{"id":"https://openalex.org/W4385800970","doi":"https://doi.org/10.1109/vtc2023-spring57618.2023.10200544","title":"Learning Beamforming for RIS-aided Systems with Permutation Equivariant Graph Neural Networks","display_name":"Learning Beamforming for RIS-aided Systems with Permutation Equivariant Graph Neural Networks","publication_year":2023,"publication_date":"2023-06-01","ids":{"openalex":"https://openalex.org/W4385800970","doi":"https://doi.org/10.1109/vtc2023-spring57618.2023.10200544"},"language":"en","primary_location":{"id":"doi:10.1109/vtc2023-spring57618.2023.10200544","is_oa":false,"landing_page_url":"https://doi.org/10.1109/vtc2023-spring57618.2023.10200544","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE 97th Vehicular Technology Conference (VTC2023-Spring)","raw_type":"proceedings-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/A5041458795","display_name":"Baichuan Zhao","orcid":"https://orcid.org/0000-0002-5654-5136"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Baichuan Zhao","raw_affiliation_strings":["Beihang University,Beijing,China","Beihang University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Beihang University,Beijing,China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082950698","display_name":"Chenyang Yang","orcid":"https://orcid.org/0000-0003-0058-0765"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chenyang Yang","raw_affiliation_strings":["Beihang University,Beijing,China","Beihang University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Beihang University,Beijing,China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5041458795"],"corresponding_institution_ids":["https://openalex.org/I82880672"],"apc_list":null,"apc_paid":null,"fwci":1.2063,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.78888903,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"5"},"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":0.9739000201225281,"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/T11133","display_name":"UAV Applications and Optimization","score":0.9527000188827515,"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":0.7211872339248657},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6659689545631409},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.6159085035324097},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5945296287536621},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.47840413451194763},{"id":"https://openalex.org/keywords/overhead","display_name":"Overhead (engineering)","score":0.43390369415283203},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.42353302240371704},{"id":"https://openalex.org/keywords/computer-engineering","display_name":"Computer engineering","score":0.32510024309158325},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3135913610458374},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.28864920139312744},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2398800253868103},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.14096200466156006},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.10687944293022156}],"concepts":[{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.7211872339248657},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6659689545631409},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.6159085035324097},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5945296287536621},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.47840413451194763},{"id":"https://openalex.org/C2779960059","wikidata":"https://www.wikidata.org/wiki/Q7113681","display_name":"Overhead (engineering)","level":2,"score":0.43390369415283203},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.42353302240371704},{"id":"https://openalex.org/C113775141","wikidata":"https://www.wikidata.org/wiki/Q428691","display_name":"Computer engineering","level":1,"score":0.32510024309158325},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3135913610458374},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.28864920139312744},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2398800253868103},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.14096200466156006},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.10687944293022156},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/vtc2023-spring57618.2023.10200544","is_oa":false,"landing_page_url":"https://doi.org/10.1109/vtc2023-spring57618.2023.10200544","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE 97th Vehicular Technology Conference (VTC2023-Spring)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W2805516822","https://openalex.org/W2971598376","https://openalex.org/W3005476696","https://openalex.org/W3010695123","https://openalex.org/W3043220753","https://openalex.org/W3089453335","https://openalex.org/W3111885788","https://openalex.org/W3160036209","https://openalex.org/W3171070969","https://openalex.org/W3189854358","https://openalex.org/W4280571452","https://openalex.org/W4310418197","https://openalex.org/W6751796012","https://openalex.org/W6846912144"],"related_works":["https://openalex.org/W4210726725","https://openalex.org/W4285192270","https://openalex.org/W2960001594","https://openalex.org/W3202446995","https://openalex.org/W4309995524","https://openalex.org/W4382139247","https://openalex.org/W4304091389","https://openalex.org/W4320029333","https://openalex.org/W3044077824","https://openalex.org/W4285708443"],"abstract_inverted_index":{"Reconfigurable":[0],"intelligent":[1],"surface":[2],"(RIS)":[3],"is":[4],"capable":[5],"of":[6,14,22,59,65,89,133,139],"controlling":[7],"environment":[8],"smartly":[9],"for":[10],"improving":[11],"the":[12,19,24,38,60,66,72,86,117,131,134,141,146],"performance":[13],"wireless":[15],"communications.":[16],"To":[17],"reduce":[18],"pilot":[20,43],"overhead":[21],"estimating":[23],"high-dimensional":[25],"channels":[26],"in":[27,45,97,137],"RIS-aided":[28,99],"systems,":[29],"deep":[30],"neural":[31,74,107],"networks":[32,75],"have":[33],"been":[34],"introduced":[35],"to":[36,115,144],"learn":[37,116],"beam-forming":[39],"policy":[40,96],"with":[41,111],"received":[42],"sequences":[44],"an":[46,90,126],"end-to-end":[47],"(E2E)":[48],"manner.":[49],"However,":[50],"existing":[51],"works":[52],"either":[53],"ignore":[54],"or":[55],"only":[56],"consider":[57],"part":[58],"permutation":[61],"equivariant":[62],"(PE)":[63],"properties":[64],"E2E":[67,91],"policy.":[68,118],"As":[69],"a":[70,98,105],"result,":[71],"designed":[73],"suffer":[76],"from":[77],"high":[78],"sample":[79,142],"complexity.":[80],"In":[81],"this":[82],"paper,":[83],"we":[84],"analyze":[85],"PE":[87],"property":[88],"active":[92],"and":[93,103],"passive":[94],"beamforming":[95],"multi-user":[100],"multi-antenna":[101],"system,":[102],"design":[104],"graph":[106],"network":[108],"(GNN)":[109],"architecture":[110],"matched":[112],"inductive":[113],"bias":[114],"By":[119],"taking":[120],"sum":[121,148],"rate":[122],"maximization":[123],"problem":[124],"as":[125],"example,":[127],"simulation":[128],"results":[129],"demonstrate":[130],"benefits":[132],"proposed":[135],"GNN":[136],"terms":[138],"reducing":[140],"complexity":[143],"achieve":[145],"expected":[147],"rate.":[149]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}