{"id":"https://openalex.org/W3179146960","doi":"https://doi.org/10.1109/tsp.2021.3094653","title":"Efficient Algorithms for Constant-Modulus Analog Beamforming","display_name":"Efficient Algorithms for Constant-Modulus Analog Beamforming","publication_year":2021,"publication_date":"2021-07-08","ids":{"openalex":"https://openalex.org/W3179146960","doi":"https://doi.org/10.1109/tsp.2021.3094653","mag":"3179146960"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2021.3094653","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tsp.2021.3094653","pdf_url":"https://ieeexplore.ieee.org/ielx7/78/9675017/09478276.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"https://ieeexplore.ieee.org/ielx7/78/9675017/09478276.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076402236","display_name":"Aakash Arora","orcid":"https://orcid.org/0000-0002-8490-7552"},"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"]}],"countries":["LU"],"is_corresponding":true,"raw_author_name":"Aakash Arora","raw_affiliation_strings":["Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg, Luxembourg, Luxembourg"],"affiliations":[{"raw_affiliation_string":"Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg, Luxembourg, Luxembourg","institution_ids":["https://openalex.org/I186903577"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074241486","display_name":"Christos G. Tsinos","orcid":"https://orcid.org/0000-0002-4790-1477"},"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"]}],"countries":["LU"],"is_corresponding":false,"raw_author_name":"Christos G. Tsinos","raw_affiliation_strings":["Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg, Luxembourg, Luxembourg"],"affiliations":[{"raw_affiliation_string":"Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg, Luxembourg, Luxembourg","institution_ids":["https://openalex.org/I186903577"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035099577","display_name":"Mallikarjun Shankar","orcid":"https://orcid.org/0000-0001-5289-7460"},"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"]}],"countries":["LU"],"is_corresponding":false,"raw_author_name":"M. R. Bhavani Shankar","raw_affiliation_strings":["Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg, Luxembourg, Luxembourg"],"affiliations":[{"raw_affiliation_string":"Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg, Luxembourg, Luxembourg","institution_ids":["https://openalex.org/I186903577"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016154330","display_name":"Symeon Chatzinotas","orcid":"https://orcid.org/0000-0001-5122-0001"},"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"]}],"countries":["LU"],"is_corresponding":false,"raw_author_name":"Symeon Chatzinotas","raw_affiliation_strings":["Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg, Luxembourg, Luxembourg"],"affiliations":[{"raw_affiliation_string":"Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg, Luxembourg, Luxembourg","institution_ids":["https://openalex.org/I186903577"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080037825","display_name":"Bj\u00f6rn Ottersten","orcid":"https://orcid.org/0000-0003-2298-6774"},"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"]}],"countries":["LU"],"is_corresponding":false,"raw_author_name":"Bjorn Ottersten","raw_affiliation_strings":["Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg, Luxembourg, Luxembourg"],"affiliations":[{"raw_affiliation_string":"Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg, Luxembourg, Luxembourg","institution_ids":["https://openalex.org/I186903577"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5076402236"],"corresponding_institution_ids":["https://openalex.org/I186903577"],"apc_list":null,"apc_paid":null,"fwci":2.0216,"has_fulltext":true,"cited_by_count":28,"citation_normalized_percentile":{"value":0.8676284,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"70","issue":null,"first_page":"756","last_page":"771"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10936","display_name":"Millimeter-Wave Propagation and Modeling","score":0.9998000264167786,"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/T10936","display_name":"Millimeter-Wave Propagation and Modeling","score":0.9998000264167786,"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":0.9994999766349792,"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/T11946","display_name":"Antenna Design and