Download - A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems
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A Discrete-Time Polynomial Model of SingleChannel Long-Haul Fiber-Optic Communication
Systems
Houbing Song and Maıte Brandt-Pearce
Charles L. Brown Department of Electrical and Computer EngineeringUniversity of Virginia, USA
[email protected], [email protected]
IEEE ICC2011Kyoto, JapanJune 7, 2011
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Outline
1 IntroductionMotivationNonlinear Schrodinger Equation
2 Model DevelopmentStep 1: Extension of VSTF to Multispan Multipulse CaseStep 2: Simplification of Triple Integral to Simple IntegralStep 3: Conversion to Time DomainStep 4: Extension to include Photodetector
3 Model Validation
4 Model Application: Constrained CodingCoding SchemePerformance Evaluation
5 Conclusion
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 2/26
![Page 3: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/3.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Outline
1 IntroductionMotivationNonlinear Schrodinger Equation
2 Model DevelopmentStep 1: Extension of VSTF to Multispan Multipulse CaseStep 2: Simplification of Triple Integral to Simple IntegralStep 3: Conversion to Time DomainStep 4: Extension to include Photodetector
3 Model Validation
4 Model Application: Constrained CodingCoding SchemePerformance Evaluation
5 Conclusion
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 3/26
![Page 4: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/4.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Dense Wavelength Division Multiplexing (DWDM)
Physical impairments in DWDM systems
DispersionFiber nonlinearitiesNoise
Signal processing for optical communications requires a model2D: time and wavelength
Intrachannel impairmentsInterchannel impairments
Discrete-time: digital communications, digital signal processing(DSP)
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 4/26
![Page 5: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/5.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Dense Wavelength Division Multiplexing (DWDM)
Physical impairments in DWDM systems
DispersionFiber nonlinearitiesNoise
Signal processing for optical communications requires a model2D: time and wavelength
Intrachannel impairmentsInterchannel impairments
Discrete-time: digital communications, digital signal processing(DSP)
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 4/26
![Page 6: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/6.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Dense Wavelength Division Multiplexing (DWDM)
Physical impairments in DWDM systems
DispersionFiber nonlinearitiesNoise
Signal processing for optical communications requires a model2D: time and wavelength
Intrachannel impairmentsInterchannel impairments
Discrete-time: digital communications, digital signal processing(DSP)
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 4/26
![Page 7: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/7.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Dense Wavelength Division Multiplexing (DWDM)
Physical impairments in DWDM systems
DispersionFiber nonlinearitiesNoise
Signal processing for optical communications requires a model2D: time and wavelength
Intrachannel impairmentsInterchannel impairments
Discrete-time: digital communications, digital signal processing(DSP)
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 4/26
![Page 8: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/8.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Dense Wavelength Division Multiplexing (DWDM)
Physical impairments in DWDM systems
DispersionFiber nonlinearitiesNoise
Signal processing for optical communications requires a model2D: time and wavelength
Intrachannel impairmentsInterchannel impairments
Discrete-time: digital communications, digital signal processing(DSP)
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 4/26
![Page 9: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/9.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Dense Wavelength Division Multiplexing (DWDM)
Physical impairments in DWDM systems
DispersionFiber nonlinearitiesNoise
Signal processing for optical communications requires a model2D: time and wavelength
Intrachannel impairmentsInterchannel impairments
Discrete-time: digital communications, digital signal processing(DSP)
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 4/26
![Page 10: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/10.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Dense Wavelength Division Multiplexing (DWDM)
Physical impairments in DWDM systems
DispersionFiber nonlinearitiesNoise
Signal processing for optical communications requires a model2D: time and wavelength
Intrachannel impairmentsInterchannel impairments
Discrete-time: digital communications, digital signal processing(DSP)
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 4/26
![Page 11: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/11.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Dense Wavelength Division Multiplexing (DWDM)
Physical impairments in DWDM systems
DispersionFiber nonlinearitiesNoise
Signal processing for optical communications requires a model2D: time and wavelength
Intrachannel impairmentsInterchannel impairments
Discrete-time: digital communications, digital signal processing(DSP)
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 4/26
![Page 12: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/12.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Dense Wavelength Division Multiplexing (DWDM)
