Abstract

We introduce a closed form equation, validated by simulations and experimental results that predicts the residual nonlinear noise ratio in mid-link OPC assisted discretely amplified systems. The model anticipates the reduction in performance enhancement achieved by mid-link OPC as the bandwidth of the modulated signals increases. The numerical analysis shows that uncompensated signal-signal interactions limit the performance improvement achieved by the introduction of additional OPCs. The numerical analysis predicts that the deployment of shorter amplifier spacing will lead to a greater performance enhancement. The numerical results are validated by experimentally testing of 2x, 4x, and 8x28Gbaud PM-QPSK systems with mid-link OPC compensation in a discretely amplified system with 100km amplifier spacing. The experimentally obtained reach enhancement (43%, 32%, and 24% for 2x28Gbaud, 4x28Gbaud, and 8x28Gbaud, respectively) confirms that the compensation efficiency of mid-link OPC is highly dependent on the number of channels (bandwidth) propagating along the system.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Full Article  |  PDF Article
OSA Recommended Articles
Experimental demonstration of 72% reach enhancement of 3.6Tbps optical transmission system using mid-link optical phase conjugation

Mohammad A. Z. Al-Khateeb, Mingming Tan, Md. Asif Iqbal, Abdallah Ali, Mary E. McCarthy, Paul Harper, and Andrew D. Ellis
Opt. Express 26(18) 23960-23968 (2018)

Analysis of the nonlinear Kerr effects in optical transmission systems that deploy optical phase conjugation

Mohammad A. Z. Al-Khateeb, Md. Asif Iqbal, Mingming Tan, Abdallah Ali, Mary McCarthy, Paul Harper, and Andrew D. Ellis
Opt. Express 26(3) 3145-3160 (2018)

Fiber nonlinearity mitigation of WDM-PDM QPSK/16-QAM signals using fiber-optic parametric amplifiers based multiple optical phase conjugations

Hao Hu, Robert M. Jopson, Alan H. Gnauck, Sebastian Randel, and S. Chandrasekhar
Opt. Express 25(3) 1618-1628 (2017)

