Maximum-Likelihood Direction Finding Under Elliptical Noise Using the EM Algorithm
Unlike subspace-based solutions of direction-of-arrival (DOA) estimation under non-Gaussian noise, where the only optional difference with the Gaussian case is the scatter/covariance matrix estimation method, maximum-likelihood (ML)-based DOA solutions need a different treatment under the non-Gaussi...
        Saved in:
      
    
          | Published in | IEEE communications letters Vol. 23; no. 6; pp. 1041 - 1044 | 
|---|---|
| Main Authors | , , | 
| Format | Journal Article | 
| Language | English | 
| Published | 
        New York
          IEEE
    
        01.06.2019
     The Institute of Electrical and Electronics Engineers, Inc. (IEEE)  | 
| Subjects | |
| Online Access | Get full text | 
| ISSN | 1089-7798 1558-2558  | 
| DOI | 10.1109/LCOMM.2019.2911518 | 
Cover
| Abstract | Unlike subspace-based solutions of direction-of-arrival (DOA) estimation under non-Gaussian noise, where the only optional difference with the Gaussian case is the scatter/covariance matrix estimation method, maximum-likelihood (ML)-based DOA solutions need a different treatment under the non-Gaussianity assumption. In this letter, we derive a particular ML-based DOA solution, called the expectation-maximization (EM) estimator, under the wide class of complex elliptically symmetric (CES) distributions. | 
    
|---|---|
| AbstractList | Unlike subspace-based solutions of direction-of-arrival (DOA) estimation under non-Gaussian noise, where the only optional difference with the Gaussian case is the scatter/covariance matrix estimation method, maximum-likelihood (ML)-based DOA solutions need a different treatment under the non-Gaussianity assumption. In this letter, we derive a particular ML-based DOA solution, called the expectation–maximization (EM) estimator, under the wide class of complex elliptically symmetric (CES) distributions. | 
    
| Author | Wang, Xiaodong Karimi, Mahmood Baktash, Ebrahim  | 
    
| Author_xml | – sequence: 1 givenname: Ebrahim orcidid: 0000-0003-3744-2139 surname: Baktash fullname: Baktash, Ebrahim email: ebrahim.baktash@gmail.com organization: School of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran – sequence: 2 givenname: Mahmood surname: Karimi fullname: Karimi, Mahmood email: karimi@shirazu.ac.ir organization: School of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran – sequence: 3 givenname: Xiaodong orcidid: 0000-0002-2945-9240 surname: Wang fullname: Wang, Xiaodong email: wangx@ee.columbia.edu organization: Electrical Engineering Department, Columbia University, New York, NY, USA  | 
    
| BookMark | eNp9kMFOwzAMQCMEEtvgB-ASiXNHnC5NcpzGBkgdkxA7R2mabhltM9JOgr-nZRMHDlxsS_az5TdE57WvLUI3QMYARN6ns9VyOaYE5JhKAAbiDA2AMRHRLpx3NREy4lyKSzRsmh0hRFAGA_S61J-uOlRR6t5t6bbe5_jBBWta52u8cHXu6g1e17kNeF6Wbt86o0v84l1j8brpm-3W4vkST8uND67dVlfootBlY69PeYTWi_nb7ClKV4_Ps2kaGSpZGzGtjTZAMy54VuQUaAKUCWImOWRykvPEAJ-YIuYMEii4BkqYFglh1maaJvEI3R337oP_ONimVTt_CHV3UlEa80RSkvBuShynTPBNE2yhjGt1_10btCsVENUbVD8GVW9QnQx2KP2D7oOrdPj6H7o9Qs5a-wuIRAKnJP4GVC19wA | 
    
| CODEN | ICLEF6 | 
    
| CitedBy_id | crossref_primary_10_1007_s11277_022_09664_4 crossref_primary_10_1109_TVT_2021_3106794 crossref_primary_10_1016_j_aej_2023_03_018 crossref_primary_10_1049_iet_rsn_2019_0584 crossref_primary_10_1109_JIOT_2022_3181683 crossref_primary_10_3233_JCM_226416  | 
    
| Cites_doi | 10.1109/TVT.2018.2794322 10.1111/j.2517-6161.1977.tb01600.x 10.1109/TSP.2012.2212433  | 
    
| ContentType | Journal Article | 
    
| Copyright | Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2019 | 
    
| Copyright_xml | – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2019 | 
    
| DBID | 97E RIA RIE AAYXX CITATION 7SP 8FD L7M  | 
    
| DOI | 10.1109/LCOMM.2019.2911518 | 
    
| DatabaseName | IEEE All-Society Periodicals Package (ASPP) 2005–Present IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Xplore (NTUSG) CrossRef Electronics & Communications Abstracts Technology Research Database Advanced Technologies Database with Aerospace  | 
    
