{"id":"https://openalex.org/W3121527341","doi":"https://doi.org/10.1109/tsp.2021.3052040","title":"Polynomial GSVD Beamforming for Two-User Frequency-Selective MIMO Channels","display_name":"Polynomial GSVD Beamforming for Two-User Frequency-Selective MIMO Channels","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3121527341","doi":"https://doi.org/10.1109/tsp.2021.3052040","mag":"3121527341"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2021.3052040","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2021.3052040","pdf_url":null,"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":null,"license_id":null,"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":"green","oa_url":"https://figshare.com/articles/journal_contribution/Polynomial_GSVD_beamforming_for_two-user_frequency-selective_MIMO_channels/13562303","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055840835","display_name":"Diyari A. Hassan","orcid":"https://orcid.org/0000-0003-0710-1923"},"institutions":[{"id":"https://openalex.org/I4391768095","display_name":"Qaiwan International University","ror":"https://ror.org/00c7kp696","country_code":null,"type":"education","lineage":["https://openalex.org/I4391768095"]}],"countries":["IQ"],"is_corresponding":false,"raw_author_name":"Diyari Hassan","raw_affiliation_strings":["Faculty of Engineering & Sciences, Qaiwan International University-UTM Franchise, Sulaymaniyah, Kurdistan Region-Iraq, Iraq"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering & Sciences, Qaiwan International University-UTM Franchise, Sulaymaniyah, Kurdistan Region-Iraq, Iraq","institution_ids":["https://openalex.org/I4391768095"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075426985","display_name":"Soydan Redif","orcid":"https://orcid.org/0000-0003-4325-1080"},"institutions":[{"id":"https://openalex.org/I116528569","display_name":"European University of Lefke","ror":"https://ror.org/00t7bpe49","country_code":"TR","type":"education","lineage":["https://openalex.org/I116528569"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Soydan Redif","raw_affiliation_strings":["Faculty of Engineering, European University of Lefke, Lefke, Northern Cyprus, Turkey"],"raw_orcid":"https://orcid.org/0000-0003-4325-1080","affiliations":[{"raw_affiliation_string":"Faculty of Engineering, European University of Lefke, Lefke, Northern Cyprus, Turkey","institution_ids":["https://openalex.org/I116528569"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5105458070","display_name":"J.G. McWhirter","orcid":"https://orcid.org/0000-0003-1810-3318"},"institutions":[{"id":"https://openalex.org/I4210162667","display_name":"University of Wales Institute Cardiff","ror":"https://ror.org/03evaaw16","country_code":"SG","type":"education","lineage":["https://openalex.org/I4210162667"]},{"id":"https://openalex.org/I79510175","display_name":"Cardiff University","ror":"https://ror.org/03kk7td41","country_code":"GB","type":"education","lineage":["https://openalex.org/I79510175"]},{"id":"https://openalex.org/I97429440","display_name":"University of Wales","ror":"https://ror.org/01se4f844","country_code":"GB","type":"education","lineage":["https://openalex.org/I97429440"]}],"countries":["GB","SG"],"is_corresponding":false,"raw_author_name":"John G. McWhirter","raw_affiliation_strings":["Electrical and Electronic, Cardiff University, Cardiff, Wales, U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Electronic, Cardiff University, Cardiff, Wales, U.K","institution_ids":["https://openalex.org/I97429440","https://openalex.org/I79510175","https://openalex.org/I4210162667"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009232291","display_name":"Sangarapillai Lambotharan","orcid":"https://orcid.org/0000-0001-5255-7036"},"institutions":[{"id":"https://openalex.org/I143804889","display_name":"Loughborough University","ror":"https://ror.org/04vg4w365","country_code":"GB","type":"education","lineage":["https://openalex.org/I143804889"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Sangarapillai Lambotharan","raw_affiliation_strings":["Signal Processing and Networks Research Group, Wolfson School, Loughborough University, Loughborough, Leicestershire, U.K"],"raw_orcid":"https://orcid.org/0000-0001-5255-7036","affiliations":[{"raw_affiliation_string":"Signal Processing and Networks Research Group, Wolfson School, Loughborough University, Loughborough, Leicestershire, U.K","institution_ids":["https://openalex.org/I143804889"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1187,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.76653658,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"69","issue":null,"first_page":"948","last_page":"959"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","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/T10148","display_name":"Advanced MIMO Systems Optimization","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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9995999932289124,"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/T11873","display_name":"PAPR reduction in OFDM","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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7545069456100464},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.7502704858779907},{"id":"https://openalex.org/keywords/orthogonal-frequency-division-multiplexing","display_name":"Orthogonal frequency-division multiplexing","score":0.6388110518455505},{"id":"https://openalex.org/keywords/beamforming","display_name":"Beamforming","score":0.5971440672874451},{"id":"https://openalex.org/keywords/mimo-ofdm","display_name":"MIMO-OFDM","score":0.5101569294929504},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.5039839148521423},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.4795224964618683},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47798436880111694},{"id":"https://openalex.org/keywords/precoding","display_name":"Precoding","score":0.4391520619392395},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.25887399911880493}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7545069456100464},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.7502704858779907},{"id":"https://openalex.org/C40409654","wikidata":"https://www.wikidata.org/wiki/Q375889","display_name":"Orthogonal