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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 23 — Nov. 8, 2010
  • pp: 23608–23619
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Simultaneous and independent multi-parameter monitoring with fault localization for DSP-based coherent communication systems

Thomas Shun Rong Shen, Alan Pak Tao Lau, and Changyuan Yu  »View Author Affiliations


Optics Express, Vol. 18, Issue 23, pp. 23608-23619 (2010)
http://dx.doi.org/10.1364/OE.18.023608


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Abstract

Digital signal processing (DSP)-based coherent communications have become standard for future high-speed optical networks. Implementing DSP-based advanced algorithms for data detection requires much more detailed knowledge of the transmission link parameters, resulting in optical performance monitoring (OPM) being even more important for next generation systems. At the same time, the DSP platform also enables new strategies for OPM. In this paper, we propose the use of pilot symbols with alternating power levels and study the statistics of the received power and phase difference to simultaneously and independently monitor the carrier frequency offset between transmitter and receiver laser, laser linewidth, number of spans, fiber nonlinearity parameters as well as optical signal-to-noise ratio (OSNR) of a transmission link. Analytical predictions are verified by simulation results for systems with full chromatic dispersion (CD) compensation per span and 10% CD under-compensation per span. In addition, we show that by monitoring the changes in the statistics of the received pilot symbols during network operation, one can locate faults or OSNR degradations along a transmission link without additional monitoring equipments at intermediate nodes, which may be useful for more efficient dynamic routing and network management.

© 2010 OSA

1. Introduction

2. Simultaneous and independent multi-parameters monitoring using pilot symbols

2.1. System model

In absence of nonlinearity and when the symbol rate of the pilot symbols is low enough so that the effects of CD and PMD are negligible, the instantaneous received signal power at time t can be expressed as
P(t)=|Pk+i=1N(nSi(t)+nDi(t))|2Pk+2PkRe{i=1N(nSi(t)+nDi(t))}      for k=1,2
(1)
where the approximation is valid for high OSNR. The variance of the received signal power Pk is then given by
σpower2(Pk)=Ε[P2(t)]Ε[P(t)]2=E[Pk2+4PkPkRe{i=1N(nSi(t)+nDi(t))}+4Pk(i=1NRe{nSi(t)+nDi(t)})2]Pk2=2PkN(σS2+σD2)                                                                               for k=1,2.   
(2)
where σS(D)2=SS(D)(f)Bf and Bf is the low-pass filter bandwidth at the receiver. It should be noted that Eq. (2) is still valid for systems with fiber nonlinearity.

The overall received phaseϕ(t)after propagating through N spans of fibers is given by
ϕ(t)=ϕASE(t)+ϕNL(t)+ϕTx(t)+ϕRx(t)+2πΔfofft+θ 
(3)
which contains ASE-induced phase noise ϕASE(t), nonlinear phase noise ϕNL(t)caused by fiber nonlinearity as well as transmitter and receiver laser phase noise ϕTx(t) and ϕRx(t). The frequency offset between the transmitter and receiver phase noise is denoted by Δfoff and θ is the relative phase of the transmitter (Tx) and receiver (Rx) laser at t = 0. For high OSNR, the ASE-induced phase noise can be approximated as
ϕASE(t)Im{i=1N[nSi(t)+nDi(t)]}Pkfork=1,2
(4)
with zero mean and variance

σASE2(Pk)=N2Pk(σS2+σD2)                          for k=1,2.
(5)

