{"id":"https://openalex.org/W4386230806","doi":"https://doi.org/10.1109/tsp.2023.3309460","title":"Half-Inverted Array Design Scheme for Large Hole-Free Fourth-Order Difference Co-Arrays","display_name":"Half-Inverted Array Design Scheme for Large Hole-Free Fourth-Order Difference Co-Arrays","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4386230806","doi":"https://doi.org/10.1109/tsp.2023.3309460"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2023.3309460","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2023.3309460","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Signal Processing","raw_type":"journal-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/A5085132596","display_name":"Yuan-Pon Chen","orcid":"https://orcid.org/0000-0002-0850-5009"},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Yuan-Pon Chen","raw_affiliation_strings":["Graduate Institute of Communication Engineering, National Taiwan University, Taipei City, Taiwan"],"raw_orcid":"https://orcid.org/0000-0002-0850-5009","affiliations":[{"raw_affiliation_string":"Graduate Institute of Communication Engineering, National Taiwan University, Taipei City, Taiwan","institution_ids":["https://openalex.org/I16733864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102758279","display_name":"Chun-Lin Liu","orcid":"https://orcid.org/0000-0003-3135-9684"},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chun-Lin Liu","raw_affiliation_strings":["Department of Electrical Engineering and the Graduate Institute of Communication Engineering, National Taiwan University, Taipei City, Taiwan"],"raw_orcid":"https://orcid.org/0000-0003-3135-9684","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and the Graduate Institute of Communication Engineering, National Taiwan University, Taipei City, Taiwan","institution_ids":["https://openalex.org/I16733864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I16733864"],"apc_list":null,"apc_paid":null,"fwci":0.6662,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.65623082,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"71","issue":null,"first_page":"3296","last_page":"3311"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11946","display_name":"Antenna Design and Optimization","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T10860","display_name":"Speech and Audio Processing","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/notation","display_name":"Notation","score":0.6710572242736816},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4703175127506256},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4298039972782135},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41517576575279236},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3903392255306244},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.341560423374176},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.15083861351013184}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6710572242736816},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4703175127506256},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4298039972782135},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41517576575279236},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3903392255306244},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.341560423374176},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.15083861351013184},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2023.3309460","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2023.3309460","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Signal Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W653761051","https://openalex.org/W1521990686","https://openalex.org/W1952629836","https://openalex.org/W1964521756","https://openalex.org/W1978318660","https://openalex.org/W2006365168","https://openalex.org/W2020524619","https://openalex.org/W2026101255","https://openalex.org/W2046053831","https://openalex.org/W2098174516","https://openalex.org/W2113638573","https://openalex.org/W2144661574","https://openalex.org/W2162654459","https://openalex.org/W2164390589","https://openalex.org/W2172082699","https://openalex.org/W2230451454","https://openalex.org/W2335128326","https://openalex.org/W2346607232","https://openalex.org/W2586607074","https://openalex.org/W2598194391","https://openalex.org/W2625286829","https://openalex.org/W2766362876","https://openalex.org/W2789263903","https://openalex.org/W2798333393","https://openalex.org/W2890483231","https://openalex.org/W2904550993","https://openalex.org/W2942508766","https://openalex.org/W3015894443","https://openalex.org/W3120344529","https://openalex.org/W3128888383","https://openalex.org/W3157811516","https://openalex.org/W3168923453","https://openalex.org/W3203592813","https://openalex.org/W4224932537","https://openalex.org/W4235373508"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2051487156","https://openalex.org/W2504004674","https://openalex.org/W1987679298","https://openalex.org/W2073681303","https://openalex.org/W2963177394","https://openalex.org/W4313359513","https://openalex.org/W2498744856","https://openalex.org/W4390482104","https://openalex.org/W322408318"],"abstract_inverted_index":{"Linear":[0],"sparse":[1],"arrays":[2,42,48,62,67,109,122,172,210],"with":[3,112,123,142],"fourth-order":[4,15],"cumulant":[5],"processing":[6],"can":[7,31],"resolve$\\mathcal{O}(N^4)$directions-of-arrival":[8],"(DOAs)":[9],"using$N$physical":[10],"sensors,":[11],"provided":[12],"that":[13],"the":[14,28,57,65,80,89,93,139,149,153,177,204],"difference":[16],"co-array$\\Delta_4$contains":[17],"a":[18,114,143,160,191,195],"contiguous":[19],"segment":[20],"of":[21,75,152,208],"size$\\mathcal{O}(N^4)$.":[22],"Furthermore,":[23],"if$\\Delta_4$has":[24],"no":[25,73],"holes,":[26],"then":[27],"received":[29],"data":[30],"be":[32],"fully":[33],"exploited":[34],"in":[35],"subspace-based":[36],"DOA":[37,205],"estimators.":[38],"However,":[39],"few":[40],"existing":[41,47,121,199,212],"attain":[43],"large":[44,161],"hole-free$\\Delta_4$.":[45,76,162],"Many":[46],"designed":[49],"for$\\Delta_4$are":[50],"constructed":[51],"from":[52],"two":[53,86],"smaller":[54],"arrays,":[55,83],"called":[56],"basis":[58,66,87,154],"arrays.":[59,155,213],"Nevertheless,":[60],"such":[61],"either":[63],"restrict":[64],"to":[68,169],"certain":[69],"types":[70],"or":[71],"have":[72],"guarantee":[74],"This":[77,117],"paper":[78],"proposes":[79],"half-inverted":[81,131,178],"(HI)":[82],"parameterized":[84],"by":[85,148],"arrays$\\mathbb{S}^{(1)}$and$\\mathbb{S}^{(2)}$,":[88],"shifting":[90],"parameter$M$,":[91],"and":[92,104,145,184,211],"scaling":[94],"parameter$\\sigma$.":[95],"An":[96],"HI":[97,108,140,171,209],"array":[98,141,179],"consists":[99],"of$\\mathbb{S}^{(1)}$and":[100],"an":[101,126,198],"inverted,":[102],"scaled,":[103],"shifted":[105],"version":[106],"of$\\mathbb{S}^{(2)}$.":[107],"are":[110],"guaranteed":[111],"hole-free$\\Delta_4$over":[113],"range":[115],"of$(M,\\sigma)$pairs.":[116],"property":[118],"unifies":[119],"several":[120],"hole-free$\\Delta_4$and":[124],"admits":[125],"optimization":[127,183],"problem":[128],"over$(M,\\sigma)$.":[129],"The":[130,156,163],"general":[132],"hole-free":[133],"(HIGH)":[134],"scheme":[135,158],"is":[136,167,188],"defined":[137],"as":[138],"closed-form":[144],"optimized$(M,\\sigma)$pair":[146],"determined":[147],"second-order":[150,182],"co-arrays":[151],"HIGH":[157],"enjoys":[159],"shift-scale":[164],"representation":[165],"(SSR)":[166],"presented":[168],"study$\\Delta_4$of":[170],"visually.":[173],"From":[174],"these":[175],"results,":[176],"based":[180],"on":[181],"extended":[185],"shift":[186],"(HI-SOES)":[187],"proposed.":[189],"For":[190],"fixed$N$,":[192],"HI-SOES":[193],"synthesizes":[194],"hole-free$\\Delta_4$larger":[196],"than":[197],"array.":[200],"Numerical":[201],"examples":[202],"demonstrate":[203],"estimation":[206],"performance":[207]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
