{"id":"https://openalex.org/W4399114362","doi":"https://doi.org/10.1109/access.2024.3406527","title":"Bi-Level Deep Unfolding Based Robust Beamforming Design for IRS-Assisted ISAC System","display_name":"Bi-Level Deep Unfolding Based Robust Beamforming Design for IRS-Assisted ISAC System","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4399114362","doi":"https://doi.org/10.1109/access.2024.3406527"},"language":"en","primary_location":{"id":"doi:10.1109/access.2024.3406527","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2024.3406527","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/10540175.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/10540175.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079966172","display_name":"Wanxian Liu","orcid":"https://orcid.org/0000-0001-6018-7899"},"institutions":[{"id":"https://openalex.org/I40963666","display_name":"Central China Normal University","ror":"https://ror.org/03x1jna21","country_code":"CN","type":"education","lineage":["https://openalex.org/I40963666"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wanxian Liu","raw_affiliation_strings":["Department of Electronics and Information Engineering, Central China Normal University, Wuhan, China","The Department of Electronics and Information Engineering, Central China Normal University, Wuhan, China"],"raw_orcid":"https://orcid.org/0000-0001-6018-7899","affiliations":[{"raw_affiliation_string":"Department of Electronics and Information Engineering, Central China Normal University, Wuhan, China","institution_ids":["https://openalex.org/I40963666"]},{"raw_affiliation_string":"The Department of Electronics and Information Engineering, Central China Normal University, Wuhan, China","institution_ids":["https://openalex.org/I40963666"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102727762","display_name":"Hongbo Xu","orcid":"https://orcid.org/0000-0003-4704-8629"},"institutions":[{"id":"https://openalex.org/I40963666","display_name":"Central China Normal University","ror":"https://ror.org/03x1jna21","country_code":"CN","type":"education","lineage":["https://openalex.org/I40963666"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongbo Xu","raw_affiliation_strings":["Department of Electronics and Information Engineering, Central China Normal University, Wuhan, China","The Department of Electronics and Information Engineering, Central China Normal University, Wuhan, China"],"raw_orcid":"https://orcid.org/0000-0003-4704-8629","affiliations":[{"raw_affiliation_string":"Department of Electronics and Information Engineering, Central China Normal University, Wuhan, China","institution_ids":["https://openalex.org/I40963666"]},{"raw_affiliation_string":"The Department of Electronics and Information Engineering, Central China Normal University, Wuhan, China","institution_ids":["https://openalex.org/I40963666"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058006389","display_name":"Xiuli He","orcid":"https://orcid.org/0000-0002-8198-2995"},"institutions":[{"id":"https://openalex.org/I40963666","display_name":"Central China Normal University","ror":"https://ror.org/03x1jna21","country_code":"CN","type":"education","lineage":["https://openalex.org/I40963666"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiuli He","raw_affiliation_strings":["Department of Electronics and Information Engineering, Central China Normal University, Wuhan, China","The Department of Electronics and Information Engineering, Central China Normal University, Wuhan, China"],"raw_orcid":"https://orcid.org/0000-0002-8198-2995","affiliations":[{"raw_affiliation_string":"Department of Electronics and Information Engineering, Central China Normal University, Wuhan, China","institution_ids":["https://openalex.org/I40963666"]},{"raw_affiliation_string":"The Department of Electronics and Information Engineering, Central China Normal University, Wuhan, China","institution_ids":["https://openalex.org/I40963666"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5096830244","display_name":"Yuchen Ye","orcid":null},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]},{"id":"https://openalex.org/I40963666","display_name":"Central China Normal University","ror":"https://ror.org/03x1jna21","country_code":"CN","type":"education","lineage":["https://openalex.org/I40963666"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuchen Ye","raw_affiliation_strings":["School of Electronic Science, National University of Defense Technology, Changsha, China","The Department of Electronics and Information Engineering, Central China Normal University, Wuhan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electronic Science, National University of Defense Technology, Changsha, China","institution_ids":["https://openalex.org/I170215575"]},{"raw_affiliation_string":"The Department of Electronics and Information Engineering, Central China Normal University, Wuhan, China","institution_ids":["https://openalex.org/I40963666"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102062746","display_name":"Aizhi Zhou","orcid":null},"institutions":[{"id":"https://openalex.org/I40963666","display_name":"Central China Normal University","ror":"https://ror.org/03x1jna21","country_code":"CN","type":"education","lineage":["https://openalex.org/I40963666"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Aizhi