OSNR 14.8 dB.

Fig. 7
Fig. 7

CD compensation with different taps number using LMS filter and FD-FIR filter at OSNR 14.8 dB. (a) 20 km fiber. (b) 600 km fiber.

Fig. 8
Fig. 8

The continuous time window TW A and discrete time window TN A.

Fig. 9
Fig. 9

CD compensation using FD-FIR filter with different sampling rate. (a) BER with OSNR. (b) BER with normalized time window at OSNR 14.8 dB.

Fig. 10
Fig. 10

CD compensation using blind look-up filter at OSNR 14.8 dB. (a) BER with different FFT size for 20 km and 40 km fiber. (b) BER with overlap for 4000 km fiber.

Fig. 11
Fig. 11

CD equalization using three filters with small fiber dispersion variation.

Fig. 12
Fig. 12

Phase noise compensation using the NLMS filter after dispersion equalization. w/o means without.

Tables (4)

Tables Icon

Table 1 The tap number in FD-FIR filter calculated by pulse broadening and anti-aliasing

Tables Icon

Table 2 The relative error between continuous time window and discrete time window

Tables Icon

Table 3 The minimum overlap size in BLU filter calculated according to pulse broadening

Tables Icon

Table 4 The computational complexity of the three digital filters

Equations (24)

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

y ( n ) = w H ( n ) x ( n )
w ( n + 1 ) = w ( n ) + μ x ( n ) e ( n )
e ( n ) = d ( n ) y ( n )
a k = j c T 2 D λ 2 z exp ( j π c T 2 D λ 2 z k 2 )
N 2 k N 2
N A = 2 × | D | λ 2 z 2 c T 2 + 1
| D | λ 2 z 2 c T t | D | λ 2 z 2 c T
T W A = 2 | D | λ 2 z 2 c T = | D | λ 2 z c T .
N A = 2 × T W A / ( 2 T ) + 1.
T W P = 2 π c T π 2 c 2 T 4 + 4 λ 4 D 2 z 2
N P = 2 × T W P 2 T + 1 = 2 × 1 π c T 2 π 2 c 2 T 4 + 4 λ 4 D 2 z 2 + 1
G c ( z , ω ) = exp ( j D λ 2 z 4 π c ω 2 )
ω N ω B L U ω N
b k = exp [ j D λ 2 z π c ( k N F F T ω N ) 2 ]
N F F T 2 k N F F T 2 1
[ x o u t ( n ) y o u t ( n ) ] = [ w x x H ( n ) w x y H ( n ) w y x H ( n ) w y y H ( n ) ] [ x i n ( n ) y i n ( n ) ]
{ w x x ( n + 1 ) = w x x ( n ) + μ p ε x ( n ) x i n * ( n ) w y x ( n + 1 ) = w y x ( n ) + μ p ε y ( n ) x i n * ( n ) w x y ( n + 1 ) = w x y ( n ) + μ p ε x ( n ) y i n * ( n ) w y y ( n + 1 ) = w y y ( n ) + μ p ε y ( n ) y i n * ( n )
{ ε x ( n ) = d x ( n ) x o u t ( n ) ε y ( n ) = d y ( n ) y o u t ( n )
w N L M S ( n + 1 ) = w N L M S ( n ) + μ P N | x P N ( n ) | 2 x P N * ( n ) ς ( n )
ς ( n ) = d P N ( n ) w N L M S ( n ) x P N ( n )
p = ( T N A T W A ) / T W A .
C L M S = L C D ( 1 + n S C ) log 2 ( M )
C F D F I R = L C D n S C 2 log 2 ( M )
C B L U = [ 1 + log 2 ( N F F T ) ] n S C log 2 ( M ) ( 1 L C D / N F F T )

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