Physical impairments in DWDM systems
DispersionFiber nonlinearitiesNoise
Signal processing for optical communications requires a model2D: time and wavelength
Intrachannel impairmentsInterchannel impairments
Discrete-time: digital communications, digital signal processing(DSP)
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 4/26
![Page 13: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/13.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Dense Wavelength Division Multiplexing (DWDM)
Physical impairments in DWDM systems
DispersionFiber nonlinearitiesNoise
Signal processing for optical communications requires a model2D: time and wavelength
Intrachannel impairmentsInterchannel impairments
Discrete-time: digital communications, digital signal processing(DSP)
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 4/26
![Page 14: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/14.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Previous Work: single span caseTriple integral
Volterra series transfer function (VSTF) method(Peddanarappagari and Brandt-Pearce, 1997)perturbation method (Ablowitz, 1998)
Single integral (Mecozzi, 2000; Essiambre, 2002) but ignoresfiber losschirpphotodetection
Our Work: a single channel multipulse multispan modelsimplifies the triple integral to a simple integral for Gaussianpulsescomputational advantage over the split-step Fourier (SSF)method with comparable accuracyeasily extendable to multichannel case and 2-polarization-modecasetakes into account the parameters ignored in the literature
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 5/26
![Page 15: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/15.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Previous Work: single span caseTriple integral
Volterra series transfer function (VSTF) method(Peddanarappagari and Brandt-Pearce, 1997)perturbation method (Ablowitz, 1998)
Single integral (Mecozzi, 2000; Essiambre, 2002) but ignoresfiber losschirpphotodetection
Our Work: a single channel multipulse multispan modelsimplifies the triple integral to a simple integral for Gaussianpulsescomputational advantage over the split-step Fourier (SSF)method with comparable accuracyeasily extendable to multichannel case and 2-polarization-modecasetakes into account the parameters ignored in the literature
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 5/26
![Page 16: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/16.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Previous Work: single span caseTriple integral
Volterra series transfer function (VSTF) method(Peddanarappagari and Brandt-Pearce, 1997)perturbation method (Ablowitz, 1998)
Single integral (Mecozzi, 2000; Essiambre, 2002) but ignoresfiber losschirpphotodetection
Our Work: a single channel multipulse multispan modelsimplifies the triple integral to a simple integral for Gaussianpulsescomputational advantage over the split-step Fourier (SSF)method with comparable accuracyeasily extendable to multichannel case and 2-polarization-modecasetakes into account the parameters ignored in the literature
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 5/26
![Page 17: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/17.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Previous Work: single span caseTriple integral
Volterra series transfer function (VSTF) method(Peddanarappagari and Brandt-Pearce, 1997)perturbation method (Ablowitz, 1998)
Single integral (Mecozzi, 2000; Essiambre, 2002) but ignoresfiber losschirpphotodetection
Our Work: a single channel multipulse multispan modelsimplifies the triple integral to a simple integral for Gaussianpulsescomputational advantage over the split-step Fourier (SSF)method with comparable accuracyeasily extendable to multichannel case and 2-polarization-modecasetakes into account the parameters ignored in the literature
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 5/26
![Page 18: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/18.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Previous Work: single span caseTriple integral
Volterra series transfer function (VSTF) method(Peddanarappagari and Brandt-Pearce, 1997)perturbation method (Ablowitz, 1998)
Single integral (Mecozzi, 2000; Essiambre, 2002) but ignoresfiber losschirpphotodetection
Our Work: a single channel multipulse multispan modelsimplifies the triple integral to a simple integral for Gaussianpulsescomputational advantage over the split-step Fourier (SSF)method with comparable accuracyeasily extendable to multichannel case and 2-polarization-modecasetakes into account the parameters ignored in the literature
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 5/26
![Page 19: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/19.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Previous Work: single span caseTriple integral
Volterra series transfer function (VSTF) method(Peddanarappagari and Brandt-Pearce, 1997)perturbation method (Ablowitz, 1998)
Single integral (Mecozzi, 2000; Essiambre, 2002) but ignoresfiber losschirpphotodetection
Our Work: a single channel multipulse multispan modelsimplifies the triple integral to a simple integral for Gaussianpulsescomputational advantage over the split-step Fourier (SSF)method with comparable accuracyeasily extendable to multichannel case and 2-polarization-modecasetakes into account the parameters ignored in the literature
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 5/26
