{"id":"https://openalex.org/W2104681550","doi":"https://doi.org/10.1109/tvt.2010.2063047","title":"Exact Evaluation of Ergodic Capacity for Multihop Variable-Gain Relay Networks: A Unified Framework for Generalized Fading Channels","display_name":"Exact Evaluation of Ergodic Capacity for Multihop Variable-Gain Relay Networks: A Unified Framework for Generalized Fading Channels","publication_year":2010,"publication_date":"2010-08-05","ids":{"openalex":"https://openalex.org/W2104681550","doi":"https://doi.org/10.1109/tvt.2010.2063047","mag":"2104681550"},"language":"en","primary_location":{"id":"doi:10.1109/tvt.2010.2063047","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvt.2010.2063047","pdf_url":null,"source":{"id":"https://openalex.org/S10936095","display_name":"IEEE Transactions on Vehicular Technology","issn_l":"0018-9545","issn":["0018-9545","1939-9359"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Vehicular Technology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035909356","display_name":"Omer Waqar","orcid":"https://orcid.org/0000-0003-1787-7100"},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Omer Waqar","raw_affiliation_strings":["School of Electronic and Electrical Engineering, University of Leeds, Leeds, U.K","Sch. of Electron. & Electr. Eng., Univ. of Leeds, Leeds, UK"],"affiliations":[{"raw_affiliation_string":"School of Electronic and Electrical Engineering, University of Leeds, Leeds, U.K","institution_ids":["https://openalex.org/I130828816"]},{"raw_affiliation_string":"Sch. of Electron. & Electr. Eng., Univ. of Leeds, Leeds, UK","institution_ids":["https://openalex.org/I130828816"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084710654","display_name":"Des McLernon","orcid":"https://orcid.org/0000-0001-8278-6171"},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"D. C. McLernon","raw_affiliation_strings":["School of Electronic and Electrical Engineering, University of Leeds, Leeds, U.K","Sch. of Electron. & Electr. Eng., Univ. of Leeds, Leeds, UK"],"affiliations":[{"raw_affiliation_string":"School of Electronic and Electrical Engineering, University of Leeds, Leeds, U.K","institution_ids":["https://openalex.org/I130828816"]},{"raw_affiliation_string":"Sch. of Electron. & Electr. Eng., Univ. of Leeds, Leeds, UK","institution_ids":["https://openalex.org/I130828816"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057324156","display_name":"Mounir Ghogho","orcid":"https://orcid.org/0000-0002-0055-7867"},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Mounir Ghogho","raw_affiliation_strings":["School of Electronic and Electrical Engineering, University of Leeds, Leeds, U.K","Sch. of Electron. & Electr. Eng., Univ. of Leeds, Leeds, UK"],"affiliations":[{"raw_affiliation_string":"School of Electronic and Electrical Engineering, University of Leeds, Leeds, U.K","institution_ids":["https://openalex.org/I130828816"]},{"raw_affiliation_string":"Sch. of Electron. & Electr. Eng., Univ. of Leeds, Leeds, UK","institution_ids":["https://openalex.org/I130828816"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035909356"],"corresponding_institution_ids":["https://openalex.org/I130828816"],"apc_list":null,"apc_paid":null,"fwci":8.1909,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.97843532,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"59","issue":"8","first_page":"4181","last_page":"4187"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12791","display_name":"Full-Duplex Wireless Communications","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.854761004447937},{"id":"https://openalex.org/keywords/fading","display_name":"Fading","score":0.8007562160491943},{"id":"https://openalex.org/keywords/moment-generating-function","display_name":"Moment-generating function","score":0.676793098449707},{"id":"https://openalex.org/keywords/relay","display_name":"Relay","score":0.6743917465209961},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.5167493224143982},{"id":"https://openalex.org/keywords/channel-state-information","display_name":"Channel state information","score":0.5117416381835938},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5047155618667603},{"id":"https://openalex.org/keywords/channel-capacity","display_name":"Channel capacity","score":0.49627238512039185},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4472009539604187},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.44314900040626526},{"id":"https://openalex.org/keywords/ergodicity","display_name":"Ergodicity","score":0.43652987480163574},{"id":"https://openalex.org/keywords/signal-to-noise-ratio","display_name":"Signal-to-noise ratio (imaging)","score":0.4335673451423645},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42210283875465393},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.2628089189529419},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.246076762676239},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12911880016326904},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0869288444519043},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07129251956939697}],"concepts":[{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.854761004447937},{"id":"https://openalex.org/C81978471","wikidata":"https://www.wikidata.org/wiki/Q1196572","display_name":"Fading","level":3,"score":0.8007562160491943},{"id":"https://openalex.org/C101796028","wikidata":"https://www.wikidata.org/wiki/Q535587","display_name":"Moment-generating function","level":3,"score":0.676793098449707},{"id":"https://openalex.org/C2778156585","wikidata":"https://www.wikidata.org/wiki/Q174053","display_name":"Relay","level":3,"score":0.6743917465209961},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.5167493224143982},{"id":"https://openalex.org/C148063708","wikidata":"https://www.wikidata.org/wiki/Q5072511","display_name":"Channel