Zhou","raw_affiliation_strings":["Department of Electronics and Information Engineering, Central China Normal University, Wuhan, China","The Department of Electronics and Information Engineering, Central China Normal University, Wuhan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics and Information Engineering, Central China Normal University, Wuhan, China","institution_ids":["https://openalex.org/I40963666"]},{"raw_affiliation_string":"The Department of Electronics and Information Engineering, Central China Normal University, Wuhan, China","institution_ids":["https://openalex.org/I40963666"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.6269,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.6193717,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"12","issue":null,"first_page":"76663","last_page":"76672"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11458","display_name":"Advanced Wireless Communication Technologies","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/T11458","display_name":"Advanced Wireless Communication Technologies","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/T11946","display_name":"Antenna Design and Optimization","score":0.9980000257492065,"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/T10891","display_name":"Radar Systems and Signal Processing","score":0.9945999979972839,"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":0.818701982498169},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6939728260040283},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6746488213539124},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.6546193957328796},{"id":"https://openalex.org/keywords/base-station","display_name":"Base station","score":0.5997978448867798},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5366119742393494},{"id":"https://openalex.org/keywords/transmitter-power-output","display_name":"Transmitter power output","score":0.5276224613189697},{"id":"https://openalex.org/keywords/channel-state-information","display_name":"Channel state information","score":0.5095763206481934},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5092600584030151},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.45372653007507324},{"id":"https://openalex.org/keywords/signal-to-noise-ratio","display_name":"Signal-to-noise ratio (imaging)","score":0.4267183840274811},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27362748980522156},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22734466195106506},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.2096056342124939},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.17810606956481934},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.1610463559627533},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.13778820633888245},{"id":"https://openalex.org/keywords/transmitter","display_name":"Transmitter","score":0.081763356924057}],"concepts":[{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.818701982498169},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6939728260040283},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6746488213539124},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.6546193957328796},{"id":"https://openalex.org/C68649174","wikidata":"https://www.wikidata.org/wiki/Q1379116","display_name":"Base station","level":2,"score":0.5997978448867798},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5366119742393494},{"id":"https://openalex.org/C65422117","wikidata":"https://www.wikidata.org/wiki/Q358527","display_name":"Transmitter power output","level":4,"score":0.5276224613189697},{"id":"https://openalex.org/C148063708","wikidata":"https://www.wikidata.org/wiki/Q5072511","display_name":"Channel state information","level":3,"score":0.5095763206481934},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5092600584030151},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.45372653007507324},{"id":"https://openalex.org/C13944312","wikidata":"https://www.wikidata.org/wiki/Q7512748","display_name":"Signal-to-noise ratio (imaging)","level":2,"score":0.4267183840274811},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27362748980522156},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22734466195106506},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.2096056342124939},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.17810606956481934},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.1610463559627533},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.13778820633888245},{"id":"https://openalex.org/C47798520","wikidata":"https://www.wikidata.org/wiki/Q190157","display_name":"Transmitter","level":3,"score":0.081763356924057},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2024.3406527","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2024.3406527","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/10540175.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:6f87f69ce0854cc6b0a7dfc7b66917aa","is_oa":true,"landing_page_url":"https://doaj.org/article/6f87f69ce0854cc6b0a7dfc7b66917aa","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 12, Pp 76663-76672 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2024.3406527","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2024.3406527","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/10540175.