{"id":"https://openalex.org/W1495128998","doi":"https://doi.org/10.1109/vtcspring.2015.7146060","title":"Richardson Method Based Linear Precoding with Low Complexity for Massive MIMO Systems","display_name":"Richardson Method Based Linear Precoding with Low Complexity for Massive MIMO Systems","publication_year":2015,"publication_date":"2015-05-01","ids":{"openalex":"https://openalex.org/W1495128998","doi":"https://doi.org/10.1109/vtcspring.2015.7146060","mag":"1495128998"},"language":"en","primary_location":{"id":"doi:10.1109/vtcspring.2015.7146060","is_oa":false,"landing_page_url":"https://doi.org/10.1109/vtcspring.2015.7146060","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE 81st Vehicular Technology Conference (VTC Spring)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5114706300","display_name":"Zhaohua Lu","orcid":"https://orcid.org/0009-0009-1761-3544"},"institutions":[{"id":"https://openalex.org/I4210098582","display_name":"ZTE (China)","ror":"https://ror.org/00rjhhq63","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210098582"]},{"id":"https://openalex.org/I75746372","display_name":"ZTE (United States)","ror":"https://ror.org/0518yg160","country_code":"US","type":"company","lineage":["https://openalex.org/I4210098582","https://openalex.org/I75746372"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Zhaohua Lu","raw_affiliation_strings":["ZTE Corporation, Shenzhen, China","ZTE Corp., Shenzhen, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ZTE Corporation, Shenzhen, China","institution_ids":["https://openalex.org/I4210098582"]},{"raw_affiliation_string":"ZTE Corp., Shenzhen, China","institution_ids":["https://openalex.org/I75746372"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062763709","display_name":"Jiaqi Ning","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210110458","display_name":"Institute of Electronics","ror":"https://ror.org/01z143507","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210110458"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiaqi Ning","raw_affiliation_strings":["Institute of Electronics, Chinese Academy of Sciences, Beijing, China","Inst. of Electron., Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Electronics, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210110458","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Inst. of Electron., Beijing, China","institution_ids":["https://openalex.org/I4210110458"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100388312","display_name":"Yi Zhang","orcid":"https://orcid.org/0000-0003-2888-4736"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yi Zhang","raw_affiliation_strings":["Department of Electronic Engineering, Tsinghua National Laboratory for Information Science and Technology (TNList), Beijing, China","Dept. of Electron. Eng., Tsinghua Nat. Lab. for Inf. Sci. & Technol. (TNList), Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Tsinghua National Laboratory for Information Science and Technology (TNList), Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Dept. of Electron. Eng., Tsinghua Nat. Lab. for Inf. Sci. & Technol. (TNList), Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058094603","display_name":"Tian Xie","orcid":"https://orcid.org/0000-0002-5445-664X"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tian Xie","raw_affiliation_strings":["Department of Electronic Engineering, Tsinghua National Laboratory for Information Science and Technology (TNList), Beijing, China","Dept. of Electron. Eng., Tsinghua Nat. Lab. for Inf. Sci. & Technol. (TNList), Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Tsinghua National Laboratory for Information Science and Technology (TNList), Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Dept. of Electron. Eng., Tsinghua Nat. Lab. for Inf. Sci. & Technol. (TNList), Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077015591","display_name":"Wenqian Shen","orcid":"https://orcid.org/0000-0003-2509-3664"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenqian Shen","raw_affiliation_strings":["Department of Electronic Engineering, Tsinghua National Laboratory for Information Science and Technology (TNList), Beijing, China","Dept. of Electron. Eng., Tsinghua Nat. Lab. for Inf. Sci. & Technol. (TNList), Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Tsinghua National Laboratory for Information Science and Technology (TNList), Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Dept. of Electron. Eng., Tsinghua Nat. Lab. for Inf. Sci. & Technol. (TNList), Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"61","issue":null,"first_page":"1","last_page":"4"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":1.0,"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":1.0,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11392","display_name":"Energy Harvesting in Wireless Networks","score":0.9991999864578247,"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/precoding","display_name":"Precoding","score":0.9611266851425171},{"id":"https://openalex.org/keywords/zero-forcing-precoding","display_name":"Zero-forcing precoding","score":0.6996445655822754},{"id":"https://openalex.org/keywords/base-station","display_name":"Base