{"id":"https://openalex.org/W2946391868","doi":"https://doi.org/10.1109/tcomm.2019.2916857","title":"Design of Asymptotically Optimal Improper Constellations With Hexagonal Packing","display_name":"Design of Asymptotically Optimal Improper Constellations With Hexagonal Packing","publication_year":2019,"publication_date":"2019-05-15","ids":{"openalex":"https://openalex.org/W2946391868","doi":"https://doi.org/10.1109/tcomm.2019.2916857","mag":"2946391868"},"language":"en","primary_location":{"id":"doi:10.1109/tcomm.2019.2916857","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcomm.2019.2916857","pdf_url":null,"source":{"id":"https://openalex.org/S196647941","display_name":"IEEE Transactions on Communications","issn_l":"0090-6778","issn":["0090-6778","1558-0857"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310316002","host_organization_name":"IEEE Communications Society","host_organization_lineage":["https://openalex.org/P4310316002","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Communications Society","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 Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10651/51647","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066416804","display_name":"Jes\u00fas A. L\u00f3pez\u2010Fern\u00e1ndez","orcid":"https://orcid.org/0000-0001-7603-9591"},"institutions":[{"id":"https://openalex.org/I165339363","display_name":"Universidad de Oviedo","ror":"https://ror.org/006gksa02","country_code":"ES","type":"education","lineage":["https://openalex.org/I165339363"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jesus Alberto Lopez-Fernandez","raw_affiliation_strings":["Department of Electrical Engineering, University of Oviedo, Gij\u00f3n, Spain"],"raw_orcid":"https://orcid.org/0000-0001-7603-9591","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Oviedo, Gij\u00f3n, Spain","institution_ids":["https://openalex.org/I165339363"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003850349","display_name":"Rafael Gonz\u00e1lez Ayestar\u00e1n","orcid":"https://orcid.org/0000-0002-9775-9448"},"institutions":[{"id":"https://openalex.org/I165339363","display_name":"Universidad de Oviedo","ror":"https://ror.org/006gksa02","country_code":"ES","type":"education","lineage":["https://openalex.org/I165339363"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Rafael Gonzalez Ayestaran","raw_affiliation_strings":["Department of Electrical Engineering, University of Oviedo, Gij\u00f3n, Spain"],"raw_orcid":"https://orcid.org/0000-0002-9775-9448","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Oviedo, Gij\u00f3n, Spain","institution_ids":["https://openalex.org/I165339363"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059078809","display_name":"Ignacio Santamar\u0131\u0301a","orcid":"https://orcid.org/0000-0003-0040-7436"},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Ignacio Santamaria","raw_affiliation_strings":["Department of Communications Engineering, University of Cantabria, Santander, Spain"],"raw_orcid":"https://orcid.org/0000-0003-0040-7436","affiliations":[{"raw_affiliation_string":"Department of Communications Engineering, University of Cantabria, Santander, Spain","institution_ids":["https://openalex.org/I13134134"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017899271","display_name":"Christian Lameiro","orcid":"https://orcid.org/0000-0003-4455-5940"},"institutions":[{"id":"https://openalex.org/I206945453","display_name":"Paderborn University","ror":"https://ror.org/058kzsd48","country_code":"DE","type":"education","lineage":["https://openalex.org/I206945453"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian Lameiro","raw_affiliation_strings":["Signal and System Theory Group, University of Paderborn, Paderborn, Germany"],"raw_orcid":"https://orcid.org/0000-0003-4455-5940","affiliations":[{"raw_affiliation_string":"Signal and System Theory Group, University of Paderborn, Paderborn, Germany","institution_ids":["https://openalex.org/I206945453"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2843,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.80346161,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"67","issue":"8","first_page":"5445","last_page":"5457"},"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/T10148","display_name":"Advanced MIMO Systems Optimization","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/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"}}],"keywords":[{"id":"https://openalex.org/keywords/quadrature-amplitude-modulation","display_name":"Quadrature amplitude modulation","score":0.6912346482276917},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6782692670822144},{"id":"https://openalex.org/keywords/constellation-diagram","display_name":"Constellation diagram","score":0.6086528897285461},{"id":"https://openalex.org/keywords/asymptotically-optimal-algorithm","display_name":"Asymptotically optimal algorithm","score":0.6041781902313232},{"id":"https://openalex.org/keywords/additive-white-gaussian-noise","display_name":"Additive