{"id":"https://openalex.org/W4365461416","doi":"https://doi.org/10.1109/msp.2023.3262366","title":"Twenty-Five Years of Advances in Beamforming: From convex and nonconvex optimization to learning techniques","display_name":"Twenty-Five Years of Advances in Beamforming: From convex and nonconvex optimization to learning techniques","publication_year":2023,"publication_date":"2023-06-01","ids":{"openalex":"https://openalex.org/W4365461416","doi":"https://doi.org/10.1109/msp.2023.3262366"},"language":"en","primary_location":{"id":"doi:10.1109/msp.2023.3262366","is_oa":true,"landing_page_url":"https://doi.org/10.1109/msp.2023.3262366","pdf_url":"https://ieeexplore.ieee.org/ielx7/79/10144695/10144712.pdf","source":{"id":"https://openalex.org/S120977877","display_name":"IEEE Signal Processing Magazine","issn_l":"1053-5888","issn":["1053-5888","1558-0792"],"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 Magazine","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://ieeexplore.ieee.org/ielx7/79/10144695/10144712.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063247145","display_name":"Ahmet M. Elbir","orcid":"https://orcid.org/0000-0003-4060-3781"},"institutions":[{"id":"https://openalex.org/I186903577","display_name":"University of Luxembourg","ror":"https://ror.org/036x5ad56","country_code":"LU","type":"education","lineage":["https://openalex.org/I186903577"]},{"id":"https://openalex.org/I54001450","display_name":"D\u00fczce \u00dcniversitesi","ror":"https://ror.org/04175wc52","country_code":"TR","type":"education","lineage":["https://openalex.org/I54001450"]}],"countries":["LU","TR"],"is_corresponding":false,"raw_author_name":"Ahmet M. Elbir","raw_affiliation_strings":["University of Luxembourg, Luxembourg City, Luxembourg","Duzce University, Duzce, Turkey"],"raw_orcid":"https://orcid.org/0000-0003-4060-3781","affiliations":[{"raw_affiliation_string":"University of Luxembourg, Luxembourg City, Luxembourg","institution_ids":["https://openalex.org/I186903577"]},{"raw_affiliation_string":"Duzce University, Duzce, Turkey","institution_ids":["https://openalex.org/I54001450"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082119521","display_name":"Kumar Vijay Mishra","orcid":"https://orcid.org/0000-0002-5386-609X"},"institutions":[{"id":"https://openalex.org/I166416128","display_name":"DEVCOM Army Research Laboratory","ror":"https://ror.org/011hc8f90","country_code":"US","type":"government","lineage":["https://openalex.org/I1304082316","https://openalex.org/I1330347796","https://openalex.org/I166416128","https://openalex.org/I2802705668","https://openalex.org/I4210154437"]},{"id":"https://openalex.org/I2802705668","display_name":"United States Army Combat Capabilities Development Command","ror":"https://ror.org/02rdkx920","country_code":"US","type":"other","lineage":["https://openalex.org/I1304082316","https://openalex.org/I1330347796","https://openalex.org/I2802705668","https://openalex.org/I4210154437"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kumar Vijay Mishra","raw_affiliation_strings":["U.S. DEVCOM Army Research Laboratory, Adelphi, MD, USA"],"raw_orcid":"https://orcid.org/0000-0002-5386-609X","affiliations":[{"raw_affiliation_string":"U.S. DEVCOM Army Research Laboratory, Adelphi, MD, USA","institution_ids":["https://openalex.org/I166416128","https://openalex.org/I2802705668"]}]},{"author_position":"middle","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 Information and Communications Engineering, Aalto University, Espoo, Finland"],"raw_orcid":"https://orcid.org/0000-0001-7249-647X","affiliations":[{"raw_affiliation_string":"Department of Information and Communications Engineering, Aalto University, Espoo, Finland","institution_ids":["https://openalex.org/I9927081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029812222","display_name":"Robert W. Heath","orcid":"https://orcid.org/0000-0002-4666-5628"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert W. Heath","raw_affiliation_strings":["North Carolina State University, Raleigh, NC, USA"],"raw_orcid":"https://orcid.org/0000-0002-4666-5628","affiliations":[{"raw_affiliation_string":"North Carolina State University, Raleigh, NC, USA","institution_ids":["https://openalex.org/I137902535"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":111.2571,"has_fulltext":true,"cited_by_count":161,"citation_normalized_percentile":{"value":0.99977809,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"40","issue":"4","first_page":"118","last_page":"131"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11946","display_name":"Antenna