{"id":"https://openalex.org/W1956919402","doi":"https://doi.org/10.1109/lsp.2015.2504386","title":"Joint Robust Transmit/Receive Adaptive Beamforming for MIMO Radar Using Probability-Constrained Optimization","display_name":"Joint Robust Transmit/Receive Adaptive Beamforming for MIMO Radar Using Probability-Constrained Optimization","publication_year":2015,"publication_date":"2015-12-04","ids":{"openalex":"https://openalex.org/W1956919402","doi":"https://doi.org/10.1109/lsp.2015.2504386","mag":"1956919402"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2015.2504386","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2015.2504386","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1508.02212","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100664346","display_name":"Weiyu Zhang","orcid":"https://orcid.org/0000-0002-4646-1991"},"institutions":[{"id":"https://openalex.org/I4210099069","display_name":"Institute of Acoustics","ror":"https://ror.org/00v8rqv75","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210099069"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["CN","FI"],"is_corresponding":true,"raw_author_name":"Weiyu Zhang","raw_affiliation_strings":["Chinese Academy of Sciences, Institute of Acoustics, Beijing, China","Department of Signal Processing and Acoustics, Aalto University, Espoo, Finland"],"affiliations":[{"raw_affiliation_string":"Chinese Academy of Sciences, Institute of Acoustics, Beijing, China","institution_ids":["https://openalex.org/I4210099069","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Department of Signal Processing and Acoustics, Aalto University, Espoo, Finland","institution_ids":["https://openalex.org/I9927081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055234860","display_name":"Sergiy A. Vorobyov","orcid":"https://orcid.org/0000-0001-7249-647X"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Sergiy A. Vorobyov","raw_affiliation_strings":["Department of Signal Processing and Acoustics, Aalto University, Espoo, Finland"],"affiliations":[{"raw_affiliation_string":"Department of Signal Processing and Acoustics, Aalto University, Espoo, Finland","institution_ids":["https://openalex.org/I9927081"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100664346"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210099069","https://openalex.org/I9927081"],"apc_list":null,"apc_paid":null,"fwci":56.9043,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.99527632,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"23","issue":"1","first_page":"112","last_page":"116"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10891","display_name":"Radar Systems and Signal Processing","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T10891","display_name":"Radar Systems and Signal Processing","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9987999796867371,"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/T11038","display_name":"Advanced SAR Imaging Techniques","score":0.992900013923645,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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":0.7585338354110718},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.6371430158615112},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6139901876449585},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5685879588127136},{"id":"https://openalex.org/keywords/second-order-cone-programming","display_name":"Second-order cone programming","score":0.566116213798523},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5508747100830078},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.47922569513320923},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4381103515625},{"id":"https://openalex.org/keywords/adaptive-beamformer","display_name":"Adaptive beamformer","score":0.42600324749946594},{"id":"https://openalex.org/keywords/robust-optimization","display_name":"Robust optimization","score":0.41953855752944946},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3586311340332031},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3127415180206299},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.22832581400871277},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.19357427954673767},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08895817399024963}],"concepts":[{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.7585338354110718},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.6371430158615112},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6139901876449585},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5685879588127136},{"id":"https://openalex.org/C111397411","wikidata":"https://www.wikidata.org/wiki/Q7442977","display_name":"Second-order cone programming","level":4,"score":0.566116213798523},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5508747100830078},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.47922569513320923},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4381103515625},{"id":"https://openalex.org/C33378366","wikidata":"https://www.wikidata.org/wiki/Q4680719","display_name":"Adaptive