| DatabaseTitle | CrossRef Technology Research Database Advanced Technologies Database with Aerospace Electronics & Communications Abstracts  | 
    
| DatabaseTitleList | Technology Research Database | 
    
| Database_xml | – sequence: 1 dbid: RIE name: IEEE Xplore (NTUSG) url: https://proxy.k.utb.cz/login?url=https://ieeexplore.ieee.org/ sourceTypes: Publisher  | 
    
| DeliveryMethod | fulltext_linktorsrc | 
    
| Discipline | Engineering | 
    
| EISSN | 1558-2558 | 
    
| EndPage | 1044 | 
    
| ExternalDocumentID | 10_1109_LCOMM_2019_2911518 8691720  | 
    
| Genre | orig-research | 
    
| GrantInformation_xml | – fundername: Shenzhen Peacock program grantid: KQTD2015071715073798 – fundername: Leading Talents Program of Guangdong Province grantid: 00201510 funderid: 10.13039/501100013069  | 
    
| GroupedDBID | -~X 0R~ 29I 4.4 5GY 5VS 6IK 97E AAJGR AARMG AASAJ AAWTH ABAZT ABQJQ ABVLG ACGFO ACIWK AENEX AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ATWAV AZLTO BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 EBS EJD HZ~ H~9 IES IFIPE IFJZH IPLJI JAVBF LAI M43 O9- OCL P2P RIA RIE RNS TN5 VH1 AAYXX CITATION 7SP 8FD L7M RIG  | 
    
| ID | FETCH-LOGICAL-c295t-5aacac12b787bfd212612580c4d1b94d76c174cf375161f7a1205a8605eeba263 | 
    
| IEDL.DBID | RIE | 
    
| ISSN | 1089-7798 | 
    
| IngestDate | Mon Jun 30 07:09:21 EDT 2025 Wed Oct 01 04:53:03 EDT 2025 Thu Apr 24 23:09:41 EDT 2025 Wed Aug 27 08:34:02 EDT 2025  | 
    
| IsPeerReviewed | true | 
    
| IsScholarly | true | 
    
| Issue | 6 | 
    
| Language | English | 
    
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html https://doi.org/10.15223/policy-029 https://doi.org/10.15223/policy-037  | 
    
| LinkModel | DirectLink | 
    
| MergedId | FETCHMERGED-LOGICAL-c295t-5aacac12b787bfd212612580c4d1b94d76c174cf375161f7a1205a8605eeba263 | 
    
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14  | 
    
| ORCID | 0000-0003-3744-2139 0000-0002-2945-9240  | 
    
| PQID | 2237692067 | 
    
| PQPubID | 85419 | 
    
| PageCount | 4 | 
    
| ParticipantIDs | crossref_citationtrail_10_1109_LCOMM_2019_2911518 crossref_primary_10_1109_LCOMM_2019_2911518 proquest_journals_2237692067 ieee_primary_8691720  | 
    
| ProviderPackageCode | CITATION AAYXX  | 
    
| PublicationCentury | 2000 | 
    
| PublicationDate | 2019-06-01 | 
    
| PublicationDateYYYYMMDD | 2019-06-01 | 
    
| PublicationDate_xml | – month: 06 year: 2019 text: 2019-06-01 day: 01  | 
    
| PublicationDecade | 2010 | 
    
| PublicationPlace | New York | 
    
| PublicationPlace_xml | – name: New York | 
    
| PublicationTitle | IEEE communications letters | 
    
| PublicationTitleAbbrev | COML | 
    
| PublicationYear | 2019 | 
    
| Publisher | IEEE The Institute of Electrical and Electronics Engineers, Inc. (IEEE)  | 
    
| Publisher_xml | – name: IEEE – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE)  | 
    
| References | harry (ref4) 2002 ref2 ref1 ref3 frahm (ref5) 2004  | 
    
| References_xml | – year: 2002 ident: ref4 publication-title: Optimum Array Processing Part IV of Detection Estimation and Modulation Theory – ident: ref1 doi: 10.1109/TVT.2018.2794322 – year: 2004 ident: ref5 article-title: Generalized elliptical distributions: Theory and applications – ident: ref3 doi: 10.1111/j.2517-6161.1977.tb01600.x – ident: ref2 doi: 10.1109/TSP.2012.2212433  | 
    
| SSID | ssj0008251 | 
    
| Score | 2.3227217 | 
    
| Snippet | Unlike subspace-based solutions of direction-of-arrival (DOA) estimation under non-Gaussian noise, where the only optional difference with the Gaussian case is... | 
    
| SourceID | proquest crossref ieee  | 
    
| SourceType | Aggregation Database Enrichment Source Index Database Publisher  | 
    
