{"id":"https://openalex.org/W2111484900","doi":"https://doi.org/10.1109/tcomm.2011.050211.100036a","title":"Cramer-Rao Lower Bounds of DOA Estimates from Square QAM-Modulated Signals","display_name":"Cramer-Rao Lower Bounds of DOA Estimates from Square QAM-Modulated Signals","publication_year":2011,"publication_date":"2011-05-09","ids":{"openalex":"https://openalex.org/W2111484900","doi":"https://doi.org/10.1109/tcomm.2011.050211.100036a","mag":"2111484900"},"language":"en","primary_location":{"id":"doi:10.1109/tcomm.2011.050211.100036a","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcomm.2011.050211.100036a","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003619912","display_name":"Faouzi Bellili","orcid":"https://orcid.org/0000-0001-6630-6561"},"institutions":[{"id":"https://openalex.org/I39481719","display_name":"Institut National de la Recherche Scientifique","ror":"https://ror.org/04td37d32","country_code":"CA","type":"education","lineage":["https://openalex.org/I39481719","https://openalex.org/I49663120"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Faouzi Bellili","raw_affiliation_strings":["Institut National de Recherche Scientifique - Energie Mat\u00e9riaux et t\u00e9l\u00e9communications (EMT), Montreal, Qc, Canada","Inst. Nat. de Rech. Sci. - Energie Mater. et Telecommun. (EMT), Montreal, QC, Canada"],"affiliations":[{"raw_affiliation_string":"Institut National de Recherche Scientifique - Energie Mat\u00e9riaux et t\u00e9l\u00e9communications (EMT), Montreal, Qc, Canada","institution_ids":["https://openalex.org/I39481719"]},{"raw_affiliation_string":"Inst. Nat. de Rech. Sci. - Energie Mater. et Telecommun. (EMT), Montreal, QC, Canada","institution_ids":["https://openalex.org/I39481719"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065385887","display_name":"Sonia Ben Hassen","orcid":"https://orcid.org/0000-0003-4997-9398"},"institutions":[{"id":"https://openalex.org/I39481719","display_name":"Institut National de la Recherche Scientifique","ror":"https://ror.org/04td37d32","country_code":"CA","type":"education","lineage":["https://openalex.org/I39481719","https://openalex.org/I49663120"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Sonia Ben Hassen","raw_affiliation_strings":["Institut National de Recherche Scientifique - Energie Mat\u00e9riaux et t\u00e9l\u00e9communications (EMT), Montreal, Qc, Canada","Inst. Nat. de Rech. Sci. - Energie Mater. et Telecommun. (EMT), Montreal, QC, Canada"],"affiliations":[{"raw_affiliation_string":"Institut National de Recherche Scientifique - Energie Mat\u00e9riaux et t\u00e9l\u00e9communications (EMT), Montreal, Qc, Canada","institution_ids":["https://openalex.org/I39481719"]},{"raw_affiliation_string":"Inst. Nat. de Rech. Sci. - Energie Mater. et Telecommun. (EMT), Montreal, QC, Canada","institution_ids":["https://openalex.org/I39481719"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076850812","display_name":"Sofi\u00e8ne Affes","orcid":"https://orcid.org/0000-0002-1729-3503"},"institutions":[{"id":"https://openalex.org/I39481719","display_name":"Institut National de la Recherche Scientifique","ror":"https://ror.org/04td37d32","country_code":"CA","type":"education","lineage":["https://openalex.org/I39481719","https://openalex.org/I49663120"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Sofiene Affes","raw_affiliation_strings":["Institut National de Recherche Scientifique - Energie Mat\u00e9riaux et t\u00e9l\u00e9communications (EMT), Montreal, Qc, Canada","Inst. Nat. de Rech. Sci. - Energie Mater. et Telecommun. (EMT), Montreal, QC, Canada"],"affiliations":[{"raw_affiliation_string":"Institut National de Recherche Scientifique - Energie Mat\u00e9riaux et t\u00e9l\u00e9communications (EMT), Montreal, Qc, Canada","institution_ids":["https://openalex.org/I39481719"]},{"raw_affiliation_string":"Inst. Nat. de Rech. Sci. - Energie Mater. et Telecommun. (EMT), Montreal, QC, Canada","institution_ids":["https://openalex.org/I39481719"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000502403","display_name":"Alex St\u00e9phenne","orcid":null},"institutions":[{"id":"https://openalex.org/I39481719","display_name":"Institut National de la Recherche Scientifique","ror":"https://ror.org/04td37d32","country_code":"CA","type":"education","lineage":["https://openalex.org/I39481719","https://openalex.org/I49663120"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Alex Stephenne","raw_affiliation_strings":["Institut National de Recherche Scientifique - Energie Mat\u00e9riaux et t\u00e9l\u00e9communications (EMT), Montreal, Qc, Canada","Inst. Nat. de Rech. Sci. - Energie Mater. et Telecommun. (EMT), Montreal, QC, Canada"],"affiliations":[{"raw_affiliation_string":"Institut National de Recherche Scientifique - Energie Mat\u00e9riaux et t\u00e9l\u00e9communications (EMT), Montreal, Qc, Canada","institution_ids":["https://openalex.org/I39481719"]},{"raw_affiliation_string":"Inst. Nat. de Rech. Sci. - Energie Mater. et Telecommun. (EMT), Montreal, QC, Canada","institution_ids":["https://openalex.org/I39481719"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5003619912"],"corresponding_institution_ids":["https://openalex.org/I39481719"],"apc_list":null,"apc_paid":null,"fwci":1.8374,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.86113514,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"59","issue":"6","first_page":"1675","last_page":"1685"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T10860","display_name":"Speech and Audio