{"id":"https://openalex.org/W4287219596","doi":"https://doi.org/10.3390/sym14081510","title":"Beamforming Optimization for Intelligent Reflecting Surface-Assisted MIMO Systems","display_name":"Beamforming Optimization for Intelligent Reflecting Surface-Assisted MIMO Systems","publication_year":2022,"publication_date":"2022-07-23","ids":{"openalex":"https://openalex.org/W4287219596","doi":"https://doi.org/10.3390/sym14081510"},"language":"en","primary_location":{"id":"doi:10.3390/sym14081510","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14081510","pdf_url":"https://www.mdpi.com/2073-8994/14/8/1510/pdf?version=1660217592","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/8/1510/pdf?version=1660217592","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066397149","display_name":"Wenjuan Zhang","orcid":"https://orcid.org/0000-0001-8281-3125"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenjuan Zhang","raw_affiliation_strings":["School of Physics and Electronics, Central South University, Changsha 410083, China"],"raw_orcid":"https://orcid.org/0000-0001-8281-3125","affiliations":[{"raw_affiliation_string":"School of Physics and Electronics, Central South University, Changsha 410083, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021520866","display_name":"Honggui Deng","orcid":null},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Honggui Deng","raw_affiliation_strings":["School of Physics and Electronics, Central South University, Changsha 410083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics and Electronics, Central South University, Changsha 410083, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026871670","display_name":"Youzhen Li","orcid":"https://orcid.org/0000-0001-8994-3627"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Youzhen Li","raw_affiliation_strings":["School of Physics and Electronics, Central South University, Changsha 410083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics and Electronics, Central South University, Changsha 410083, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067668433","display_name":"Zaoxing Zhu","orcid":"https://orcid.org/0000-0003-4239-3749"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zaoxing Zhu","raw_affiliation_strings":["School of Physics and Electronics, Central South University, Changsha 410083, China"],"raw_orcid":"https://orcid.org/0000-0003-4239-3749","affiliations":[{"raw_affiliation_string":"School of Physics and Electronics, Central South University, Changsha 410083, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010278474","display_name":"Chengzuo Peng","orcid":"https://orcid.org/0009-0001-7072-9302"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chengzuo Peng","raw_affiliation_strings":["School of Physics and Electronics, Central South University, Changsha 410083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics and Electronics, Central South University, Changsha 410083, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100412392","display_name":"Gang Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]},{"id":"https://openalex.org/I3130607311","display_name":"Changsha Normal University","ror":"https://ror.org/02sqk3z62","country_code":"CN","type":"education","lineage":["https://openalex.org/I3130607311"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gang Liu","raw_affiliation_strings":["College of Information Science and Engineering, Changsha Normal University, Changsha 410100, China","School of Physics and Electronics, Central South University, Changsha 410083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Information Science and Engineering, Changsha Normal University, Changsha 410100, China","institution_ids":["https://openalex.org/I3130607311"]},{"raw_affiliation_string":"School of Physics and Electronics, Central South University, Changsha 410083, China","institution_ids":["https://openalex.org/I139660479"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5021520866"],"corresponding_institution_ids":["https://openalex.org/I139660479"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.6466,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.66449703,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"14","issue":"8","first_page":"1510","last_page":"1510"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11458","display_name":"Advanced Wireless Communication Technologies","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/T11458","display_name":"Advanced Wireless Communication Technologies","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/T10069","display_name":"Antenna Design and Analysis","score":0.9923999905586243,"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/T11383","display_name":"Advanced Antenna and Metasurface Technologies","score":0.9907000064849854,"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":0.8182317018508911},{"id":"https://openalex.org/keywords/precoding","display_name":"Precoding","score":0.7637820839881897},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.5816277861595154},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5692082643508911},{"id":"https://openalex.org/keywords/spectral-efficiency","display_name":"Spectral efficiency","score":0.4993324279785156},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.4964445233345032},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4917755424976349},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4897325038909912},{"id":"https://openalex.org/keywords/minimum-mean-square-error","display_name":"Minimum mean square