The Kolmogorov-Zakharov Model for Optical Fiber Communication
A mathematical framework is presented to study the evolution of multi-point cumulants in nonlinear dispersive partial differential equations with random input data, based on the theory of weak wave turbulence (WWT). This framework is used to explain how energy is distributed among Fourier modes in t...
Gespeichert in:
| Veröffentlicht in: | IEEE transactions on information theory 2017-01, Vol.63 (1), p.377-391 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 391 |
|---|---|
| container_issue | 1 |
| container_start_page | 377 |
| container_title | IEEE transactions on information theory |
| container_volume | 63 |
| creator | Yousefi, Mansoor I. |
| description | A mathematical framework is presented to study the evolution of multi-point cumulants in nonlinear dispersive partial differential equations with random input data, based on the theory of weak wave turbulence (WWT). This framework is used to explain how energy is distributed among Fourier modes in the nonlinear Schrödinger equation. This is achieved by considering interactions among four Fourier modes and studying the role of the resonant, non-resonant, and trivial quartets in the dynamics. As an application, a power spectral density is suggested for calculating the interference power in dense wavelength-division multiplexed optical systems, based on the kinetic equation of the WWT. This power spectrum, termed the Kolmogorov-Zakharov (KZ) model, results in a better estimate of the signal spectrum in optical fiber, compared with the so-called Gaussian noise model. The KZ model is generalized to non-stationary inputs and multi-span optical systems. |
| doi_str_mv | 10.1109/TIT.2016.2620985 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_RIE</sourceid><recordid>TN_cdi_proquest_journals_2174327179</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>7676314</ieee_id><sourcerecordid>4288742791</sourcerecordid><originalsourceid>FETCH-LOGICAL-c319t-e34bf9829e79b1891fbfa90eee219c0d8861b732a2e1ad63f7504d2b9fa0c0823</originalsourceid><addsrcrecordid>eNp9kLtOwzAUQC0EEqWwI7FEYk7x9dsDA6ooVBR1CQuL5SQ2TUnq4qRI_D2uWjEy3YfOfeggdA14AoD1XTEvJgSDmBBBsFb8BI2Ac5lrwdkpGmEMKteMqXN00ffrVDIOZITui5XLXkLbhY8Qw3f-bj9XNiXZa6hdm_kQs-V2aCrbZrOmdDGbhq7bbVJjaMLmEp152_bu6hjH6G32WEyf88XyaT59WOQVBT3kjrLSa0W0k7oEpcGX3mrsnCOgK1wrJaCUlFjiwNaCeskxq0mpvcUVVoSO0e1h7zaGr53rB7MOu7hJJw0BySiRIPV_FChOJSFS80ThA1XF0PfRebONTWfjjwFs9ipNUmn2Ks1RZRq5OYw06eU_XAopKDD6Cw_Bbb0</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1853722795</pqid></control><display><type>article</type><title>The Kolmogorov-Zakharov Model for Optical Fiber Communication</title><source>IEEE Electronic Library (IEL)</source><creator>Yousefi, Mansoor I.</creator><creatorcontrib>Yousefi, Mansoor I.</creatorcontrib><description>A mathematical framework is presented to study the evolution of multi-point cumulants in nonlinear dispersive partial differential equations with random input data, based on the theory of weak wave turbulence (WWT). This framework is used to explain how energy is distributed among Fourier modes in the nonlinear Schrödinger equation. This is achieved by considering interactions among four Fourier modes and studying the role of the resonant, non-resonant, and trivial quartets in the dynamics. As an application, a power spectral density is suggested for calculating the interference power in dense wavelength-division multiplexed optical systems, based on the kinetic equation of the WWT. This power spectrum, termed the Kolmogorov-Zakharov (KZ) model, results in a better estimate of the signal spectrum in optical fiber, compared with the so-called Gaussian noise model. The KZ model is generalized to non-stationary inputs and multi-span optical systems.