{"id":"https://openalex.org/W2290254791","doi":"https://doi.org/10.1109/tit.2018.2812885","title":"Capacity Scaling in MIMO Systems With General Unitarily Invariant Random Matrices","display_name":"Capacity Scaling in MIMO Systems With General Unitarily Invariant Random Matrices","publication_year":2018,"publication_date":"2018-03-07","ids":{"openalex":"https://openalex.org/W2290254791","doi":"https://doi.org/10.1109/tit.2018.2812885","mag":"2290254791"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2018.2812885","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2812885","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1306.2595","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087063228","display_name":"Burak \u00c7akmak","orcid":"https://orcid.org/0000-0001-5089-8873"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Burak Cakmak","raw_affiliation_strings":["Department of Computer Science, Technical University of Berlin, Berlin, Germany","Department of Electronic Systems, Aalborg University, Aalborg, Germany"],"raw_orcid":"https://orcid.org/0000-0001-5089-8873","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Technical University of Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"Department of Electronic Systems, Aalborg University, Aalborg, Germany","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026710677","display_name":"Ralf R. M\u00fcller","orcid":"https://orcid.org/0000-0003-3780-9308"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ralf R. Muller","raw_affiliation_strings":["Institute for Digital Communications, Friedrich-Alexander Universit\u00e4t Erlangen-N\u00fcrnberg, Erlangen, Germany","Institute for Digital Communications, Friedrich-Alexander-Universita\u0308t Erlangen-Nu\u0308rnberg, Erlangen, Germany"],"raw_orcid":"https://orcid.org/0000-0003-3780-9308","affiliations":[{"raw_affiliation_string":"Institute for Digital Communications, Friedrich-Alexander Universit\u00e4t Erlangen-N\u00fcrnberg, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]},{"raw_affiliation_string":"Institute for Digital Communications, Friedrich-Alexander-Universita\u0308t Erlangen-Nu\u0308rnberg, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064657299","display_name":"Bernard H. Fleury","orcid":"https://orcid.org/0000-0002-9061-3083"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bernard H. Fleury","raw_affiliation_strings":["Department of Electronic Systems, Aalborg University, Aalborg, Germany"],"raw_orcid":"https://orcid.org/0000-0002-9061-3083","affiliations":[{"raw_affiliation_string":"Department of Electronic Systems, Aalborg University, Aalborg, Germany","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00400091,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"64","issue":"5","first_page":"3825","last_page":"3841"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9750999808311462,"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":0.9750999808311462,"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/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9718999862670898,"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.9693999886512756,"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/mathematics","display_name":"Mathematics","score":0.6436789035797119},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.6204695701599121},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5948094129562378},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.5659693479537964},{"id":"https://openalex.org/keywords/ergodicity","display_name":"Ergodicity","score":0.5325068235397339},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.5314962267875671},{"id":"https://openalex.org/keywords/channel-capacity","display_name":"Channel capacity","score":0.49039173126220703},{"id":"https://openalex.org/keywords/mutual-information","display_name":"Mutual information","score":0.4772481918334961},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4517955780029297},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4454430937767029},{"id":"https://openalex.org/keywords/transmitter","display_name":"Transmitter","score":0.4377821981906891},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3457314968109131},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.34534952044487},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3241835832595825},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.23093262314796448},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.178728848695755},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.15209606289863586},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1376889944076538},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13079676032066345},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09319907426834106}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6436789035797119},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.6204695701599121},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5948094129562378},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.5659693479537964},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.5325068235397339},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.5314962267875671},{"id":"https://openalex.org/C97744766","wikidata":"https://www.wikidata.org/wiki/Q870845","display_name":"Channel