![Page 20: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/20.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Previous Work: single span caseTriple integral
Volterra series transfer function (VSTF) method(Peddanarappagari and Brandt-Pearce, 1997)perturbation method (Ablowitz, 1998)
Single integral (Mecozzi, 2000; Essiambre, 2002) but ignoresfiber losschirpphotodetection
Our Work: a single channel multipulse multispan modelsimplifies the triple integral to a simple integral for Gaussianpulsescomputational advantage over the split-step Fourier (SSF)method with comparable accuracyeasily extendable to multichannel case and 2-polarization-modecasetakes into account the parameters ignored in the literature
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 5/26
![Page 21: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/21.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Previous Work: single span caseTriple integral
Volterra series transfer function (VSTF) method(Peddanarappagari and Brandt-Pearce, 1997)perturbation method (Ablowitz, 1998)
Single integral (Mecozzi, 2000; Essiambre, 2002) but ignoresfiber losschirpphotodetection
Our Work: a single channel multipulse multispan modelsimplifies the triple integral to a simple integral for Gaussianpulsescomputational advantage over the split-step Fourier (SSF)method with comparable accuracyeasily extendable to multichannel case and 2-polarization-modecasetakes into account the parameters ignored in the literature
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 5/26
![Page 22: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/22.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Previous Work: single span caseTriple integral
Volterra series transfer function (VSTF) method(Peddanarappagari and Brandt-Pearce, 1997)perturbation method (Ablowitz, 1998)
Single integral (Mecozzi, 2000; Essiambre, 2002) but ignoresfiber losschirpphotodetection
Our Work: a single channel multipulse multispan modelsimplifies the triple integral to a simple integral for Gaussianpulsescomputational advantage over the split-step Fourier (SSF)method with comparable accuracyeasily extendable to multichannel case and 2-polarization-modecasetakes into account the parameters ignored in the literature
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 5/26
![Page 23: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/23.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Previous Work: single span caseTriple integral
Volterra series transfer function (VSTF) method(Peddanarappagari and Brandt-Pearce, 1997)perturbation method (Ablowitz, 1998)
Single integral (Mecozzi, 2000; Essiambre, 2002) but ignoresfiber losschirpphotodetection
Our Work: a single channel multipulse multispan modelsimplifies the triple integral to a simple integral for Gaussianpulsescomputational advantage over the split-step Fourier (SSF)method with comparable accuracyeasily extendable to multichannel case and 2-polarization-modecasetakes into account the parameters ignored in the literature
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 5/26
![Page 24: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/24.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Previous Work: single span caseTriple integral
Volterra series transfer function (VSTF) method(Peddanarappagari and Brandt-Pearce, 1997)perturbation method (Ablowitz, 1998)
Single integral (Mecozzi, 2000; Essiambre, 2002) but ignoresfiber losschirpphotodetection
Our Work: a single channel multipulse multispan modelsimplifies the triple integral to a simple integral for Gaussianpulsescomputational advantage over the split-step Fourier (SSF)method with comparable accuracyeasily extendable to multichannel case and 2-polarization-modecasetakes into account the parameters ignored in the literature
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 5/26
![Page 25: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/25.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Previous Work: single span caseTriple integral
Volterra series transfer function (VSTF) method(Peddanarappagari and Brandt-Pearce, 1997)perturbation method (Ablowitz, 1998)
Single integral (Mecozzi, 2000; Essiambre, 2002) but ignoresfiber losschirpphotodetection
Our Work: a single channel multipulse multispan modelsimplifies the triple integral to a simple integral for Gaussianpulsescomputational advantage over the split-step Fourier (SSF)method with comparable accuracyeasily extendable to multichannel case and 2-polarization-modecasetakes into account the parameters ignored in the literature
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 5/26
![Page 26: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/26.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Motivation
Previous Work: single span caseTriple integral
Volterra series transfer function (VSTF) method(Peddanarappagari and Brandt-Pearce, 1997)perturbation method (Ablowitz, 1998)
Single integral (Mecozzi, 2000; Essiambre, 2002) but ignoresfiber losschirpphotodetection
Our Work: a single channel multipulse multispan modelsimplifies the triple integral to a simple integral for Gaussianpulsescomputational advantage over the split-step Fourier (SSF)method with comparable accuracyeasily extendable to multichannel case and 2-polarization-modecasetakes into account the parameters ignored in the literature
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 5/26
![Page 27: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/27.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Nonlinear Schrodinger Equation