Design and Optimization","score":0.9997000098228455,"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/T11946","display_name":"Antenna Design and Optimization","score":0.9997000098228455,"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/T10326","display_name":"Indoor and Outdoor Localization Technologies","score":0.9993000030517578,"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/T10931","display_name":"Direction-of-Arrival Estimation Techniques","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":0.9089484214782715},{"id":"https://openalex.org/keywords/sonar","display_name":"Sonar","score":0.6989573240280151},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6255297064781189},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.5828393697738647},{"id":"https://openalex.org/keywords/radar","display_name":"Radar","score":0.5440880060195923},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5158295035362244},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4662685990333557},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.4517951011657715},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3475234806537628},{"id":"https://openalex.org/keywords/electronic-engineering","display_name":"Electronic engineering","score":0.3450692892074585},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3069249391555786},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.29308193922042847},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2877834737300873},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.23182576894760132},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.17337152361869812},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10185512900352478},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.07446184754371643}],"concepts":[{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.9089484214782715},{"id":"https://openalex.org/C555745239","wikidata":"https://www.wikidata.org/wiki/Q133220","display_name":"Sonar","level":2,"score":0.6989573240280151},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6255297064781189},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.5828393697738647},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.5440880060195923},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5158295035362244},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4662685990333557},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4517951011657715},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3475234806537628},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.3450692892074585},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3069249391555786},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.29308193922042847},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2877834737300873},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.23182576894760132},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.17337152361869812},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10185512900352478},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.07446184754371643},{"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/msp.2023.3262366","is_oa":true,"landing_page_url":"https://doi.org/10.1109/msp.2023.3262366","pdf_url":"https://ieeexplore.ieee.org/ielx7/79/10144695/10144712.pdf","source":{"id":"https://openalex.org/S120977877","display_name":"IEEE Signal Processing Magazine","issn_l":"1053-5888","issn":["1053-5888","1558-0792"],"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 Magazine","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1109/msp.2023.3262366","is_oa":true,"landing_page_url":"https://doi.org/10.1109/msp.2023.3262366","pdf_url":"https://ieeexplore.ieee.org/ielx7/79/10144695/10144712.pdf","source":{"id":"https://openalex.org/S120977877","display_name":"IEEE Signal Processing Magazine","issn_l":"1053-5888","issn":["1053-5888","1558-0792"],"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 Magazine","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320338295","display_name":"Army Research