capacity","level":3,"score":0.49039173126220703},{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.4772481918334961},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4517955780029297},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4454430937767029},{"id":"https://openalex.org/C47798520","wikidata":"https://www.wikidata.org/wiki/Q190157","display_name":"Transmitter","level":3,"score":0.4377821981906891},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3457314968109131},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.34534952044487},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3241835832595825},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.23093262314796448},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.178728848695755},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.15209606289863586},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1376889944076538},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13079676032066345},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09319907426834106},{"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/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tit.2018.2812885","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2812885","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1306.2595","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1306.2595","pdf_url":"https://arxiv.org/pdf/1306.2595","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},{"id":"pmh:oai:pure.atira.dk:publications/7b1949fd-b215-4a06-8a48-d438ec9dff00","is_oa":true,"landing_page_url":"https://vbn.aau.dk/da/publications/7b1949fd-b215-4a06-8a48-d438ec9dff00","pdf_url":"http://arxiv.org/pdf/1306.2595","source":{"id":"https://openalex.org/S4306401731","display_name":"VBN Forskningsportal (Aalborg Universitet)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I891191580","host_organization_name":"Aalborg University","host_organization_lineage":["https://openalex.org/I891191580"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Cakmak , B , Muller , R R &amp; Fleury , B H 2018 , ' Capacity scaling in MIMO systems with general unitarily invariant random matrices ' , IEEE Transactions on Information Theory , vol. 64 , no. 5 , pp. 3825-3841 . https://doi.org/10.1109/TIT.2018.2812885","raw_type":"article"},{"id":"mag:2290254791","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1306.2595.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1306.2595","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1306.2595","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1306.2595","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1306.2595","pdf_url":"https://arxiv.org/pdf/1306.2595","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W615589970","https://openalex.org/W1516287220","https://openalex.org/W1965180197","https://openalex.org/W1966600169","https://openalex.org/W1997834106","https://openalex.org/W2063361547","https://openalex.org/W2094933406","https://openalex.org/W2095712621","https://openalex.org/W2099111195","https://openalex.org/W2109286020","https://openalex.org/W2120339991","https://openalex.org/W2130509920","https://openalex.org/W2134186144","https://openalex.org/W2136979582","https://openalex.org/W2139474620","https://openalex.org/W2151716519","https://openalex.org/W2159312879","https://openalex.org/W2181292907","https://openalex.org/W2198712087","https://openalex.org/W2588048611","https://openalex.org/W4206442507","https://openalex.org/W4229746864","https://openalex.org/W4247891181","https://openalex.org/W4253567193","https://openalex.org/W6675880906"],"related_works":["https://openalex.org/W2293867623","https://openalex.org/W2111473018","https://openalex.org/W1782860950","https://openalex.org/W2951985090","https://openalex.org/W2951714206","https://openalex.org/W3102122722","https://openalex.org/W2607913557","https://openalex.org/W2101781652","https://openalex.org/W1976109068","https://openalex.org/W2105151164","https://openalex.org/W1661479849","https://openalex.org/W2784902909","https://openalex.org/W2949671731","https://openalex.org/W2136478832","https://openalex.org/W1972826915","https://openalex.org/W2084870045","https://openalex.org/W3019652833","https://openalex.org/W2151673148","https://openalex.org/W3080476703","https://openalex.org/W2803592714"],"abstract_inverted_index":{"We":[0,185],"investigate":[1],"the":[2,9,18,23,29,52,68,74,79,97,103,116,122,146,155,166,181,191,198,203,209,212],"capacity":[3],"scaling":[4],"of":[5,25,83,99,102,197,211],"multiple-input-multiple-output":[6],"systems":[7],"with":[8,46,154,178],"system":[10,38,66,199,213],"dimensions.":[11],"To":[12],"that":[13],"end,":[14],"we":[15,50],"quantify":[16,187],"how":[17,190],"mutual":[19,84,192],"information":[20,85,193],"varies":[21],"when":[22],"number":[24],"antennas":[26,45,59],"(at":[27],"either":[28],"receiver":[30],"or":[31],"transmitter":[32],"side)":[33],"is":[34,119,126],"altered.":[35],"For":[36],"a":[37,64,195],"comprising":[39],"R":[40,47,151,171],"receive":[41,58],"and":[42,72,96,188],"T":[43],"transmit":[44],">":[48],"T,":[49,95,150],"find":[51],"following:":[53],"by":[54,128,170],"removing":[55],"as":[56,60,194],"many":[57],"needed":[61],"to":[62,175],"obtain":[63],"square":[65],"(provided":[67],"channel":[69,105],"matrices":[70],"before":[71],"after":[73],"removal":[75],"have":[76],"full":[77],"rank)":[78],"maximum":[80],"resulting":[81],"loss":[82,125,168],"over":[86],"all":[87],"signal-to-noise":[88],"ratios":[89],"(SNRs)":[90],"depends":[91],"only":[92],"on":[93,109],"R,":[94],"matrix":[98,118],"left-singular":[100],"vectors":[101],"initial":[104],"matrix,":[106],"but":[107],"not":[108],"its":[110],"singular":[111],"values.":[112],"In":[113],"particular,":[114],"if":[115,149],"latter":[117],"Haar":[120],"distributed":[121],"ergodic":[123],"rate":[124,167],"given":[127],"\u03a3":[129,136],"<sub":[130,137,158],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[131,134,138,141,159,162],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">t=1</sub>":[132],"<sup":[133,140,161],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">T</sup>":[135],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">r=T+1</sub>":[139],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">R</sup>":[142],"1/r-t":[143],"nats.":[144],"Under":[145],"same":[147],"assumption,":[148],"\u2192":[152],"\u221e":[153],"ratio":[156],"\u03c6":[157],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">=</sub>":[160],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u0394</sup>":[163],"T/R":[164],"fixed,":[165],"normalized":[169],"converges":[172],"almost":[173],"surely":[174],"H(\u03c6)":[176],"bits":[177],"H(\u00b7)":[179],"denoting":[180],"binary":[182],"entropy":[183],"function.":[184],"also":[186],"study":[189],"function":[196],"dimensions":[200,214],"deviates":[201],"from":[202],"traditionally":[204],"assumed":[205],"linear":[206],"growth":[207],"in":[208],"minimum":[210],"at":[215],"high":[216],"SNR.":[217]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}