References

  • View by:
  • |
  • |
  • |

  1. A. Yariv, D. Fekete, and D. M. Pepper, “Compensation for channel dispersion by nonlinear optical phase conjugation,” Opt. Lett. 4(2), 52 (1979).
    [Crossref] [PubMed]
  2. W. Shieh and Xi Chen, “Information spectral efficiency and launch power density limits due to fiber nonlinearity for coherent optical OFDM systems,” IEEE Photonics J. 3(2), 158–173 (2011).
    [Crossref]
  3. K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “Cw three-wave mixing in single-mode optical fibers,” J. Appl. Phys. 49(10), 5098–5106 (1978).
    [Crossref]
  4. A. D. Ellis and W. A. Stallard, “Four wave mixing in ultra long transmission systems incorporating linear amplifiers,” in IEE Colloquium on Non-Linear Effects in Fibre Communications. p. 6/1–6/4, 1990.
  5. K. Inoue, “Phase-mismatching characteristic of four-wave mixing in fiber lines with multistage optical amplifiers,” Opt. Lett. 17(11), 801–803 (1992).
    [Crossref] [PubMed]
  6. S. Radic, G. Pendock, A. Srivastava, P. Wysocki, and A. Chraplyvy, “Four-wave mixing in optical links using quasi-distributed optical amplifiers,” J. Lightwave Technol. 19(5), 636–645 (2001).
    [Crossref]
  7. M. A. Z. Al-Khateeb, M. A. Iqbal, M. Tan, A. Ali, M. McCarthy, P. Harper, and A. D. Ellis, “Analysis of the nonlinear Kerr effects in optical transmission systems that deploy optical phase conjugation,” Opt. Express 26(3), 3145–3160 (2018).
    [Crossref] [PubMed]
  8. A. D. Ellis, M. E. McCarthy, M. A. Z. Al Khateeb, M. Sorokina, and N. J. Doran, “Performance limits in optical communications due to fiber nonlinearity,” Adv. Opt. Photonics 9(3), 429–503 (2017).
    [Crossref]
  9. M. E. McCarthy, M. A. Z. Al Kahteeb, F. M. Ferreira, and A. D. Ellis, “PMD tolerant nonlinear compensation using in-line phase conjugation,” Opt. Express 24(4), 3385–3392 (2016).
    [Crossref] [PubMed]
  10. D. Rafique and A. D. Ellis, “Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems,” Opt. Express 19(4), 3449–3454 (2011).
    [Crossref] [PubMed]
  11. M. A. Z. Al-Khateeb, M. McCarthy, C. Sánchez, and A. Ellis, “Effect of second order signal-noise interactions in nonlinearity compensated optical transmission systems,” Opt. Lett. 41(8), 1849–1852 (2016).
    [Crossref] [PubMed]
  12. A. D. Ellis, M. E. McCarthy, M. A. Z. Al-Khateeb, and S. Sygletos, “Capacity limits of systems employing multiple optical phase conjugators,” Opt. Express 23(16), 20381–20393 (2015).
    [Crossref] [PubMed]
  13. M. A. Z. Al-Khateeb, M. E. Mccarthy, and A. Ellis, “Performance enhancement prediction for optical phase Conjugation in Systems with 100km Amplifier Spacing,” in Proc. European Conference and Exhibition on Optical Communication (ECOC) (2017), p. Th.1.F.4.
    [Crossref]
  14. K. Solis-Trapala, M. Pelusi, H. N. Tan, T. Inoue, and S. Namiki, “Optimized WDM Transmission Impairment Mitigation by Multiple Phase Conjugations,” J. Lightwave Technol. 34(2), 431–440 (2016).
    [Crossref]
  15. H. Hu, R. M. Jopson, A. H. Gnauck, S. Randel, and S. Chandrasekhar, “Fiber nonlinearity mitigation of WDM-PDM QPSK/16-QAM signals using fiber-optic parametric amplifiers based multiple optical phase conjugations,” Opt. Express 25(3), 1618–1628 (2017).
    [Crossref] [PubMed]
  16. E. Desurvire, Erbium Doped Fiber Amplifiers: Principles and Applications, John Wiley & Sons, N.Y., 1994.
  17. M. H. Shoreh, “Compensation of nonlinearity impairments in coherent optical OFDM systems using multiple optical phase conjugate modules,” J. Opt. Commun. Netw. 6(6), 549–558 (2014).
    [Crossref]
  18. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
    [Crossref]
  19. A. D. Ellis and N. J. Doran, “Optical link design for Minimum Power Consumption and Maximum Capacity,” in 39th European Conference and Exhibition on Optical Communication (ECOC 2013) (Institution of Engineering and Technology, 2013), pp. 1068–1070.
  20. P. Poggiolini, “The GN model of non-linear propagation in uncompensated coherent optical systems,” J. Lightwave Technol. 30(24), 3857–3879 (2012).
    [Crossref]
  21. S. Yoshima, Y. Sun, Z. Liu, K. R. H. Bottrill, F. Parmigiani, D. J. Richardson, and P. Petropoulos, “Mitigation of nonlinear effects on WDM QAM signals enabled by optical phase conjugation with efficient bandwidth utilization,” J. Light. Technol. 35, 971 (2017).
  22. M. Morshed, L. B. Du, B. Foo, M. D. Pelusi, B. Corcoran, and A. J. Lowery, “Experimental demonstrations of dual polarization CO-OFDM using mid-span spectral inversion for nonlinearity compensation,” Opt. Express 22(9), 10455–10466 (2014).
    [Crossref] [PubMed]
  23. I. Phillips, M. Tan, M. F. Stephens, M. McCarthy, E. Giacoumidis, S. Sygletos, P. Rosa, S. Fabbri, S. T. Le, T. Kanesan, S. K. Turitsyn, N. J. Doran, P. Harper, and A. D. Ellis, “Exceeding the nonlinear-Shannon limit using Raman laser based amplification and optical phase conjugation,” in Optical Fiber Communication Conference (2014), p. M3C.1.
  24. I. Sackey, F. Da Ros, J. Karl Fischer, T. Richter, M. Jazayerifar, C. Peucheret, K. Petermann, and C. Schubert, “Kerr nonlinearity mitigation: mid-link spectral inversion versus digital backpropagation in 5×28-GBd PDM 16-QAM signal transmission,” J. Lightwave Technol. 33(9), 1821–1827 (2015).
    [Crossref]
  25. I. Sackey, R. Elschner, C. Schmidt-Langhorst, T. Kato, T. Tanimura, S. Watanabe, T. Hoshida, C. Schubert, and C. Schubert, “Novel wavelength-shift-free optical phase conjugator used for fiber nonlinearity mitigation in 200-Gb/s PDM-16QAM transmission,” in Optical Fiber Communication Conference (OSA,2017), p. Th3J.1.

