{"id":"https://openalex.org/W2590602772","doi":"https://doi.org/10.1109/cns.2016.7860563","title":"Ergodic secrecy sum rate for multiuser MIMO downlink systems using block diagonalization","display_name":"Ergodic secrecy sum rate for multiuser MIMO downlink systems using block diagonalization","publication_year":2016,"publication_date":"2016-10-01","ids":{"openalex":"https://openalex.org/W2590602772","doi":"https://doi.org/10.1109/cns.2016.7860563","mag":"2590602772"},"language":"en","primary_location":{"id":"doi:10.1109/cns.2016.7860563","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cns.2016.7860563","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE Conference on Communications and Network Security (CNS)","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/A5020497698","display_name":"Xuanxuan Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I2800274787","display_name":"Fraunhofer Institute for Telecommunications, Heinrich Hertz Institute","ror":"https://ror.org/02tbr6331","country_code":"DE","type":"facility","lineage":["https://openalex.org/I2800274787","https://openalex.org/I4923324"]},{"id":"https://openalex.org/I4210156404","display_name":"Institute of Information Engineering","ror":"https://ror.org/04r53se39","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]}],"countries":["CN","DE"],"is_corresponding":false,"raw_author_name":"Xuanxuan Wang","raw_affiliation_strings":["Chinese Academy of Sciences, Institute of Information Engineering, China","Fraunhofer Institute for Telecommunications, Heinrich Hertz Institute, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chinese Academy of Sciences, Institute of Information Engineering, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]},{"raw_affiliation_string":"Fraunhofer Institute for Telecommunications, Heinrich Hertz Institute, Germany","institution_ids":["https://openalex.org/I2800274787"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038203207","display_name":"Rafael F. Schaefer","orcid":"https://orcid.org/0000-0002-1702-9075"},"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":"Rafael F. Schaefer","raw_affiliation_strings":["Information Theory and Applications Chair, Technische Universit\u00e4t, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information Theory and Applications Chair, Technische Universit\u00e4t, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107839122","display_name":"Lars Thiele","orcid":null},"institutions":[{"id":"https://openalex.org/I2800274787","display_name":"Fraunhofer Institute for Telecommunications, Heinrich Hertz Institute","ror":"https://ror.org/02tbr6331","country_code":"DE","type":"facility","lineage":["https://openalex.org/I2800274787","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Lars Thiele","raw_affiliation_strings":["Fraunhofer Institute for Telecommunications, Heinrich Hertz Institute, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fraunhofer Institute for Telecommunications, Heinrich Hertz Institute, Germany","institution_ids":["https://openalex.org/I2800274787"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109187976","display_name":"Thomas Haustein","orcid":null},"institutions":[{"id":"https://openalex.org/I2800274787","display_name":"Fraunhofer Institute for Telecommunications, Heinrich Hertz Institute","ror":"https://ror.org/02tbr6331","country_code":"DE","type":"facility","lineage":["https://openalex.org/I2800274787","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thomas Haustein","raw_affiliation_strings":["Fraunhofer Institute for Telecommunications, Heinrich Hertz Institute, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fraunhofer Institute for Telecommunications, Heinrich Hertz Institute, Germany","institution_ids":["https://openalex.org/I2800274787"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060385264","display_name":"Yongming Wang","orcid":"https://orcid.org/0000-0001-8287-6986"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210156404","display_name":"Institute of Information Engineering","ror":"https://ror.org/04r53se39","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongming Wang","raw_affiliation_strings":["Chinese Academy of Sciences, Institute of Information Engineering, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chinese Academy of Sciences, Institute of Information Engineering, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"1","issue":null,"first_page":"636","last_page":"640"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":1.0,"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":0.9986000061035156,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.998199999332428,"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/telecommunications-link","display_name":"Telecommunications link","score":0.8517323136329651},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.8196377754211426},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.6822608113288879},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6130358576774597},{"id":"https://openalex.org/keywords/secrecy","display_name":"Secrecy","score":0.5676587820053101},{"id":"https://openalex.org/keywords/transmitter","display_name":"Transmitter","score":0.5489686727523804},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.501854658126831},{"id":"https://openalex.org/keywords/multi-user-mimo","display_name":"Multi-user