Abstract

We propose a novel and unified algorithm that estimates linear impairments in optical transmission systems from tap coefficients of an adaptive finite-impulse response (FIR) filter in a coherent optical receiver. Measurable impairments include chromatic dispersion (CD), differential group delay (DGD) between two principal states of polarization, second-order polarization-mode dispersion (second-order PMD), and polarization-dependent loss (PDL). We validate our multi-impairment monitoring algorithm by dual-polarization quadrature phase-shift keying (QPSK) transmission experiments.

© 2010 OSA

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  1. K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation of with digital carrier phase estimation,” IEEE J. Sel. Top. Quantum Electron. 12(4), 563–570 (2006).
    [CrossRef]
  2. K. Kikuchi, Optical Fiber Telecommunication V B (Academic press, 2008), Chap. 3.
  3. D. C. Kilper, R. Bach, D. J. Blumenthal, D. Einstein, T. Landolsi, L. Ostar, M. Preiss, and A. E. Willner, “Optical performance monitoring,” J. Lightwave Technol. 22(1), 294–304 (2004).
    [CrossRef]
  4. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-2-804 .
    [CrossRef] [PubMed]
  5. F. N. Hauske, J. C. Geyer, M. Kuschnerov, K. Piyawanno, T. Duthel, C. R. S. Fludger, D. van den Borne, E.-D. Schmidt, B. Spinnler, H. de Waardt, and B. Lankl, “Optical performance monitoring from FIR filter co-efficients in coherent receivers,” Optical Fiber Communication Conference (OFC 2008), San Diego, CA, USA, paper OThW2 (2008).
  6. J. C. Geyer, F. N. Hauske, C. R. S. Fludger, T. Duthel, C. Schulien, M. Kuschnerov, K. Piyawanno, D. van den Borne, E.-D. Schmidt, B. Spinnler, B. Lankl, and B. Schmauss, “Channel parameter estimation for polarization diverse coherent receives,” IEEE Photon. Technol. Lett. 20(10), 776–778 (2008).
    [CrossRef]
  7. J. C. Geyer, C. R. S. Fludger, T. Duthel, C. Schulien, and B. Schmauss, “Performance monitoring using coherent receiver,” Optical Fiber Communication Conference (OFC 2008), San Diego, CA, USA, paper OThH5 (2009).
  8. F. N. Hauske, M. Kuschnerov, B. Spinnler, and B. Lankl, “Optical performance monitoring in digital coherent receivers,” J. Lightwave Technol. 27(16), 3623–3631 (2009).
    [CrossRef]
  9. Md. S. Faruk, Y. Mori, C. Zhang and K. Kikuchi, “Proper polarization demultiplexing in coherent optical receiver using constant modulus algorithm with training mode,” Optoelectronics and Communication Conference (OECC 2010), Sapporo, Japan, paper 9B3–3 (2010).
  10. G. J. Foschini and C. D. Poole, “Statistical theory of polarization dispersion in single mode fibers,” J. Lightwave Technol. 9(11), 1439–1456 (1991).
    [CrossRef]
  11. G. J. Foschini, L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Probability densities of second-order polarization mode dispersion including polarization dependent chromatic fiber dispersion,” IEEE Photon. Technol. Lett. 12(3), 293–295 (2000).
    [CrossRef]
  12. G. J. Foschini, L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Statistics of second-order PMD depolarization,” J. Lightwave Technol. 19(12), 1882–1886 (2001).
    [CrossRef]
  13. L. Yan, X. T. Yao, M. C. Hauer, and A. E. Willner, “Practical solutions to polarization-mode-dispersion emulation and compensation,” J. Lightwave Technol. 24(11), 3992–4005 (2006).
    [CrossRef]

2009 (1)

2008 (2)

S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-2-804 .
[CrossRef] [PubMed]

J. C. Geyer, F. N. Hauske, C. R. S. Fludger, T. Duthel, C. Schulien, M. Kuschnerov, K. Piyawanno, D. van den Borne, E.-D. Schmidt, B. Spinnler, B. Lankl, and B. Schmauss, “Channel parameter estimation for polarization diverse coherent receives,” IEEE Photon. Technol. Lett. 20(10), 776–778 (2008).
[CrossRef]

2006 (2)

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

L. Yan, X. T. Yao, M. C. Hauer, and A. E. Willner, “Practical solutions to polarization-mode-dispersion emulation and compensation,” J. Lightwave Technol. 24(11), 3992–4005 (2006).
[CrossRef]

2004 (1)

2001 (1)

2000 (1)

G. J. Foschini, L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Probability densities of second-order polarization mode dispersion including polarization dependent chromatic fiber dispersion,” IEEE Photon. Technol. Lett. 12(3), 293–295 (2000).
[CrossRef]

1991 (1)

G. J. Foschini and C. D. Poole, “Statistical theory of polarization dispersion in single mode fibers,” J. Lightwave Technol. 9(11), 1439–1456 (1991).
[CrossRef]

Bach, R.

