{"id":"https://openalex.org/W2907649467","doi":"https://doi.org/10.1109/pimrc.2018.8580814","title":"Zero-forcing Precoding for the MU-MISO Downlink: How Many Antennas Do We Need?","display_name":"Zero-forcing Precoding for the MU-MISO Downlink: How Many Antennas Do We Need?","publication_year":2018,"publication_date":"2018-09-01","ids":{"openalex":"https://openalex.org/W2907649467","doi":"https://doi.org/10.1109/pimrc.2018.8580814","mag":"2907649467"},"language":"en","primary_location":{"id":"doi:10.1109/pimrc.2018.8580814","is_oa":false,"landing_page_url":"https://doi.org/10.1109/pimrc.2018.8580814","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE 29th Annual International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)","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/A5102972825","display_name":"Xiaoyong Wu","orcid":"https://orcid.org/0000-0002-2965-0504"},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoyong Wu","raw_affiliation_strings":["Ministry of Education, Beijing University of Posts and Telecommunications, Beijing Laboratory of Advanced Information Network, Beijing Key Laboratory of Network System Architecture and Convergence, Key Laboratory of Universal Wireless Communications, Beijing, 100876, China","Ministry of Education, Beijing University of Posts and Telecommunications, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ministry of Education, Beijing University of Posts and Telecommunications, Beijing Laboratory of Advanced Information Network, Beijing Key Laboratory of Network System Architecture and Convergence, Key Laboratory of Universal Wireless Communications, Beijing, 100876, China","institution_ids":["https://openalex.org/I139759216"]},{"raw_affiliation_string":"Ministry of Education, Beijing University of Posts and Telecommunications, Beijing, China","institution_ids":["https://openalex.org/I139759216"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048802154","display_name":"Danpu Liu","orcid":"https://orcid.org/0000-0003-4296-5209"},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Danpu Liu","raw_affiliation_strings":["Ministry of Education, Beijing University of Posts and Telecommunications, Beijing Laboratory of Advanced Information Network, Beijing Key Laboratory of Network System Architecture and Convergence, Key Laboratory of Universal Wireless Communications, Beijing, 100876, China","Ministry of Education, Beijing University of Posts and Telecommunications, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ministry of Education, Beijing University of Posts and Telecommunications, Beijing Laboratory of Advanced Information Network, Beijing Key Laboratory of Network System Architecture and Convergence, Key Laboratory of Universal Wireless Communications, Beijing, 100876, China","institution_ids":["https://openalex.org/I139759216"]},{"raw_affiliation_string":"Ministry of Education, Beijing University of Posts and Telecommunications, Beijing, China","institution_ids":["https://openalex.org/I139759216"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101676900","display_name":"Zhe Zheng","orcid":"https://orcid.org/0000-0002-1379-3068"},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhe Zheng","raw_affiliation_strings":["Ministry of Education, Beijing University of Posts and Telecommunications, Beijing Laboratory of Advanced Information Network, Beijing Key Laboratory of Network System Architecture and Convergence, Key Laboratory of Universal Wireless Communications, Beijing, 100876, China","Ministry of Education, Beijing University of Posts and Telecommunications, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ministry of Education, Beijing University of Posts and Telecommunications, Beijing Laboratory of Advanced Information Network, Beijing Key Laboratory of Network System Architecture and Convergence, Key Laboratory of Universal Wireless Communications, Beijing, 100876, China","institution_ids":["https://openalex.org/I139759216"]},{"raw_affiliation_string":"Ministry of Education, Beijing University of Posts and Telecommunications, Beijing, China","institution_ids":["https://openalex.org/I139759216"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15031119,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"61","issue":null,"first_page":"1433","last_page":"1439"},"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":0.9994999766349792,"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/precoding","display_name":"Precoding","score":0.8753522634506226},{"id":"https://openalex.org/keywords/telecommunications-link","display_name":"Telecommunications link","score":0.762042760848999},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.623721182346344},{"id":"https://openalex.org/keywords/zero-forcing-precoding","display_name":"Zero-forcing precoding","score":0.6041740775108337},{"id":"https://openalex.org/keywords/channel-state-information","display_name":"Channel state information","score":0.5563948750495911},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5371603965759277},{"id":"https://openalex.org/keywords/rayleigh-fading","display_name":"Rayleigh fading","score":0.48885101079940796},{"id":"https://openalex.org/keywords/signal-to-noise-ratio","display_name":"Signal-to-noise ratio (imaging)","score":0.48184335231781006},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.44278684258461},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4266365170478821},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.415977418422699},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38063371181488037},{"id":"https://openalex.org/keywords/electronic-engineering","display_name":"Electronic