| StartPage | 1041 | 
    
| SubjectTerms | Algorithms Arrays CES noise Covariance matrix Direction finding Direction of arrival Direction-of-arrival estimation DOA estimation Economic models EM method Generators Maximum likelihood estimation Normal distribution Probability density function Random noise Symmetric matrices  | 
    
| Title | Maximum-Likelihood Direction Finding Under Elliptical Noise Using the EM Algorithm | 
    
| URI | https://ieeexplore.ieee.org/document/8691720 https://www.proquest.com/docview/2237692067  | 
    
| Volume | 23 | 
    
| hasFullText | 1 | 
    
| inHoldings | 1 | 
    
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVIEE databaseName: IEEE Xplore (NTUSG) customDbUrl: eissn: 1558-2558 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0008251 issn: 1089-7798 databaseCode: RIE dateStart: 19970101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE  | 
    
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV3PS8MwFA5zJz34a4rTKTl403Zt2qbJcYyNIesEcbBbadJUy7Z2bB2If71J2pWhIt56SEvIS977Xvq97wFwnzgERT4jBnEYNlyJaA3KUWzEwhdx4toJ1mLVwQSPpu7TzJs1wGNdCyOE0OQzYapH_S8_zvlWXZV1CZbJBZIJ-oFPcFmrVXtdVYJZkumpRIyU7ApkLNod95-DQLG4qInk2fZUg4-9IKS7qvxwxTq-DE9AsJtZSSuZm9uCmfzzm2jjf6d-Co4roAl75c44Aw2RnYOjPfnBFngJoo90uV0a43QuFqkSOIaVC8wzOEx1wQvUnZGg4nas9L03nOTpRkDNNYASPsJBAHuLt3ydFu_LCzAdDl77I6PqsWBwRL3C8KKIR9xGTB5clsQykCnIQyzuxjajbuxjLnMWnji-J7Fh4kc2sryIyCRICBYh7FyCZpZn4gpA6ToTIVRPKx9LWJAQwjGX-NF1MJMR0GoDe7foIa8EyFUfjEWoExGLhtpQoTJUWBmqDR7qd1al_Mafo1tq5euR1aK3QWdn27A6oZsQKToQVeL117-_dQMO1bdLWlgHNIv1VtxKAFKwO73zvgBFq9TN | 
    
| linkProvider | IEEE | 
    
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1LS8QwEB4WPagH3-L6zMGbdm3TNE2OIrusul1BVvBWmjTVso-KdkH89SZpd1lUxFsPKQ2ZZOab9JtvAM4yn-EkFMxhvqAO0YjW4RKnTqpClWbEy6gVq476tPtIbp-CpwZczGthlFKWfKZa5tH-y08LOTVXZZeM6uQC6wR9OSCEBFW11tzvmiLMik7PNWbkbFYi4_LL3vV9FBkeF29hfboD0-JjIQzZvio_nLGNMJ0NiGZzq4glw9a0FC35-U228b-T34T1Gmqiq2pvbEFDTbZhbUGAcAceouQjH0_HTi8fqlFuJI5R7QSLCerktuQF2d5IyLA7Xu3NN-oX-btClm2ANIBE7QhdjZ6Lt7x8Ge_CY6c9uO46dZcFR2IelE6QJDKRHhb66Ios1aHMgB7mSpJ6gpM0pFJnLTLzw0CjwyxMPOwGCdNpkFIiwdTfg6VJMVH7gLTzzJQyXa1CqoFBxpikUiNI4lOhY6DbBG-26LGsJchNJ4xRbFMRl8fWULExVFwbqgnn83deKwGOP0fvmJWfj6wXvQlHM9vG9Rl9j7EhBHEjX3_w-1unsNIdRL24d9O_O4RV852KJHYES-XbVB1rOFKKE7sLvwCWt9ga | 
    
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Maximum-Likelihood+Direction+Finding+Under+Elliptical+Noise+Using+the+EM+Algorithm&rft.jtitle=IEEE+communications+letters&rft.au=Baktash%2C+Ebrahim&rft.au=Karimi%2C+Mahmood&rft.au=Wang%2C+Xiaodong&rft.date=2019-06-01&rft.pub=The+Institute+of+Electrical+and+Electronics+Engineers%2C+Inc.+%28IEEE%29&rft.issn=1089-7798&rft.eissn=1558-2558&rft.volume=23&rft.issue=6&rft.spage=1041&rft_id=info:doi/10.1109%2FLCOMM.2019.2911518&rft.externalDBID=NO_FULL_TEXT | 
    
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1089-7798&client=summon | 
    
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1089-7798&client=summon | 
    
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1089-7798&client=summon |