Processing","score":0.9994000196456909,"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/T10891","display_name":"Radar Systems and Signal Processing","score":0.9984999895095825,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quadrature-amplitude-modulation","display_name":"Quadrature amplitude modulation","score":0.7683555483818054},{"id":"https://openalex.org/keywords/cram\u00e9r\u2013rao-bound","display_name":"Cram\u00e9r\u2013Rao bound","score":0.7329938411712646},{"id":"https://openalex.org/keywords/qam","display_name":"QAM","score":0.6832337379455566},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.634452223777771},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.49457451701164246},{"id":"https://openalex.org/keywords/additive-white-gaussian-noise","display_name":"Additive white Gaussian noise","score":0.4813964366912842},{"id":"https://openalex.org/keywords/fisher-information","display_name":"Fisher information","score":0.41197511553764343},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.38344356417655945},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.37853357195854187},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.36699000000953674},{"id":"https://openalex.org/keywords/bit-error-rate","display_name":"Bit error rate","score":0.22192785143852234},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.12921449542045593}],"concepts":[{"id":"https://openalex.org/C32409245","wikidata":"https://www.wikidata.org/wiki/Q749753","display_name":"Quadrature amplitude modulation","level":4,"score":0.7683555483818054},{"id":"https://openalex.org/C4978587","wikidata":"https://www.wikidata.org/wiki/Q1138810","display_name":"Cram\u00e9r\u2013Rao bound","level":3,"score":0.7329938411712646},{"id":"https://openalex.org/C59030546","wikidata":"https://www.wikidata.org/wiki/Q7265371","display_name":"QAM","level":5,"score":0.6832337379455566},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.634452223777771},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49457451701164246},{"id":"https://openalex.org/C169334058","wikidata":"https://www.wikidata.org/wiki/Q353292","display_name":"Additive white Gaussian noise","level":3,"score":0.4813964366912842},{"id":"https://openalex.org/C29406490","wikidata":"https://www.wikidata.org/wiki/Q1420659","display_name":"Fisher information","level":2,"score":0.41197511553764343},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.38344356417655945},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.37853357195854187},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.36699000000953674},{"id":"https://openalex.org/C56296756","wikidata":"https://www.wikidata.org/wiki/Q840922","display_name":"Bit error rate","level":3,"score":0.22192785143852234},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.12921449542045593}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcomm.2011.050211.100036a","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcomm.2011.050211.100036a","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W263517893","https://openalex.org/W1514558801","https://openalex.org/W1965392255","https://openalex.org/W1990740914","https://openalex.org/W2009647803","https://openalex.org/W2019202918","https://openalex.org/W2076764958","https://openalex.org/W2116414176","https://openalex.org/W2140675727","https://openalex.org/W2167626406","https://openalex.org/W2169013630"],"related_works":["https://openalex.org/W4297911919","https://openalex.org/W4390873927","https://openalex.org/W3111419928","https://openalex.org/W2159438609","https://openalex.org/W2900995485","https://openalex.org/W2147334234","https://openalex.org/W2122253935","https://openalex.org/W4247508912","https://openalex.org/W2117555526","https://openalex.org/W2979776991"],"abstract_inverted_index":{"In":[0],"this":[1,55],"paper,":[2],"we":[3],"derive":[4],"for":[5,11,60,66,75],"the":[6,12,24,50,61,67,76,80,85,97,107,112,118,122,126,131,134,142],"first":[7,62],"time":[8,63],"analytical":[9,64],"expressions":[10,65],"inphase/quadrature":[13],"(I/Q)":[14],"non-data-aided":[15],"(NDA)":[16],"Cram\u00e9r-Rao":[17],"lower":[18],"bounds":[19],"(I/Q":[20],"NDA":[21,68,81,113,127],"CRLBs)":[22],"of":[23,26,79,87,99,121,133],"direction":[25],"arrival":[27],"(DOA)":[28],"estimates":[29,83,115],"from":[30,146],"square":[31,88],"quadrature":[32],"amplitude":[33],"(QAM)-modulated":[34],"signals":[35],"corrupted":[36],"by":[37,54],"additive":[38],"white":[39],"circular":[40],"complex":[41],"Gaussian":[42],"noise":[43],"(AWCCGN)":[44],"with":[45],"any":[46,100],"antenna":[47],"configuration.":[48],"Yet":[49],"main":[51],"contribution":[52],"embodied":[53],"paper":[56],"consists":[57],"in":[58,84,96,130,141],"deriving":[59],"Fisher":[69],"information":[70],"matrix":[71],"(FIM)":[72],"and":[73],"then":[74],"stochastic":[77],"CRLB":[78],"DOA":[82,114],"case":[86],"QAM-modulated":[89],"signals.":[90],"It":[91],"will":[92],"be":[93],"shown":[94],"that":[95],"presence":[98],"unknown":[101],"phase":[102,135],"offset":[103,136],"(i.e.,":[104,137],"non-coherent":[105],"estimation),":[106],"ultimate":[108],"achievable":[109],"performance":[110],"on":[111],"holds":[116],"almost":[117],"same":[119],"irrespectively":[120],"modulation":[123,148],"order.":[124],"However,":[125],"CRLBs":[128],"obtained":[129],"absence":[132],"coherent":[138],"estimation)":[139],"vary,":[140],"high":[143],"SNR":[144],"region,":[145],"one":[147],"order":[149],"to":[150],"another.":[151]},"counts_by_year":[{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":3},{"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"}