∂A
∂z= −α
2A− iβ2
2
∂2A
∂t2+ iγ|A|2A
A = A(t, z): slowly varying complex envelope
t: propagation time
z : propagation distance
α: attenuation constant
β2: group-velocity dispersion (GVD) parameter
γ: nonlinear parameter
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 6/26
![Page 28: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/28.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Nonlinear Schrodinger Equation
∂A
∂z= −α
2A− iβ2
2
∂2A
∂t2+ iγ|A|2A
A = A(t, z): slowly varying complex envelope
t: propagation time
z : propagation distance
α: attenuation constant
β2: group-velocity dispersion (GVD) parameter
γ: nonlinear parameter
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 6/26
![Page 29: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/29.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Nonlinear Schrodinger Equation
∂A
∂z= −α
2A− iβ2
2
∂2A
∂t2+ iγ|A|2A
A = A(t, z): slowly varying complex envelope
t: propagation time
z : propagation distance
α: attenuation constant
β2: group-velocity dispersion (GVD) parameter
γ: nonlinear parameter
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 6/26
![Page 30: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/30.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Nonlinear Schrodinger Equation
∂A
∂z= −α
2A− iβ2
2
∂2A
∂t2+ iγ|A|2A
A = A(t, z): slowly varying complex envelope
t: propagation time
z : propagation distance
α: attenuation constant
β2: group-velocity dispersion (GVD) parameter
γ: nonlinear parameter
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 6/26
![Page 31: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/31.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Nonlinear Schrodinger Equation
∂A
∂z= −α
2A− iβ2
2
∂2A
∂t2+ iγ|A|2A
A = A(t, z): slowly varying complex envelope
t: propagation time
z : propagation distance
α: attenuation constant
β2: group-velocity dispersion (GVD) parameter
γ: nonlinear parameter
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 6/26
![Page 32: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/32.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Nonlinear Schrodinger Equation
∂A
∂z= −α
2A− iβ2
2
∂2A
∂t2+ iγ|A|2A
A = A(t, z): slowly varying complex envelope
t: propagation time
z : propagation distance
α: attenuation constant
β2: group-velocity dispersion (GVD) parameter
γ: nonlinear parameter
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 6/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Fiber Nonlinearities
Multipulse: A =∑K−1
k=0 Ak
K−1∑k=0
(∂Ak
∂z+α
2Ak + i
β2
2
∂2Ak
∂t2) = iγ
K−1∑l ,m,n=0
AlA∗mAn
Time-matching location: (l −m + n)T
l = m = n: self phase modulation (SPM) ⇒ spectralbroadeningl = m 6= n or l 6= m = n: intrachannel cross phase modulation(IXPM) ⇒ timing jitterl 6= m 6= n or l = n 6= m: intrachannel four wave mixing(IFWM) ⇒ amplitude jitter and ghost pulse
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 7/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Fiber Nonlinearities
Multipulse: A =∑K−1
k=0 Ak
K−1∑k=0
(∂Ak
∂z+α
2Ak + i
β2
2
∂2Ak
∂t2) = iγ
K−1∑l ,m,n=0
AlA∗mAn
Time-matching location: (l −m + n)T
l = m = n: self phase modulation (SPM) ⇒ spectralbroadeningl = m 6= n or l 6= m = n: intrachannel cross phase modulation(IXPM) ⇒ timing jitterl 6= m 6= n or l = n 6= m: intrachannel four wave mixing(IFWM) ⇒ amplitude jitter and ghost pulse
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 7/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Fiber Nonlinearities
Multipulse: A =∑K−1
k=0 Ak
K−1∑k=0
(∂Ak
∂z+α
2Ak + i
β2
2
∂2Ak
∂t2) = iγ
K−1∑l ,m,n=0
AlA∗mAn
Time-matching location: (l −m + n)T
l = m = n: self phase modulation (SPM) ⇒ spectralbroadeningl = m 6= n or l 6= m = n: intrachannel cross phase modulation(IXPM) ⇒ timing jitterl 6= m 6= n or l = n 6= m: intrachannel four wave mixing(IFWM) ⇒ amplitude jitter and ghost pulse
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 7/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Fiber Nonlinearities
Multipulse: A =∑K−1
k=0 Ak
K−1∑k=0
(∂Ak
∂z+α
2Ak + i
β2
2
∂2Ak
∂t2) = iγ
K−1∑l ,m,n=0
AlA∗mAn
Time-matching location: (l −m + n)T
l = m = n: self phase modulation (SPM) ⇒ spectralbroadeningl = m 6= n or l 6= m = n: intrachannel cross phase modulation(IXPM) ⇒ timing jitterl 6= m 6= n or l = n 6= m: intrachannel four wave mixing(IFWM) ⇒ amplitude jitter and ghost pulse
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 7/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
3rd-order VSTF model
A(ω, L)=H1(ω, L)A(ω, 0) +
∫ +∞
−∞
∫ +∞
−∞H3(ω1, ω2, ω−ω1+ω2, L)
A(ω1, 0)A∗(ω2, 0)A(ω − ω1 + ω2, 0)dω1dω2
where
H1(ω, L) = exp(−α2L + i
β2
2ω2L),
H3(ω1, ω2, ω − ω1 + ω2, L)=iγ
4π2H1(ω, L)
∫ L
0exp[−αz +
iβ2z(ω1 − ω)(ω1 − ω2)]dz
A(ω, z) : Fourier transform of A(t, z)H1(ω, L): linear transfer functionH3(ω1, ω2, ω − ω1 + ω2, L): nonlinear transfer function
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 8/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
3rd-order VSTF model
A(ω, L)=H1(ω, L)A(ω, 0) +
∫ +∞
−∞
∫ +∞
−∞H3(ω1, ω2, ω−ω1+ω2, L)
A(ω1, 0)A∗(ω2, 0)A(ω − ω1 + ω2, 0)dω1dω2
where
H1(ω, L) = exp(−α2L + i
β2
2ω2L),
H3(ω1, ω2, ω − ω1 + ω2, L)=iγ
4π2H1(ω, L)
∫ L
0exp[−αz +
iβ2z(ω1 − ω)(ω1 − ω2)]dz
A(ω, z) : Fourier transform of A(t, z)H1(ω, L): linear transfer functionH3(ω1, ω2, ω − ω1 + ω2, L): nonlinear transfer function
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 8/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
3rd-order VSTF model
A(ω, L)=H1(ω, L)A(ω, 0) +
∫ +∞
−∞
