{"id":"https://openalex.org/W2548211615","doi":"https://doi.org/10.1109/wifs.2012.6412662","title":"Optimality of beamforming for secrecy capacity of MIMO wiretap channels","display_name":"Optimality of beamforming for secrecy capacity of MIMO wiretap channels","publication_year":2012,"publication_date":"2012-12-01","ids":{"openalex":"https://openalex.org/W2548211615","doi":"https://doi.org/10.1109/wifs.2012.6412662","mag":"2548211615"},"language":"en","primary_location":{"id":"doi:10.1109/wifs.2012.6412662","is_oa":false,"landing_page_url":"https://doi.org/10.1109/wifs.2012.6412662","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Workshop on Information Forensics and Security (WIFS)","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/A5053441128","display_name":"Jiangyuan Li","orcid":"https://orcid.org/0000-0002-2147-5908"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jiangyuan Li","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Rutgers-The State University of New Jersey, New Brunswick, NJ"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Rutgers-The State University of New Jersey, New Brunswick, NJ","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004201783","display_name":"Athina P. Petropulu","orcid":"https://orcid.org/0000-0001-7380-7815"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Athina P. Petropulu","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Rutgers-The State University of New Jersey, New Brunswick, NJ"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Rutgers-The State University of New Jersey, New Brunswick, NJ","institution_ids":["https://openalex.org/I102322142"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5053441128"],"corresponding_institution_ids":["https://openalex.org/I102322142"],"apc_list":null,"apc_paid":null,"fwci":0.982,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.79944955,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"276","last_page":"281"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9959999918937683,"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/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9890999794006348,"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/beamforming","display_name":"Beamforming","score":0.9065617322921753},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.7541970014572144},{"id":"https://openalex.org/keywords/transmitter","display_name":"Transmitter","score":0.6386462450027466},{"id":"https://openalex.org/keywords/secrecy","display_name":"Secrecy","score":0.6043931841850281},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5599377751350403},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5227506160736084},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.48840993642807007},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.48686379194259644},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.45635464787483215},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.41417670249938965},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3357810080051422},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.3161661624908447},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.12725049257278442},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07860764861106873}],"concepts":[{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.9065617322921753},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.7541970014572144},{"id":"https://openalex.org/C47798520","wikidata":"https://www.wikidata.org/wiki/Q190157","display_name":"Transmitter","level":3,"score":0.6386462450027466},{"id":"https://openalex.org/C2776452267","wikidata":"https://www.wikidata.org/wiki/Q1503443","display_name":"Secrecy","level":2,"score":0.6043931841850281},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5599377751350403},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5227506160736084},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.48840993642807007},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.48686379194259644},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.45635464787483215},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.41417670249938965},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3357810080051422},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.3161661624908447},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.12725049257278442},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07860764861106873},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/wifs.2012.6412662","is_oa":false,"landing_page_url":"https://doi.org/10.1109/wifs.2012.6412662","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Workshop on Information Forensics and Security (WIFS)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.75,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1527687627","https://openalex.org/W1598269389","https://openalex.org/W1970616625","https://openalex.org/W1991614769","https://openalex.org/W1993873761","https://openalex.org/W2043769961","https://openalex.org/W2060756156","https://openalex.org/W2072563372","https://openalex.org/W2092086200","https://openalex.org/W2104562009","https://openalex.org/W2128153585","https://openalex.org/W2144007657","https://openalex.org/W2156214717","https://openalex.org/W2607549630","https://openalex.org/W2620656463","https://openalex.org/W2797925981","https://openalex.org/W2949672874","https://openalex.org/W4250589301","https://openalex.org/W4301621763","https://openalex.org/W6673604286"],"related_works":["https://openalex.org/W2493929861","https://openalex.org/W2016567611","https://openalex.org/W2475541339","https://openalex.org/W565335793","https://openalex.org/W2363071176","https://openalex.org/W2107199751","https://openalex.org/W4243812570","https://openalex.org/W4300441478","https://openalex.org/W2059045613","https://openalex.org/W2724724053"],"abstract_inverted_index":{"A":[0],"Gaussian":[1],"multiple-input":[2],"multiple-output":[3],"(MIMO)":[4],"wiretap":[5],"channel":[6,69],"model":[7],"is":[8,38,78,89,98,104,121],"considered,":[9],"where":[10],"there":[11],"exists":[12],"a":[13,15],"transmitter,":[14],"legitimate":[16,66],"receiver":[17],"and":[18,40,67,117],"an":[19,107],"eavesdropper":[20,68],"each":[21],"equipped":[22],"with":[23],"multiple":[24],"antennas.":[25],"The":[26,52],"optimality":[27],"of":[28,65,110],"beamforming":[29,45,77,97,118],"for":[30,44],"secrecy":[31,102,115,119],"capacity":[32,103,116],"subject":[33],"to":[34,46],"sum":[35],"power":[36],"constraint":[37],"studied,":[39],"two":[41],"sufficient":[42,54,83],"conditions":[43],"be":[47],"globally":[48,79,99],"optimal":[49],"are":[50],"given.":[51],"first":[53],"condition":[55],"states":[56],"that":[57],"when":[58],"the":[59,62,93,101,111,114],"difference":[60,112],"between":[61,113],"Gram":[63],"matrices":[64,70],"has":[71],"exactly":[72],"one":[73],"positive":[74],"eigenvalue,":[75],"then":[76],"optimal.":[80],"An":[81],"alternative":[82],"condition,":[84],"which":[85,96],"involves":[86],"convex":[87],"optimization,":[88],"also":[90],"provided.":[91,122],"For":[92],"case":[94],"in":[95],"optimal,":[100],"obtained.":[105],"Otherwise,":[106],"upper":[108],"bound":[109],"rate":[120]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