Blumenthal, D. J.

Duthel, T.

J. C. Geyer, F. N. Hauske, C. R. S. Fludger, T. Duthel, C. Schulien, M. Kuschnerov, K. Piyawanno, D. van den Borne, E.-D. Schmidt, B. Spinnler, B. Lankl, and B. Schmauss, “Channel parameter estimation for polarization diverse coherent receives,” IEEE Photon. Technol. Lett. 20(10), 776–778 (2008).
[CrossRef]

Einstein, D.

Fludger, C. R. S.

J. C. Geyer, F. N. Hauske, C. R. S. Fludger, T. Duthel, C. Schulien, M. Kuschnerov, K. Piyawanno, D. van den Borne, E.-D. Schmidt, B. Spinnler, B. Lankl, and B. Schmauss, “Channel parameter estimation for polarization diverse coherent receives,” IEEE Photon. Technol. Lett. 20(10), 776–778 (2008).
[CrossRef]

Foschini, G. J.

G. J. Foschini, L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Statistics of second-order PMD depolarization,” J. Lightwave Technol. 19(12), 1882–1886 (2001).
[CrossRef]

G. J. Foschini, L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Probability densities of second-order polarization mode dispersion including polarization dependent chromatic fiber dispersion,” IEEE Photon. Technol. Lett. 12(3), 293–295 (2000).
[CrossRef]

G. J. Foschini and C. D. Poole, “Statistical theory of polarization dispersion in single mode fibers,” J. Lightwave Technol. 9(11), 1439–1456 (1991).
[CrossRef]

Geyer, J. C.

J. C. Geyer, F. N. Hauske, C. R. S. Fludger, T. Duthel, C. Schulien, M. Kuschnerov, K. Piyawanno, D. van den Borne, E.-D. Schmidt, B. Spinnler, B. Lankl, and B. Schmauss, “Channel parameter estimation for polarization diverse coherent receives,” IEEE Photon. Technol. Lett. 20(10), 776–778 (2008).
[CrossRef]

Hauer, M. C.

Hauske, F. N.

F. N. Hauske, M. Kuschnerov, B. Spinnler, and B. Lankl, “Optical performance monitoring in digital coherent receivers,” J. Lightwave Technol. 27(16), 3623–3631 (2009).
[CrossRef]

J. C. Geyer, F. N. Hauske, C. R. S. Fludger, T. Duthel, C. Schulien, M. Kuschnerov, K. Piyawanno, D. van den Borne, E.-D. Schmidt, B. Spinnler, B. Lankl, and B. Schmauss, “Channel parameter estimation for polarization diverse coherent receives,” IEEE Photon. Technol. Lett. 20(10), 776–778 (2008).
[CrossRef]

Jopson, R. M.

G. J. Foschini, L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Statistics of second-order PMD depolarization,” J. Lightwave Technol. 19(12), 1882–1886 (2001).
[CrossRef]

G. J. Foschini, L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Probability densities of second-order polarization mode dispersion including polarization dependent chromatic fiber dispersion,” IEEE Photon. Technol. Lett. 12(3), 293–295 (2000).
[CrossRef]

Kikuchi, K.

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

Kilper, D. C.

Kogelnik, H.

G. J. Foschini, L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Statistics of second-order PMD depolarization,” J. Lightwave Technol. 19(12), 1882–1886 (2001).
[CrossRef]

G. J. Foschini, L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Probability densities of second-order polarization mode dispersion including polarization dependent chromatic fiber dispersion,” IEEE Photon. Technol. Lett. 12(3), 293–295 (2000).
[CrossRef]

Kuschnerov, M.

F. N. Hauske, M. Kuschnerov, B. Spinnler, and B. Lankl, “Optical performance monitoring in digital coherent receivers,” J. Lightwave Technol. 27(16), 3623–3631 (2009).
[CrossRef]

J. C. Geyer, F. N. Hauske, C. R. S. Fludger, T. Duthel, C. Schulien, M. Kuschnerov, K. Piyawanno, D. van den Borne, E.-D. Schmidt, B. Spinnler, B. Lankl, and B. Schmauss, “Channel parameter estimation for polarization diverse coherent receives,” IEEE Photon. Technol. Lett. 20(10), 776–778 (2008).
[CrossRef]

Landolsi, T.

Lankl, B.

