{"id":"https://openalex.org/W1981874147","doi":"https://doi.org/10.1109/wcnc.2012.6214432","title":"On achievable rate and ergodic capacity of non-symmetric half-duplex NAF relay channels","display_name":"On achievable rate and ergodic capacity of non-symmetric half-duplex NAF relay channels","publication_year":2012,"publication_date":"2012-04-01","ids":{"openalex":"https://openalex.org/W1981874147","doi":"https://doi.org/10.1109/wcnc.2012.6214432","mag":"1981874147"},"language":"en","primary_location":{"id":"doi:10.1109/wcnc.2012.6214432","is_oa":false,"landing_page_url":"https://doi.org/10.1109/wcnc.2012.6214432","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE Wireless Communications and Networking Conference (WCNC)","raw_type":"proceedings-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/A5080774708","display_name":"Leonardo Jim\u00e9nez Rodr\u00edguez","orcid":"https://orcid.org/0000-0003-1666-1164"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Leonardo Jimenez Rodriguez","raw_affiliation_strings":["Department of Electrical & Computer Engineering, McGill University, Montr\u00e9al, Canada","department of Electrical and Computer Engineering, McGill University, Montreal, QC, Canada#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical & Computer Engineering, McGill University, Montr\u00e9al, Canada","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"department of Electrical and Computer Engineering, McGill University, Montreal, QC, Canada#TAB#","institution_ids":["https://openalex.org/I5023651"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045721364","display_name":"Nghi H. Tran","orcid":"https://orcid.org/0000-0002-4246-0190"},"institutions":[{"id":"https://openalex.org/I110152177","display_name":"University of Akron","ror":"https://ror.org/02kyckx55","country_code":"US","type":"education","lineage":["https://openalex.org/I110152177"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nghi H. Tran","raw_affiliation_strings":["University of Akron, Akron, OH, US","Department of Electrical & Computer Engineering, University of Akron, Akron, OH, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Akron, Akron, OH, US","institution_ids":["https://openalex.org/I110152177"]},{"raw_affiliation_string":"Department of Electrical & Computer Engineering, University of Akron, Akron, OH, USA","institution_ids":["https://openalex.org/I110152177"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026464766","display_name":"Tho Le\u2010Ngoc","orcid":"https://orcid.org/0000-0002-9308-8894"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Tho Le-Ngoc","raw_affiliation_strings":["Department of Electrical & Computer Engineering, McGill University, Montr\u00e9al, Canada","department of Electrical and Computer Engineering, McGill University, Montreal, QC, Canada#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical & Computer Engineering, McGill University, Montr\u00e9al, Canada","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"department of Electrical and Computer Engineering, McGill University, Montreal, QC, Canada#TAB#","institution_ids":["https://openalex.org/I5023651"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10223515,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"565","last_page":"569"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9998000264167786,"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/T11392","display_name":"Energy Harvesting in Wireless Networks","score":0.9927999973297119,"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":0.874683141708374},{"id":"https://openalex.org/keywords/relay","display_name":"Relay","score":0.7657245993614197},{"id":"https://openalex.org/keywords/rayleigh-fading","display_name":"Rayleigh fading","score":0.6324838995933533},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.621574342250824},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.600795328617096},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5790417194366455},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.5631735920906067},{"id":"https://openalex.org/keywords/channel-capacity","display_name":"Channel capacity","score":0.5135672092437744},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4573076069355011},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.45417237281799316},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44324833154678345},{"id":"https://openalex.org/keywords/fading","display_name":"Fading","score":0.35609036684036255},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33083614706993103},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.2690010666847229},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17153596878051758},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1506834328174591},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12516486644744873}],"concepts":[{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.874683141708374},{"id":"https://openalex.org/C2778156585","wikidata":"https://www.wikidata.org/wiki/Q174053","display_name":"Relay","level":3,"score":0.7657245993614197},{"id":"https://openalex.org/C56985126","wikidata":"https://www.wikidata.org/wiki/Q854039","display_name":"Rayleigh