2018 (1)

2017 (3)

A. D. Ellis, M. E. McCarthy, M. A. Z. Al Khateeb, M. Sorokina, and N. J. Doran, “Performance limits in optical communications due to fiber nonlinearity,” Adv. Opt. Photonics 9(3), 429–503 (2017).
[Crossref]

H. Hu, R. M. Jopson, A. H. Gnauck, S. Randel, and S. Chandrasekhar, “Fiber nonlinearity mitigation of WDM-PDM QPSK/16-QAM signals using fiber-optic parametric amplifiers based multiple optical phase conjugations,” Opt. Express 25(3), 1618–1628 (2017).
[Crossref] [PubMed]

S. Yoshima, Y. Sun, Z. Liu, K. R. H. Bottrill, F. Parmigiani, D. J. Richardson, and P. Petropoulos, “Mitigation of nonlinear effects on WDM QAM signals enabled by optical phase conjugation with efficient bandwidth utilization,” J. Light. Technol. 35, 971 (2017).

2016 (3)

2015 (2)

2014 (2)

2012 (1)

2011 (2)

D. Rafique and A. D. Ellis, “Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems,” Opt. Express 19(4), 3449–3454 (2011).
[Crossref] [PubMed]

W. Shieh and Xi Chen, “Information spectral efficiency and launch power density limits due to fiber nonlinearity for coherent optical OFDM systems,” IEEE Photonics J. 3(2), 158–173 (2011).
[Crossref]

2010 (1)

2001 (1)

1992 (1)

1979 (1)

1978 (1)

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “Cw three-wave mixing in single-mode optical fibers,” J. Appl. Phys. 49(10), 5098–5106 (1978).
[Crossref]

Al Kahteeb, M. A. Z.

Al Khateeb, M. A. Z.

A. D. Ellis, M. E. McCarthy, M. A. Z. Al Khateeb, M. Sorokina, and N. J. Doran, “Performance limits in optical communications due to fiber nonlinearity,” Adv. Opt. Photonics 9(3), 429–503 (2017).
[Crossref]

Ali, A.

Al-Khateeb, M. A. Z.

Bottrill, K. R. H.

S. Yoshima, Y. Sun, Z. Liu, K. R. H. Bottrill, F. Parmigiani, D. J. Richardson, and P. Petropoulos, “Mitigation of nonlinear effects on WDM QAM signals enabled by optical phase conjugation with efficient bandwidth utilization,” J. Light. Technol. 35, 971 (2017).

Chandrasekhar, S.

Chraplyvy, A.

Corcoran, B.

Da Ros, F.

Doran, N. J.

A. D. Ellis, M. E. McCarthy, M. A. Z. Al Khateeb, M. Sorokina, and N. J. Doran, “Performance limits in optical communications due to fiber nonlinearity,” Adv. Opt. Photonics 9(3), 429–503 (2017).
[Crossref]

Du, L. B.

Ellis, A.

M. A. Z. Al-Khateeb, M. McCarthy, C. Sánchez, and A. Ellis, “Effect of second order signal-noise interactions in nonlinearity compensated optical transmission systems,” Opt. Lett. 41(8), 1849–1852 (2016).
[Crossref] [PubMed]

M. A. Z. Al-Khateeb, M. E. Mccarthy, and A. Ellis, “Performance enhancement prediction for optical phase Conjugation in Systems with 100km Amplifier Spacing,” in Proc. European Conference and Exhibition on Optical Communication (ECOC) (2017), p. Th.1.F.4.
[Crossref]

Ellis, A. D.

Essiambre, R.-J.

Fekete, D.

Ferreira, F. M.