Optimization","score":0.9993000030517578,"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":0.7566721439361572},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6874499320983887},{"id":"https://openalex.org/keywords/coordinate-descent","display_name":"Coordinate descent","score":0.5812991261482239},{"id":"https://openalex.org/keywords/antenna","display_name":"Antenna (radio)","score":0.5187599658966064},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5049884915351868},{"id":"https://openalex.org/keywords/antenna-array","display_name":"Antenna array","score":0.4859001040458679},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.474604070186615},{"id":"https://openalex.org/keywords/karush\u2013kuhn\u2013tucker-conditions","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","score":0.46014130115509033},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4278584420681},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4158562421798706},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3182492256164551},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.30565160512924194},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.22550922632217407}],"concepts":[{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.7566721439361572},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6874499320983887},{"id":"https://openalex.org/C157553263","wikidata":"https://www.wikidata.org/wiki/Q5168004","display_name":"Coordinate descent","level":2,"score":0.5812991261482239},{"id":"https://openalex.org/C21822782","wikidata":"https://www.wikidata.org/wiki/Q131214","display_name":"Antenna (radio)","level":2,"score":0.5187599658966064},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5049884915351868},{"id":"https://openalex.org/C62191587","wikidata":"https://www.wikidata.org/wiki/Q4771249","display_name":"Antenna array","level":3,"score":0.4859001040458679},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.474604070186615},{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.46014130115509033},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4278584420681},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4158562421798706},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3182492256164551},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30565160512924194},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.22550922632217407},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tsp.2021.3094653","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tsp.2021.3094653","pdf_url":"https://ieeexplore.ieee.org/ielx7/78/9675017/09478276.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:orbilu.uni.lu:10993/47891","is_oa":true,"landing_page_url":"https://ieeexplore.ieee.org/document/9478276","pdf_url":"http://orbilu.uni.lu/handle/10993/47891","source":{"id":"https://openalex.org/S4306401815","display_name":"Open Repository and Bibliography (University of Luxembourg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I186903577","host_organization_name":"University of Luxembourg","host_organization_lineage":["https://openalex.org/I186903577"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Signal Processing (2021)","raw_type":"peer reviewed"}],"best_oa_location":{"id":"doi:10.1109/tsp.2021.3094653","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tsp.2021.3094653","pdf_url":"https://ieeexplore.ieee.org/ielx7/78/9675017/09478276.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.800000011920929}],"awards":[{"id":"https://openalex.org/G1902004651","display_name":null,"funder_award_id":"11607283","funder_id":"https://openalex.org/F4320321038","funder_display_name":"Fonds National de la Recherche Luxembourg"},{"id":"https://openalex.org/G8610186197","display_name":null,"funder_award_id":"ECLECTIC","funder_id":"https://openalex.org/F4320321038","funder_display_name":"Fonds National de la Recherche Luxembourg"}],"funders":[{"id":"https://openalex.org/F4320321038","display_name":"Fonds National de la Recherche Luxembourg","ror":"https://ror.org/039z13y21"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3179146960.pdf","grobid_xml":"https://content.openalex.org/works/W3179146960.