beamformer","level":3,"score":0.42600324749946594},{"id":"https://openalex.org/C193254401","wikidata":"https://www.wikidata.org/wiki/Q2160088","display_name":"Robust optimization","level":2,"score":0.41953855752944946},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3586311340332031},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3127415180206299},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.22832581400871277},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.19357427954673767},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08895817399024963},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/lsp.2015.2504386","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2015.2504386","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1508.02212","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1508.02212","pdf_url":"https://arxiv.org/pdf/1508.02212","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":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1508.02212","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1508.02212","pdf_url":"https://arxiv.org/pdf/1508.02212","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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W65255600","https://openalex.org/W322920824","https://openalex.org/W653761051","https://openalex.org/W1540764732","https://openalex.org/W1599703818","https://openalex.org/W1622825395","https://openalex.org/W1667165204","https://openalex.org/W1923730267","https://openalex.org/W1964590153","https://openalex.org/W1968644212","https://openalex.org/W1989979908","https://openalex.org/W2000317822","https://openalex.org/W2005602327","https://openalex.org/W2014020284","https://openalex.org/W2018744547","https://openalex.org/W2044000385","https://openalex.org/W2050968963","https://openalex.org/W2057077708","https://openalex.org/W2061788339","https://openalex.org/W2083506609","https://openalex.org/W2087005409","https://openalex.org/W2093225945","https://openalex.org/W2097254749","https://openalex.org/W2100693051","https://openalex.org/W2107811524","https://openalex.org/W2109012875","https://openalex.org/W2113168978","https://openalex.org/W2122420047","https://openalex.org/W2122852420","https://openalex.org/W2124733114","https://openalex.org/W2129640939","https://openalex.org/W2132065358","https://openalex.org/W2132506160","https://openalex.org/W2132679193","https://openalex.org/W2138352074","https://openalex.org/W2145686608","https://openalex.org/W2147556173","https://openalex.org/W2150273584","https://openalex.org/W2155951048","https://openalex.org/W2158844568","https://openalex.org/W2159659869","https://openalex.org/W2159810364","https://openalex.org/W2162862209","https://openalex.org/W2166117654","https://openalex.org/W2168200870","https://openalex.org/W2171576754","https://openalex.org/W2186637489","https://openalex.org/W2196292687","https://openalex.org/W4237205459","https://openalex.org/W6636669794","https://openalex.org/W6640196398","https://openalex.org/W6674619943"],"related_works":["https://openalex.org/W2724724053","https://openalex.org/W818226659","https://openalex.org/W2009075871","https://openalex.org/W2132841313","https://openalex.org/W2105408150","https://openalex.org/W1976800395","https://openalex.org/W2365713954","https://openalex.org/W2606661315","https://openalex.org/W2548445082","https://openalex.org/W2081621768"],"abstract_inverted_index":{"In":[0],"this":[1],"letter,":[2],"a":[3,72,86],"joint":[4,123],"robust":[5,58,125],"transmit/receive":[6,124],"adaptive":[7,126],"beamforming":[8,59,112,127],"for":[9,129],"multiple-input":[10],"multiple-output":[11],"(MIMO)":[12],"radar":[13],"based":[14,91],"on":[15,92],"probability-constrained":[16,57],"optimization":[17],"approach":[18],"is":[19,48,61,96],"developed":[20,97],"in":[21,31],"the":[22,33,45,76,100,110,117],"case":[23],"of":[24,44,109],"Gaussian":[25],"and":[26,35,63,82,119],"arbitrary":[27],"distributed":[28],"mismatches":[29],"present":[30],"both":[32],"transmit":[34,81],"receive":[36,83],"signal":[37],"steering":[38],"vectors.":[39],"A":[40],"tight":[41],"lower":[42],"bound":[43],"probability":[46,77],"constraint":[47,78],"also":[49],"derived":[50],"by":[51],"using":[52],"duality":[53],"theory.":[54],"The":[55],"formulated":[56],"problem":[60],"nonconvex":[62],"NP-hard.":[64],"However,":[65],"we":[66],"reformulate":[67],"its":[68],"cost":[69],"function":[70,74],"into":[71,80],"bi-quadratic":[73],"while":[75],"splits":[79],"parts.":[84],"Then,":[85],"block":[87],"coordinate":[88],"descent":[89],"method":[90,113],"second-order":[93],"cone":[94],"programming":[95],"to":[98,116],"address":[99],"biconvex":[101],"problem.":[102],"Simulation":[103],"results":[104],"show":[105],"an":[106],"improved":[107],"robustness":[108],"proposed":[111],"as":[114],"compared":[115],"worst-case":[118],"other":[120],"existing":[121],"state-of-the-art":[122],"methods":[128],"MIMO":[130],"radar.":[131]},"counts_by_year":[{"year":2023,"cited_by_count":6},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":5}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