MIMO","score":0.41993576288223267},{"id":"https://openalex.org/keywords/antenna","display_name":"Antenna (radio)","score":0.41202202439308167},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.32700371742248535},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3023068308830261},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.2838219106197357},{"id":"https://openalex.org/keywords/beamforming","display_name":"Beamforming","score":0.17585769295692444},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.0711388885974884},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.0633639395236969},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.061997830867767334}],"concepts":[{"id":"https://openalex.org/C138660444","wikidata":"https://www.wikidata.org/wiki/Q5607897","display_name":"Telecommunications link","level":2,"score":0.8517323136329651},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.8196377754211426},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.6822608113288879},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6130358576774597},{"id":"https://openalex.org/C2776452267","wikidata":"https://www.wikidata.org/wiki/Q1503443","display_name":"Secrecy","level":2,"score":0.5676587820053101},{"id":"https://openalex.org/C47798520","wikidata":"https://www.wikidata.org/wiki/Q190157","display_name":"Transmitter","level":3,"score":0.5489686727523804},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.501854658126831},{"id":"https://openalex.org/C91330434","wikidata":"https://www.wikidata.org/wiki/Q738298","display_name":"Multi-user MIMO","level":4,"score":0.41993576288223267},{"id":"https://openalex.org/C21822782","wikidata":"https://www.wikidata.org/wiki/Q131214","display_name":"Antenna (radio)","level":2,"score":0.41202202439308167},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.32700371742248535},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3023068308830261},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.2838219106197357},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.17585769295692444},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0711388885974884},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0633639395236969},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.061997830867767334},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cns.2016.7860563","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cns.2016.7860563","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE Conference on Communications and Network Security (CNS)","raw_type":"proceedings-article"},{"id":"pmh:oai:publica.fraunhofer.de:publica/398106","is_oa":false,"landing_page_url":"https://publica.fraunhofer.de/handle/publica/398106","pdf_url":null,"source":{"id":"https://openalex.org/S4306400318","display_name":"Fraunhofer-Publica (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"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":"conference paper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W949353694","https://openalex.org/W1551587481","https://openalex.org/W1836938175","https://openalex.org/W1993039929","https://openalex.org/W1997834106","https://openalex.org/W2035759913","https://openalex.org/W2051990156","https://openalex.org/W2072184935","https://openalex.org/W2072563372","https://openalex.org/W2079364662","https://openalex.org/W2117041221","https://openalex.org/W2130509920","https://openalex.org/W2132035967","https://openalex.org/W2139794367","https://openalex.org/W2151716519","https://openalex.org/W2167200713","https://openalex.org/W2269066968","https://openalex.org/W4293702014"],"related_works":["https://openalex.org/W2493929861","https://openalex.org/W2016567611","https://openalex.org/W2548963335","https://openalex.org/W2475541339","https://openalex.org/W2159941915","https://openalex.org/W565335793","https://openalex.org/W2363071176","https://openalex.org/W2761879201","https://openalex.org/W2556017705","https://openalex.org/W2059045613"],"abstract_inverted_index":{"To":[0],"date,":[1],"the":[2,42,47,52,63,67,71,76,84,90,93,106,118,121],"achievable":[3,64],"ergodic":[4,85],"secrecy":[5,86],"sum":[6,87],"rate":[7,65,74,88],"has":[8],"been":[9],"studied":[10],"for":[11,66,75,89],"multiuser":[12,25],"MIMO":[13,26],"downlink":[14,27],"systems":[15,28],"with":[16,29],"single-antenna":[17,35],"receivers":[18,31],"only.":[19],"In":[20],"this":[21],"paper,":[22],"we":[23,79],"study":[24],"multiple-antenna":[30],"and":[32,58,70,95,99,111],"an":[33],"external":[34],"eavesdropper":[36],"to":[37,54],"be":[38],"kept":[39],"ignorant":[40],"of":[41,62,83,108,120],"transmitted":[43],"messages.":[44],"We":[45],"adopt":[46],"block":[48],"diagonalization":[49],"technique":[50],"at":[51],"transmitter":[53],"remove":[55],"inter-user":[56],"interference,":[57],"derive":[59],"closed-form":[60],"expressions":[61],"intended":[68],"users":[69],"information":[72],"leakage":[73],"eavesdropper.":[77],"Furthermore,":[78],"analyze":[80],"asymptotic":[81],"characteristics":[82],"system":[91],"in":[92,105],"high":[94],"low":[96],"SNR":[97],"regime,":[98],"obtain":[100],"a":[101],"tight":[102],"lower":[103],"bound":[104],"regime":[107],"large":[109],"transmit":[110],"receive":[112],"antennas.":[113],"Finally,":[114],"numerical":[115],"results":[116],"validate":[117],"accuracy":[119],"theoretical":[122],"analysis.":[123]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}