∫ +∞
−∞H3(ω1, ω2, ω−ω1+ω2, L)
A(ω1, 0)A∗(ω2, 0)A(ω − ω1 + ω2, 0)dω1dω2
where
H1(ω, L) = exp(−α2L + i
β2
2ω2L),
H3(ω1, ω2, ω − ω1 + ω2, L)=iγ
4π2H1(ω, L)
∫ L
0exp[−αz +
iβ2z(ω1 − ω)(ω1 − ω2)]dz
A(ω, z) : Fourier transform of A(t, z)H1(ω, L): linear transfer functionH3(ω1, ω2, ω − ω1 + ω2, L): nonlinear transfer function
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 8/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Outline
1 IntroductionMotivationNonlinear Schrodinger Equation
2 Model DevelopmentStep 1: Extension of VSTF to Multispan Multipulse CaseStep 2: Simplification of Triple Integral to Simple IntegralStep 3: Conversion to Time DomainStep 4: Extension to include Photodetector
3 Model Validation
4 Model Application: Constrained CodingCoding SchemePerformance Evaluation
5 Conclusion
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 9/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Model Development
Laser Diode
Modulator Dispersion Compensator Amplifier Photo
DetectorDecision Device
Threshold
Sample at time
{ }∧
kb( )ts ( )tr ( )ty ( )qty
qTtq =
{ }kb
λ
( )( )0,tA n ( )( )LtA n , ( ) ( )0,1 tA n+
n th span
Encoder
Figure: Schematic of a typical fiber-optic communication system
Assumptions:
Noiseless
No predetection optical filering
Input-output model: {ak} ⇒ y(tq)
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 10/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Model Development
Laser Diode
Modulator Dispersion Compensator Amplifier Photo
DetectorDecision Device
Threshold
Sample at time
{ }∧
kb( )ts ( )tr ( )ty ( )qty
qTtq =
{ }kb
λ
( )( )0,tA n ( )( )LtA n , ( ) ( )0,1 tA n+
n th span
Encoder
Figure: Schematic of a typical fiber-optic communication system
Assumptions:
Noiseless
No predetection optical filering
Input-output model: {ak} ⇒ y(tq)
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 10/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Step 1: Extension of VSTF to Multispan Multipulse Case
Dispersion Compensation + Amplification:
H−11 (ω, L) = exp(
α
2L− i
β2
2ω2L)
Multipulse:
S(ω) =K−1∑k=0
akP12
0
√2πT0 exp
[−ω
2T 20
2− iωkT + iΦk
]
where
P0: launched peak power
T 20 =
T 20
1+iC , where T0 is pulse width and C is chirp parameter
T = 1/Rs , where Rs is symbol rate
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 11/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Step 1: Extension of VSTF to Multispan Multipulse Case
Dispersion Compensation + Amplification:
H−11 (ω, L) = exp(
α
2L− i
β2
2ω2L)
Multipulse:
S(ω) =K−1∑k=0
akP12
0
√2πT0 exp
[−ω
2T 20
2− iωkT + iΦk
]
where
P0: launched peak power
T 20 =
T 20
1+iC , where T0 is pulse width and C is chirp parameter
T = 1/Rs , where Rs is symbol rate
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 11/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Step 1: Extension of VSTF to Multispan Multipulse Case
Dispersion Compensation + Amplification:
H−11 (ω, L) = exp(
α
2L− i
β2
2ω2L)
Multipulse:
S(ω) =K−1∑k=0
akP12
0
√2πT0 exp
[−ω
2T 20
2− iωkT + iΦk
]
where
P0: launched peak power
T 20 =
T 20
1+iC , where T0 is pulse width and C is chirp parameter
T = 1/Rs , where Rs is symbol rate
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 11/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Step 2: Triple Integral ⇒ Simple Integral
R(ω) =√
2πK−1∑k=0
akP12
0 T0 exp
(−ω
2T 20
2− iωkT + iΦk
)
+ iNγ√
2πT 20 exp
(−3ω2T 2
0
2
)K−1∑l=0
K−1∑m=0
K−1∑n=0
ala∗man
P32
0 exp[−iω(l −m + n)T + i(Φl − Φm + Φn)]
∫ L
0
exp
{−αz +
[2ωT 20 +i(l−m)T ][2ωT 2
0 +i(n−m)T ]3T 2
0 +iβ2z
}√
3T 20 +
β22z
2
T 20
− i2β2z
exp
[− (l − n)2T 2
3T 20 + β2
2z2/T 2
0 − i2β2z
]dz
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 12/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Step 3: Conversion to Time Domain
r(t) =K−1∑k=0
akP12
0 exp
[−(t − kT )2
2T 20
+ iΦk
]+ iNγ
K−1∑l=0
K−1∑m=0
K−1∑n=0
ala∗manP
32
0 exp[i(Φl − Φm + Φn)]
exp
(−
t2NL
6T 20
)∫ L
0exp[−αz−K2(z , l , n)]
exp
{−
3{
2tNL3
+(l−m)T}{
2tNL3
+(n−m)T}
T 20 +i3β2z
}K1(z)
dz
wheretNL = t − (l −m + n)T
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 13/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Step 3 (Con.)
Introduce:
ISI coefficient (effect of pulse k on pulse q):
ρISIq,k = exp[−(q − k)2T 2/2T 2
0
]SPM, IXPM, IFWM coefficient:
ρSPM(IXPM,IFWM)l ,m,n = iγ
∫ L
0
exp [−αz − K2(z , l , n)]
K1(z)
exp
{−3(l −m)(n −m)T 2
T 20 + i3β2z
}dz
where
K1(z) =
√1 + i2β2z/T 2
0 + 3β22z
2/T 40
K2(z , l , n) =(l − n)2T 2
T 20 + i2β2z + 3β2
2z2/T 2
0A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 14/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Step 3 (Con.)
Introduce:
ISI coefficient (effect of pulse k on pulse q):
ρISIq,k = exp[−(q − k)2T 2/2T 2
0
]SPM, IXPM, IFWM coefficient:
ρSPM(IXPM,IFWM)l ,m,n = iγ
∫ L
0
exp [−αz − K2(z , l , n)]
K1(z)
exp
{−3(l −m)(n −m)T 2
T 20 + i3β2z
}dz
where
K1(z) =
√1 + i2β2z/T 2
0 + 3β22z
2/T 40
K2(z , l , n) =(l − n)2T 2
T 20 + i2β2z + 3β2
2z2/T 2
0A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 14/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Step 3 (Con.)
Discrete-time polynomial model:
r(tq) = aqP12
0 exp(iΦq) + P12
0
K−1∑k=0;k 6=q
akρISIq,k exp(iΦk)
+ N|aq|2aqP32
0 ρSPM exp(iΦq)
+ NP32
0
∑l=m 6=n;l 6=m=n
ala∗manρ
IXPMl ,m,n exp[i(Φl − Φm + Φn)]
+ NP32
0
∑l 6=m 6=n;l=n 6=m
ala∗manρ
IFWMl ,m,n exp[i(Φl − Φm + Φn)]
Advantages:
Reduce computational complexity
Isolate any individual physical impairment
Analyze impact of system, fiber, and pulse parametersA Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 15/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Step 3 (Con.)