engineering","score":0.3355519771575928},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.3307915925979614},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3257310390472412},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.26986098289489746},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.13654181361198425},{"id":"https://openalex.org/keywords/fading","display_name":"Fading","score":0.10221976041793823},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08737191557884216},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07974159717559814}],"concepts":[{"id":"https://openalex.org/C160562895","wikidata":"https://www.wikidata.org/wiki/Q7239557","display_name":"Precoding","level":4,"score":0.8753522634506226},{"id":"https://openalex.org/C138660444","wikidata":"https://www.wikidata.org/wiki/Q5607897","display_name":"Telecommunications link","level":2,"score":0.762042760848999},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.623721182346344},{"id":"https://openalex.org/C155437304","wikidata":"https://www.wikidata.org/wiki/Q8069444","display_name":"Zero-forcing precoding","level":5,"score":0.6041740775108337},{"id":"https://openalex.org/C148063708","wikidata":"https://www.wikidata.org/wiki/Q5072511","display_name":"Channel state information","level":3,"score":0.5563948750495911},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5371603965759277},{"id":"https://openalex.org/C56985126","wikidata":"https://www.wikidata.org/wiki/Q854039","display_name":"Rayleigh fading","level":4,"score":0.48885101079940796},{"id":"https://openalex.org/C13944312","wikidata":"https://www.wikidata.org/wiki/Q7512748","display_name":"Signal-to-noise ratio (imaging)","level":2,"score":0.48184335231781006},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.44278684258461},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4266365170478821},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.415977418422699},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38063371181488037},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.3355519771575928},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.3307915925979614},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3257310390472412},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.26986098289489746},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.13654181361198425},{"id":"https://openalex.org/C81978471","wikidata":"https://www.wikidata.org/wiki/Q1196572","display_name":"Fading","level":3,"score":0.10221976041793823},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08737191557884216},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07974159717559814},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/pimrc.2018.8580814","is_oa":false,"landing_page_url":"https://doi.org/10.1109/pimrc.2018.8580814","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE 29th Annual International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.4699999988079071,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1423052447","https://openalex.org/W1971443733","https://openalex.org/W1982306920","https://openalex.org/W2072184935","https://openalex.org/W2084304524","https://openalex.org/W2103749601","https://openalex.org/W2128513990","https://openalex.org/W2147601077","https://openalex.org/W2166579323","https://openalex.org/W2238937638","https://openalex.org/W2558927171","https://openalex.org/W3106282754"],"related_works":["https://openalex.org/W2111825998","https://openalex.org/W2326544815","https://openalex.org/W1973158664","https://openalex.org/W1731022149","https://openalex.org/W1996933839","https://openalex.org/W2000226056","https://openalex.org/W4386858283","https://openalex.org/W1976511355","https://openalex.org/W2082469387","https://openalex.org/W1985632843"],"abstract_inverted_index":{"In":[0,67],"this":[1],"study,":[2],"we":[3,32],"consider":[4],"zero-forcing":[5],"(ZF)":[6],"precoding":[7],"under":[8],"uncorrelated":[9],"Rayleigh":[10],"channels":[11],"with":[12,58],"both":[13],"perfect":[14,30],"channel":[15],"state":[16],"information":[17],"(CSI)":[18],"and":[19,97],"pilot-based":[20,107],"CSI":[21],"in":[22],"a":[23,48],"multi-user":[24],"multiple-input":[25],"single-output":[26],"(MU-MISO)":[27],"system.":[28],"Using":[29],"CSI,":[31],"first":[33],"demonstrate":[34],"that":[35,77,113],"the":[36,40,52,59,62,69,72,82,93,98,104,106,118,122],"needed":[37,73],"number":[38,84,94],"of":[39,51,61,71,81,85,95,103,124],"transmit":[41,63,74],"antennas":[42,75,86],"for":[43,87,127],"ZF":[44],"precoder":[45],"to":[46,92,111],"achieve":[47],"certain":[49],"percentage":[50],"maximal":[53],"achievable":[54],"sum-rate":[55],"monotonically":[56],"decreases":[57],"increase":[60],"signal-to-noise":[64],"ratio":[65],"(SNR).":[66],"addition,":[68],"analysis":[70],"shows":[76],"an":[78],"upper":[79],"bound":[80],"required":[83],"easy":[88],"calculation":[89],"only":[90],"relates":[91],"users":[96],"target":[99],"percentage.":[100],"For":[101],"completeness":[102],"research,":[105],"case":[108],"is":[109,130],"analyzed":[110],"examine":[112],"how":[114],"pilots":[115],"will":[116],"affect":[117],"aforementioned":[119],"results.":[120,134],"Finally,":[121],"concept":[123],"massive":[125],"MIMO":[126],"practical":[128],"deployment":[129],"discussed":[131],"via":[132],"simulation":[133]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}