F. N. Hauske, M. Kuschnerov, B. Spinnler, and B. Lankl, “Optical performance monitoring in digital coherent receivers,” J. Lightwave Technol. 27(16), 3623–3631 (2009).
[CrossRef]

J. C. Geyer, F. N. Hauske, C. R. S. Fludger, T. Duthel, C. Schulien, M. Kuschnerov, K. Piyawanno, D. van den Borne, E.-D. Schmidt, B. Spinnler, B. Lankl, and B. Schmauss, “Channel parameter estimation for polarization diverse coherent receives,” IEEE Photon. Technol. Lett. 20(10), 776–778 (2008).
[CrossRef]

Nelson, L. E.

G. J. Foschini, L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Statistics of second-order PMD depolarization,” J. Lightwave Technol. 19(12), 1882–1886 (2001).
[CrossRef]

G. J. Foschini, L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Probability densities of second-order polarization mode dispersion including polarization dependent chromatic fiber dispersion,” IEEE Photon. Technol. Lett. 12(3), 293–295 (2000).
[CrossRef]

Ostar, L.

Piyawanno, K.

J. C. Geyer, F. N. Hauske, C. R. S. Fludger, T. Duthel, C. Schulien, M. Kuschnerov, K. Piyawanno, D. van den Borne, E.-D. Schmidt, B. Spinnler, B. Lankl, and B. Schmauss, “Channel parameter estimation for polarization diverse coherent receives,” IEEE Photon. Technol. Lett. 20(10), 776–778 (2008).
[CrossRef]

Poole, C. D.

G. J. Foschini and C. D. Poole, “Statistical theory of polarization dispersion in single mode fibers,” J. Lightwave Technol. 9(11), 1439–1456 (1991).
[CrossRef]

Preiss, M.

Savory, S. J.

Schmauss, B.

J. C. Geyer, F. N. Hauske, C. R. S. Fludger, T. Duthel, C. Schulien, M. Kuschnerov, K. Piyawanno, D. van den Borne, E.-D. Schmidt, B. Spinnler, B. Lankl, and B. Schmauss, “Channel parameter estimation for polarization diverse coherent receives,” IEEE Photon. Technol. Lett. 20(10), 776–778 (2008).
[CrossRef]

Schmidt, E.-D.

J. C. Geyer, F. N. Hauske, C. R. S. Fludger, T. Duthel, C. Schulien, M. Kuschnerov, K. Piyawanno, D. van den Borne, E.-D. Schmidt, B. Spinnler, B. Lankl, and B. Schmauss, “Channel parameter estimation for polarization diverse coherent receives,” IEEE Photon. Technol. Lett. 20(10), 776–778 (2008).
[CrossRef]

Schulien, C.

J. C. Geyer, F. N. Hauske, C. R. S. Fludger, T. Duthel, C. Schulien, M. Kuschnerov, K. Piyawanno, D. van den Borne, E.-D. Schmidt, B. Spinnler, B. Lankl, and B. Schmauss, “Channel parameter estimation for polarization diverse coherent receives,” IEEE Photon. Technol. Lett. 20(10), 776–778 (2008).
[CrossRef]

Spinnler, B.

F. N. Hauske, M. Kuschnerov, B. Spinnler, and B. Lankl, “Optical performance monitoring in digital coherent receivers,” J. Lightwave Technol. 27(16), 3623–3631 (2009).
[CrossRef]

J. C. Geyer, F. N. Hauske, C. R. S. Fludger, T. Duthel, C. Schulien, M. Kuschnerov, K. Piyawanno, D. van den Borne, E.-D. Schmidt, B. Spinnler, B. Lankl, and B. Schmauss, “Channel parameter estimation for polarization diverse coherent receives,” IEEE Photon. Technol. Lett. 20(10), 776–778 (2008).
[CrossRef]

van den Borne, D.

J. C. Geyer, F. N. Hauske, C. R. S. Fludger, T. Duthel, C. Schulien, M. Kuschnerov, K. Piyawanno, D. van den Borne, E.-D. Schmidt, B. Spinnler, B. Lankl, and B. Schmauss, “Channel parameter estimation for polarization diverse coherent receives,” IEEE Photon. Technol. Lett. 20(10), 776–778 (2008).
[CrossRef]

Willner, A. E.

Yan, L.

Yao, X. T.