white Gaussian noise","score":0.5886732339859009},{"id":"https://openalex.org/keywords/constellation","display_name":"Constellation","score":0.5378090739250183},{"id":"https://openalex.org/keywords/ellipse","display_name":"Ellipse","score":0.44912198185920715},{"id":"https://openalex.org/keywords/qam","display_name":"QAM","score":0.42975443601608276},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4284361004829407},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42516931891441345},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.4216029942035675},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3914913833141327},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3750660717487335},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.2825045883655548},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21517980098724365},{"id":"https://openalex.org/keywords/bit-error-rate","display_name":"Bit error rate","score":0.1778758466243744},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.17710688710212708},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1619318425655365},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.15421298146247864},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14014971256256104}],"concepts":[{"id":"https://openalex.org/C32409245","wikidata":"https://www.wikidata.org/wiki/Q749753","display_name":"Quadrature amplitude modulation","level":4,"score":0.6912346482276917},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6782692670822144},{"id":"https://openalex.org/C185837786","wikidata":"https://www.wikidata.org/wiki/Q1782940","display_name":"Constellation diagram","level":4,"score":0.6086528897285461},{"id":"https://openalex.org/C181789720","wikidata":"https://www.wikidata.org/wiki/Q4812191","display_name":"Asymptotically optimal algorithm","level":2,"score":0.6041781902313232},{"id":"https://openalex.org/C169334058","wikidata":"https://www.wikidata.org/wiki/Q353292","display_name":"Additive white Gaussian noise","level":3,"score":0.5886732339859009},{"id":"https://openalex.org/C70352696","wikidata":"https://www.wikidata.org/wiki/Q8928","display_name":"Constellation","level":2,"score":0.5378090739250183},{"id":"https://openalex.org/C74261601","wikidata":"https://www.wikidata.org/wiki/Q40112","display_name":"Ellipse","level":2,"score":0.44912198185920715},{"id":"https://openalex.org/C59030546","wikidata":"https://www.wikidata.org/wiki/Q7265371","display_name":"QAM","level":5,"score":0.42975443601608276},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4284361004829407},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42516931891441345},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.4216029942035675},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3914913833141327},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3750660717487335},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.2825045883655548},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21517980098724365},{"id":"https://openalex.org/C56296756","wikidata":"https://www.wikidata.org/wiki/Q840922","display_name":"Bit error rate","level":3,"score":0.1778758466243744},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.17710688710212708},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1619318425655365},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.15421298146247864},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14014971256256104},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tcomm.2019.2916857","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcomm.2019.2916857","pdf_url":null,"source":{"id":"https://openalex.org/S196647941","display_name":"IEEE Transactions on Communications","issn_l":"0090-6778","issn":["0090-6778","1558-0857"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310316002","host_organization_name":"IEEE Communications Society","host_organization_lineage":["https://openalex.org/P4310316002","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Communications Society","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 Communications","raw_type":"journal-article"},{"id":"pmh:oai:dnet:ucreareposit::e5425e7b61f68b3ee501f2cb43ee988b","is_oa":false,"landing_page_url":"http://hdl.handle.net/10902/17958","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"IEEE Transactions on Communications, 2019, 67(8), 5445-5457","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:digibuo.uniovi.es:10651/51647","is_oa":true,"landing_page_url":"http://hdl.handle.net/10651/51647","pdf_url":null,"source":{"id":"https://openalex.org/S4306402334","display_name":"Consultation of the Doctoral Thesis Database (TESEO) (Ministerio de Educaci\u00f3n, Cultura y Deporte)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801976130","host_organization_name":"Ministerio de Educaci\u00f3n Cultura y Deporte","host_organization_lineage":["https://openalex.org/I2801976130"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:zenodo.org:10641307","is_oa":true,"landing_page_url":"https://doi.org/10.1109/TCOMM.2019.2916857","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Communications, 