{"id":"https://openalex.org/W2163470941","doi":"https://doi.org/10.1109/tsp.2009.2025823","title":"On Low Complexity Robust Beamforming With Positive Semidefinite Constraints","display_name":"On Low Complexity Robust Beamforming With Positive Semidefinite Constraints","publication_year":2009,"publication_date":"2009-06-25","ids":{"openalex":"https://openalex.org/W2163470941","doi":"https://doi.org/10.1109/tsp.2009.2025823","mag":"2163470941"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2009.2025823","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2009.2025823","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-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/A5008383657","display_name":"Chengwen Xing","orcid":"https://orcid.org/0000-0003-4941-3503"},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Chengwen Xing","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong, China"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong, China","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053586699","display_name":"Shaodan Ma","orcid":"https://orcid.org/0000-0001-5521-3650"},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Shaodan Ma","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong, China"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong, China","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085964667","display_name":"Yik\u2010Chung Wu","orcid":"https://orcid.org/0000-0002-2738-0387"},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Yik-Chung Wu","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong, China"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong, China","institution_ids":["https://openalex.org/I889458895"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5008383657"],"corresponding_institution_ids":["https://openalex.org/I889458895"],"apc_list":null,"apc_paid":null,"fwci":2.8568,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.9127321,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"57","issue":"12","first_page":"4942","last_page":"4945"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10860","display_name":"Speech and Audio Processing","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/beamforming","display_name":"Beamforming","score":0.6884722709655762},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.6022882461547852},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.5888537764549255},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.573261559009552},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.567434549331665},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.5169036388397217},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5069044232368469},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5068843960762024},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4930283725261688},{"id":"https://openalex.org/keywords/adaptive-beamformer","display_name":"Adaptive beamformer","score":0.4665282368659973},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.45896032452583313},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4380556643009186},{"id":"https://openalex.org/keywords/minimum-variance-unbiased-estimator","display_name":"Minimum-variance unbiased estimator","score":0.43416231870651245},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.4249546527862549},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4103434085845947},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11820653080940247},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.0847901999950409},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.07101026177406311},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.06720426678657532}],"concepts":[{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.6884722709655762},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.6022882461547852},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.5888537764549255},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.573261559009552},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.567434549331665},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.5169036388397217},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5069044232368469},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5068843960762024},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4930283725261688},{"id":"https://openalex.org/C33378366","wikidata":"https://www.wikidata.org/wiki/Q4680719","display_name":"Adaptive beamformer","level":3,"score":0.4665282368659973},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.45896032452583313},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4380556643009186},{"id":"https://openalex.org/C165646398","wikidata":"https://www.wikidata.org/wiki/Q3755281","display_name":"Minimum-variance unbiased estimator","level":3,"score":0.43416231870651245},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.4249546527862549},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4103434085845947},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11820653080940247},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0847901999950409},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.07101026177406311},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.06720426678657532},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tsp.2009.2025823","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2009.2025823","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.380.8173","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.380.8173","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.eee.hku.hk/~ycwu/publication_download/ycwu_TSP_2009_beamforming.pdf","raw_type":"text"},{"id":"pmh:oai:hub.hku.hk:10722/73912","is_oa":false,"landing_page_url":"http://hdl.handle.net/10722/73912","pdf_url":null,"source":{"id":"https://openalex.org/S4377196271","display_name":"The HKU Scholars Hub (University of Hong Kong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I889458895","host_organization_name":"University of Hong Kong","host_organization_lineage":["https://openalex.org/I889458895"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1503221585","https://openalex.org/W1546493376","https://openalex.org/W1568307856","https://openalex.org/W1602659231","https://openalex.org/W2045021643","https://openalex.org/W2125739803","https://openalex.org/W2139419267","https://openalex.org/W2150835235","https://openalex.org/W2296319761","https://openalex.org/W2475682732","https://openalex.org/W3147528989","https://openalex.org/W4206383846","https://openalex.org/W4250589301"],"related_works":["https://openalex.org/W3013496310","https://openalex.org/W2807497897","https://openalex.org/W2761218246","https://openalex.org/W4225264158","https://openalex.org/W2019022680","https://openalex.org/W2951676025","https://openalex.org/W2242301815","https://openalex.org/W2793870329","https://openalex.org/W2392382502","https://openalex.org/W2037962720"],"abstract_inverted_index":{"This":[0],"paper":[1],"addresses":[2],"the":[3,17,31,49,58,68,75,86],"problem":[4],"of":[5,52,72,77,85],"robust":[6,38],"beamforming":[7],"for":[8],"general-rank":[9],"signal":[10,21],"models":[11],"with":[12,65],"norm":[13],"bounded":[14],"uncertainties":[15],"in":[16,42],"desired":[18],"and":[19,82],"received":[20],"covariance":[22,32],"matrices":[23],"as":[24,26],"well":[25],"positive":[27],"semidefinite":[28],"constraints":[29],"on":[30],"matrices.":[33],"Two":[34],"novel":[35],"minimum":[36],"variance":[37],"beamformers":[39,88],"are":[40,89],"derived":[41],"closed-form.":[43],"The":[44,80],"first":[45,69],"one":[46,60],"basically":[47],"is":[48],"closed-form":[50],"version":[51],"an":[53],"existing":[54],"iterative":[55],"algorithm,":[56],"while":[57],"second":[59],"offers":[61],"even":[62],"better":[63],"performance":[64,83],"respect":[66],"to":[67],"one.":[70],"Both":[71],"them":[73],"have":[74],"advantage":[76],"low":[78],"complexity.":[79],"effectiveness":[81],"improvement":[84],"proposed":[87],"verified":[90],"by":[91],"simulation":[92],"results.":[93]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":6},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