station","score":0.6617215871810913},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.6244804859161377},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5211289525032043},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.48427289724349976},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.47837725281715393},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4613490402698517},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4589591324329376},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.44102826714515686},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.36517012119293213},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3491503596305847},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3376529812812805},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3374156355857849},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.33414265513420105},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.2401120960712433},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.09820017218589783}],"concepts":[{"id":"https://openalex.org/C160562895","wikidata":"https://www.wikidata.org/wiki/Q7239557","display_name":"Precoding","level":4,"score":0.9611266851425171},{"id":"https://openalex.org/C155437304","wikidata":"https://www.wikidata.org/wiki/Q8069444","display_name":"Zero-forcing precoding","level":5,"score":0.6996445655822754},{"id":"https://openalex.org/C68649174","wikidata":"https://www.wikidata.org/wiki/Q1379116","display_name":"Base station","level":2,"score":0.6617215871810913},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.6244804859161377},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5211289525032043},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48427289724349976},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.47837725281715393},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4613490402698517},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4589591324329376},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.44102826714515686},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.36517012119293213},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3491503596305847},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3376529812812805},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3374156355857849},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.33414265513420105},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.2401120960712433},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.09820017218589783},{"id":"https://openalex.org/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/vtcspring.2015.7146060","is_oa":false,"landing_page_url":"https://doi.org/10.1109/vtcspring.2015.7146060","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE 81st Vehicular Technology Conference (VTC Spring)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W637574335","https://openalex.org/W1747072732","https://openalex.org/W1971443733","https://openalex.org/W1976109068","https://openalex.org/W2011736561","https://openalex.org/W2020203407","https://openalex.org/W2021582374","https://openalex.org/W2022318697","https://openalex.org/W2046114564","https://openalex.org/W2052321444","https://openalex.org/W2072184935","https://openalex.org/W2081274544","https://openalex.org/W2097234978","https://openalex.org/W2099781940","https://openalex.org/W2103972037","https://openalex.org/W2128513990","https://openalex.org/W2129459483","https://openalex.org/W2130877546","https://openalex.org/W2139693953","https://openalex.org/W3104535788","https://openalex.org/W3106282754","https://openalex.org/W4229746864","https://openalex.org/W6643128684"],"related_works":["https://openalex.org/W2111825998","https://openalex.org/W2326544815","https://openalex.org/W2489379490","https://openalex.org/W1973158664","https://openalex.org/W1731022149","https://openalex.org/W1996933839","https://openalex.org/W2000226056","https://openalex.org/W4386858283","https://openalex.org/W3190864439","https://openalex.org/W1979957996"],"abstract_inverted_index":{"For":[0],"massive":[1],"MIMO":[2],"system":[3],"with":[4,123],"hundreds":[5],"of":[6,34,66,92,101,107,120,128],"antennas":[7,103],"at":[8],"the":[9,19,24,50,61,72,89,99,105,117],"base":[10],"station":[11],"(BS),":[12],"zero":[13],"forcing":[14],"(ZF)":[15],"precoding":[16,47,114,122],"can":[17,59,78,115],"achieve":[18,116],"near-optimal":[20,118],"capacity":[21],"due":[22],"to":[23,48,76,87],"asymptotically":[25],"orthogonal":[26],"channel,":[27],"but":[28],"it":[29],"involves":[30],"complicated":[31,51],"matrix":[32,52],"inversion":[33,53],"large":[35],"size.":[36],"In":[37],"this":[38],"paper,":[39],"we":[40],"propose":[41],"a":[42,82,125],"Richardson":[43],"Method":[44],"(RM)":[45],"based":[46],"avoid":[49],"in":[54],"an":[55],"iterative":[56],"way,":[57],"which":[58,95],"reduce":[60],"complexity":[62],"by":[63,81],"one":[64],"order":[65],"magnitude.":[67],"We":[68],"also":[69],"prove":[70],"that":[71,112],"optimal":[73],"relaxation":[74],"parameter":[75],"RM":[77],"be":[79],"approached":[80],"simple":[83],"and":[84,104],"quantified":[85],"value":[86],"maximize":[88],"convergence":[90],"rate":[91],"RM-based":[93,113],"precoding,":[94],"only":[96,124],"depends":[97],"on":[98],"number":[100,106,127],"BS":[102],"users.":[108],"Simulation":[109],"results":[110],"show":[111],"performance":[119],"ZF":[121],"small":[126],"iterations.":[129]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