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4399114362.pdf"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W2042599231","https://openalex.org/W2140960275","https://openalex.org/W2766953637","https://openalex.org/W2883094398","https://openalex.org/W2908498346","https://openalex.org/W3010167864","https://openalex.org/W3031701267","https://openalex.org/W3034281970","https://openalex.org/W3040368914","https://openalex.org/W3045871138","https://openalex.org/W3119152637","https://openalex.org/W3133902371","https://openalex.org/W3152519267","https://openalex.org/W3187913739","https://openalex.org/W3200205254","https://openalex.org/W3200820186","https://openalex.org/W3209801506","https://openalex.org/W3212208169","https://openalex.org/W4206633299","https://openalex.org/W4214923099","https://openalex.org/W4224925138","https://openalex.org/W4285189033","https://openalex.org/W4285208261","https://openalex.org/W4285306829","https://openalex.org/W4291910413","https://openalex.org/W4312051213","https://openalex.org/W4312330321","https://openalex.org/W4315474376","https://openalex.org/W4322706724","https://openalex.org/W4361801433","https://openalex.org/W4378697233","https://openalex.org/W4380030971","https://openalex.org/W4380763437","https://openalex.org/W4383220453","https://openalex.org/W4386703483","https://openalex.org/W4386825118","https://openalex.org/W4388505414","https://openalex.org/W4389922377","https://openalex.org/W4390534227","https://openalex.org/W4392024918","https://openalex.org/W4395470959","https://openalex.org/W4401990339","https://openalex.org/W6860955195"],"related_works":["https://openalex.org/W3087844490","https://openalex.org/W3090699061","https://openalex.org/W2088352174","https://openalex.org/W4387546583","https://openalex.org/W4286695888","https://openalex.org/W3084132786","https://openalex.org/W4327661444","https://openalex.org/W2161061958","https://openalex.org/W2034991012","https://openalex.org/W2051762234"],"abstract_inverted_index":{"In":[0,110,272],"this":[1,114,140],"paper,":[2],"an":[3],"intelligent":[4],"reflecting":[5],"surface":[6],"(IRS)-assisted":[7],"integrated":[8],"sensing":[9,30,84,220],"and":[10,28,50,69,102,129,174,189,217,235,244,262,269,278,287],"communication":[11,24],"(ISAC)":[12],"system":[13],"is":[14,35,163,227],"considered,":[15],"where":[16],"the":[17,23,39,57,61,66,90,97,103,119,132,145,153,159,168,184,190,195,201,214,228,236,241,255,274,284,288,298,301],"ISAC":[18],"base":[19],"station":[20],"(BS)":[21],"serves":[22],"user":[25,46],"equipments":[26,47],"(UEs)":[27],"tracks":[29],"targets":[31,85],"simultaneously.":[32],"Unfortunately,":[33],"it":[34],"challenging":[36],"to":[37,89,112,138,181,212],"obtain":[38],"perfect":[40],"channel":[41],"state":[42],"information":[43],"(CSI)":[44],"of":[45,83,106,219,266,300],"(UEs)-related":[48],"links":[49],"target":[51,71],"directions":[52],"in":[53],"practice.":[54],"To":[55],"address":[56],"imperfection,":[58],"we":[59,77,117,143,247],"investigate":[60],"robust":[62,120,303],"beamforming":[63,121,233,304],"design":[64,122,234,305],"under":[65],"statistical":[67],"CSI":[68,216,243],"bounded":[70],"direction":[72],"uncertainty":[73],"models.With":[74],"these":[75],"considerations,":[76],"formulate":[78,118,144],"a":[79,124,148],"Cram\u00e9r-Rao":[80],"bound":[81],"(CRB)":[82],"minimization":[86],"problem,":[87,116],"subject":[88],"signal-to-interference-plus-noise":[91],"ratio":[92],"(SINR)":[93],"outage":[94,155],"probability":[95,156],"constraint,":[96,192],"maximum":[98,185],"transmit":[99,186],"power":[100,187],"limits":[101],"unit-modulus":[104,191],"constraint":[105,157,188],"each":[107,263],"IRS":[108],"element.":[109],"order":[111],"solve":[113,139],"non-convex":[115],"as":[123,200,283],"bi-level":[125,202],"optimization":[126,177,203,239,293],"(BLO)":[127,204],"problem":[128,146,150,196,226,230],"then":[130],"apply":[131,248],"double-loop":[133,249],"deep":[134],"unfolding":[135],"(DU)":[136],"approach":[137],"problem.":[141,205],"Specifically,":[142],"into":[147,158,259],"primal-dual":[149,229],"by":[151,166,232],"integrating":[152],"SINR":[154],"objective":[160],"function":[161],"which":[162,253],"further":[164],"approximated":[165],"using":[167],"worst-case":[169,215],"SINR.":[170],"The":[171,206,222],"projection":[172],"method":[173,178],"Riemannian":[175],"manifold":[176],"are":[179,281],"used":[180],"deal":[182],"with":[183,240],"respectively.":[193],"Therefore,":[194],"can":[197],"be":[198],"reformulated":[199],"lower":[207],"level":[208,224],"(LL)":[209],"problems":[210],"aim":[211],"find":[213],"angle":[218],"targets.":[221],"upper":[223],"(UL)":[225],"solved":[231],"Lagrange":[237],"multipliers":[238],"certain":[242],"angle.":[245],"Then,":[246],"DU":[250],"neural":[251],"network":[252,285,289],"unfolds":[254],"iterative":[256],"gradient":[257],"descent":[258],"multi-layer":[260],"structure,":[261],"layer":[264],"consists":[265],"UL":[267],"loop":[268],"LL":[270],"loop.":[271],"addition,":[273],"trainable":[275],"step":[276],"sizes":[277],"offset":[279],"parameters":[280],"introduced":[282],"parameters,":[286],"ultimately":[290],"outputs":[291],"optimal":[292],"variables.":[294],"Simulation":[295],"results":[296],"demonstrate":[297],"effectiveness":[299],"proposed":[302],"algorithm.":[306]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}