error","score":0.4501707851886749},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44803616404533386},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.43712061643600464},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35996729135513306},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3344678282737732},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.22213128209114075}],"concepts":[{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.8182317018508911},{"id":"https://openalex.org/C160562895","wikidata":"https://www.wikidata.org/wiki/Q7239557","display_name":"Precoding","level":4,"score":0.7637820839881897},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.5816277861595154},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5692082643508911},{"id":"https://openalex.org/C137246740","wikidata":"https://www.wikidata.org/wiki/Q583970","display_name":"Spectral efficiency","level":3,"score":0.4993324279785156},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.4964445233345032},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4917755424976349},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4897325038909912},{"id":"https://openalex.org/C90652560","wikidata":"https://www.wikidata.org/wiki/Q11091747","display_name":"Minimum mean square error","level":3,"score":0.4501707851886749},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44803616404533386},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.43712061643600464},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35996729135513306},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3344678282737732},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.22213128209114075},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14081510","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14081510","pdf_url":"https://www.mdpi.com/2073-8994/14/8/1510/pdf?version=1660217592","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:13e1af5d21684549b0e8d9cbb5a3fc3b","is_oa":true,"landing_page_url":"https://doaj.org/article/13e1af5d21684549b0e8d9cbb5a3fc3b","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 8, p 1510 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/8/1510/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14081510","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14081510","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14081510","pdf_url":"https://www.mdpi.com/2073-8994/14/8/1510/pdf?version=1660217592","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4300000071525574,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4287219596.pdf","grobid_xml":"https://content.openalex.org/works/W4287219596.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W2031281790","https://openalex.org/W2053521124","https://openalex.org/W2789683520","https://openalex.org/W2891354184","https://openalex.org/W2963460596","https://openalex.org/W2964076076","https://openalex.org/W2975820893","https://openalex.org/W2981792785","https://openalex.org/W2985466239","https://openalex.org/W2990747873","https://openalex.org/W3005476696","https://openalex.org/W3007159123","https://openalex.org/W3007669596","https://openalex.org/W3032095193","https://openalex.org/W3035386068","https://openalex.org/W3039402952","https://openalex.org/W3040433108","https://openalex.org/W3041653465","https://openalex.org/W3091842477","https://openalex.org/W3094164592","https://openalex.org/W3129486236","https://openalex.org/W3159735193","https://openalex.org/W3189764254","https://openalex.org/W4212813195"],"related_works":["https://openalex.org/W2152088989","https://openalex.org/W2756419127","https://openalex.org/W4366493479","https://openalex.org/W2905893439","https://openalex.org/W3135374966","https://openalex.org/W2554517556","https://openalex.org/W4214571564","https://openalex.org/W4311950697","https://openalex.org/W2538872159","https://openalex.org/W4390584137"],"abstract_inverted_index":{"To":[0],"improve":[1],"the":[2,17,39,68,78,93,102,106,113,119],"spectral":[3,50,136],"efficiency":[4,51,137],"of":[5],"symmetry-based":[6],"intelligent":[7],"reconfigurable":[8],"surface":[9],"(IRS)-assisted":[10],"MIMO":[11,28],"communication":[12],"systems,":[13],"this":[14],"paper":[15],"investigates":[16],"joint":[18],"precoding":[19,108],"and":[20,33,57,122,133],"passive":[21,94,104],"beamforming":[22,95],"optimization":[23,89],"problem":[24,71],"for":[25],"millimeter-wave":[26],"point-to-point":[27],"systems":[29],"under":[30],"both":[31],"ideal":[32,40],"practical":[34,79],"IRS":[35,41,80],"phase":[36,42,81],"shifts.":[37],"For":[38,77],"shifts":[43,82],"setup,":[44,83],"we":[45,84],"derive":[46],"a":[47,59,73,86],"simplified":[48,69],"approximate":[49],"expression":[52],"based":[53],"on":[54,118],"Jensen\u2019s":[55],"inequality":[56],"propose":[58,85],"minimum":[60],"mean":[61],"square":[62],"error":[63],"(MMSE)-based":[64],"algorithm":[65,90],"to":[66,91,143],"transform":[67],"non-convex":[70],"into":[72],"solvable":[74],"convex":[75],"function.":[76],"multi-start":[87],"stepwise":[88,97],"obtain":[92],"by":[96,111],"iterative":[98],"search.":[99],"Finally,":[100],"with":[101],"above-obtained":[103],"beamforming,":[105],"optimal":[107],"is":[109],"derived":[110],"performing":[112],"singular":[114],"value":[115],"decomposition":[116],"(SVD)":[117],"effective":[120],"channel":[121],"water-filling":[123],"power":[124],"allocation.":[125],"The":[126],"simulation":[127],"results":[128],"verify":[129],"our":[130],"performance":[131],"analysis":[132],"demonstrate":[134],"that":[135],"can":[138],"be":[139],"effectively":[140],"improved":[141],"compared":[142],"various":[144],"benchmark":[145],"schemes.":[146]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