Discrete-time polynomial model:
r(tq) = aqP12
0 exp(iΦq) + P12
0
K−1∑k=0;k 6=q
akρISIq,k exp(iΦk)
+ N|aq|2aqP32
0 ρSPM exp(iΦq)
+ NP32
0
∑l=m 6=n;l 6=m=n
ala∗manρ
IXPMl ,m,n exp[i(Φl − Φm + Φn)]
+ NP32
0
∑l 6=m 6=n;l=n 6=m
ala∗manρ
IFWMl ,m,n exp[i(Φl − Φm + Φn)]
Advantages:
Reduce computational complexity
Isolate any individual physical impairment
Analyze impact of system, fiber, and pulse parametersA Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 15/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Step 3 (Con.)
Discrete-time polynomial model:
r(tq) = aqP12
0 exp(iΦq) + P12
0
K−1∑k=0;k 6=q
akρISIq,k exp(iΦk)
+ N|aq|2aqP32
0 ρSPM exp(iΦq)
+ NP32
0
∑l=m 6=n;l 6=m=n
ala∗manρ
IXPMl ,m,n exp[i(Φl − Φm + Φn)]
+ NP32
0
∑l 6=m 6=n;l=n 6=m
ala∗manρ
IFWMl ,m,n exp[i(Φl − Φm + Φn)]
Advantages:
Reduce computational complexity
Isolate any individual physical impairment
Analyze impact of system, fiber, and pulse parametersA Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 15/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Step 4: Extension to include Photodetector
y(tq) = |aq|2P0 + P0
∣∣∣∣∣∣K−1∑
k=0;k 6=q
akρISIq,k exp(iΦk)
∣∣∣∣∣∣2
+ 2P0Re
aq
K−1∑k=0;k 6=q
ak(ρISIq,k)∗ exp[i(Φq − Φk)]
+ 2NP2
0Re{aq(ρSPM)∗
}+ N2|aq|6P3
0
∣∣∣ρSPM ∣∣∣2+ 2NP2
0Re{aq∑
ala∗man(ρIXPMl ,m,n )∗K3(l ,m, n)}
+ 2NP20Re{aq
∑ala∗man(ρIFWM
l ,m,n )∗K3(l ,m, n)}
+ N2P60
(∣∣∣∑ ala∗manρ
IXPMl ,m,n
∣∣∣2 +∣∣∣∑ ala
∗manρ
IFWMl ,m,n
∣∣∣2)A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 16/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
where
K3(l ,m, n) = exp
{− [q − (l −m + n)]2T 2
6(T 20 )∗
}exp{i [Φq − (Φl − Φm + Φn)]}
Mapping: binary input vector ⇒ sampled photodetectoroutput vector
intrachannel interference (ICI): ICI{bk},q
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 17/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
where
K3(l ,m, n) = exp
{− [q − (l −m + n)]2T 2
6(T 20 )∗
}exp{i [Φq − (Φl − Φm + Φn)]}
Mapping: binary input vector ⇒ sampled photodetectoroutput vector
intrachannel interference (ICI): ICI{bk},q
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 17/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Outline
1 IntroductionMotivationNonlinear Schrodinger Equation
2 Model DevelopmentStep 1: Extension of VSTF to Multispan Multipulse CaseStep 2: Simplification of Triple Integral to Simple IntegralStep 3: Conversion to Time DomainStep 4: Extension to include Photodetector
3 Model Validation
4 Model Application: Constrained CodingCoding SchemePerformance Evaluation
5 Conclusion
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 18/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Model Validation (Model vs SSF simulation)
Normalized squared deviation (NSD):
NSD(N) =
∫ KT0 |rModel(t)− rSSF (t)|2dt∫ KT
0 |rSSF (t)|2dt
2 4 6 8 10 12 14 16
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
x 10−4
Number of Spans
Nor
mal
ized
Squ
ared
Dev
iatio
n
P0=1 mW; OOKP0=3 mW; OOKP0=10 mW; OOKP0=1 mW; DBPSKP0=3 mW; DBPSKP0=10 mW; DBPSK
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 19/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Outline
1 IntroductionMotivationNonlinear Schrodinger Equation
2 Model DevelopmentStep 1: Extension of VSTF to Multispan Multipulse CaseStep 2: Simplification of Triple Integral to Simple IntegralStep 3: Conversion to Time DomainStep 4: Extension to include Photodetector
3 Model Validation
4 Model Application: Constrained CodingCoding SchemePerformance Evaluation
5 Conclusion
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 20/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Coding Scheme
Using a constrained code to avoid bit patterns that will most likelybe detected incorrectly
Metric (Bit pattern): ICI{bk} =∑K−1
q=0 |ICI{bk},q|Scheme:
Rank the bit patterns in order of increasing ICIMap every K-bit pattern with bad ICI metric to one of K+1-bitpatterns with good ICI metric
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 21/26
![Page 60: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/60.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Coding Scheme
Using a constrained code to avoid bit patterns that will most likelybe detected incorrectly
Metric (Bit pattern): ICI{bk} =∑K−1
q=0 |ICI{bk},q|Scheme:
Rank the bit patterns in order of increasing ICIMap every K-bit pattern with bad ICI metric to one of K+1-bitpatterns with good ICI metric
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 21/26
![Page 61: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/61.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Coding Scheme
Using a constrained code to avoid bit patterns that will most likelybe detected incorrectly
Metric (Bit pattern): ICI{bk} =∑K−1
q=0 |ICI{bk},q|Scheme:
Rank the bit patterns in order of increasing ICIMap every K-bit pattern with bad ICI metric to one of K+1-bitpatterns with good ICI metric
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 21/26
![Page 62: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/62.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Coding Scheme
Using a constrained code to avoid bit patterns that will most likelybe detected incorrectly
Metric (Bit pattern): ICI{bk} =∑K−1
q=0 |ICI{bk},q|Scheme:
Rank the bit patterns in order of increasing ICIMap every K-bit pattern with bad ICI metric to one of K+1-bitpatterns with good ICI metric
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 21/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Evaluation Method
For a given proportion of bit patterns constrained,
Calculate Q factor before coding: Qbefore = µ1−µ0σ1+σ0
whereµi = E [y(tq)|aq = i ], i = 0, 1
