{"id":"https://openalex.org/W2055748786","doi":"https://doi.org/10.1109/iswcs.2011.6125288","title":"Spectral analysis of the amplify and forward relay network as the number of relay layers increases","display_name":"Spectral analysis of the amplify and forward relay network as the number of relay layers increases","publication_year":2011,"publication_date":"2011-11-01","ids":{"openalex":"https://openalex.org/W2055748786","doi":"https://doi.org/10.1109/iswcs.2011.6125288","mag":"2055748786"},"language":"en","primary_location":{"id":"doi:10.1109/iswcs.2011.6125288","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iswcs.2011.6125288","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 8th International Symposium on Wireless Communication Systems","raw_type":"proceedings-article"},"type":"conference-paper","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/A5083981154","display_name":"Gabriel H. Tucci","orcid":null},"institutions":[{"id":"https://openalex.org/I72090969","display_name":"Nokia (United States)","ror":"https://ror.org/038km2573","country_code":"US","type":"company","lineage":["https://openalex.org/I2738502077","https://openalex.org/I72090969"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Gabriel H. Tucci","raw_affiliation_strings":["Bell Laboratories, Alcatel-Lucent, Murray Hill, NJ, USA","Bell Labs, Alcatel-Lucent, 600 Mountain Aveniue, Murray Hill, NJ 07974, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bell Laboratories, Alcatel-Lucent, Murray Hill, NJ, USA","institution_ids":[]},{"raw_affiliation_string":"Bell Labs, Alcatel-Lucent, 600 Mountain Aveniue, Murray Hill, NJ 07974, USA","institution_ids":["https://openalex.org/I72090969"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5083981154"],"corresponding_institution_ids":["https://openalex.org/I72090969"],"apc_list":null,"apc_paid":null,"fwci":1.0172,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.75959368,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":null,"first_page":"879","last_page":"883"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9868000149726868,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9861000180244446,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.8541164398193359},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.7307982444763184},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6008803844451904},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5402829647064209},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5297138690948486},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.513207197189331},{"id":"https://openalex.org/keywords/relay","display_name":"Relay","score":0.507373034954071},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.44868528842926025},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44330644607543945},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4401569366455078},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.42742472887039185},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.417555570602417},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4028357267379761},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.3859022557735443},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2996084690093994},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.136249840259552},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12562361359596252},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.08009743690490723}],"concepts":[{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.8541164398193359},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.7307982444763184},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6008803844451904},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5402829647064209},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5297138690948486},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.513207197189331},{"id":"https://openalex.org/C2778156585","wikidata":"https://www.wikidata.org/wiki/Q174053","display_name":"Relay","level":3,"score":0.507373034954071},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.44868528842926025},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44330644607543945},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4401569366455078},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.42742472887039185},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.417555570602417},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4028357267379761},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.3859022557735443},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2996084690093994},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.136249840259552},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12562361359596252},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.08009743690490723},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/iswcs.2011.6125288","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iswcs.2011.6125288","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 8th International Symposium on Wireless Communication Systems","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W45441657","https://openalex.org/W1708958458","https://openalex.org/W1965748679","https://openalex.org/W1999913024","https://openalex.org/W2002364903","https://openalex.org/W2047962726","https://openalex.org/W2064052856","https://openalex.org/W2072184935","https://openalex.org/W2086605818","https://openalex.org/W2102015892","https://openalex.org/W2106084579","https://openalex.org/W2153077717","https://openalex.org/W2156048454","https://openalex.org/W2333504782","https://openalex.org/W2607689712","https://openalex.org/W2610053348","https://openalex.org/W2949954798","https://openalex.org/W3104359459","https://openalex.org/W6637511679","https://openalex.org/W6666498509","https://openalex.org/W6682745690"],"related_works":["https://openalex.org/W2306553012","https://openalex.org/W2539674285","https://openalex.org/W4251417359","https://openalex.org/W1998322187","https://openalex.org/W1038122923","https://openalex.org/W2952514781","https://openalex.org/W4229993731","https://openalex.org/W2282205043","https://openalex.org/W2934566931","https://openalex.org/W4288376261"],"abstract_inverted_index":{"In":[0],"this":[1],"work":[2],"we":[3,97],"address":[4],"the":[5,9,14,25,28,47,51,62,65,74,88,104,113,116,146,160,164,169],"problem":[6,108],"of":[7,13,16,30,43,50,64,76,90,115,163,171],"determining":[8],"asymptotic":[10],"spectral":[11,48],"measure":[12,49,60,85,105],"product":[15,52,170],"independent,":[17],"Gaussian":[18,173],"random":[19],"matrices":[20,66],"with":[21,119],"correlated":[22],"entries,":[23],"as":[24,87],"dimension":[26,63],"and":[27,125],"number":[29,42,89],"multiplicative":[31,44,91],"terms":[32,45,92],"goes":[33],"to":[34,56,81,94],"infinity.":[35,95],"We":[36,70],"show":[37,72],"that":[38,73,139],"for":[39,103,112],"a":[40,57,82,122,149,154],"fixed":[41],"n":[46],"converges":[53],"in":[54,79,135,144,148],"distribution":[55,80],"compactly":[58,83],"supported":[59,84],"vnas":[61],"N":[67],"\u2192":[68],"\u221e.":[69],"also":[71],"sequence":[75],"measures":[77],"vnconverges":[78],"v":[86],"increases":[93],"Moreover,":[96],"deduce":[98],"an":[99],"exact":[100],"closed-form":[101],"expression":[102],"v.":[106],"This":[107],"is":[109,128,142,166],"fundamentally":[110],"important":[111],"analysis":[114],"wireless":[117],"network":[118,152],"fading":[120],"when":[121],"single":[123,155],"source":[124,156],"destination":[126,157],"pair":[127],"considered.":[129],"For":[130],"instance,":[131],"it":[132],"was":[133],"studied":[134],"[4,":[136],"5,":[137],"9]":[138],"if":[140],"one":[141],"interested":[143],"exploring":[145],"performance":[147],"layered":[150],"relay":[151],"having":[153],"pair,":[158],"then":[159],"effective":[161],"channel":[162],"system":[165],"given":[167],"by":[168],"independent":[172],"matrices.":[174]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}