Let γS and γDbe the nonlinear coefficients of the SMF and DCF, and Leff,S and Leff,D be the effective lengths of SMF and DCF respectively. Defining ΛS=γSLeff,S and ΛD=γDLeff,D, the overall nonlinear phase shift at the receiver is given by
ϕNL(t)=ΛS|Pk|2+ΛD|Pk+nS1(t)|2               +ΛS|Pk+nS1(t)+nD1(t)|2+ΛD|Pk+nS1(t)+nD1(t)+nS2(t)|2+               +ΛS|Pk+nS1(t)+nSN1(t)+nD1(t)++nDN1(t)|2               +ΛD|Pk+nS1(t)+nSN(t)+nD1(t)++nDN1(t)|2           =i=1N(ΛD|Pk+l=1inSl(t)+m=1i1nDm(t)|2+ΛS|Pk+m=1i1nSm(t)+m=1i1nDm(t)|2)           i=1NΛD(Pk+2PkRe{l=1inSl(t)+m=1i1nDm(t)})              +i=1NΛS(Pk+2PkRe{l=1i1nSl(t)+m=1i1nDm(t)})                        for k=1,2.
(6)
where the approximation is valid for high OSNR. In this case, the mean and variance of the nonlinear phase shiftϕNL(t)is given by
ϕNL(Pk)¯=PkN(ΛS+ΛD)                          for k=1,2
(7)
and
σNL2(Pk)=Ε[ϕNL2(Pk)]Ε[ϕNL(Pk)]2            =2Pk(ΛS+ΛD)2σD2[(N1)2+(N2)2++1]               +2PkσS2{[ΛS(N1)+ΛDN]2+[ΛS(N2)+ΛD(N1)]2++ΛD2}            =2Pk(ΛS+ΛD)2σD2i=1N1i2+2PkσS2(ΛS2i=1N1i2+ΛD2i=1Ni2)               +4ΛSΛDPkσS2i=0N1(Ni)24ΛSΛDPkσS2i=0N1(Ni)              for k=1,2.
As i=1Ni2=N(N+1)(2N+1)6 andi=1Ni=N(N+1)2,
σNL2(Pk)=2Pk(ΛS+ΛD)2σD2N(N1)(2N1)6               +2PkσS2[ΛS2N(N1)(2N1)6+ΛD2N(N+1)(2N+1)6]               +4ΛSΛDPkσS2[N(N+1)(2N+1)6N(N+1)2]            =2Pk(ΛS+ΛD)2(σS2+σD2)(13N312N2+16N)               +2PkσS2[ΛD2N2+ΛSΛD(N2N)]                                      for k=1,2.
(8)
Assuming Tx and Rx lasers with identical linewidth, the spectrum of the laser output ejϕTx(Rx)(t)can be modeled as a Lorentzian lineshape with 3-dB linewidth ΔfLWin which

E[ej(ϕTx(Rx)(t1)ϕTx(Rx)(t2))]=exp(πΔfLW|t1t2|).
(9)

Equivalently, the phase noise ϕTx(Rx)(t)can be modeled as a Wiener process in which ϕTx(Rx)(t2)ϕTx(Rx)(t1)is Gaussian distributed with zero mean and variance

σLW2=2πΔfLW|t1t2|.
(10)

2.2. Simultaneous and independent multi-parameter monitoring

The frequency offset between the Tx and Rx lasers and their linewidths can be obtained from the statistics of the phase difference between samples within a pilot symbol. Without loss of generality, let ϕ(t) andϕ(t+w1Ts)belong to the same pilot symbol with power Pk and ϕ(t)being the first sample of the symbol. The phase difference between these two samples is given by
Δϕ(w1)=ϕ(t+w1Ts)ϕ(t)     =[ϕASE(t)+ϕNL(t)+ϕTx(t)+ϕRx(t)]-              [ϕASE(t+w1Ts)+ϕNL(t+w1Ts)+ϕTx(t+w1Ts)+ϕRx(t+w1Ts)]+2πΔfoffw1Ts 
where w1=1,2,η1 and η=T/Ts is the number of samples per symbol. AsϕASE(t) and ϕNL(t) are uncorrelated with each other [17

17. A. P. T. Lau and J. M. Kahn, “Design of inline amplifier gains and spacings to minimize the phase noise in optical transmission systems,” J. Lightwave Technol. 24(3), 1334–1341 (2006). [CrossRef]