σ2i = E{[y(tq)− µi ]2|aq = i}, i = 0, 1
Constrained coding
Calculate Q factor after coding: Qafter
Q factor improvement: Qimprovement(dB) = 20log10QafterQbefore
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 22/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Evaluation Method
For a given proportion of bit patterns constrained,
Calculate Q factor before coding: Qbefore = µ1−µ0σ1+σ0
whereµi = E [y(tq)|aq = i ], i = 0, 1
σ2i = E{[y(tq)− µi ]2|aq = i}, i = 0, 1
Constrained coding
Calculate Q factor after coding: Qafter
Q factor improvement: Qimprovement(dB) = 20log10QafterQbefore
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 22/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Evaluation Method
For a given proportion of bit patterns constrained,
Calculate Q factor before coding: Qbefore = µ1−µ0σ1+σ0
whereµi = E [y(tq)|aq = i ], i = 0, 1
σ2i = E{[y(tq)− µi ]2|aq = i}, i = 0, 1
Constrained coding
Calculate Q factor after coding: Qafter
Q factor improvement: Qimprovement(dB) = 20log10QafterQbefore
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 22/26
![Page 66: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/66.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Evaluation Method
For a given proportion of bit patterns constrained,
Calculate Q factor before coding: Qbefore = µ1−µ0σ1+σ0
whereµi = E [y(tq)|aq = i ], i = 0, 1
σ2i = E{[y(tq)− µi ]2|aq = i}, i = 0, 1
Constrained coding
Calculate Q factor after coding: Qafter
Q factor improvement: Qimprovement(dB) = 20log10QafterQbefore
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 22/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Evaluation Result
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.56
8
10
12
14
16
18
20
22
24
Proportion of Sequences Constrained
Q fa
ctor
(dB
)
OOK; 1 mW
OOK; 3 mW
OOK; 10 mW
DBPSK; 1 mW
DBPSK; 3 mW
DBPSK; 10 mW
OOK; 1 mW
OOK; 3 mW
OOK; 10 mW
DBPSK; 1 mW
DBPSK; 3 mW
DBPSK; 10 mW
Encoded
Uncoded
Figure: Q factor improvementA Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 23/26
![Page 68: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/68.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Outline
1 IntroductionMotivationNonlinear Schrodinger Equation
2 Model DevelopmentStep 1: Extension of VSTF to Multispan Multipulse CaseStep 2: Simplification of Triple Integral to Simple IntegralStep 3: Conversion to Time DomainStep 4: Extension to include Photodetector
3 Model Validation
4 Model Application: Constrained CodingCoding SchemePerformance Evaluation
5 Conclusion
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 24/26
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Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Conclusion
Development, validation and application of a discrete-timetime model of single channel multipulse multispan systemswith periodic amplification and dispersion management2D model
”Range of Influence of Physical Impairments in WDMSystems”, GLOBECOM 2011 (Under Review)”A Two-Dimensional Discrete-Time Model of PhysicalImpairments in WDM Systems”, The IEEE/OSA Journal ofLightwave Technology (JLT) (Submitted)
Extending to the general case, including ASE noise andpostdetection electrical filteringPotential Applications
multichannel signal processing for intersymbol and interchannelinterference mitigationmultiuser coding, multichannel detection and path-diversity forall-optical networksconstrained coding for WDM systems
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 25/26
![Page 70: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/70.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Conclusion
Development, validation and application of a discrete-timetime model of single channel multipulse multispan systemswith periodic amplification and dispersion management2D model
”Range of Influence of Physical Impairments in WDMSystems”, GLOBECOM 2011 (Under Review)”A Two-Dimensional Discrete-Time Model of PhysicalImpairments in WDM Systems”, The IEEE/OSA Journal ofLightwave Technology (JLT) (Submitted)
Extending to the general case, including ASE noise andpostdetection electrical filteringPotential Applications
multichannel signal processing for intersymbol and interchannelinterference mitigationmultiuser coding, multichannel detection and path-diversity forall-optical networksconstrained coding for WDM systems
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 25/26
![Page 71: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/71.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Conclusion
Development, validation and application of a discrete-timetime model of single channel multipulse multispan systemswith periodic amplification and dispersion management2D model
”Range of Influence of Physical Impairments in WDMSystems”, GLOBECOM 2011 (Under Review)”A Two-Dimensional Discrete-Time Model of PhysicalImpairments in WDM Systems”, The IEEE/OSA Journal ofLightwave Technology (JLT) (Submitted)
Extending to the general case, including ASE noise andpostdetection electrical filteringPotential Applications
multichannel signal processing for intersymbol and interchannelinterference mitigationmultiuser coding, multichannel detection and path-diversity forall-optical networksconstrained coding for WDM systems
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 25/26
![Page 72: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/72.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Conclusion
Development, validation and application of a discrete-timetime model of single channel multipulse multispan systemswith periodic amplification and dispersion management2D model