67(8), 5445-5457, (2019-08)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:digibuo.uniovi.es:10651/51647","is_oa":true,"landing_page_url":"http://hdl.handle.net/10651/51647","pdf_url":null,"source":{"id":"https://openalex.org/S4306402334","display_name":"Consultation of the Doctoral Thesis Database (TESEO) (Ministerio de Educaci\u00f3n, Cultura y Deporte)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801976130","host_organization_name":"Ministerio de Educaci\u00f3n Cultura y Deporte","host_organization_lineage":["https://openalex.org/I2801976130"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3863520210","display_name":null,"funder_award_id":"LA 4107/1-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G4077028854","display_name":null,"funder_award_id":"TEC2016-75067-C4-4-R (CARMEN)","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G4211686769","display_name":null,"funder_award_id":"GRUPIN-IDI-2018-000191","funder_id":"https://openalex.org/F4320313141","funder_display_name":"Gobierno del Principado de Asturias"},{"id":"https://openalex.org/G6811234217","display_name":null,"funder_award_id":"TEC2015-69648-REDC (Red COMONSENS)","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"}],"funders":[{"id":"https://openalex.org/F4320313141","display_name":"Gobierno del Principado de Asturias","ror":"https://ror.org/05mj4yh71"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W639989723","https://openalex.org/W1969165241","https://openalex.org/W1996124484","https://openalex.org/W1999666226","https://openalex.org/W2029236670","https://openalex.org/W2030127857","https://openalex.org/W2046079909","https://openalex.org/W2067489830","https://openalex.org/W2071238091","https://openalex.org/W2080450804","https://openalex.org/W2098234850","https://openalex.org/W2098918476","https://openalex.org/W2099111195","https://openalex.org/W2100440346","https://openalex.org/W2103604544","https://openalex.org/W2128552251","https://openalex.org/W2129124464","https://openalex.org/W2136180028","https://openalex.org/W2138293524","https://openalex.org/W2139996618","https://openalex.org/W2153782647","https://openalex.org/W2164654926","https://openalex.org/W2167705656","https://openalex.org/W2168048200","https://openalex.org/W2240505936","https://openalex.org/W2294288691","https://openalex.org/W2322960615","https://openalex.org/W2354913050","https://openalex.org/W2409390797","https://openalex.org/W2478708596","https://openalex.org/W2607860961","https://openalex.org/W2783165102","https://openalex.org/W2798333393","https://openalex.org/W2999275664","https://openalex.org/W4211251910","https://openalex.org/W4237963784","https://openalex.org/W4289709047","https://openalex.org/W4293860921"],"related_works":["https://openalex.org/W2380145154","https://openalex.org/W2776889143","https://openalex.org/W2103491754","https://openalex.org/W3139451426","https://openalex.org/W2737715209","https://openalex.org/W2318644031","https://openalex.org/W2253476804","https://openalex.org/W1976196557","https://openalex.org/W2108175840","https://openalex.org/W2107360574"],"abstract_inverted_index":{"This":[0],"paper":[1],"addresses":[2],"the":[3,19,31,46,63,68,72,75,84,136],"problem":[4],"of":[5,43,49,65,74,122,138],"designing":[6],"asymptotically":[7],"optimal":[8,29,69],"improper":[9,99,112,140],"constellations":[10,27,103,141],"with":[11,78,108],"a":[12,40,118,123,143],"given":[13],"circularity":[14,85],"coefficient":[15,17],"(correlation":[16],"between":[18],"constellation":[20,70],"and":[21,38],"its":[22],"complex":[23],"conjugate).":[24],"The":[25,101],"designed":[26],"are":[28],"in":[30,146],"sense":[32],"that,":[33],"at":[34],"high":[35],"signal-to-noise-ratio":[36],"(SNR)":[37],"for":[39,56],"large":[41],"number":[42,64],"symbols,":[44],"yield":[45],"lowest":[47],"probability":[48],"error":[50],"under":[51],"an":[52,79,94,131,147],"average":[53],"power":[54],"constraint":[55],"additive":[57],"white":[58],"Gaussian":[59],"noise":[60],"channels.":[61],"As":[62,130],"symbols":[66],"grows,":[67],"is":[71],"intersection":[73],"hexagonal":[76],"lattice":[77],"ellipse":[80],"whose":[81],"eccentricity":[82],"determines":[83],"coefficient.":[86],"Based":[87],"on":[88],"this":[89],"asymptotic":[90],"result,":[91],"we":[92,134],"propose":[93],"algorithm":[95],"to":[96,110],"design":[97],"finite":[98],"constellations.":[100],"proposed":[102],"provide":[104],"significant":[105],"SNR":[106],"gains":[107],"respect":[109],"previous":[111],"designs,":[113],"which":[114],"were":[115],"generated":[116],"through":[117],"widely":[119],"linear":[120],"transformation":[121],"standard":[124],"M-ary":[125],"quadrature":[126],"amplitude":[127],"modulation":[128],"constellation.":[129],"application":[132],"example,":[133],"study":[135],"use":[137],"these":[139],"by":[142],"secondary":[144],"user":[145],"underlay":[148],"cognitive":[149],"radio":[150],"network.":[151]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}