] and ϕASE(NL)(t) and ϕASE(NL)(t+w1Ts)are also uncorrelated if we choose the filter bandwidth Bf=12Ts, the mean and variance of Δϕ(w1) is given by
Δϕ(w1)¯=2πΔfoffw1Ts
(11)
and
σΔϕ,k2(w1)=2σNL2(Pk)+2σASE2(Pk)+2×2πΔfLWw1Ts
(12)
It is obvious from Eq. (12) that the linear and nonlinear phase noise variance σASE2(Pk) and σNL2(Pk) do not depend on w1. Therefore, for two values w1 and w2 such that ϕ(t),ϕ(t+w1Ts) and ϕ(t+w2Ts)belong to the same pilot symbol, the difference between σΔϕ,k2(w1) and σΔϕ,k2(w2)can be expressed as
σΔϕ,k2(w1)σΔϕ,k2(w2)=2×2πΔfLW(w1w2)Ts
(13)
With (11) and (13), the frequency offset and laser linewidth of the Tx and Rx lasers can be estimated by
Δfoff=Δϕ¯(w1)2πw1Ts 
(14)
and
ΔfLW=σΔϕ,k2(w2)σΔϕ,k2(w1)4π(w2w1)Ts
(15)
The statistics of the phase difference Δϕ(w1)also allow us to simultaneously and independently monitor the number of spans N, fiber nonlinear parameters as well as OSNR of the link. In particular, if we choose w1=η, the two samples ϕ(t) and ϕ(t+w1Ts)will belong to different pilot symbols with different power levels. In this case, the mean of the phase difference will be given by
Δϕ(η)¯=(P2P1)N(ΛS+ΛD)+2πΔfoffT
(16)
assuming the signal power at time t is P(t)=P1.

As the parameters of SMF such as length, attenuation and nonlinear coefficients are usually known and relatively more consistent across a network compared to those of DCF in practice, we will assume the knowledge ofσS2 and ΛS when monitoring the number of span N, fiber nonlinear coefficient and OSNR of the link. With Eqs. (2), (5), (8), (12)-(16) and some algebraic manipulations, one obtain
2(P1+P2)σS2(ΛS2ΛSΛφ(η)¯P1P2)N3+[(P1+P2)Λφ(η)¯2σpower2(P1)3(P1P2)2P1+2(P1+P2)σS2Λφ(η)¯2(P1P2)22(P1+P2)ΛSσS2Δφ(η)¯P1P+σpower2(P1)4P1(1P1+1P2)(σΔφ,12(w1)+σΔφ,22(w2))]N2(P1+P2)Δφ(η)¯2σpower2(P1)2P1(P1P2)2N+(P1+P2)Δφ(η)¯2σpower2(P1)6P1(P1P2)2=0
which is a cubic function of N. Subsequently, the fiber nonlinear parameter ΛD and OSNR can be calculated by
ΛD=Δϕ(η)¯-2πΔfoffT(P1P2)N -ΛS
(18)
and

OSNR=PkN(σS2+σD2)=Pkσpower22Pk=2Pk2σpower2                     for k=1,2.
(19)

3. Simulation Results and Discussions

Simulations are conducted to investigate the monitoring performance of Δfoff,ΔfLW,N, ΛD and OSNR. Pilot sequences with 106 symbols with NRZ pulse shape are transmitted at two arbitrarily chosen power levels of P1=3dBm and P2=2dBm. The symbol rate is chosen to be 50 MSym/s so that the effects of CD and PMD become negligible. The sampling rate is set to be 25 GHz and thus η=500. In our simulations, high analog-to-digital converter resolution (ADC) and timing recovery are assumed and other channel parameters are listed in Table 1. To maximize the monitoring range of Δfofffor a given sampling rate, w1 is chosen to be 1. In addition, we arbitrarily set w2=3for laser linewidth monitoring. Simulation results for frequency offset and laser linewidth monitoring for a 15-span system are shown in Figs. 4(a)
Fig. 4 (a) Estimated frequency offset vs. true frequency offset (b) Estimated laser linewidth vs. true laser linewidth for a 15-span system. Samples from106symbols are used for each estimate and the error bars indicate standard deviations of 10 independent estimates.
and 4(b) for full CD compensated and 10% CD under-compensated links. The means and standard deviations of the estimates are obtained from 10 independent trials with independent ASE noise. From the figures, the proposed technique enables a wide monitoring range from −10 GHz to 10GHz, more than sufficient for worst cases of ±5GHz reported in practical systems [18

18. T. Tanimura, et al., “Digital clock recovery algorithm for optical coherent receivers operating independent of laser frequency offset,” in 34th European Conference on Optical Communication (ECOC), (2008), Paper Mo.3.D.2.