Laboratory","ror":"https://ror.org/011hc8f90"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4365461416.pdf","grobid_xml":"https://content.openalex.org/works/W4365461416.grobid-xml"},"referenced_works_count":62,"referenced_works":["https://openalex.org/W1981044874","https://openalex.org/W2005602327","https://openalex.org/W2025624431","https://openalex.org/W2030077956","https://openalex.org/W2037791815","https://openalex.org/W2044342600","https://openalex.org/W2053521124","https://openalex.org/W2060108923","https://openalex.org/W2066218102","https://openalex.org/W2075148031","https://openalex.org/W2078637887","https://openalex.org/W2082038839","https://openalex.org/W2093225945","https://openalex.org/W2103049885","https://openalex.org/W2111937449","https://openalex.org/W2113168978","https://openalex.org/W2121484391","https://openalex.org/W2124733114","https://openalex.org/W2133257086","https://openalex.org/W2134883135","https://openalex.org/W2139184248","https://openalex.org/W2145486800","https://openalex.org/W2150835235","https://openalex.org/W2153750271","https://openalex.org/W2154354807","https://openalex.org/W2166117654","https://openalex.org/W2167704502","https://openalex.org/W2182943128","https://openalex.org/W2189661557","https://openalex.org/W2195693430","https://openalex.org/W2196292687","https://openalex.org/W2259391824","https://openalex.org/W2272804037","https://openalex.org/W2395565466","https://openalex.org/W2526144952","https://openalex.org/W2905402910","https://openalex.org/W2917210985","https://openalex.org/W2943928690","https://openalex.org/W2950636122","https://openalex.org/W2964468371","https://openalex.org/W2969424089","https://openalex.org/W2972473258","https://openalex.org/W2992096220","https://openalex.org/W3003168191","https://openalex.org/W3034441334","https://openalex.org/W3080694619","https://openalex.org/W3090927150","https://openalex.org/W3099560594","https://openalex.org/W3101999018","https://openalex.org/W3129331719","https://openalex.org/W3162509564","https://openalex.org/W3185298575","https://openalex.org/W3200205254","https://openalex.org/W3204308155","https://openalex.org/W3205802379","https://openalex.org/W4231961563","https://openalex.org/W4281645007","https://openalex.org/W4293370729","https://openalex.org/W4312680196","https://openalex.org/W4361757154","https://openalex.org/W6686149489","https://openalex.org/W6711977273"],"related_works":["https://openalex.org/W2129421807","https://openalex.org/W4286569445","https://openalex.org/W4236087151","https://openalex.org/W2761543104","https://openalex.org/W4302353319","https://openalex.org/W2047743558","https://openalex.org/W2756132392","https://openalex.org/W3035814349","https://openalex.org/W2084892497","https://openalex.org/W4285101096"],"abstract_inverted_index":{"Beamforming":[0],"is":[1,74],"a":[2,21,57,110,119],"signal":[3,115],"processing":[4,116],"technique":[5],"to":[6,81,100,105],"steer,":[7],"shape,":[8],"and":[9,41,52,103,128],"focus":[10],"an":[11,16],"electromagnetic":[12],"(EM)":[13],"wave":[14],"using":[15],"array":[17],"of":[18,46,91,121],"sensors":[19],"toward":[20],"desired":[22],"direction.":[23],"It":[24,108],"has":[25,55],"been":[26,56],"used":[27],"in":[28,60,93],"many":[29],"engineering":[30],"applications,":[31],"such":[32],"as":[33],"radar,":[34],"sonar,":[35],"acoustics,":[36],"astronomy,":[37],"seismology,":[38],"medical":[39],"imaging,":[40],"communications.":[42],"With":[43],"the":[44,89,94],"advent":[45],"multiantenna":[47],"technologies":[48],"in,":[49],"say,":[50],"radar":[51],"communication,":[53],"there":[54],"great":[58],"interest":[59],"designing":[61],"beamformers":[62],"by":[63],"exploiting":[64],"convex":[65,99],"or":[66],"nonconvex":[67,101],"optimization":[68,102,104],"methods.":[69],"Recently,":[70],"machine":[71],"learning":[72,106],"(ML)":[73],"also":[75],"leveraged":[76],"for":[77,118],"obtaining":[78],"attractive":[79],"solutions":[80],"more":[82],"complex":[83],"beamforming":[84,92],"scenarios.":[85],"This":[86],"article":[87],"captures":[88],"evolution":[90],"last":[95],"25":[96],"years":[97],"from":[98],"approaches.":[107],"provides":[109],"glimpse":[111],"into":[112],"these":[113],"important":[114],"algorithms":[117],"variety":[120],"transmit\u2013receive":[122],"architectures,":[123],"propagation":[124,126],"zones,":[125],"paths,":[127],"multidisciplinary":[129],"applications.":[130]},"counts_by_year":[{"year":2026,"cited_by_count":18},{"year":2025,"cited_by_count":60},{"year":2024,"cited_by_count":58},{"year":2023,"cited_by_count":25}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2023-04-15T00:00:00"}