frequency-division multiplexing","level":3,"score":0.6388110518455505},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.5971440672874451},{"id":"https://openalex.org/C130946814","wikidata":"https://www.wikidata.org/wiki/Q5988271","display_name":"MIMO-OFDM","level":4,"score":0.5101569294929504},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5039839148521423},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.4795224964618683},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47798436880111694},{"id":"https://openalex.org/C160562895","wikidata":"https://www.wikidata.org/wiki/Q7239557","display_name":"Precoding","level":4,"score":0.4391520619392395},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.25887399911880493},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"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:10.1109/tsp.2021.3052040","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2021.3052040","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:figshare.com:article/13562303","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Polynomial_GSVD_beamforming_for_two-user_frequency-selective_MIMO_channels/13562303","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":"","raw_type":"Text"},{"id":"pmh:oai:https://orca.cardiff.ac.uk:142864","is_oa":false,"landing_page_url":"https://orca.cardiff.ac.uk/id/eprint/142864/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401195","display_name":"ORCA Online Research @Cardiff (Cardiff University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79510175","host_organization_name":"Cardiff University","host_organization_lineage":["https://openalex.org/I79510175"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/13562303","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Polynomial_GSVD_beamforming_for_two-user_frequency-selective_MIMO_channels/13562303","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4078854928","display_name":null,"funder_award_id":"EP/R006385/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6997114215","display_name":"Communications Signal Processing Based Solutions for Massive Machine-to-Machine Networks (M3NETs)","funder_award_id":"EP/R006385/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W186507531","https://openalex.org/W1977271127","https://openalex.org/W1977803797","https://openalex.org/W1985852691","https://openalex.org/W1992758506","https://openalex.org/W1997834106","https://openalex.org/W2033128271","https://openalex.org/W2045966546","https://openalex.org/W2055307618","https://openalex.org/W2060198758","https://openalex.org/W2063862284","https://openalex.org/W2069354344","https://openalex.org/W2095706820","https://openalex.org/W2107792943","https://openalex.org/W2125624993","https://openalex.org/W2136126519","https://openalex.org/W2142690499","https://openalex.org/W2147792942","https://openalex.org/W2155847893","https://openalex.org/W2165344682","https://openalex.org/W2165682245","https://openalex.org/W2344963878","https://openalex.org/W2403379548","https://openalex.org/W2554137461","https://openalex.org/W2555516797","https://openalex.org/W2609583227","https://openalex.org/W2788735937","https://openalex.org/W2795109180","https://openalex.org/W2903169964","https://openalex.org/W2905374532","https://openalex.org/W2938584951","https://openalex.org/W2962886963","https://openalex.org/W2969328877","https://openalex.org/W2994710153","https://openalex.org/W3148453925","https://openalex.org/W6607639225"],"related_works":["https://openalex.org/W2124087336","https://openalex.org/W3206079451","https://openalex.org/W2611513238","https://openalex.org/W2165879876","https://openalex.org/W2155862235","https://openalex.org/W2101639217","https://openalex.org/W2137138698","https://openalex.org/W2132393855","https://openalex.org/W3146064192","https://openalex.org/W2750780858"],"abstract_inverted_index":{"In":[0],"this":[1,131],"paper,":[2],"we":[3,97,115],"propose":[4,117],"a":[5,40],"generalized":[6],"singular":[7],"value":[8],"decomposition":[9],"(GSVD)":[10],"for":[11,23,110,151],"polynomial":[12,15],"matrices,":[13],"or":[14],"GSVD":[16,67],"(PGSVD).":[17],"We":[18],"then":[19],"consider":[20],"PGSVD-based":[21,61,126],"beamforming":[22],"two-user,":[24],"frequency-selective,":[25],"multiple-input":[26],"multiple-output":[27],"(MIMO)":[28],"multicasting.":[29],"The":[30],"PGSVD":[31],"can":[32,84],"jointly":[33],"factorize":[34],"two":[35],"frequency-selective":[36],"MIMO":[37,107,137],"channels,":[38],"producing":[39],"set":[41],"of":[42,58,66,73,104,145],"virtual":[43],"channels":[44,49,53],"(VCs),":[45],"split":[46],"into:":[47],"private":[48],"(PCs)":[50],"and":[51,122,135,149],"common":[52],"(CCs).":[54],"An":[55],"important":[56],"advantage":[57,144],"the":[59,64,74,99],"proposed":[60],"beamformer,":[62],"over":[63],"application":[65],"independently":[68],"to":[69,91,130,142],"each":[70],"frequency":[71,76],"bin":[72],"orthogonal":[75],"division":[77],"multiplexing":[78],"(OFDM)":[79],"scheme,":[80],"is":[81],"that":[82,124],"it":[83],"facilitate":[85],"different":[86,111],"modulation":[87,148],"and/or":[88],"access":[89,150],"schemes":[90],"various":[92,152],"users.":[93,153],"Using":[94],"computer":[95],"simulations,":[96],"characterize":[98],"bit":[100],"error":[101],"rate":[102],"performance":[103],"our":[105,125],"two-user":[106],"multicasting":[108],"system":[109],"PCs/CCs":[112],"configurations.":[113],"Here,":[114],"also":[116],"an":[118],"OFDM-GSVD":[119],"benchmark":[120,132],"system,":[121],"show":[123],"beamformer":[127],"compares":[128],"favorably":[129],"under":[133],"erroneous":[134],"uncertain":[136],"channel":[138],"conditions,":[139],"in":[140],"addition":[141],"its":[143],"facilitating":[146],"heterogeneous":[147]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