]. The corresponding maximum estimation error is below 6 MHz. For laser linewidth monitoring, a wide dynamic range of 100 kHz to 10 MHz with corresponding maximum estimation error below 1% is achieved. Such monitoring performance is comparable to others reported in the literature [4

4. T. Duthel, G. Clarici, C. R. S. Fludger, J. C. Geyer, C. Schulien, and S. Wiese, “Laser Linewidth Estimation by Means of Coherent Detection,” IEEE Photon. Technol. Lett. 21(20), 1568–1570 (2009). [CrossRef]

] that only monitors laser linewidths. It is also noted that the monitoring performance does not depend on the dispersion map of the transmission link.

4. Receiver-based fault localization using statistics of received pilot symbols

A calibration graph of the fault locations indexed according to the number of span starting from the transmitter vs. ΔσΔϕ,k2(1)for different Δσi2is given in Fig. 6
Fig. 6 Change in variance of phase differenceΔσΔϕ2(1)vs. fault location with Δσi2=, 8 and 10 dB for a 20-span link. Samples from106symbols are used for each estimate and the error bars indicate standard deviations of 10 independent estimates.
for a 20-span link. The other parameters of the pilot sequence and the channel used in the simulation are identical to those in Section 3. From the figure, for a given Δσi2, the change in variance of phase difference ΔσΔϕ,k2(1)is distinct for different fault locations. In a network where fault locations are detected through other means, the proposed method may provide additional information about the status of the network and simplify network layer communication protocols and enhance efficiencies in network management.

5. Conclusions

Acknowledgments

The authors would like to acknowledge the support of the Hong Kong Government General Research Fund under project number 519910.

References and links

1.

Z. Q. Pan, C. Y. Yu, and A. E. Willner, “Optical performance monitoring for the next generation optical communication networks,” Opt. Fiber Technol. 16(1), 20–45 (2010). [CrossRef]

2.

S. Zhang, et al., “Novel ultra wide-range frequency offset estimation for digital coherent optical receiver,” in Optical Fiber Communication/National Fiber Optic Engineers Conference, (OFC/NFOEC), 2010, Paper OWV3.

3.

Y. Cao, S. Yu, J. Shen, W. Gu, and Y. Ji, “Frequency Estimation for Optical Coherent MPSK System Without Removing Modulated Data Phase,” IEEE Photon. Technol. Lett. 22(10), 691–693 (2010). [CrossRef]

4.

T. Duthel, G. Clarici, C. R. S. Fludger, J. C. Geyer, C. Schulien, and S. Wiese, “Laser Linewidth Estimation by Means of Coherent Detection,” IEEE Photon. Technol. Lett. 21(20), 1568–1570 (2009). [CrossRef]

5.

A. P. T. Lau and J. M. Kahn, “Signal design and detection in presence of nonlinear phase noise,” J. Lightwave Technol. 25(10), 3008–3016 (2007). [CrossRef]

6.

K. P. Ho and J. M. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” J. Lightwave Technol. 22(3), 779–783 (2004). [CrossRef]

7.

A. P. T. Lau, S. Rabbani, and J. M. Kahn, “On the Statistics of Intrachannel Four-Wave Mixing in Phase-Modulated Optical Communication Systems,” J. Lightwave Technol. 26(14), 2128–2135 (2008). [CrossRef]

8.

E. Ip and J. M. Kahn, “Compensation of Dispersion and Nonlinear Impairments Using Digital Backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008). [CrossRef]

9.

E. F. Mateo and G. F. Li, “Compensation of interchannel nonlinearities using enhanced coupled equations for digital backward propagation,” Appl. Opt. 48(25), F6–F10 (2009). [CrossRef] [PubMed]

10.

K. S. Kim, R. H. Stolen, W. A. Reed, and K. W. Quoi, “Measurement of the nonlinear index of silica-core and dispersion-shifted fibers,” Opt. Lett. 19(4), 257–259 (1994). [CrossRef] [PubMed]

11.

T. Kato, Y. Suetsugu, M. Takagi, E. Sasaoka, and M. Nishimura, “Measurement of the nonlinear refractive index in optical fiber by the cross-phase-modulation method with depolarized pump light,” Opt. Lett. 20(9), 988–990 (1995). [CrossRef] [PubMed]

12.

L. Prigent and J. P. Hamaide, “Measurement of Fiber Nonlinear Kerr Coefficient by four-Wave-Mixing,” IEEE Photon. Technol. Lett. 5(9), 1092–1095 (1993). [CrossRef]

13.