Foo, B.

Foschini, G. J.

Gnauck, A. H.

Goebel, B.

Harper, P.

Hill, K. O.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “Cw three-wave mixing in single-mode optical fibers,” J. Appl. Phys. 49(10), 5098–5106 (1978).
[Crossref]

Hu, H.

Inoue, K.

Inoue, T.

Iqbal, M. A.

Jazayerifar, M.

Johnson, D. C.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “Cw three-wave mixing in single-mode optical fibers,” J. Appl. Phys. 49(10), 5098–5106 (1978).
[Crossref]

Jopson, R. M.

Karl Fischer, J.

Kawasaki, B. S.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “Cw three-wave mixing in single-mode optical fibers,” J. Appl. Phys. 49(10), 5098–5106 (1978).
[Crossref]

Kramer, G.

Liu, Z.

S. Yoshima, Y. Sun, Z. Liu, K. R. H. Bottrill, F. Parmigiani, D. J. Richardson, and P. Petropoulos, “Mitigation of nonlinear effects on WDM QAM signals enabled by optical phase conjugation with efficient bandwidth utilization,” J. Light. Technol. 35, 971 (2017).

Lowery, A. J.

MacDonald, R. I.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “Cw three-wave mixing in single-mode optical fibers,” J. Appl. Phys. 49(10), 5098–5106 (1978).
[Crossref]

McCarthy, M.

McCarthy, M. E.

A. D. Ellis, M. E. McCarthy, M. A. Z. Al Khateeb, M. Sorokina, and N. J. Doran, “Performance limits in optical communications due to fiber nonlinearity,” Adv. Opt. Photonics 9(3), 429–503 (2017).
[Crossref]

M. E. McCarthy, M. A. Z. Al Kahteeb, F. M. Ferreira, and A. D. Ellis, “PMD tolerant nonlinear compensation using in-line phase conjugation,” Opt. Express 24(4), 3385–3392 (2016).
[Crossref] [PubMed]

A. D. Ellis, M. E. McCarthy, M. A. Z. Al-Khateeb, and S. Sygletos, “Capacity limits of systems employing multiple optical phase conjugators,” Opt. Express 23(16), 20381–20393 (2015).
[Crossref] [PubMed]

M. A. Z. Al-Khateeb, M. E. Mccarthy, and A. Ellis, “Performance enhancement prediction for optical phase Conjugation in Systems with 100km Amplifier Spacing,” in Proc. European Conference and Exhibition on Optical Communication (ECOC) (2017), p. Th.1.F.4.
[Crossref]

Morshed, M.

Namiki, S.

Parmigiani, F.

S. Yoshima, Y. Sun, Z. Liu, K. R. H. Bottrill, F. Parmigiani, D. J. Richardson, and P. Petropoulos, “Mitigation of nonlinear effects on WDM QAM signals enabled by optical phase conjugation with efficient bandwidth utilization,” J. Light. Technol. 35, 971 (2017).

Pelusi, M.

Pelusi, M. D.

Pendock, G.

Pepper, D. M.

Petermann, K.

Petropoulos, P.

S. Yoshima, Y. Sun, Z. Liu, K. R. H. Bottrill, F. Parmigiani, D. J. Richardson, and P. Petropoulos, “Mitigation of nonlinear effects on WDM QAM signals enabled by optical phase conjugation with efficient bandwidth utilization,” J. Light. Technol. 35, 971 (2017).

Peucheret, C.

Poggiolini, P.

Radic, S.

Rafique, D.

Randel, S.

Richardson, D. J.

S. Yoshima, Y. Sun, Z. Liu, K. R. H. Bottrill, F. Parmigiani, D. J. Richardson, and P. Petropoulos, “Mitigation of nonlinear effects on WDM QAM signals enabled by optical phase conjugation with efficient bandwidth utilization,” J. Light. Technol. 35, 971 (2017).

Richter, T.

Sackey, I.

Sánchez, C.

Schubert, C.

Shieh, W.

W. Shieh and Xi Chen, “Information spectral efficiency and launch power density limits due to fiber nonlinearity for coherent optical OFDM systems,” IEEE Photonics J. 3(2), 158–173 (2011).
[Crossref]

Shoreh, M. H.

