{"id":"https://openalex.org/W2091674039","doi":"https://doi.org/10.1109/isit.2011.6034112","title":"Optimal lattices for MIMO precoding","display_name":"Optimal lattices for MIMO precoding","publication_year":2011,"publication_date":"2011-07-01","ids":{"openalex":"https://openalex.org/W2091674039","doi":"https://doi.org/10.1109/isit.2011.6034112","mag":"2091674039"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2011.6034112","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2011.6034112","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE International Symposium on Information Theory Proceedings","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/A5033255554","display_name":"D\u017eevdan Kapetanovi\u0107","orcid":null},"institutions":[{"id":"https://openalex.org/I187531555","display_name":"Lund University","ror":"https://ror.org/012a77v79","country_code":"SE","type":"education","lineage":["https://openalex.org/I187531555"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Dzevdan Kapetanovic","raw_affiliation_strings":["Department of Electrical and Information Technology, Lund University, Lund, Sweden","Department of Electrical and Information Technology, Lund University, P. O. Box 118, 22100, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Information Technology, Lund University, Lund, Sweden","institution_ids":["https://openalex.org/I187531555"]},{"raw_affiliation_string":"Department of Electrical and Information Technology, Lund University, P. O. Box 118, 22100, Sweden","institution_ids":["https://openalex.org/I187531555"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081375588","display_name":"Hei Victor Cheng","orcid":"https://orcid.org/0000-0001-8432-3779"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]},{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Hei Victor Cheng","raw_affiliation_strings":["Department of Computer and Electronic Engineering, Hong Kong University of Science and Technology, Hong Kong, China","[Department of Computer and Electronic Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong]"],"affiliations":[{"raw_affiliation_string":"Department of Computer and Electronic Engineering, Hong Kong University of Science and Technology, Hong Kong, China","institution_ids":["https://openalex.org/I200769079"]},{"raw_affiliation_string":"[Department of Computer and Electronic Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong]","institution_ids":["https://openalex.org/I200769079","https://openalex.org/I889458895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065074102","display_name":"Wai Ho Mow","orcid":"https://orcid.org/0000-0003-1804-0476"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]},{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Wai Ho Mow","raw_affiliation_strings":["Department of Computer and Electronic Engineering, Hong Kong University of Science and Technology, Hong Kong, China","[Department of Computer and Electronic Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong]"],"affiliations":[{"raw_affiliation_string":"Department of Computer and Electronic Engineering, Hong Kong University of Science and Technology, Hong Kong, China","institution_ids":["https://openalex.org/I200769079"]},{"raw_affiliation_string":"[Department of Computer and Electronic Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong]","institution_ids":["https://openalex.org/I200769079","https://openalex.org/I889458895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002140807","display_name":"Fredrik Rusek","orcid":"https://orcid.org/0000-0002-2077-3858"},"institutions":[{"id":"https://openalex.org/I187531555","display_name":"Lund University","ror":"https://ror.org/012a77v79","country_code":"SE","type":"education","lineage":["https://openalex.org/I187531555"]},{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]},{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK","SE"],"is_corresponding":false,"raw_author_name":"Fredrik Rusek","raw_affiliation_strings":["Department of Electrical and Information Technology, Lund University, Lund, Sweden","[Department of Computer and Electronic Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong]"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Information Technology, Lund University, Lund, Sweden","institution_ids":["https://openalex.org/I187531555"]},{"raw_affiliation_string":"[Department of Computer and Electronic Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong]","institution_ids":["https://openalex.org/I200769079","https://openalex.org/I889458895"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5033255554"],"corresponding_institution_ids":["https://openalex.org/I187531555"],"apc_list":null,"apc_paid":null,"fwci":1.5898,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.84980547,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"a","issue":null,"first_page":"2924","last_page":"2928"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10125","display_name":"Advanced Wireless Communication Techniques","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/T10125","display_name":"Advanced Wireless Communication Techniques","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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9998000264167786,"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/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9988999962806702,"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":0.6713411808013916},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.6655005812644958},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.6169646978378296},{"id":"https://openalex.org/keywords/additive-white-gaussian-noise","display_name":"Additive white Gaussian noise","score":0.5872786641120911},{"id":"https://openalex.org/keywords/lattice-reduction","display_name":"Lattice