{"id":"https://openalex.org/W7160495351","doi":"https://doi.org/10.48550/arxiv.2605.04545","title":"Z-Opt: A Near-Optimal Reduced-Complexity Two-Dimensional Grassmannian Constellation","display_name":"Z-Opt: A Near-Optimal Reduced-Complexity Two-Dimensional Grassmannian Constellation","publication_year":2026,"publication_date":"2026-05-06","ids":{"openalex":"https://openalex.org/W7160495351","doi":"https://doi.org/10.48550/arxiv.2605.04545"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.04545","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.04545","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.04545","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135586640","display_name":"Kotaro Shigenaga","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shigenaga, Kotaro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135630192","display_name":"Hiroki Iimori","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Iimori, Hiroki","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014303858","display_name":"Yuto Hama","orcid":"https://orcid.org/0000-0002-0852-5085"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hama, Yuto","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135598529","display_name":"Chandan Pradhan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pradhan, Chandan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083468980","display_name":"Szabolcs Malomsoky","orcid":"https://orcid.org/0009-0007-9013-860X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Malomsoky, Szabolcs","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5088245484","display_name":"Naoki Ishikawa","orcid":"https://orcid.org/0000-0001-8978-4849"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ishikawa, Naoki","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10232","display_name":"Optical Network Technologies","score":0.3950999975204468,"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/T10232","display_name":"Optical Network Technologies","score":0.3950999975204468,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.1298999935388565,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.0917000025510788,"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/grassmannian","display_name":"Grassmannian","score":0.8392000198364258},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.64410001039505},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.47119998931884766},{"id":"https://openalex.org/keywords/constellation","display_name":"Constellation","score":0.45980000495910645},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.39160001277923584},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.3873000144958496},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.362199991941452}],"concepts":[{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.8392000198364258},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7110000252723694},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.64410001039505},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.47119998931884766},{"id":"https://openalex.org/C70352696","wikidata":"https://www.wikidata.org/wiki/Q8928","display_name":"Constellation","level":2,"score":0.45980000495910645},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.39160001277923584},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.3873000144958496},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.362199991941452},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35589998960494995},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.3377000093460083},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3287999927997589},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3224000036716461},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.3174999952316284},{"id":"https://openalex.org/C81978471","wikidata":"https://www.wikidata.org/wiki/Q1196572","display_name":"Fading","level":3,"score":0.3084000051021576},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.301800012588501},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.2867000102996826},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C94915269","wikidata":"https://www.wikidata.org/wiki/Q1834857","display_name":"Detector","level":2,"score":0.26460000872612}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.04545","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.04545","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.04545","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.04545","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.7174489498138428}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Grassmannian":[0,34,137],"constellations":[1,35,138],"are":[2,58],"known":[3,64],"to":[4,84,135],"achieve":[5],"the":[6,16,53,61,66,75,79,85,89,101,105,119,124,148,156,161,166,172,176,179,189,198,203,215,222,227],"capacity":[7],"of":[8,36,150,217],"noncoherent":[9],"communications":[10],"over":[11,202],"Rayleigh":[12],"fading":[13],"channels":[14],"in":[15,39,69],"high-SNR":[17],"regime,":[18],"yet":[19],"their":[20],"efficient":[21],"construction":[22,31,54],"remains":[23],"challenging.":[24],"In":[25],"this":[26],"paper,":[27],"we":[28],"propose":[29],"two":[30,49],"methods":[32],"for":[33,123,230],"one-dimensional":[37],"subspaces":[38],"a":[40,94],"two-dimensional":[41],"space,":[42],"termed":[43],"S-Opt":[44,110,130,177],"and":[45,55,92,117,141,153,192],"Z-Opt,":[46],"along":[47],"with":[48,147,155,214],"low-complexity":[50],"detectors.":[51],"Both":[52],"detection":[56,163,224],"procedures":[57],"performed":[59],"on":[60,78,88,100,104,139,171,188],"unit":[62],"sphere,":[63,191],"as":[65,165,226],"Bloch":[67,90,190],"sphere":[68,91],"quantum":[70],"computing.":[71],"We":[72],"show":[73],"that":[74],"chordal":[76,107,195],"distance":[77,87,196],"Grassmann":[80],"manifold":[81],"is":[82,112,182],"proportional":[83],"Euclidean":[86],"derive":[93],"corresponding":[95],"theoretical":[96],"upper":[97,121,200],"bound":[98,103,122,201],"based":[99,170],"Fejes--T\u00f3th":[102],"minimum":[106,194],"distance.":[108],"The":[109,129,207],"constellation":[111,157,181,205],"constructed":[113,183],"from":[114],"sphere-packing":[115],"solutions":[116],"attains":[118],"derived":[120,199],"optimal":[125],"Bloch-sphere":[126],"packings":[127],"considered.":[128],"detector":[131,229],"can":[132],"be":[133],"applied":[134],"arbitrary":[136],"$\\mathcal{G}(2,1)$,":[140],"its":[142,193],"time":[143,210],"complexity":[144,211],"scales":[145,212],"linearly":[146,213],"number":[149,216],"receive":[151,218],"antennas":[152],"logarithmically":[154],"size,":[158],"while":[159,220],"yielding":[160,221],"same":[162,223],"performance":[164,225],"GLRT":[167,228],"detector.":[168],"Furthermore,":[169],"insight":[173],"obtained":[174],"through":[175],"construction,":[178],"Z-Opt":[180,208],"by":[184],"stacking":[185],"regular":[186],"polygons":[187],"approaches":[197],"evaluated":[204],"sizes.":[206],"detector's":[209],"antennas,":[219],"Z-Opt.":[231]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-08T00:00:00"}