Solis-Trapala, K.

Sorokina, M.

A. D. Ellis, M. E. McCarthy, M. A. Z. Al Khateeb, M. Sorokina, and N. J. Doran, “Performance limits in optical communications due to fiber nonlinearity,” Adv. Opt. Photonics 9(3), 429–503 (2017).
[Crossref]

Srivastava, A.

Sun, Y.

S. Yoshima, Y. Sun, Z. Liu, K. R. H. Bottrill, F. Parmigiani, D. J. Richardson, and P. Petropoulos, “Mitigation of nonlinear effects on WDM QAM signals enabled by optical phase conjugation with efficient bandwidth utilization,” J. Light. Technol. 35, 971 (2017).

Sygletos, S.

Tan, H. N.

Tan, M.

Winzer, P. J.

Wysocki, P.

Xi Chen,

W. Shieh and Xi Chen, “Information spectral efficiency and launch power density limits due to fiber nonlinearity for coherent optical OFDM systems,” IEEE Photonics J. 3(2), 158–173 (2011).
[Crossref]

Yariv, A.

Yoshima, S.

S. Yoshima, Y. Sun, Z. Liu, K. R. H. Bottrill, F. Parmigiani, D. J. Richardson, and P. Petropoulos, “Mitigation of nonlinear effects on WDM QAM signals enabled by optical phase conjugation with efficient bandwidth utilization,” J. Light. Technol. 35, 971 (2017).

Adv. Opt. Photonics (1)

A. D. Ellis, M. E. McCarthy, M. A. Z. Al Khateeb, M. Sorokina, and N. J. Doran, “Performance limits in optical communications due to fiber nonlinearity,” Adv. Opt. Photonics 9(3), 429–503 (2017).
[Crossref]

IEEE Photonics J. (1)

W. Shieh and Xi Chen, “Information spectral efficiency and launch power density limits due to fiber nonlinearity for coherent optical OFDM systems,” IEEE Photonics J. 3(2), 158–173 (2011).
[Crossref]

J. Appl. Phys. (1)

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “Cw three-wave mixing in single-mode optical fibers,” J. Appl. Phys. 49(10), 5098–5106 (1978).
[Crossref]

J. Light. Technol. (1)

S. Yoshima, Y. Sun, Z. Liu, K. R. H. Bottrill, F. Parmigiani, D. J. Richardson, and P. Petropoulos, “Mitigation of nonlinear effects on WDM QAM signals enabled by optical phase conjugation with efficient bandwidth utilization,” J. Light. Technol. 35, 971 (2017).

J. Lightwave Technol. (5)

J. Opt. Commun. Netw. (1)

Opt. Express (6)

Opt. Lett. (3)

Other (6)

A. D. Ellis and W. A. Stallard, “Four wave mixing in ultra long transmission systems incorporating linear amplifiers,” in IEE Colloquium on Non-Linear Effects in Fibre Communications. p. 6/1–6/4, 1990.

M. A. Z. Al-Khateeb, M. E. Mccarthy, and A. Ellis, “Performance enhancement prediction for optical phase Conjugation in Systems with 100km Amplifier Spacing,” in Proc. European Conference and Exhibition on Optical Communication (ECOC) (2017), p. Th.1.F.4.
[Crossref]

E. Desurvire, Erbium Doped Fiber Amplifiers: Principles and Applications, John Wiley & Sons, N.Y., 1994.

A. D. Ellis and N. J. Doran, “Optical link design for Minimum Power Consumption and Maximum Capacity,” in 39th European Conference and Exhibition on Optical Communication (ECOC 2013) (Institution of Engineering and Technology, 2013), pp. 1068–1070.

I. Phillips, M. Tan, M. F. Stephens, M. McCarthy, E. Giacoumidis, S. Sygletos, P. Rosa, S. Fabbri, S. T. Le, T. Kanesan, S. K. Turitsyn, N. J. Doran, P. Harper, and A. D. Ellis, “Exceeding the nonlinear-Shannon limit using Raman laser based amplification and optical phase conjugation,” in Optical Fiber Communication Conference (2014), p. M3C.1.