</description><identifier>ISSN: 0018-9448</identifier><identifier>EISSN: 1557-9654</identifier><identifier>DOI: 10.1109/TIT.2016.2620985</identifier><identifier>CODEN: IETTAW</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Correlation ; cumulants ; Division ; Fiber-optic communication ; Information theory ; Interference ; Kinetic equations ; Kinetic theory ; Mathematical model ; Modulation ; moments ; Nonlinear equations ; Nonlinear optics ; Normal distribution ; Optical communication ; Optical fibers ; Partial differential equations ; perturbation theory ; Power spectral density ; Random noise ; Schrodinger equation ; Turbulence ; Wavelength division multiplexing ; weak wave turbulence</subject><ispartof>IEEE transactions on information theory, 2017-01, Vol.63 (1), p.377-391</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Jan 2017</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-e34bf9829e79b1891fbfa90eee219c0d8861b732a2e1ad63f7504d2b9fa0c0823</citedby><cites>FETCH-LOGICAL-c319t-e34bf9829e79b1891fbfa90eee219c0d8861b732a2e1ad63f7504d2b9fa0c0823</cites><orcidid>0000-0003-4899-4609</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/7676314$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/7676314$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Yousefi, Mansoor I.</creatorcontrib><title>The Kolmogorov-Zakharov Model for Optical Fiber Communication</title><title>IEEE transactions on information theory</title><addtitle>TIT</addtitle><description>A mathematical framework is presented to study the evolution of multi-point cumulants in nonlinear dispersive partial differential equations with random input data, based on the theory of weak wave turbulence (WWT). This framework is used to explain how energy is distributed among Fourier modes in the nonlinear Schrödinger equation. This is achieved by considering interactions among four Fourier modes and studying the role of the resonant, non-resonant, and trivial quartets in the dynamics. As an application, a power spectral density is suggested for calculating the interference power in dense wavelength-division multiplexed optical systems, based on the kinetic equation of the WWT. This power spectrum, termed the Kolmogorov-Zakharov (KZ) model, results in a better estimate of the signal spectrum in optical fiber, compared with the so-called Gaussian noise model. The KZ model is generalized to non-stationary inputs and multi-span optical systems.</description><subject>Correlation</subject><subject>cumulants</subject><subject>Division</subject><subject>Fiber-optic communication</subject><subject>Information theory</subject><subject>Interference</subject><subject>Kinetic equations</subject><subject>Kinetic theory</subject><subject>Mathematical model</subject><subject>Modulation</subject><subject>moments</subject><subject>Nonlinear equations</subject><subject>Nonlinear optics</subject><subject>Normal distribution</subject><subject>Optical communication</subject><subject>Optical fibers</subject><subject>Partial differential equations</subject><subject>perturbation theory</subject><subject>Power spectral density</subject><subject>Random noise</subject><subject>Schrodinger equation</subject><subject>Turbulence</subject><subject>Wavelength division multiplexing</subject><subject>weak wave turbulence</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kLtOwzAUQC0EEqWwI7FEYk7x9dsDA6ooVBR1CQuL5SQ2TUnq4qRI_D2uWjEy3YfOfeggdA14AoD1XTEvJgSDmBBBsFb8BI2Ac5lrwdkpGmEMKteMqXN00ffrVDIOZITui5XLXkLbhY8Qw3f-bj9XNiXZa6hdm_kQs-V2aCrbZrOmdDGbhq7bbVJjaMLmEp152_bu6hjH6G32WEyf88XyaT59WOQVBT3kjrLSa0W0k7oEpcGX3mrsnCOgK1wrJaCUlFjiwNaCeskxq0mpvcUVVoSO0e1h7zaGr53rB7MOu7hJJw0BySiRIPV_FChOJSFS80ThA1XF0PfRebONTWfjjwFs9ipNUmn2Ks1RZRq5OYw06eU_XAopKDD6Cw_Bbb0</recordid><startdate>201701</startdate><enddate>201701</enddate><creator>Yousefi, Mansoor I.</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0003-4899-4609</orcidid></search><sort><creationdate>201701</creationdate><title>The Kolmogorov-Zakharov Model for Optical Fiber Communication</title><author>Yousefi, Mansoor I.