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W1967790992","https://openalex.org/W1978423571","https://openalex.org/W1996215314","https://openalex.org/W2007104311","https://openalex.org/W2045089915","https://openalex.org/W2050968963","https://openalex.org/W2053521124","https://openalex.org/W2073955633","https://openalex.org/W2111953900","https://openalex.org/W2113842230","https://openalex.org/W2118799287","https://openalex.org/W2126381689","https://openalex.org/W2141415498","https://openalex.org/W2144070955","https://openalex.org/W2149358222","https://openalex.org/W2149414429","https://openalex.org/W2164064673","https://openalex.org/W2168265940","https://openalex.org/W2196484074","https://openalex.org/W2324740189","https://openalex.org/W2489539531","https://openalex.org/W2508393166","https://openalex.org/W2544090110","https://openalex.org/W2578438628","https://openalex.org/W2586063770","https://openalex.org/W2617507432","https://openalex.org/W2639082558","https://openalex.org/W2771808324","https://openalex.org/W2773442076","https://openalex.org/W2780206593","https://openalex.org/W2780231131","https://openalex.org/W2794455363","https://openalex.org/W2803170239","https://openalex.org/W2809272045","https://openalex.org/W2810939342","https://openalex.org/W2885627765","https://openalex.org/W2891388456","https://openalex.org/W2917232082","https://openalex.org/W2962834015","https://openalex.org/W2991873439","https://openalex.org/W3003750314","https://openalex.org/W3015001943","https://openalex.org/W4253515568","https://openalex.org/W4254313632"],"related_works":["https://openalex.org/W2807256486","https://openalex.org/W2391309548","https://openalex.org/W2123675486","https://openalex.org/W117224218","https://openalex.org/W3038961962","https://openalex.org/W2900428495","https://openalex.org/W2134293600","https://openalex.org/W2947894078","https://openalex.org/W2791039104","https://openalex.org/W3164429027"],"abstract_inverted_index":{"The":[0],"use":[1],"of":[2,13,52,98,111,129,144,240,243],"a":[3,44,70,142,190,205,210],"large-scale":[4],"antenna":[5,37],"array":[6],"(LSAA)":[7],"has":[8,39],"become":[9],"an":[10],"important":[11],"characteristic":[12],"multi-antenna":[14],"communication":[15],"systems":[16,27],"to":[17,28,40,116,177,204],"achieve":[18],"beamforming":[19,67,81,86],"gains":[20],"such":[21,34],"as":[22,141],"in":[23,122,181,238],"designing":[24],"millimeter-wave":[25],"(mmWave)":[26],"combat":[29],"severe":[30],"propagation":[31],"losses.":[32],"In":[33,73,102],"applications,":[35],"each":[36,182],"element":[38],"be":[41],"driven":[42],"by":[43,94],"radio":[45],"frequency":[46],"(RF)":[47],"chain":[48],"for":[49],"the":[50,57,78,91,103,107,112,117,123,127,130,135,145,156,163,167,171,179,198,217,223,228,230,241,246],"implementation":[51],"fully-digital":[53],"beamformers,":[54],"significantly":[55],"increasing":[56],"hardware":[58],"cost,":[59],"complexity,":[60],"and":[61,89,109,166,170,245],"power":[62],"consumption.":[63],"Therefore,":[64],"constant-modulus":[65,84,146],"analog":[66,80,85],"(CMAB)":[68,87],"becomes":[69],"viable":[71],"solution.":[72],"this":[74],"paper,":[75],"we":[76,201],"consider":[77],"scaled":[79],"(SAB)":[82],"or":[83],"architecture":[88],"design":[90],"system":[92],"parameters":[93],"solving":[95],"two":[96],"variants":[97],"beampattern":[99,113,120,131,136],"matching":[100,137],"problem.":[101,149],"first":[104],"case,":[105,125],"both":[106],"magnitude":[108,128],"phase":[110],"are":[114,139],"matched":[115],"given":[118],"desired":[119],"whereas":[121],"second":[124],"only":[126],"is":[132],"matched.":[133],"Both":[134],"problems":[138],"cast":[140],"variant":[143],"least-squares":[147],"(CLS)":[148],"We":[150,184],"provide":[151],"efficient":[152],"algorithms":[153,176,187,200,219,232,248],"based":[154,188,194],"on":[155,189],"alternating":[157,164],"majorization-minimization":[158],"(AMM)":[159],"framework":[160],"that":[161,216],"combines":[162],"minimization":[165],"MM":[168],"frameworks":[169],"conventional-cyclic":[172],"coordinate":[173],"descent":[174],"(C-CCD)":[175],"solve":[178],"problem":[180],"case.":[183],"also":[185],"propose":[186],"new":[191],"modified-CCD":[192],"(M-CCD)":[193],"approach.":[195],"For":[196],"all":[197,227],"developed":[199],"prove":[202],"convergence":[203,235],"Karush-Kuhn-Tucker":[206],"(KKT)":[207],"point":[208],"(or":[209],"stationary":[211],"point).":[212],"Numerical":[213],"results":[214],"demonstrate":[215],"proposed":[218],"converge":[220],"faster":[221,234],"than":[222],"state-of-the-art":[224],"solutions.":[225],"Among":[226],"algorithms,":[229],"M-CCD-based":[231],"have":[233],"when":[236],"evaluated":[237],"terms":[239],"number":[242],"iterations":[244],"AMM-based":[247],"offer":[249],"lower":[250],"complexity.":[251]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}