”Range of Influence of Physical Impairments in WDMSystems”, GLOBECOM 2011 (Under Review)”A Two-Dimensional Discrete-Time Model of PhysicalImpairments in WDM Systems”, The IEEE/OSA Journal ofLightwave Technology (JLT) (Submitted)
Extending to the general case, including ASE noise andpostdetection electrical filteringPotential Applications
multichannel signal processing for intersymbol and interchannelinterference mitigationmultiuser coding, multichannel detection and path-diversity forall-optical networksconstrained coding for WDM systems
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 25/26
![Page 73: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/73.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Conclusion
Development, validation and application of a discrete-timetime model of single channel multipulse multispan systemswith periodic amplification and dispersion management2D model
”Range of Influence of Physical Impairments in WDMSystems”, GLOBECOM 2011 (Under Review)”A Two-Dimensional Discrete-Time Model of PhysicalImpairments in WDM Systems”, The IEEE/OSA Journal ofLightwave Technology (JLT) (Submitted)
Extending to the general case, including ASE noise andpostdetection electrical filteringPotential Applications
multichannel signal processing for intersymbol and interchannelinterference mitigationmultiuser coding, multichannel detection and path-diversity forall-optical networksconstrained coding for WDM systems
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 25/26
![Page 74: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/74.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Conclusion
Development, validation and application of a discrete-timetime model of single channel multipulse multispan systemswith periodic amplification and dispersion management2D model
”Range of Influence of Physical Impairments in WDMSystems”, GLOBECOM 2011 (Under Review)”A Two-Dimensional Discrete-Time Model of PhysicalImpairments in WDM Systems”, The IEEE/OSA Journal ofLightwave Technology (JLT) (Submitted)
Extending to the general case, including ASE noise andpostdetection electrical filteringPotential Applications
multichannel signal processing for intersymbol and interchannelinterference mitigationmultiuser coding, multichannel detection and path-diversity forall-optical networksconstrained coding for WDM systems
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 25/26
![Page 75: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/75.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Conclusion
Development, validation and application of a discrete-timetime model of single channel multipulse multispan systemswith periodic amplification and dispersion management2D model
”Range of Influence of Physical Impairments in WDMSystems”, GLOBECOM 2011 (Under Review)”A Two-Dimensional Discrete-Time Model of PhysicalImpairments in WDM Systems”, The IEEE/OSA Journal ofLightwave Technology (JLT) (Submitted)
Extending to the general case, including ASE noise andpostdetection electrical filteringPotential Applications
multichannel signal processing for intersymbol and interchannelinterference mitigationmultiuser coding, multichannel detection and path-diversity forall-optical networksconstrained coding for WDM systems
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 25/26
![Page 76: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/76.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Conclusion
Development, validation and application of a discrete-timetime model of single channel multipulse multispan systemswith periodic amplification and dispersion management2D model
”Range of Influence of Physical Impairments in WDMSystems”, GLOBECOM 2011 (Under Review)”A Two-Dimensional Discrete-Time Model of PhysicalImpairments in WDM Systems”, The IEEE/OSA Journal ofLightwave Technology (JLT) (Submitted)
Extending to the general case, including ASE noise andpostdetection electrical filteringPotential Applications
multichannel signal processing for intersymbol and interchannelinterference mitigationmultiuser coding, multichannel detection and path-diversity forall-optical networksconstrained coding for WDM systems
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 25/26
![Page 77: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/77.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Conclusion
Development, validation and application of a discrete-timetime model of single channel multipulse multispan systemswith periodic amplification and dispersion management2D model
”Range of Influence of Physical Impairments in WDMSystems”, GLOBECOM 2011 (Under Review)”A Two-Dimensional Discrete-Time Model of PhysicalImpairments in WDM Systems”, The IEEE/OSA Journal ofLightwave Technology (JLT) (Submitted)
Extending to the general case, including ASE noise andpostdetection electrical filteringPotential Applications
multichannel signal processing for intersymbol and interchannelinterference mitigationmultiuser coding, multichannel detection and path-diversity forall-optical networksconstrained coding for WDM systems
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 25/26
![Page 78: A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems](https://reader034.vdocument.in/reader034/viewer/2022052602/55a0b9f91a28abd5608b47d2/html5/thumbnails/78.jpg)
Outline Introduction Model Development Model Validation Model Application: Constrained Coding Conclusion
Thank You
A Discrete-Time Polynomial Model of Single Channel Long-Haul Fiber-Optic Communication Systems:Houbing Song and Maıte Brandt-Pearce, University of Virginia 26/26