fading","level":4,"score":0.6324838995933533},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.621574342250824},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.600795328617096},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5790417194366455},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.5631735920906067},{"id":"https://openalex.org/C97744766","wikidata":"https://www.wikidata.org/wiki/Q870845","display_name":"Channel capacity","level":3,"score":0.5135672092437744},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4573076069355011},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.45417237281799316},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44324833154678345},{"id":"https://openalex.org/C81978471","wikidata":"https://www.wikidata.org/wiki/Q1196572","display_name":"Fading","level":3,"score":0.35609036684036255},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33083614706993103},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.2690010666847229},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17153596878051758},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1506834328174591},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12516486644744873},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/wcnc.2012.6214432","is_oa":false,"landing_page_url":"https://doi.org/10.1109/wcnc.2012.6214432","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE Wireless Communications and Networking Conference (WCNC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.49000000953674316,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1971536606","https://openalex.org/W2098969228","https://openalex.org/W2102934991","https://openalex.org/W2106470018","https://openalex.org/W2106801259","https://openalex.org/W2111354185","https://openalex.org/W2120062331","https://openalex.org/W2125434467","https://openalex.org/W2130509920","https://openalex.org/W2136209931","https://openalex.org/W2142353524","https://openalex.org/W2145060291","https://openalex.org/W2167447263"],"related_works":["https://openalex.org/W2116044594","https://openalex.org/W2101999641","https://openalex.org/W2795180473","https://openalex.org/W1503152075","https://openalex.org/W301676527","https://openalex.org/W2052600062","https://openalex.org/W2090373650","https://openalex.org/W2124541664","https://openalex.org/W2383416193","https://openalex.org/W289296924"],"abstract_inverted_index":{"In":[0],"this":[1,186],"paper,":[2],"we":[3,130],"investigate":[4],"the":[5,27,35,47,51,71,77,88,91,99,110,117,121,137,155,161],"achievable":[6,78,138],"rate":[7,79],"and":[8,43,67,73,93,127,151,178,183],"ergodic":[9,156],"capacity":[10,157],"of":[11,70,102,125,136],"a":[12,55,61],"general":[13],"non-symmetric":[14],"half-duplex":[15],"non-orthogonal":[16],"amplify-and-forward":[17],"(NAF)":[18],"single-relay":[19],"channel":[20,28],"in":[21,98,108,185],"Rayleigh":[22],"fading":[23],"environments,":[24],"assuming":[25],"that":[26,147],"state":[29],"information":[30],"is":[31,96,144,158,163],"only":[32],"available":[33],"at":[34,148,176],"destination.":[36],"The":[37,181],"considered":[38],"channel,":[39],"which":[40,104],"captures":[41],"pathloss":[42],"shadowing":[44],"effects":[45],"over":[46,173],"transmission":[48,175],"links,":[49],"includes":[50],"symmetric":[52],"one":[53],"as":[54],"special":[56],"case.":[57],"At":[58],"first,":[59],"for":[60],"given":[62],"power":[63,112],"allocation":[64,113],"scheme,":[65],"simple":[66],"closed-form":[68],"expressions":[69],"upper":[72,92],"lower":[74,94],"bounds":[75,95],"on":[76,120,194],"are":[80],"derived.":[81],"As":[82],"shown":[83],"by":[84],"various":[85],"numerical":[86],"examples,":[87],"gap":[89],"between":[90],"small":[97],"entire":[100],"range":[101],"SNRs,":[103,129],"makes":[105],"them":[106],"useful":[107],"finding":[109],"optimal":[111],"solution":[114],"to":[115],"achieve":[116],"capacity.":[118],"Focusing":[119],"two":[122],"extreme":[123],"cases":[124],"low":[126,152,177],"high":[128,150,179],"then":[131,145],"provide":[132,189],"relatively":[133],"tight":[134],"approximations":[135],"rate.":[139],"Using":[140],"these":[141],"approximations,":[142],"it":[143],"revealed":[146],"both":[149],"SNR":[153],"regimes,":[154],"achieved":[159],"when":[160],"relay":[162],"inactive.":[164],"Equivalently,":[165],"NAF":[166,195],"relaying":[167],"does":[168],"not":[169],"yield":[170],"any":[171],"advantage":[172],"direct":[174],"SNRs.":[180],"results":[182],"observations":[184],"paper":[187],"therefore":[188],"some":[190],"further":[191],"important":[192],"insights":[193],"relaying.":[196]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