reduction","score":0.5311533212661743},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5227420330047607},{"id":"https://openalex.org/keywords/transmitter","display_name":"Transmitter","score":0.49039316177368164},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.444053590297699},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.36782872676849365},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35203883051872253},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2946627140045166},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.27468281984329224},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.2682037055492401},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2535099983215332},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.21782314777374268}],"concepts":[{"id":"https://openalex.org/C160562895","wikidata":"https://www.wikidata.org/wiki/Q7239557","display_name":"Precoding","level":4,"score":0.6713411808013916},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.6655005812644958},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.6169646978378296},{"id":"https://openalex.org/C169334058","wikidata":"https://www.wikidata.org/wiki/Q353292","display_name":"Additive white Gaussian noise","level":3,"score":0.5872786641120911},{"id":"https://openalex.org/C44274781","wikidata":"https://www.wikidata.org/wiki/Q6497132","display_name":"Lattice reduction","level":4,"score":0.5311533212661743},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5227420330047607},{"id":"https://openalex.org/C47798520","wikidata":"https://www.wikidata.org/wiki/Q190157","display_name":"Transmitter","level":3,"score":0.49039316177368164},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.444053590297699},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.36782872676849365},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35203883051872253},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2946627140045166},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.27468281984329224},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.2682037055492401},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2535099983215332},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.21782314777374268},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/isit.2011.6034112","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2011.6034112","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE International Symposium on Information Theory Proceedings","raw_type":"proceedings-article"},{"id":"pmh:oai:lup.lub.lu.se:7a35dda4-1c0b-4ef1-afa9-32b0cb2adc02","is_oa":false,"landing_page_url":"https://lup.lub.lu.se/record/2494443","pdf_url":null,"source":{"id":"https://openalex.org/S4306400536","display_name":"Lund University Publications (Lund University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I187531555","host_organization_name":"Lund University","host_organization_lineage":["https://openalex.org/I187531555"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-47548","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-47548","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Conference paper"},{"id":"pmh:oai:repository.ust.hk:1783.1-47548","is_oa":false,"landing_page_url":"http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=LinksAMR&SrcApp=PARTNER_APP&DestLinkType=FullRecord&DestApp=WOS&KeyUT=000297465103062","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference paper"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8700000047683716,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1995990042","https://openalex.org/W2049285480","https://openalex.org/W2098113380","https://openalex.org/W2098234850","https://openalex.org/W2107740059","https://openalex.org/W2125901036","https://openalex.org/W2130509920","https://openalex.org/W2130667916","https://openalex.org/W2144552676","https://openalex.org/W2156264702","https://openalex.org/W2162819547","https://openalex.org/W2312344881","https://openalex.org/W4292408570"],"related_works":["https://openalex.org/W2489379490","https://openalex.org/W2141031289","https://openalex.org/W2543308263","https://openalex.org/W1995289652","https://openalex.org/W2059045613","https://openalex.org/W1969034288","https://openalex.org/W2132991559","https://openalex.org/W2389865855","https://openalex.org/W2051551367","https://openalex.org/W2136616653"],"abstract_inverted_index":{"Consider":[0],"the":[1,37,44,47,53,61,76,94,115,119,128,135],"communication":[2],"model":[3],"\u0233":[4,35],"=":[5],"HF":[6,78,149],"x\u0304":[7,16,65],"+":[8],"n\u0304,":[9],"where":[10],"H;":[11,140],"F":[12,64,107,146],"are":[13,91],"real-valued":[14,24],"matrices,":[15],"is":[17,29,36,41,66,144,150],"a":[18,87,103,151],"data":[19],"vector":[20],"drawn":[21],"from":[22],"some":[23],"lattice":[25,120],"(e.g.":[26],"M-PAM),":[27],"n\u0304":[28],"additive":[30],"white":[31],"Gaussian":[32],"noise":[33],"and":[34,46,59,89],"received":[38],"vector.":[39],"It":[40],"assumed":[42],"that":[43,60,85,148],"transmitter":[45],"receiver":[48],"have":[49],"perfect":[50],"knowledge":[51],"of":[52,75,97,118,130],"channel":[54],"matrix":[55,77],"H":[56],"(perfect":[57],"CSI)":[58],"transmitted":[62],"signal":[63],"subject":[67],"to":[68],"an":[69,109,145],"average":[70,110],"energy":[71,111],"constraint.":[72],"The":[73,142],"columns":[74],"can":[79],"be":[80],"viewed":[81],"as":[82],"basis":[83],"vectors":[84],"span":[86],"lattice,":[88],"we":[90],"interested":[92],"in":[93],"minimum":[95,116],"distance":[96,117],"this":[98],"lattice.":[99,153],"More":[100],"precisely,":[101],"for":[102,137],"given":[104],"H,":[105],"which":[106],"under":[108],"constraint":[112],"will":[113],"maximize":[114],"HF?":[121],"This":[122,132],"particular":[123],"question":[124],"remains":[125],"open":[126],"within":[127],"theory":[129],"lattices.":[131],"work":[133],"provides":[134],"solution":[136],"2\u00d72":[138],"matrices":[139],"F.":[141],"answer":[143],"such":[147],"hexagonal":[152]},"counts_by_year":[{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}