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(4), 563–570 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

J. C. Geyer, F. N. Hauske, C. R. S. Fludger, T. Duthel, C. Schulien, M. Kuschnerov, K. Piyawanno, D. van den Borne, E.-D. Schmidt, B. Spinnler, B. Lankl, and B. Schmauss, “Channel parameter estimation for polarization diverse coherent receives,” IEEE Photon. Technol. Lett. 20(10), 776–778 (2008).
[CrossRef]

G. J. Foschini, L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Probability densities of second-order polarization mode dispersion including polarization dependent chromatic fiber dispersion,” IEEE Photon. Technol. Lett. 12(3), 293–295 (2000).
[CrossRef]

J. Lightwave Technol. (5)

Opt. Express (1)

Other (4)

F. N. Hauske, J. C. Geyer, M. Kuschnerov, K. Piyawanno, T. Duthel, C. R. S. Fludger, D. van den Borne, E.-D. Schmidt, B. Spinnler, H. de Waardt, and B. Lankl, “Optical performance monitoring from FIR filter co-efficients in coherent receivers,” Optical Fiber Communication Conference (OFC 2008), San Diego, CA, USA, paper OThW2 (2008).

K. Kikuchi, Optical Fiber Telecommunication V B (Academic press, 2008), Chap. 3.

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

J. C. Geyer, C. R. S. Fludger, T. Duthel, C. Schulien, and B. Schmauss, “Performance monitoring using coherent receiver,” Optical Fiber Communication Conference (OFC 2008), San Diego, CA, USA, paper OThH5 (2009).

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Figures (4)

Fig. 1
Fig. 1

Definition of second-order PMD vector. (a): Two PMD vectors at angular frequencies ω and ω + Δ ω are shown in the Stokes space. (b): Corresponding second-order PMD vector with its perpendicular and parallel components. This is given as the derivative of the first-order PMD vector with respect to the angular frequency ω.

Fig. 2
Fig. 2

Schematics of the dual-polarization QPSK transmission system for verifications of the proposed impairment-monitoring algorithm.

Fig. 3
Fig. 3

Monitoring results. (a): CD monitoring result with 20-ps DGD and 3-dB PDL. (b): DGD monitoring result with 1600-ps/nm CD and 3-dB PDL. (c): PDL monitoring result with 1600-ps/nm CD and 20-ps DGD.

Fig. 4
Fig. 4

Probability densities of the first- and second-order PMD. (a): DGD Δ τ , (b): PCD | τ ω | , (c): DEP | τ ω | , and (d): the magnitude of second-order PMD | τ ω | . Bars show those estimated from monitored values and solid curves are theoretical ones.

Equations (24)

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H f i b e r ( ω ) = D ( ω ) U ( ω ) K T ,
D ( ω ) = e j ω 2 β 2 z / 2 ,
U ( ω ) = R 1 1 [ e j ω Δ τ / 2 0 0 e j ω Δ τ / 2 ]   R 1 ,
K = R 2 1 [ Γ max 0 0 Γ min ] R 2 ,
M ( ω ) H f i b e r ( ω ) = { D F T [ h x x ( n ) h x y ( n ) h y x ( n ) h y y ( n ) ] } 1 .
d e t { M ( ω ) } = D 2 ( ω ) d e t { U ( ω ) } d e t ( K ) d e t ( T ) .
det { M ( ω ) } = D 2 ( ω ) Γ m a x Γ m i n .
τ = Δ τ p ^ ,
τ ω = d τ d ω = Δ τ ω p ^ + Δ τ p ^ ω :
M ( ω + Δ ω ) M 1 ( ω ) = D ( ω + Δ ω ) U ( ω + Δ ω ) K T { D ( ω ) U ( ω ) K T } 1
= D ( ω + Δ ω ) D * ( ω ) U ( ω + Δ ω ) K T ( K T ) 1 U 1 ( ω )
= c U ( ω + Δ ω ) U ( ω ) ,
M ( ω + Δ ω ) M 1 ( ω ) = c R 1 1 [ e j Δ ω Δ τ / 2 0 0 e j Δ ω Δ τ / 2 ]   R 1 .
Δ τ = | arg ( ρ 1 / ρ 2 ) Δ ω | .
| τ ω | = Δ τ ( ω + Δ ω ) Δ τ ( ω ) Δ ω .
S = [ s x s x * s y s y * ,       s x s y * + s x * s y ,       j ( s x s y * s x * s y ) ] ,
| p ^ ω | = 1 2 cos 1 { p ^ ( ω + Δ ω ) p ^ ( ω ) } Δ ω .
| τ ω | = Δ τ | p ^ ω |
| τ ω | = | τ ω | | | 2 + | τ ω | 2 .
M ( ω ) M ( ω ) = { D ( ω ) U ( ω ) K T } { D ( ω ) U ( ω ) K T }
= D * ( ω ) D ( ω ) { K T } U ( ω ) U ( ω ) { K T }
= T K K T
M ( ω ) M ( ω ) = ( T R 2 ) 1 [ Γ max 0 0 Γ min ] ( T R 2 ) .
P D L d B = 10 log 10 ( α 1 α 2 ) .

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