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-e34bf9829e79b1891fbfa90eee219c0d8861b732a2e1ad63f7504d2b9fa0c0823</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Correlation</topic><topic>cumulants</topic><topic>Division</topic><topic>Fiber-optic communication</topic><topic>Information theory</topic><topic>Interference</topic><topic>Kinetic equations</topic><topic>Kinetic theory</topic><topic>Mathematical model</topic><topic>Modulation</topic><topic>moments</topic><topic>Nonlinear equations</topic><topic>Nonlinear optics</topic><topic>Normal distribution</topic><topic>Optical communication</topic><topic>Optical fibers</topic><topic>Partial differential equations</topic><topic>perturbation theory</topic><topic>Power spectral density</topic><topic>Random noise</topic><topic>Schrodinger equation</topic><topic>Turbulence</topic><topic>Wavelength division multiplexing</topic><topic>weak wave turbulence</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yousefi, Mansoor I.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>IEEE transactions on information theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Yousefi, Mansoor I.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Kolmogorov-Zakharov Model for Optical Fiber Communication</atitle><jtitle>IEEE transactions on information theory</jtitle><stitle>TIT</stitle><date>2017-01</date><risdate>2017</risdate><volume>63</volume><issue>1</issue><spage>377</spage><epage>391</epage><pages>377-391</pages><issn>0018-9448</issn><eissn>1557-9654</eissn><coden>IETTAW</coden><abstract>A mathematical framework is presented to study the evolution of multi-point cumulants in nonlinear dispersive partial differential equations with random input data, based on the theory of weak wave turbulence (WWT). This framework is used to explain how energy is distributed among Fourier modes in the nonlinear Schrödinger equation. This is achieved by considering interactions among four Fourier modes and studying the role of the resonant, non-resonant, and trivial quartets in the dynamics. As an application, a power spectral density is suggested for calculating the interference power in dense wavelength-division multiplexed optical systems, based on the kinetic equation of the WWT. This power spectrum, termed the Kolmogorov-Zakharov (KZ) model, results in a better estimate of the signal spectrum in optical fiber, compared with the so-called Gaussian noise model. The KZ model is generalized to non-stationary inputs and multi-span optical systems.</abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/TIT.2016.2620985</doi><tpages>15</tpages><orcidid>https://orcid.org/0000-0003-4899-4609</orcidid></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | ISSN: 0018-9448 |
| ispartof | IEEE transactions on information theory, 2017-01, Vol.63 (1), p.377-391 |
| issn | 0018-9448 1557-9654 |
| language | eng |
| recordid | cdi_proquest_journals_2174327179 |
| source | IEEE Electronic Library (IEL) |
| subjects | Correlation cumulants Division Fiber-optic communication Information theory Interference Kinetic equations Kinetic theory Mathematical model Modulation moments Nonlinear equations Nonlinear optics Normal distribution Optical communication Optical fibers Partial differential equations perturbation theory Power spectral density Random noise Schrodinger equation Turbulence Wavelength division multiplexing weak wave turbulence |
| title | The Kolmogorov-Zakharov Model for Optical Fiber Communication |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-28T15%3A33%3A09IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_RIE&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20Kolmogorov-Zakharov%20Model%20for%20Optical%20Fiber%20Communication&rft.jtitle=IEEE%20transactions%20on%20information%20theory&rft.au=Yousefi,%20Mansoor%20I.&rft.date=2017-01&rft.volume=63&rft.issue=1&rft.spage=377&rft.epage=391&rft.pages=377-391&rft.issn=0018-9448&rft.eissn=1557-9654&rft.coden=IETTAW&rft_id=info:doi/10.1109/TIT.2016.2620985&rft_dat=%3Cproquest_RIE%3E4288742791%3C/proquest_RIE%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1853722795&rft_id=info:pmid/&rft_ieee_id=7676314&rfr_iscdi=true |