I. Sackey, R. Elschner, C. Schmidt-Langhorst, T. Kato, T. Tanimura, S. Watanabe, T. Hoshida, C. Schubert, and C. Schubert, “Novel wavelength-shift-free optical phase conjugator used for fiber nonlinearity mitigation in 200-Gb/s PDM-16QAM transmission,” in Optical Fiber Communication Conference (OSA,2017), p. Th3J.1.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1 Definition of segments in OPC assisted optical transmission systems. (a) Single segment spaced OPCs, (b) double segment spaced OPCs.
Fig. 2
Fig. 2 Q2 as a function of signal power for discretely amplified 2400km transmission system with uniform amplifier spacing of: (a) 24x100km, (b) 48x50km, (c) 96x25km, (d) 192x12.5km, and (e) 384x6.25km.
Fig. 3
Fig. 3 (a) Maximum Q2 factor, as a function of span length and bandwidth without OPC compensation. (b) Improvement in the maximum Q2 factor can be achieved by 1-OPC.
Fig. 4
Fig. 4 (a) Q2 as a function of signal power in 24x100km discretely amplified system. (b) maximum Q2 achieved by EDC system as a function of the signal bandwidth, (c) Q2 improvement with mid-link OPC as a function of signal bandwidth.
Fig. 5
Fig. 5 Experimental setup of OPC-assisted discretely amplified transmission system.
Fig. 6
Fig. 6 (a) Experimental setup of dual band, polarization insensitive, dual pump OPC, (b) the optical spectrum measured at the input and output 1% on each signal path.
Fig. 7
Fig. 7 Q2 as a function of signal power (top), constellation of received signal at the optimum launch power (bottom); measured at 3000km with and without OPC. The figure contains the results for 2 channels (a), 4 channels (b), and 8 channels (c).
Fig. 8
Fig. 8 Q2 as a function of distance (top), constellation of received signal at the distance marked by the black circle (bottom). The figure contains the results for 2 channels (a), 4 channels (b), and 8 channels (c).
Fig. 9
Fig. 9 Optical spectrum and BER per channel at the maximum distance (at which BER>2x10−3), for 2-channel system (a), 4-channel system (b), and 8-channel system (c); with and without OPC.

Equations (9)

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

SNR= I s N I ASE +κ I s 3 η ss ( N )+3 I s 2 I ASE η sn ( N ) ,
N I ASE = N P ASE B w =2 n sp hυN( G1 )
η ss ( N )=3 γ 2 0 B w /2 0 B w /2 [ α 2 L eff 2 α 2 +Δ β 2 ][ 1+ 4 e ( αL ) sin 2 ( ΔβL/2 ) ( 1 e ( αL ) ) 2 ] [ sin 2 ( ΔβNL/2 ) sin 2 ( ΔβL/2 ) ]d f 1 d f 2 .
κ η ss ( N )=3 γ 2 N seg 2 0 B w /2 0 B w /2 [ α( e αL +1 )sin( ΔβL/2 )+αΔβ L eff cos( ΔβL/2 ) α 2 +Δ β 2 ] 2 [ sin 2 ( ΔβNL/[ 2 N seg ] ) sin 2 ( ΔβL/2 ) ]d f 1 d f 2 ,
η ss ( N )= 3 γ 2 N 8π| β'' |α log( 2 π 2 | β'' | B w 2 α ).
κ 4 B w 2 0 B w /2 0 B w /2 ( 4 π 2 β'' f 1 f 2 ) 2 α 2 + ( 4 π 2 β'' f 1 f 2 ) 2 d f 1 d f 2 1 2α π 2 | β'' | B w 2 asinh( π 2 | β'' | B w 2 2α ).
η sn ( N )= N seg [ n=1 N/ N seg η ss ( n ) +3 I s 2 η ss ( 1 ) n=1 N/ N seg i=1 n1 η ss ( i ) ],
η sn ( N )= 3 γ 2 N N seg ( N N seg +1 ) 8πα| β '' | log( 2 π 2 | β'' | B w 2 α )[ 1+ 9 γ 2 I s 2 ( N N seg 1 ) 8πα| β '' | log( 2 π 2 | β'' | B w 2 α ) ].
B w = B ch M 2 B ch /Δf .

Metrics