C. Xu and X. Liu, “Postnonlinearity compensation with data-driven phase modulators in phase-shift keying transmission,” Opt. Lett. 27(18), 1619–1621 (2002). [CrossRef]

14.

M. N. Petersen and M. L. Nielsen, “Experimental and theoretical demonstration of launch power optimisation using subcarrier fibre nonlinearity monitor,” Electron. Lett. 41(5), 268–269 (2005). [CrossRef]

15.

M. Mayrock and H. Haunstein, “Monitoring of Linear and Nonlinear Signal Distortion in Coherent Optical OFDM Transmission,” J. Lightwave Technol. 27(16), 3560–3566 (2009). [CrossRef]

16.

T. Takahito, et al., “Semi-Blind Nonlinear Equalization in Coherent Multi-Span Transmission System with Inhomogeneous Span Parameters,” in Optical Fiber Communication/National Fiber Optic Engineers Conference, (OFC/NFOEC), 2010, Paper OMR6.

17.

A. P. T. Lau and J. M. Kahn, “Design of inline amplifier gains and spacings to minimize the phase noise in optical transmission systems,” J. Lightwave Technol. 24(3), 1334–1341 (2006). [CrossRef]

18.

T. Tanimura, et al., “Digital clock recovery algorithm for optical coherent receivers operating independent of laser frequency offset,” in 34th European Conference on Optical Communication (ECOC), (2008), Paper Mo.3.D.2.

19.

Y. G. Wen, V. W. S. Chan, and L. Z. Zheng, “Efficient fault-diagnosis algorithms for all-optical WDM networks with probabilistic link failures,” J. Lightwave Technol. 23(10), 3358–3371 (2005). [CrossRef]

20.

J. H. Park, J. S. Baik, and C. H. Lee, “Fault-localization in WDM-PONs,” in Optical Fiber Communication/National Fiber Optic Engineers Conference (OFC/NFOEC), 2006, Paper JThB79.

21.

S. S. Ahuja, S. Ramasubramanian, and M. Krunz, “Single-Link Failure Detection in All-Optical Networks using Monitoring Cycles and Paths,” IEEE/ACM Transactions on Networking, 17, 1080–1093 (2009).

22.

A. V. Sichani and H. T. Mouftah, “Limited-perimeter vector matching fault-localization protocol for transparent all-optical communication networks,” IET Communications 1(3), 472–478 (2007). [CrossRef]

23.

M. Khair, B. Kantarci, J. Zheng, and H. T. Mouftah, “Optimization for Fault Localization in All-Optical Networks,” J. Lightwave Technol. 27(21), 4832–4840 (2009). [CrossRef]

OCIS Codes
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(060.1660) Fiber optics and optical communications : Coherent communications
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: September 27, 2010
Revised Manuscript: October 21, 2010
Manuscript Accepted: October 21, 2010
Published: October 26, 2010

Citation
Thomas Shun Rong Shen, Alan Pak Tao Lau, and Changyuan Yu, "Simultaneous and independent multi-parameter monitoring with fault localization for DSP-based coherent communication systems," Opt. Express 18, 23608-23619 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-23-23608