state information","level":3,"score":0.5117416381835938},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5047155618667603},{"id":"https://openalex.org/C97744766","wikidata":"https://www.wikidata.org/wiki/Q870845","display_name":"Channel capacity","level":3,"score":0.49627238512039185},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4472009539604187},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.44314900040626526},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.43652987480163574},{"id":"https://openalex.org/C13944312","wikidata":"https://www.wikidata.org/wiki/Q7512748","display_name":"Signal-to-noise ratio (imaging)","level":2,"score":0.4335673451423645},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42210283875465393},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.2628089189529419},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.246076762676239},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12911880016326904},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0869288444519043},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07129251956939697},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tvt.2010.2063047","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvt.2010.2063047","pdf_url":null,"source":{"id":"https://openalex.org/S10936095","display_name":"IEEE Transactions on Vehicular Technology","issn_l":"0018-9545","issn":["0018-9545","1939-9359"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Vehicular Technology","raw_type":"journal-article"},{"id":"pmh:oai:alma.44SUR_INST:11138640540002346","is_oa":false,"landing_page_url":"https://openresearch.surrey.ac.uk/esploro/outputs/journalArticle/Exact-evaluation-of-ergodic-capacity-for/99511913402346","pdf_url":null,"source":{"id":"https://openalex.org/S4210197018","display_name":"View","issn_l":"2688-268X","issn":["2688-268X","2688-3988"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:epubs.surrey.ac.uk:834861","is_oa":false,"landing_page_url":"http://epubs.surrey.ac.uk/834861/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400680","display_name":"Surrey Research Insight Open Access (The University of Surrey)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28290843","host_organization_name":"University of Surrey","host_organization_lineage":["https://openalex.org/I28290843"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W598996319","https://openalex.org/W604181985","https://openalex.org/W1522045078","https://openalex.org/W1667165204","https://openalex.org/W1967280221","https://openalex.org/W2047511481","https://openalex.org/W2090499479","https://openalex.org/W2107921121","https://openalex.org/W2110590629","https://openalex.org/W2116770744","https://openalex.org/W2117145663","https://openalex.org/W2139887674","https://openalex.org/W2143186099","https://openalex.org/W2145520942","https://openalex.org/W2145891098","https://openalex.org/W2149454297","https://openalex.org/W2151544711","https://openalex.org/W2152205538","https://openalex.org/W2170422354","https://openalex.org/W3008609509"],"related_works":["https://openalex.org/W2009962825","https://openalex.org/W1972942382","https://openalex.org/W1722744795","https://openalex.org/W124275629","https://openalex.org/W2950014027","https://openalex.org/W4250397825","https://openalex.org/W964575223","https://openalex.org/W2952991236","https://openalex.org/W4296948412","https://openalex.org/W2358718285"],"abstract_inverted_index":{"The":[0,76],"closed-form":[1,152],"expressions":[2,153],"of":[3,20,38,57,91,104,126,136,140,154,186],"the":[4,10,14,31,35,53,73,83,89,122,137,151,175],"probability":[5],"density":[6],"function":[7,12],"(pdf)":[8],"and":[9,97,106,146,179],"moment-generating":[11],"for":[13,26,34,52,100,107,159],"exact":[15,32,54,84,123,172],"end-to-end":[16,85],"signal-to-noise":[17],"ratio":[18],"(SNR)":[19],"variable-gain":[21,62,128],"relay":[22,129],"networks":[23,59,130],"are":[24,112,156],"unknown":[25],"generalized":[27],"fading":[28,109],"models;":[29],"thus,":[30],"evaluation":[33],"ergodic":[36,55,124,138],"capacity":[37,56,125],"these":[39],"systems":[40],"is":[41,69,80,87,98,170],"cumbersome.":[42],"In":[43],"this":[44],"paper,":[45],"we":[46,119,166],"develop":[47],"a":[48,92,183],"new":[49],"unified":[50],"framework":[51],"multihop":[58],"equipped":[60],"with":[61],"relays,":[63],"assuming":[64],"that":[65,111,121,168],"channel-state":[66],"information":[67],"(CSI)":[68],"available":[70,158],"only":[71],"at":[72],"receiving":[74],"terminals.":[75],"resulting":[77],"expression":[78],"(which":[79],"based":[81],"on":[82],"SNR)":[86],"in":[88,115,134],"form":[90],"single":[93],"truncated":[94],"infinite":[95],"series":[96],"valid":[99],"an":[101,171],"arbitrary":[102],"number":[103],"hops":[105],"various":[108],"models":[110],"typically":[113],"encountered":[114],"realistic":[116],"scenarios.":[117],"Furthermore,":[118],"show":[120,167],"dual-hop":[127],"can":[131],"be":[132],"written":[133],"terms":[135],"capacities":[139],"two":[141],"equivalent":[142],"single-input-single-output":[143],"(SISO)":[144],"channels":[145],"one":[147],"single-input-multiple-output":[148],"channel":[149],"(SIMO),":[150],"which":[155],"already":[157],"many":[160],"commonly":[161],"used":[162],"fading/shadowing":[163],"models.":[164],"Finally,":[165],"there":[169],"match":[173],"between":[174],"Monte":[176],"Carlo":[177],"simulation":[178],"theoretical":[180],"results":[181],"over":[182],"whole":[184],"range":[185],"per-hop":[187],"average":[188],"SNR.":[189]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":12}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