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References

  1. Z. Q. Pan, C. Y. Yu, and A. E. Willner, “Optical performance monitoring for the next generation optical communication networks,” Opt. Fiber Technol. 16(1), 20–45 (2010). [CrossRef]
  2. S. Zhang, et al., “Novel ultra wide-range frequency offset estimation for digital coherent optical receiver,” in Optical Fiber Communication/National Fiber Optic Engineers Conference, (OFC/NFOEC), 2010, Paper OWV3.
  3. Y. Cao, S. Yu, J. Shen, W. Gu, and Y. Ji, “Frequency Estimation for Optical Coherent MPSK System Without Removing Modulated Data Phase,” IEEE Photon. Technol. Lett. 22(10), 691–693 (2010). [CrossRef]
  4. T. Duthel, G. Clarici, C. R. S. Fludger, J. C. Geyer, C. Schulien, and S. Wiese, “Laser Linewidth Estimation by Means of Coherent Detection,” IEEE Photon. Technol. Lett. 21(20), 1568–1570 (2009). [CrossRef]
  5. A. P. T. Lau and J. M. Kahn, “Signal design and detection in presence of nonlinear phase noise,” J. Lightwave Technol. 25(10), 3008–3016 (2007). [CrossRef]
  6. K. P. Ho and J. M. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” J. Lightwave Technol. 22(3), 779–783 (2004). [CrossRef]
  7. A. P. T. Lau, S. Rabbani, and J. M. Kahn, “On the Statistics of Intrachannel Four-Wave Mixing in Phase-Modulated Optical Communication Systems,” J. Lightwave Technol. 26(14), 2128–2135 (2008). [CrossRef]
  8. E. Ip and J. M. Kahn, “Compensation of Dispersion and Nonlinear Impairments Using Digital Backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008). [CrossRef]
  9. E. F. Mateo and G. F. Li, “Compensation of interchannel nonlinearities using enhanced coupled equations for digital backward propagation,” Appl. Opt. 48(25), F6–F10 (2009). [CrossRef] [PubMed]
  10. K. S. Kim, R. H. Stolen, W. A. Reed, and K. W. Quoi, “Measurement of the nonlinear index of silica-core and dispersion-shifted fibers,” Opt. Lett. 19(4), 257–259 (1994). [CrossRef] [PubMed]
  11. T. Kato, Y. Suetsugu, M. Takagi, E. Sasaoka, and M. Nishimura, “Measurement of the nonlinear refractive index in optical fiber by the cross-phase-modulation method with depolarized pump light,” Opt. Lett. 20(9), 988–990 (1995). [CrossRef] [PubMed]
  12. L. Prigent and J. P. Hamaide, “Measurement of Fiber Nonlinear Kerr Coefficient by four-Wave-Mixing,” IEEE Photon. Technol. Lett. 5(9), 1092–1095 (1993). [CrossRef]
  13. C. Xu and X. Liu, “Postnonlinearity compensation with data-driven phase modulators in phase-shift keying transmission,” Opt. Lett. 27(18), 1619–1621 (2002). [CrossRef]
  14. M. N. Petersen and M. L. Nielsen, “Experimental and theoretical demonstration of launch power optimisation using subcarrier fibre nonlinearity monitor,” Electron. Lett. 41(5), 268–269 (2005). [CrossRef]
  15. M. Mayrock and H. Haunstein, “Monitoring of Linear and Nonlinear Signal Distortion in Coherent Optical OFDM Transmission,” J. Lightwave Technol. 27(16), 3560–3566 (2009). [CrossRef]
  16. T. Takahito, et al., “Semi-Blind Nonlinear Equalization in Coherent Multi-Span Transmission System with Inhomogeneous Span Parameters,” in Optical Fiber Communication/National Fiber Optic Engineers Conference, (OFC/NFOEC), 2010, Paper OMR6.
  17. A. P. T. Lau and J. M. Kahn, “Design of inline amplifier gains and spacings to minimize the phase noise in optical transmission systems,” J. Lightwave Technol. 24(3), 1334–1341 (2006). [CrossRef]
  18. T. Tanimura, et al., “Digital clock recovery algorithm for optical coherent receivers operating independent of laser frequency offset,” in 34th European Conference on Optical Communication (ECOC), (2008), Paper Mo.3.D.2.
  19. Y. G. Wen, V. W. S. Chan, and L. Z. Zheng, “Efficient fault-diagnosis algorithms for all-optical WDM networks with probabilistic link failures,” J. Lightwave Technol. 23(10), 3358–3371 (2005). [CrossRef]
  20. J. H. Park, J. S. Baik, and C. H. Lee, “Fault-localization in WDM-PONs,” in Optical Fiber Communication/National Fiber Optic Engineers Conference (OFC/NFOEC), 2006, Paper JThB79.
  21. S. S. Ahuja, S. Ramasubramanian, and M. Krunz, “Single-Link Failure Detection in All-Optical Networks using Monitoring Cycles and Paths,” IEEE/ACM Transactions on Networking, 17, 1080–1093 (2009).
  22. A. V. Sichani and H. T. Mouftah, “Limited-perimeter vector matching fault-localization protocol for transparent all-optical communication networks,” IET Communications 1(3), 472–478 (2007). [CrossRef]
  23. M. Khair, B. Kantarci, J. Zheng, and H. T. Mouftah, “Optimization for Fault Localization in All-Optical Networks,” J. Lightwave Technol. 27(21), 4832–4840 (2009). [CrossRef]

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